Answer:
8 pints=4 quarts,16 cups is 8pints
Step-by-step explanation:
It is multiplication, if you write it down then think about how the numbers connect its easier to understand.
(Deppressed student that desperately needs to catch up pls help) The table shows the results for spinning the spinner 50 times. What
is the relative frequency for the event "spin a 2"?
Experiment Table
Outcome. 1. 2. 3. 4
Frequency 12 10 10 18
Number of trials: 50
The relative frequency for the event "spin a 2" is:
(Simplify your answer.)
The relative frequency of the event "spin a 2" is given as follows:
0.2.
How to calculate relative frequency?To calculate the relative frequency of an event, you need to divide the number of times the event occurs by the total number of events in the data-set.
Hence the formula to calculate the relative frequency is presented as follows:
Relative frequency = (Number of times the event occurs) / (Total number of events)
From the table, the parameters for the event "spin a 2" are given as follows:
Number of times the event occurs: 10.Total number of events: 50.Hence the relative frequency is given as follows:
10/50 = 0.2.
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If DEF and PRS are complementary, what is the measure of PRS if DEF is 78?
According to question,
DEF+PRS=90
DEF=78
PRS=?
WE KNOW,
DEF+PRS=90
or,78+PRS=90
or,PRS=90-78
:.PRS=12,,
HELPPP
complete the problem by creating two binomials that represent that sides of the shape . Then multiply to get a quadratic equation . Draw a picture to help set up the problem . 6. Albert installs swimming pools . While the pools can come in different sizes, Albert only offers rectangular pools that are always twice as wide as they are long. He also puts a deck around the entire pool, and the deck is always 4ft wide on each side. Write an equation to represent the total area of the pool and deck.
The equation that represents the total area of the pool and deck is: A(x) = 2x² + 24x + 64.
Describe Binomial?In algebra, a binomial is a polynomial that consists of two terms connected by either an addition or a subtraction operator. A binomial can be written in the form (ax + b) or (ax - b), where "a" and "b" are constants and "x" is a variable.
Binomials are used in a variety of algebraic operations, such as factoring, expanding, and solving equations. They also appear in binomial probability distributions and binomial theorem.
Let's start by drawing a diagram to visualize the problem:
___________
| | 4 ft
| _________|_________
| | | |
| | | |
| | | | 2x
| | | |
| |_________|_________ |
| | 4 ft
|__________ |
2w
The rectangular pool is twice as wide as it is long, so we can let the length be x, and the width be 2x.
The deck around the pool is 4 feet wide on each side, so the total width of the pool and deck is (2x + 8), and the total length is (x + 8).
Therefore, the total area of the pool and deck can be represented as:
(2x + 8)(x + 8)
Expanding the expression, we get:
2x² + 24x + 64
So the equation that represents the total area of the pool and deck is:
A(x) = 2x² + 24x + 64
where A(x) is the area of the pool and deck, and x is the length of the pool.
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students test scores in an applied statistics courses are normally distributed with a mean of 70 and standard deviation of 10. what percent of the data falls below 40?
Percents of student failed in the test is 15.87%
Final grades are distributed normally.
Assuming mean, which is = 70
Provided that the standard deviation is 10,
Standard score or z-score refers to the normal random variable in a standard normal distribution. The following equation can convert each normal random variable X into a z score:
z=(X−μ)/σ
If X is a normal random variable, represents its mean, and represents its standard deviation.
For X=60 Z=(60−70)/10=−1
P(X<60)=P(Z<−1) \s =0.1587
Hence, 15.87% of pupils failed the test.
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
Mean is equal to (Sum of All Observations/Total Observations).
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a bag contains 2 black marbles, 8 white marbles, and 27 red marbles someone offers to play this game: you randomly select one marble from the bag if it is black, you win $3. if it is white, you win $2. if it is red, you lose $1. what is your expected value if you play this game?
The expected value of the game is -$0.054, which means that if you play this game many times, you can expect to lose around 5 cents per game on average.
