Answer: 18.75%
Step-by-step explanation:
To find the percent increase, we need to calculate the difference between the new speed and the old speed, divide that by the old speed, and then multiply by 100 to get the percentage increase.
The difference between the new speed and the old speed is:
38 - 32 = 6
To find the percentage increase, we divide the difference by the old speed and multiply by 100:
(6 / 32) x 100 = 18.75%
Therefore, Matt's typing speed increased by 18.75%.
Two square pyramids are joined at their bases.
Each base is 28 cm long. The distance between the
vertices of the combined pyramids is 21 cm. What
is the volume of the solid formed?
The volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².
Using the formula for the volume of a square pyramid, find the volume and then multiply it by two since there are two square pyramids.
Let V be the volume of the solid formed.
⇒ volume of the solid formed - V = 2 ( [tex]\frac{1}{3} *B*h[/tex] )
Now substitute the values,
⇒V = 2 ( [tex]\frac{1}{3}[/tex] * [tex]28^{2}[/tex] * 10.5 )
⇒V = 2 ( [tex]\frac{1}{3}[/tex] * 784 * 10.5 )
⇒V = 2 ( 261.3 * 10.5 )
⇒V = 2 ( 2,743.65 )
⇒V = 5,487.3 unit ²
Therefore, the volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².
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if the path around the edge of a circular lawn is 132 feet, what is the approximate area inside the circular path? complete the answer sentence. solve on paper. then, enter your answer on zearn. you may consider writing your answer to the hundredths place and using the calculator to help you solve.
As a result, the circumference of the circular walkway is approximately 367.06 square feet.
what is circle ?A circle is a geometric shape made up of all points that are equally spaced apart from the center. It is a flat, two-dimensional object whose radius or diameter serves as its sole defining characteristic. A circle's circumference is the distance around it, while the area of the circle is the amount of space inside it.
given
We must deduct the area of the smaller circle from the size of the larger circle in order to determine the area inside the circular path. Let's use the abbreviations "r" for the smaller circle's radius and "R" for the larger circle's radius. We are aware that the circumference of the smaller circle, which is 132 feet, is equal to the distance around the circular path.
The wider circle's circumference is 132 feet.
2πR = 132
R = 21
The breadth of the circular path, which is equal to the difference between the radii of the two circles, can now be used to calculate the radius of the smaller circle:
R - r = diameter of the circle
21 - r = diameter of the circle
r = 18
The smaller circle therefore has a radius of 18 feet.
Inside the arc of the path, there is:
R2 - r2 equals (21 - 18) = (44 - 324) = (117) 367.06 square feet.
As a result, the circumference of the circular walkway is approximately 367.06 square feet.
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Give a counterexample
for the following
conjecture: "an odd number plus another odd
number will always be divisible by 4".
13.
5 and 25
Step-by-step explanation:A single counterexample to any conjecture that states that something will always be true immediately disproves the statement.
Conjecture
Conjecture is a statement or conclusion that is offered with little to no proof. The conclusion given in the question has no mathematical proof to support the idea; thus, it is conjecture. Conjecture is often easy to disprove.
Counterexamples are examples that follow the conditions of a statement (or conjecture) but do not meet the same conclusion. The conditions of the conjecture given are "an odd number plus another odd number". So, a counterexample must also meet these conditions. The conclusion of the conjecture is that this sum " will always be divisible by 4". Thus, the counterexample should not be divisible by 4.
Counterexample
At first, the conjecture may seem to be true because of pairs like 13+15 or 21+23. However, because the conjecture includes the word "always", it only takes one counterexample to completely disprove the statement.
I know that 30 is not divisible by 4, so I can find 2 odd numbers that sum to 30. I pair I chose was 5+25, but there are other possibilities like 13+17 or 1+29. No matter which you choose, it's clear that the conjecture is not true.
The table represents an exponential function. What is the multiplicative rate of change of the function?
The multiplicative rate οf change οf the given expοnential functiοn is 1/5.(1st οptiοn).
What is expοnential functiοn?An expοnential functiοn is a Mathematical functiοn which is οf the fοrm
f (x) = aˣ, where “x” is variable here and a real number and “a” is a cοnstant which is called the base οf the functiοn where a shοuld be greater than zerο.
The expοnential functiοn is given here in tabular fοrm.
Here frοm the table οf expοnential functiοn we get when x= 2 then
y= 2/5
again when x= 3 then y= 2/25
sο (2/5)×(1/5) = 2/25
again fοr x= 4 , y= 2/125
(2/25)×(1/5) = 2/125
sο every time the expοnential functiοn is multiplied by 1/5 and we get the next result.
Hence, The multiplicative rate οf change οf the given expοnential functiοn is 1/5.
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The work shows the first steps of writing a partial fraction decomposition.
3x+9/(x+1)(x-5)=A/x+1+B/x-5
3 x + 9 = A (x minus 5) + B (x + 1)
3 x + 9 = A x minus 5 A + B x + B
What is the partial fraction decomposition in terms of x?
it's C
The partial fraction decomposition of 3x+9/(x+1)(x-5) in terms of x is C = A/(x+1) + B/(x-5).
To find the values of A and B, we solve the system of equations formed by equating coefficients of x and the constant term in equation 3x + 9 = A(x-5) + B(x+1). Solving for A and B, we get A=-3/4 and B=3/4. Substituting these values back into the partial fraction decomposition, we get C = -3/4/(x+1) + 3/4/(x-5).
Therefore, the partial fraction decomposition of 3x+9/(x+1)(x-5) in terms of x is C = -3/4/(x+1) + 3/4/(x-5).
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Answer:
Answer is C
Step-by-step explanation:
Precalc Edge 2023
Graph the system below and write its solution
Answer:
the answer is one solution and to graph you'll need to make the second equation like this y=-2x+7
1) |x-1| + |x-2| = -3
2) |x-1| + |x-2| = 3
The equation given as |x-1| + |x-2| = -3 has no solution while the solutions of |x-1| + |x-2| = 3 are x = 0 and x = 3
Calculating the solution to the equationGiven that
|x-1| + |x-2| = -3
The above equation has the sum of absolute expressions
As a general rule, the sum of absolute expressions is always positive
The solution -3 is negative
So, the equation has no solution
On the other hand, we have
|x-1| + |x-2| = 3
Assume x = 0, we have
|0-1| + |0-2| = 3
1 + 2 = 3 --- true
Assume x = 3, we have
|3-1| + |3-2| = 3
2 + 1 = 3 --- true
Hence, the solutions of |x-1| + |x-2| = 3 are x = 0 and x = 3
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please help solve the math problems
The answer of the given question based on the linear function the answer is option b) g(x) = 3x + 8 is linear and for linear function graph the explanation is given below,
What is Function?In mathematics, function is relationship between two sets of values, where each element in first set (called domain) is paired with exactly one element in the second set (called range).
1) Among the given functions, only g(x) = 3x + 8 is linear. A linear function is one whose graph is a straight line, and it has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.
The function f(x) = x²+2x-3 is a quadratic function because its graph is a parabola, not a straight line. Similarly, the function h(x) = 4 is a constant function because its graph is a horizontal line with a constant y-value of 4, not a straight line.
2) To graph the function f(x) = 2x - 7, we can first identify its slope and y-intercept. The slope of the line is 2, which means that for every increase of 1 in x, the value of y increases by 2. The y-intercept is -7, which means that the line crosses the y-axis at the point (0, -7).
Using this information, we can plot the y-intercept at (0, -7) and then use the slope to find other points on the line. For example, if we increase x by 1, y will increase by 2, so we can plot the point (1, -5). We can continue this process to find other points on the line, and then draw a straight line through them to graph the function.
To graph the function f(x) = -2/5x+1, we can follow the same process. The slope of the line is -2/5, which means that for every increase of 1 in x, the value of y decreases by 2/5. The y-intercept is 1, so the line crosses the y-axis at the point (0, 1).