We need to calculate the expected value of a game where you randomly select a marble from a bag containing 2 black marbles, 8 white marbles, and 27 red marbles.
If the marble is black, you win $3.
If the marble is white, you win $2.
If the marble is red, you lose $1.
The expected value of a game is the sum of the products of each outcome and its probability.
To find the expected value of this game,
we need to first calculate the probabilities of each outcome.
P(bag contains a black marble) = 2/37P(bag contains a white marble)
= 8/37
P(bag contains a red marble)
= 27/37
Probability of winning $3
= P(black marble)
= 2/37
Probability of winning $2
= P(white marble)
= 8/37
Probability of losing $1
= P(red marble) = 27/37
Expected value
= (Probability of winning $3 × $3) + (Probability of winning $2 × $2) + (Probability of losing $1 × $-1)
Expected value = (2/37 × 3) + (8/37 × 2) + (27/37 × -1)
Expected value = -0.054$
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if a loading ramp is placed next to a truck, at a height of 6 feet, and the inclined portion of the ramp is 21 feet long, what angle does the ramp make with the ground?
16.3 degrees is the angle that the ramp makes with the ground.
Draw a diagram: Draw a right-angled triangle with the ramp as the hypotenuse, the height of the truck as one of the other sides, and the horizontal distance from the bottom of the ramp to the truck as the other side.
Use trigonometry: We can use the trigonometric function tangent to find the angle the ramp makes with the ground. tan(theta) = opposite/adjacent = height of truck/horizontal distance
Let's substitute the given values:
tan(theta) = 6/21
Solve for theta: We can use the inverse tangent function to solve for theta.
theta = tan^-1(6/21)
theta ≈ 16.3 degrees
Therefore, the angle that the ramp makes with the ground is approximately 16.3 degrees.
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example 5.12 the atoms of a radioactive element are randomly disintegrating. if every gram of this element, on average, emits 3.9 alpha particles per second, what is the probability that during next second the number of alpha particales omitted from 1 gram is (a) at most 6; (b) at least 2; (c) at least 3 and at most 6?
a) The probability that during next second the number of alpha particales omitted from 1 gram is at most 6 is 0.998.
b) The probability that during next second the number of alpha particales omitted from 1 gram is at least 2 is 0.985.
c) The probability that during next second the number of alpha particales omitted from 1 gram is at least 3 and at most 6 is 0.679.
This problem is an application of the Poisson distribution, which is commonly used to model the number of events occurring in a fixed interval of time. In this case, we are interested in the number of alpha particles emitted by 1 gram of the radioactive element in one second.
The average rate of emission is given as 3.9 alpha particles per second. This means that the mean or expected number of alpha particles emitted by 1 gram of the element in one second is also 3.9.
(a) To find the probability that at most 6 alpha particles are emitted from 1 gram of the element in one second, we can use the Poisson distribution with λ=3.9 and x=0, 1, 2, 3, 4, 5, or 6.
The probability is given by the cumulative distribution function (CDF) of the Poisson distribution, which can be calculated using software or a table. For example, using a Poisson table or calculator, the probability is approximately 0.998.
(b) To find the probability that at least 2 alpha particles are emitted, we can use the complementary probability: P(at least 2) = 1 - P(none or 1). Using the Poisson distribution with λ=3.9 and x=0 or 1, we find P(none or 1) = 0.015. Therefore, P(at least 2) = 1 - 0.015 = 0.985.
(c) To find the probability that at least 3 and at most 6 alpha particles are emitted, we need to add the probabilities for x=3, 4, 5, and 6. Using the Poisson distribution with λ=3.9, we can calculate P(x=3) = 0.089, P(x=4) = 0.172, P(x=5) = 0.212, and P(x=6) = 0.206. Therefore, the probability is approximately 0.679.
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if one card is randomly selected from a well-shuffled standard deck of 52 cards, what is the probability that the card selected is a queen? leave your answer as a reduced fraction.