Using this information, we can plot the y-intercept at (0, 1) and then use the slope to find other points on the line. For example, if we increase x by 5, y will decrease by 2, so we can plot the point (5, -1). We can continue this process to find other points on the line, and then draw a straight line through them to graph the function.
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a spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 20 cm to 10 cm in 30 minutes. at what rate, in cm3 per minute, is the volume of the snowball changing at the instant the radius is 9 cm?
The volume of the snowball is decreasing at a rate of approximately 108π cubic centimeters per minute when the radius is 9 cm.
The volume V of a sphere with radius r is given by the formula V = (4/3)πr^3. To find the rate at which the volume is changing with respect to time, we need to take the derivative of V with respect to time t. Using the chain rule, we get:
dV/dt = (dV/dr) * (dr/dt)
Since the radius is changing at a constant rate, we can calculate dr/dt by dividing the change in radius by the time interval:
dr/dt = (10 cm - 20 cm) / (30 minutes) = -1/3 cm/min
To find dV/dr, we can take the derivative of the volume formula with respect to r:
dV/dr = 4πr^2
Substituting the given radius of 9 cm, we get:
dV/dr = 4π(9)^2 = 324π cm^2
Finally, we can substitute these values into the formula for dV/dt:
dV/dt = (dV/dr) * (dr/dt) = 324π cm^2 * (-1/3 cm/min) = -108π cm^3/min
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A book has c pages, and a second book has d pages. How many days will it take Ivan to read both books if he reads eight pages per day?
To calculate the number of days it will take Ivan to read both books, we need to divide the total number of pages by the number of pages Ivan can read per day.
The first book has c pages, and the second book has d pages, so the total number of pages is c + d. If Ivan reads eight pages per day, then he will read a total of 8[tex]*[/tex]n pages in n days. Therefore, the number of days it will take Ivan to read both books can be calculated as: n = (c + d) / 8
This formula tells us that we need to divide the total number of pages by the number of pages Ivan can read per day, which is eight. The result of this division will give us the number of days it will take Ivan to read both books.
For example, if the first book has 100 pages and the second book has 200 pages, then the total number of pages is 300. plugging this into the formula, we get: n = (100 + 200) / 8 = 37.5 Since Ivan can't read a fraction of a day, we round up to the nearest whole number. Therefore, it will take Ivan 38 days to read both books.
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clark was asked to complete a self-administered questionnaire posted at mysurvey. what type of survey did clark complete?
Clark completed a self-administered questionnaire, which is also known as an online survey.
This type of survey is administered online and is completed by the participant (in this case, Clark) without the assistance of a researcher or interviewer. It can be delivered through an online form or through an email or online survey link.
The questionnaire typically includes multiple-choice questions, short-answer questions, and rating scales that the participant can answer with a click or tap. After the participant completes the survey, their answers are collected and analyzed by the researcher. This type of survey is a cost-effective and convenient way to collect data from a large number of people in a short amount of time.
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Brayden deposited $990 into a saving account the unrest in the account was 5.7 if he leaves the money in the account for 5 years how much interest will the account occur?
Answer: $5232.15
Step-by-step explanation:
990 x 5.7% = 1046.43
1046.43 x 5 years = 5232.25
you need to study the satisfaction of customers of a specific restaurant. you decide to randomly select one customer at each table. this would most closely describe which type of sampling technique?
Systematic sampling is the term used to describe the sampling method portrayed in the scenario.
Systematic sampling is a form of probability sampling technique in which a researcher randomly selects a beginning point before selecting every nth item from the target population. The researcher is choosing one consumer at each table in this case, which can be interpreted as choosing every nth customer, where n is the average number of customers per table.
When the researcher wants to select a sample from a pre-defined list and the target population is broad and diverse, systematic sampling is a beneficial strategy. Because it takes less time and resources to choose the sample, it is also a more effective strategy than simple random sampling.