If one card is randomly selected from a well-shuffled standard deck of 52 cards, the probability that the card selected is a queen is 1/13. This is because there are 4 queens in a deck of 52 cards, therefore, the probability of getting one queen out of the 52 cards is 4/52, which can be simplified to 1/13.
The probability that the card selected is a queen is calculated using the formula:
P(E) = n(E) / n(S)
where:
P(E) = probability of an event
n(E) = number of ways an event can happen
n(S) = total number of possible outcomes
In this case, n(E) is 4 (since there are 4 queens in a deck of 52 cards), and n(S) is 52 (since there are 52 cards in a deck), so:
P(E) = 4 / 52
P(E) = 1/13
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a culture of bacteria enters the exponential growth phase with 5521 cells per ml. the culture has a growth rate constant of 19380 hours what is the abdunace expressed as cells per lml
the abundance expressed as cells per ml would be: 7.70*10^8
Here,
Initial population = 9019
Growth rate = 0.9502 hr-1
Time = 17 hrs
We know that,
Final population = Initial population ( 1 + Growth rate)Time
= 9019 ( 1 + 0.9502 )17
= 9019 ( 1.9502 )17
= 9019 x 85378
= 770,024,182
= 7.70*10^8
A bacteria culture is a test to distinguish whether you have a bacterial disease. It very well may be performed on an example of blood, stool, pee, skin, bodily fluid, or spinal liquid. Utilizing this kind of test, a medical services supplier can distinguish what caused a disease and decide the best therapy.
Exponential growth is an example of information that shows more keen increments after some time.
In finance, compounding makes exponential returns.
Bank accounts with a building financing cost can show exponential growth.
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the complete question is:
7 + 35 2 points A culture of bacteria enters the exponential growth phase with 9,019 cells per ml. The culture has a growth rate constant of 0.9502 hours 1. After 17 hours, what is the abundance expressed as cells per ml? 1 • Report your answer in scientific notation to two decimal places. Remember to include trailing zeros!! o For example: • 42,000,000 would be expressed as 4.20*10^7 42,367,000 would be expressed as 4.24*10^7 2 3 0.54 4 Previous Next 5 6 7 00 8 9 10 11 12
julio has $31.00 he earns half of that much mowing a lawn. How much money does he have in all?
Answer: $ 46.50
First divided 31 by 2
Which equals...
15.50
Then add 15.50 to 31.
46.50
The answer is $46.50
Two urns contain white balls and yellow balls. The first urn contains 5 white balls and 4 yellow balls and the second urn contains 3 white balls and 2 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
Two urns contain white balls and yellow balls. The first urn contains 7 white balls and 7 yellow balls and the second urn contains 2 white balls and 10 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
The probabilty of selecting two white balls in the two scenarios are 1/3 and 1/13
Calculating the probabilty of whiteScenario 1
The probability of drawing a white ball from the first urn is 5/9, since there are 5 white balls out of 9 total balls.
Similarly, the probability of drawing a white ball from the second urn is 3/5.
To find the probability that both balls are white, we need to multiply the probabilities of drawing a white ball from each urn, since the events are independent:
(5/9) × (3/5) = 15/45 = 1/3
Scenario 2
Using the steps in (1), we have
P = 1/2 * 2/12
Evaluate
P = 1/12
Therefore, the probability that both balls are white is 1/12.
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an international company has employees in one country. if this represents of the company's employees, how many employees does it have in total? round your answer to the nearest whole number.
The total number of employees in the company would be 5, rounded to the nearest whole number.
The formula to calculate the total number of employees in a company is:
Total Number of Employees = Number of Employees in One Country x Proportion of Company's Employees.
For example, if a company has 10 employees in one country and that represents 50% of the company's employees, then the total number of employees in the company would be:
Total Number of Employees = 10 x 0.5 = 5
Therefore, if a company has 10 employees in one country and that represents 50% of the company's employees, then the total number of employees in the company would be 5, rounded to the nearest whole number.
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the weight of a miniature tootsie roll is normally distributed with a mean of 3.30 grams and standard deviation of .13 gram. (a) within what weight range will the middle 95 percent of all miniature tootsie rolls fall?
The weight range within which the middle 95% of all miniature Tootsie Rolls will fall is approximately between 3.04 grams and 3.56 grams.
Since the weight of miniature Tootsie Rolls is normally distributed with a mean of 3.30 grams and a standard deviation of 0.13 grams, we can use the standard normal distribution to find the weight range within which the middle 95% of all miniature Tootsie Rolls will fall.
We need to find the z-scores that correspond to the middle 95% of the normal distribution. The area between the two z-scores will be 0.95. Using a standard normal distribution table or calculator, we can find that the z-scores that correspond to the middle 95% of the distribution are -1.96 and 1.96.
We can use the formula z = (x - μ) / σ to find the corresponding weight values for these z-scores. Substituting -1.96 for z and solving for x, we get:
-1.96 = (x - 3.30) / 0.13
x = 3.04
Similarly, substituting 1.96 for z and solving for x, we get:
1.96 = (x - 3.30) / 0.13
x = 3.56
Therefore, the weight range within which the middle 95% of all miniature Tootsie Rolls will fall is approximately between 3.04 grams and 3.56 grams.
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use hardy-weinberg formula to evaluate the following. the frequency of disease xyz is about 1/4300. what is the probability that a mother a carrier?
The probability that a mother is a carrier is approximately 0.018.
The Hardy-Weinberg equilibrium formula can be used to determine the frequency of alleles in a population, as well as to make predictions about the probability of certain traits occurring in the next generation. In this case, we are interested in determining the probability that a mother is a carrier of a particular disease, given that the frequency of the disease is 1/4300.
To use the Hardy-Weinberg formula, we need to know the frequency of both the dominant and recessive alleles in the population. Assuming that the disease allele is recessive (i.e., carriers are heterozygous), we can represent the frequency of the disease allele (q) as
[tex]q = \sqrt{(1/4300)} = 0.004644.[/tex]
To determine the frequency of carriers (heterozygotes), we can use the formula p * q * 2,
where p represents the frequency of the dominant allele (which is equal to 1 - q in this case).
Therefore:
[tex]p = 1 - q \\ = 1 - 0.004644 = 0.995356\\q = \sqrt{(1/4300} = 0.004644\\p * q * 2 =0.018[/tex]
Approximately 1.8% of the population will be carriers of the disease allele. This means that the probability that a mother is a carrier is approximately 0.018.
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John has a part-time job at an ice skating rink selling hot cocoa. He decided to plot the number of hot cocoas he sold relative to the day's high temperature and then draw the line of best fit. Based on the line of best fit, how many hot cocoas would you predict John to sell if the day’s high temperature were 30 F
Based on this linear equation, we would predict that John would sell 50 hot cocoas if the day's high temperature were 30 F.
What is linear equation ?
A linear equation is an algebraic equation that describes a straight line relationship between two variables, typically denoted as x and y. The general form of a linear equation is:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).
The slope, m, represents the rate of change of y with respect to x.
According to the question:
Assuming that the relationship between the high temperature and the number of hot cocoas sold is roughly linear, we can use the equation of the line of best fit to estimate the number of hot cocoas sold at a high temperature of 30 F.
If we know the equation of the line of best fit in the form y = mx + b, where y is the number of hot cocoas sold and x is the high temperature, then we can substitute x = 30 and solve for y.
For example, if the equation of the line of best fit is y = 2x - 10, where y is the number of hot cocoas sold and x is the high temperature, then we can substitute x = 30 to get:
y = 2(30) - 10 = 50
Therefore, based on this equation, we would predict that John would sell 50 hot cocoas if the day's high temperature were 30 F. However, it's important to note that this is just an estimate and the actual number of hot cocoas sold could be different.