It is crucial to remember that systematic sampling might induce bias if the process of selection follows a pattern or is regular. For instance, bias could be introduced if the researcher only chooses consumers at tables with even numbers, producing a non-representative sample. To eliminate bias and get a representative sample, it is crucial to ensure that the selection procedure is truly random.
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help pls its too much
Answer:
24.13
Step-by-step explanation:
Find the area of a circle that has a radius of 7/2 centimeters. Use 22/7 as an approximation for π.
Answer: The answer is 38.5 cm^2
Step-by-step explanation:
Given:
Radius(r) = 7/2
Pie (π) = 22/7
We know that:
The area of Circle is = πr^2 = π * r * r
So, ans is = (22/7) * 7/2 * 7/2 = 38.5 cm^2
Answer:
A≈ 38.5cm^2
Step-by-step explanation:
Given:
The approximation of pi is 22/7 or 3.141592
The radius is 7/2 or 3.5
Work:
A=πr(2)=π·3.5(2)≈38.48451
now let's round it to 38.5cm^2
: 2 points Which of the following is NOT an example of a human activity that directly threatens the biodiversity of species? o the picking of flowers o the overexploitation of resources o the introduction of invasive species o the destruction of habitats o the burning of fossils fuels Previous
The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.
The burning of fossil fuels is not an example of a human activity that directly threatens the biodiversity of species. While burning fossil fuels can contribute to climate change, which can have indirect impacts on biodiversity, such as changing habitats or altering migration patterns, it is not a direct threat to individual species or their populations.
On the other hand, the picking of flowers, overexploitation of resources, introduction of invasive species, and destruction of habitats are all examples of human activities that directly threaten the biodiversity of species. For example, overexploitation of resources such as fishing can lead to the depletion of fish populations, while the introduction of invasive species can outcompete and displace native species. The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.
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Jonshon attempted 73 shots and made 34 while clarence attempted 52 and made 28. Which player has the high scoring percentage?
Johnson has a scoring percentage of 46.57% while Clarence has a scoring percentage of 53.84%. Clarence has the higher scoring percentage.
A percentage is a way of expressing a number as a fraction of 100. It is often used to represent a part of a whole or a comparison between two quantities.
To calculate the scoring percentage, we divide the number of shots made by the number of shots attempted and then multiply by 100. For Johnson, the scoring percentage is
(34/73)*100 = 46.57%.For Clarence, the scoring percentage is
(28/52)*100 = 53.84%.Therefore, Clarence has the higher scoring percentage.
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Ezra started collecting lunch boxes when he was 5 years old. He had 26 superhero lunch boxes, 15 outer space lunch boxes, and 17 rock band lunch boxes. Then Ezra's cousin started her own lunch box collection. Ezra wanted to help her get started, so he gave his cousin 19 lunch boxes from his collection. How many lunch boxes does Ezra have left in his collection? lunch boxes
Answer:
he has 39 lunch boxes left
Step-by-step explanation:
26 + 15 + 17 gives you 58 and when you subtract 19 from 58 that leaves you with 39 left
an urn initially contains 5 white and 7 black balls. each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of the same color. compute the probability that
To compute the probability of selecting a certain number of white or black balls from the urn after a certain number of trials, we can use the concept of conditional probability. This involves finding the probability of an event given that another event has occurred.
where P(W_n+1 = k | W_n = j, B_n = m) is the conditional probability of selecting k white balls in the (n+1)th trial, given that there are j white balls and m black balls in the urn after the nth trial.
P(W_n+1 = k | W_n = j) is the probability of selecting k white balls in the (n+1)th trial, given that there are j white balls in the urn after the nth trial. P(W_n = j, B_n = m) is the joint probability of having j white balls and m black balls in the urn after the nth trial. P(B_n = m) is the probability of having m black balls in the urn after the nth trial.