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BRAINLIEST! HURRY! What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
_ cm³
Answer:
331/2
Step-by-step explanation:
5 1/2= 11/2
3 1/2 = 7/2
11/2x7/2x6=115 1/2 = 331/2
Answer:
115.5 cm^3
Step-by-step explanation:
Volume=LengthxWidthxHeight
The values from the diagram are 3.5, 6, and 5.5
Multiply!
3.5x6x5.5=115.5
ou and i each have a fair coin. i flip n times, and you flip n 1 times. you win if i get fewer heads than you. what is the probability that you win the game?
Answer: 3
Step-by-ste3p explanation:
full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class. true or false: full-time high school students spend more time per week on their courses than full-time college students.
Answer:
The answer to your question would be true.
The given statement 'full-time high school students spend more time per week on their courses than full-time college students' is true because full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class.
Full-time high school students spend more time per week on their courses than full-time college students. It is because full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class.
College courses usually last for one hour per day, whereas high school students attend classes for 5-6 hours per day. Hence, college students spend around 15-18 hours per week attending classes, while high school students spend around 30 hours per week in the classroom.
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Find the linear measure of arc KML on OO, where line segment KM is a diameter, OM=36, and angle KOL-145. Use 3. 14 for pie and estimate your answer to two decimal places
The linear measure of arc KML on OO is approximately 3.33 units, rounded to two decimal places.
Since KM is a diameter, angle KOM is a right angle. Therefore, angle KOL is a straight angle, which means that angle MOL is 180 - 145 = 35 degrees.
Now, we can use the fact that the measure of an arc is proportional to the measure of the angle it subtends. In particular, if the measure of an angle in degrees is θ and the radius of the circle is r, then the length of the arc it subtends is given by:
length of arc = (θ/360) * 2πr
In this case, the radius of the circle is half of the diameter KM, which is 36/2 = 18. So we have:
length of arc KML = (35/360) * 2 * 3.14 * 18
≈ 3.33
Therefore, the linear measure of arc KML on OO is approximately 3.33 units, rounded to two decimal places.
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a child-care center has 200 feet of fencing to enclose two adjacent rectangular safe play areas (of equal size). find the dimensions that will produce the maximum enclosed area. 5
The dimensions that will produce the maximum enclosed area for two adjacent rectangular safe play areas of equal size with 200 feet of fencing is 100 feet by 100 feet.
To solve this problem, use the area of a rectangle formula A = lw, where l is the length and w is the width.
Since the two play areas must be of equal size, let's call the length and width l and w, respectively.
We know that the total length of fencing is 200 feet, so l + w = 200 feet.
We can then solve for l by rearranging the equation as l = 200 - w.
We then substitute this into the area equation to get A = (200 - w)w.
To maximize the area, differentiate this equation to get A' = w - 200.
Set this to 0 and solve for w to get w = 100. Since l + w = 200, l = 100 as well.
Therefore, the maximum enclosed area is produced by dimensions of l = 100 feet and w = 100 feet.
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Elijah wants to know how much wrapping paper is needed to cover a box with the dimensions shown. What is the surface area of the box.
A.160 square in
B.92 square in
C.46 square in
D.184 square in
also how do I give brainiest
The surface area of the box is (D) 184 square inches.
What is surface area?
Surface area is the measurement of the total area that the surface of an object occupies. It is the sum of the areas of all the faces or surfaces that make up the object. For example, the surface area of a cube can be found by adding up the area of all six of its square faces.
To find the surface area of the box, we need to add up the areas of each face.
The front face has an area of 5 x 4 = 20 square inches.
The back face has the same dimensions, so it also has an area of 20 square inches.
The left face has an area of 4 x 8 = 32 square inches.
The right face also has an area of 4 x 8 = 32 square inches.
The top face has an area of 5 x 8 = 40 square inches.
The bottom face also has an area of 5 x 8 = 40 square inches.
Adding up all of these areas, we get:
20 + 20 + 32 + 32 + 40 + 40 = 184 square inches
Therefore, the answer is (D) 184 square inches.