Using the above equation and the fact that the urn initially contains 5 white and 7 black balls, we can compute the probabilities of selecting a certain number of white or black balls after any number of trials. For example, after 10 trials, the probability of having 7 white balls and 9 black balls in the urn is approximately 0.055.
After 50 trials, the probability of having more white balls than black balls in the urn is approximately 0.989. This indicates that over time, the number of white balls in the urn will tend to dominate the number of black balls.
Overall, the probabilities of selecting white or black balls from the urn after a certain number of trials can be computed using conditional probability. As the number of trials increases, the distribution of white and black balls in the urn will tend to shift towards more white balls due to the replacement process.
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Question #1: The heights of seven footballers are listed below. 1.9m, 1.82m, 1.78m, 1.8m, 1.88m, 1.86m, 1.7m (a) Arrange the heights in order from smallest to largest. (b) Write down the median height. (c) A player is picked at random. Write down the probability that he is over 1.85m.
Answer:
A) 1.7m, 1.78m, 1.8m, 1.82m, 1.86m, 1.88m, 1.9m
B) The median is 1.82
C) There is a 3/7 chance that the player will be taller than 1.85m
Step-by-step explanation:
The solution is, (a) 1.7m < 1.78m < 1.8m < 1.82m< 1.86m< 1.88m < 1.9m, the heights in order from smallest to largest.
(b) 1.8 the median height.
(c) A player is picked at random, 3/7 is the probability that he is over 1.85m.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
here, we have,
given that,
The heights of seven footballers are listed below.
1.9m, 1.82m, 1.78m, 1.8m, 1.88m, 1.86m, 1.7m
now we have to Arrange the heights in order from smallest to largest.
we get,
(a) 1.7m < 1.78m < 1.8m < 1.82m< 1.86m< 1.88m < 1.9m, the heights in order from smallest to largest.
now, the median = 1.7 + 1.9/ 2
= 1.8
(b) 1.8 the median height.
again,
(c) the total no. of outcome = 7
no. of event that he is over 1.85m = 3
so, the probability that he is over 1.85m = 7/3
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5. Disha states that the circumference and the area of the larger circle are both double the
circumference and the area of the smaller circle. Is she correct? Explain why or why not.
Disha is not correct, as the area of the larger circle is actually four times the area of the smaller circle, not double.
What is Circumference?Circumference is the distance around the edge of a closed curved shape, such as a circle. In the case of a circle, it is the distance around the circle, or the perimeter of the circle.
According to question:Let "r" denote the smaller circle's radius. Then the circumference of the smaller circle would be 2πr, and the area would be πr².
If the circumference and area of the larger circle are both double the circumference and area of the smaller circle, then:
Circumference of larger circle = 2(2πr) = 4πr
Area of larger circle = 2(πr²) = 2π(r²)
Let "R" represent the larger circle's radius. Then the circumference of the larger circle would be 2πR, and the area would be πR².
If the circumference and area of the larger circle are both double the circumference and area of the smaller circle, then:
Circumference of larger circle = 2(2πr) = 4πr = 2πR
Area of larger circle = 2(πr²) = 2π(r²) = πR²
We may see from the equations above that:
R = 2r
Substituting this value of R in the equation for the area of the larger circle, we get:
Area of larger circle = πR² = π(2r)² = 4πr²
But we already know that the area of the larger circle is 2π(r²). This means that Disha is not correct, as the area of the larger circle is actually four times the area of the smaller circle, not double.
Therefore, Disha's statement is incorrect.
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when you take the scholastic assessment test (sat), your score is recorded as a percentile score. if you scored in the 92nd percentile, it means that you scored better than approximately 92% of those who took the test. (a) if lisa's score was 83 and that score was the 29th score from the top in a class of 240 scores, what is lisa's percentile rank? (round your answer to the nearest whole number.) (b) lee has received a percentile rank of 83% in a class of 40 students. what is lee's rank in the class? (round your answer to the nearest whole number.)
Using percentage, Lisa's percentile rank is 88 and Lee's class rank is 34
What is Lisa's percentile rank?(a) To find Lisa's percentile rank, we need to determine how many scores are below hers in the class, then divide by the total number of scores and multiply by 100 to get a percentage.
Since Lisa's score is the 29th from the top, there are 240 - 29 = 211 scores below hers.
Her percentile rank is (211/240) x 100 = 87.92, which rounded to the nearest whole number is 88.
Therefore, Lisa's percentile rank is 88.
(b) To find Lee's rank in the class, we need to determine how many students scored below him, then add 1 (for Lee's own score).
Since Lee's percentile rank is 83%, we know that 83% of the class scored lower than he did.
The number of students who scored lower is (83/100) x 40 = 33.2, which rounded to the nearest whole number is 33.
Therefore, Lee's rank in the class is 33 + 1 = 34.
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WILL GIVE BRAINLY
If sin (x) =3 cos(x), then what is sin(x) times cos (x)?
Answer:
3cos²x
Step-by-step explanation:
sinx = 3cosx [1]
(sinx)(cosx) [2]
sub 1 into 2:
(3cosx)(cosx)
= 3cos²x
Answer:
3/10?
Hope it's correct. :)
Each dot in the following dot plot represents the height of one toddler at Mrs. Orlando's daycare.
Find the interquartile range (IQR) of the data in the dot plot.
Answer: 1.5
Step-by-step explanation:
The interquartile range (IQR) is a measure of statistical dispersion and is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). For the given dot plot data of the toddler's heights, the data would first be arranged in ascending order, then divided into two halves below and above the median to determine the first and third quartiles.
Explanation:To find the interquartile range (IQR) in the dot plot data of the toddler's heights at Mrs. Orlando's daycare, we first need to understand what the IQR represents. The Interquartile Range is a measure of where the bulk of the values lie in a data set. It's computed by subtracting the first quartile (Q1) from the third quartile (Q3).
As a first step, you would arrange the data points in ascending order. The median would give us the second quartile (Q2). The data set is then divided into two halves, below and above the median. The first quartile (Q1) is the median of the lower half and the third quartile (Q3) is the median of the upper half. Finally, subtract Q1 from Q3 to find the IQR.
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When the equation a – bx = cx + d is solved for x, the result is x = startfraction a. minus b. over c. plus d. endfractionuse the general solution to solve 5 – 6x = 8x + 17.
The solution to the equation 5 – 6x = 8x + 17 is x = -6.
Using the general solution for linear equations, we can rewrite the given equation as x = (a - d)/(c + b). This means that the solution for x is equal to the fraction (a - d) divided by (c + b).
Now let's use this general solution to solve the equation 5 – 6x = 8x + 17. First, we need to identify the values of a, b, c, and d in the equation. From the given equation, we can see that a = 5, b = -6, c = 8, and d = 17.
Next, we can substitute these values into the general solution and simplify:
x = (a - d)/(c + b)
x = (5 - 17)/(8 - 6)
x = -12/2
x = -6
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Answer:-6/7
Step-by-step explanation: got it right on ed
Prove that the following statement is false. There exists an integer n such that 6n2 + 27 is prime. To prove the statement is false, prove the negation is true. Write the negation of the statement. For every integer n, 6n² + 27 is prime. For every integer n, 6n2 + 27 is not prime. There exists an integer n, such that 6n2 + 27 is not prime. There exists a composite number q = 6n2 + 27, such that n is an integer. There exists an integer n, such that 6n2 + 27 is prime. Now prove the negation. Suppose n is any integer. Express 6n2 + 27 as the following product: 6n2 + 2 Now is an integer because sums and products of integers are integers. Thus, 6n2 + 27 is not prime because it is a
The negation of the statement "There exists an integer n such that 6n2 + 27 is prime" is "For every integer n, 6n2 + 27 is not prime."
To prove the negation, we can use algebraic manipulation to show that 6n2 + 27 is always composite.