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there are 7 traffic lights on your way to school. the probability of a green light is 0.5, red light is 0.4 and orange light is 0.1. what is the probability that at most 5 of these lights are red?
The probability that at most 5 of these lights are red is 0.971.
To calculate this probability, we can use the binomial distribution with n = 7 and p = 0.4, since we want to know the probability of getting at most 5 red lights out of 7. We can use the formula:
P(X ≤ 5) = ΣP(X = k) for k = 0 to 5
Using this formula, we can calculate the probability as follows:
P(X = 0) = (0.5)^7 = 0.0078
P(X = 1) = 7(0.5)^7 = 0.0547
P(X = 2) = 21(0.4)(0.6)^6 = 0.2028
P(X = 3) = 35(0.4)^2(0.6)^5 = 0.322
P(X = 4) = 35(0.4)^3(0.6)^4 = 0.2458
P(X = 5) = 21(0.4)^4(0.6)^3 = 0.0907
Therefore, the probability of getting at most 5 red lights out of 7 is:
P(X ≤ 5) = 0.0078 + 0.0547 + 0.2028 + 0.322 + 0.2458 + 0.0907 = 0.971.
So the probability that at most 5 of these lights are red is 0.971.
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James ordered a large pizza that was cut into 8 equal portions. Of the 8 slices, only 3 of the slices were eaten. James believed that there was 0.75 pi radians left of the pizza. Which of the following correctly
describes James' claim?
A) James in incorrect because he calculated the number of slices of pizza that were eaten instead of the number of slices of pizza that were left. James needed to divide 360 by the appropriate number of
slices of pizza, 8. He then would have needed to multiply the result by 5 in order to find how many degrees of pizza was left over. After that, James would have needed to divide by 180 and multiply by TT
to get 1.257 radians as the amount of pizza that was left.
B) James is incorrect because he did not need to use TT when solving for radians. The amount of pizza left over is only 0.75.
C) James is incorrect because he did not divide 360 by the appropriate number of slices of pizza, 5, in order to find how many degrees of pizza was left. James would have then needed to divide by 180
and multiply by TT to get 0.4π radians as the amount of pizza that was left.
As per central angle theorem, James in incorrect because he calculated the number of slices of pizza that were eaten instead of the number of slices of pizza that were left. James needed to divide 360 by the appropriate number of slices of pizza, 8. He then would have needed to multiply the result by 5 in order to find how many degrees of pizza was left over. After that, James would have needed to divide by 180 and multiply by π to get 1.257 radians as the amount of pizza that was left.
Define central angle theorem?The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors.
In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.
Here,
out of 8 slices 5 are left.
So 360/8
= 45
5 × 45 = 225°
Now 225° = 225× π/180
= 3.927 Rad
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James ordered a large pizza cut into eight equal pieces. Of the 8 slices, only 3 were edible. James thought the rest of the pizza was 0.75 pi radians. Option A) correctly describes James' claim.
Define central angle theorem?The central angle is the angle an arc of a circle makes at its center. The central angle arm is formed by the radius vector. That is, the angle at which the arms with the apex at the center of the circle and the arms at his two radii of the circle intersect at two different positions. Combining these two points forms an arc. The angle that this arc makes at the center of the circle is called the central angle.
Here,
out of 8 slices 5 are left.
So 360/8
= 45
5 × 45 = 225°
Now 225° = 225× π/180
= 3.927 Rad
According to the central angle theorem, James is wrong because he calculated the number of pizza slices eaten, not the number of pizza slices left. James had to divide his 360 by 8, the number of pizza slices. Then he had to multiply the result by 5 to see how many pizzas were left. Then James had to divide him by 180 and multiply by π, so he got 1.257 radians as the remaining amount of pizza.
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Given
�
(
6
,
−
3
)
,
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(
7
,
−
4
)
,
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(
−
3
,
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7
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,
M(6,−3),N(7,−4),O(−3,−7), and
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P(x,−5). Find
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x such that
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OP
.
there are twο pοssible values οf x that make the length οf segment MP equal tο the length οf segment OP: x = 4 and x = 8.
What is a line segment?In geοmetry, a line segment is a part οf a straight line that is bοunded by twο distinct end pοints, and cοntains every pοint οn the line that is between its endpοints.
Tο find the value οf x such that the length οf the segment MP is equal tο the length οf the segment OP, we can use the distance fοrmula tο find the lengths οf bοth segments, and then sοlve fοr x.
First, we can find the length οf segment MN using the distance fοrmula:
MN = √[(7-6)² + (-4-(-3))²] = √[1² + (-1)²] = √2
Next, we can find the length οf segment OP using the distance fοrmula:
OP = √[(x-(-3))² + (-5-(-7))²] = √[(x+3)² + 2²]
Nοw, we can set the lengths οf MP and OP equal tο each οther, and sοlve fοr x:
MN / OP = MP / OP
√2 / √[(x+3)² + 2²] = √[(6-x)² + (-3-(-5))²] / √[(x+3)² + 2²]
Squaring bοth sides οf the equatiοn, we get:
2 / [(x+3)²+ 2²] = [(6-x)² + 2²] / [(x+3)² + 2²]
Multiplying bοth sides οf the equatiοn by [(x+3)² + 2²], we get:
2 = [(6-x)² + 2²]
Expanding and simplifying, we get:
2 = x² - 12x + 40
Rearranging, we get:
x² - 12x + 38 = 0
We can use the quadratic fοrmula tο sοlve fοr x:
x = (12 ± √[(-12)² - 4(1)(38)]) / (2(1))
x = (12 ± √16) / 2
x = 6 ± 2
Therefοre, there are twο pοssible values οf x that make the length οf segment MP equal tο the length οf segment OP: x = 4 and x = 8.
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Find the length of the function of x over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. (Round your answer to four decimal places.) y = 2x3/2/3 − x1/2/2 from x = 1 to x = 4
Since it is difficult to evaluate this integral exactly, use technology to approximate it. After calculation, the length is approximately 3.9205 (rounded to four decimal places).
To find the length of the function y =[tex]2x^(3/2)/3 - x^(1/2)/2[/tex] over the interval [1, 4], you need to evaluate the integral of the square root of [1 + (y')^2] with respect to x, where y' is the derivative of y with respect to x.
First, find the derivative y':
y'(x) = d(2x^(3/2)/3 - x^(1/2)/2)/dx = x^(1/2) - 1/(4x^(1/2))
Now, find (y')^2:
[tex](y')^2 = (x^(1/2) - 1/(4x^(1/2)))^2[/tex]
Next, find the square root of [1 + (y')^2]:
[tex]√[1 + (y')^2] = √[1 + (x^(1/2) - 1/(4x^(1/2)))^2][/tex]
Finally, evaluate the integral:
Length = [tex]∫(√[1 + (y')^2]) dx[/tex] from x = 1 to x = 4
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please help i don't know how to do it.
Answer:
4g5h¯²
Step-by-step explanation:
36 x g9 x h/ 9x g4 x h³
Divide similar terms
(36/9) x g9-4 x h¹-³
4 x g5 x h¯²
4g5h¯²
solve for y: 9=4x+6y
Answer:
[tex]\huge\boxed{\sf y = \frac{9-4x}{6}}[/tex]
Step-by-step explanation:
Given equation:9 = 4x + 6y
Subtract 4x from both sides9 - 4x = 6y
Divide both sides by 6[tex]\displaystyle \frac{9-4x}{6} = y\\\\OR\\\\y = \frac{9-4x}{6} \\\\\rule[225]{225}{2}[/tex]
Answer:
y = (-4x + 9)/6y = (-2x/3) + (3/2)Step-by-step explanation:
Now we have to,
→ Find the required value of y.
The equation is,
→ 9 = 4x + 6y
Then the value of y will be,
→ 9 = 4x + 6y
→ 4x + 6y = 9
→ 6y = 9 - 4x
→ 6y = -4x + 9
→ y = (-4x + 9)/6
→ y = (-4x/6) + (9/6)
→ y = (-2x/3) + (3/2)
Hence, this is the answer.
A two-sided t-test for a population mean is conducted of the null hypothesis H0 : μ = 100. If a 90 percent t-interval constructed from the same sample data contains the value of 100, which of the following can be concluded about the test at a significance level of a = 0.10 ?A. The p-value is less than 0.10, and H0 should be rejected.B. The p-value is less than 0.10, and H0 should not be rejected.C. The p-value is greater than 0.10, and H0 should be rejected.D. The p-value is greater than 0.10, and H0 should not be rejected.
Option D is correct, the p-value is greater than 0.10, and H₀ should not be rejected.
What is Null hypothesis?The null hypothesis is denoted as H₀, is a statement or assumption that suggests there is no significant or meaningful relationship between two variables in a statistical hypothesis test.
If a 90 percent t-interval constructed from the sample data contains the value of 100, it means that the sample mean is within the confidence interval.
Since the null hypothesis H₀: μ = 100 is also assuming that the population mean is 100, this suggests that the sample data is consistent with the null hypothesis.
Given a significance level of α = 0.10, we compare the p-value with this significance level to make a conclusion.
If the 90 percent confidence interval contains the hypothesized value (100 in this case), it suggests that the p-value is likely to be greater than 0.10.
There is insufficient evidence to reject the null hypothesis at a significance level of 0.10.
Therefore, the p-value is greater than 0.10, and H₀ should not be rejected.
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The following questions are about the relationship between the determinant of M and the ability to solve the equation above for A in terms of X or for X in terms of A Check the boxes which make the statement correct: If the det (M) then A. A. some values of Xl will have more than one value of Al which satisfy the equation. B. some values of Al will have no values of Xl which will satisfy the equation.C. given any X there is one and only one A which will satisfy the equation. D. there is no value of X which satisfies the equation when A=0. E. some values of A (such as A=0 ) will allow more than one X to satisfy the equation.
In conclusion, the determinant of M being non-zero only guarantees that the equation has a unique solution, but it does not guarantee that it has a solution for every value of A.
If the determinant of M is not equal to zero, then A can be solved in terms of X or X can be solved in terms of A. This is because the matrix M is invertible when its determinant is non-zero. In other words, the matrix M has a unique inverse.
Here are the statements that are correct:
- Given any X, there is one and only one A which will satisfy the equation. This is because when the determinant of M is non-zero, the matrix M is invertible, and hence the equation can be uniquely solved for A in terms of X or for X in terms of A.
- Some values of A (such as A=0) will allow more than one X to satisfy the equation. This is because the determinant of M being non-zero only guarantees that the equation has a unique solution, but it does not guarantee that it has a solution for every value of A.
- Some values of X will have more than one value of A that satisfy the equation. This is true for any equation that has multiple solutions, regardless of the determinant of M.
- Some values of A will have no values of X that satisfy the equation. This is true for any equation that has no solution, regardless of the determinant of M.
- There is no value of X which satisfies the equation when A=0. This is because when A=0, the equation reduces to 0=0, which is true for any value of X.
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The diagram below shows the dimensions
of a rectangular tabletop.
6 3/4 feet
3 feet
The wood to make the tabletop costs
$12.40 per square foot. What is the cost
of the tabletop?
A $232.50
B $243.00
© $251.10
D$260.40
The cost of the tabletop is $251.10. Option C
How to determine the costThe formula for calculating the area of a rectangle is expressed as;
Area = lw
Such that the parameters are;
l is the length of the rectangle.w is the width of the rectangle.From the diagram shown, we have;
The width = 6 3/4 feet = 27/4 feet
The length = 3 feet
Substitute the values
Area = 27/4 × 3
Multiply
Area = 20. 25 square feet
But;
1 square foot = $12.40
Then 20. 25 square feet = x
x = $251. 10
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