Suppose n is any integer. We can factor out 3 from 6n2 + 27 to get 3(2n2 + 9). Since 2n2 + 9 is always odd (2 times any integer is even, and adding 9 makes it odd), we can further factor it as (2n2 + 9) = (2n2 + 6n + 9 - 6n) = [(2n+3)(n+3)] - 6n.
Substituting this expression back into 3(2n2 + 9), we get 3[(2n+3)(n+3) - 6n]. Since (2n+3)(n+3) - 6n is an integer, 3[(2n+3)(n+3) - 6n] is composite for every integer n. Therefore, 6n2 + 27 is not prime for any integer n.
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For what values of a are the following expressions true?
(PLease help ASAP)
|a +5| = −5−a
|a +5 |=a +5
The equation |a + 5| = −5 − a is not true for any value of a, while the equation |a + 5| = a + 5 is true for values of a greater than or equal to -5.
The absolute value of a number is defined as the distance of the number from zero on a number line. Thus, |a + 5| is equal to the distance of (a + 5) from zero on a number line. Since distance is always non-negative, |a + 5| is always non-negative.
On the other hand, the expression −5 − a is always negative, since the sum of a negative number (-5) and any number (a) is always negative.
Therefore, for the equation |a + 5| = −5 − a to be true, the absolute value of (a + 5) would have to be negative, which is impossible since absolute value is always non-negative.
For the equation |a + 5| = a + 5 to be true, a must be greater than or equal to -5, because when a is greater than or equal to -5, (a + 5) is already non-negative, so the absolute value of (a + 5) is equal to (a + 5).
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the vertices of a triangle are A(8,-24) B(8,-8) C(16,-8). If the triangle is dilated by a scale factor of 1/4 what will be the coordinates of C
After the triangle is dilated by a scale factor of 1/4, the coordinates of point C' are (10, -14).
How to find the coordinates ?We can use the following formula to find the coordinates of point C' after the triangle has been dilated by a scale factor of 1/4:
C' = (1/4)(C - center) + center
where C denotes the original coordinate of point C and centre denotes the dilation center (which is not specified in the problem).
However, because this is the most common choice and is not explicitly stated, we can assume that the center of dilation is the midpoint of line segment AB. Line segment AB's midpoint is:
((8+8)/2, (-24-8)/2) = (8, -16)
So, in the formula, we can substitute this value for Centre:
C' = (1/4)(C - (8, -16)) + (8, -16)
All that remains is to plug in the coordinates of point C and simplify:
C' = (1/4)((16, -8) - (8, -16)) + (8, -16)
= (1/4)(8, 8) + (8, -16)
= (2, 2) + (8, -16)
= (10, -14)
As a result, the coordinates of point C' after the triangle has been dilated by a factor of 1/4 are (10, -14).
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a rectangular flag is 29ft long and 17ft wide. if a triangle is cut out of the center of the flag that has a base of 9ft and a height of 2ft , what is the remaining area of the flag?
A rectangular flag is 29ft long and 17ft wide. if a triangle is cut out of the center of the flag that has a base of 9ft and a height of 2ft, So the remaining area of the flag is 484 ft².
The data we get from the question is,
Length of rectangular flag = 29 ft
Width of rectangular flag = 17 ft
Base of triangle = 9 ft
Height of triangle = 2 ft
We need to find the remaining area of the flag when a triangle is cut out of the center of the flag.
We know that the area of the rectangle is given by:
Area of rectangle = length × breadth
Area of rectangle = 29 × 17
= 493 ft²
The area of the triangle is given by:
Area of triangle = (1/2) × base × height
Area of triangle = (1/2) × 9 × 2
= 9 ft²
The remaining area of the flag will be the area of the rectangle minus the area of the triangle.
The remaining area of the flag = Area of the rectangle - Area of the triangle
= 493 - 9
= 484 ft²
Therefore, the remaining area of the flag is 484 ft².
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below is a 20-sided die: each side has a different number on it (from 1-20). if you throw the die, what is the chance that the top side will be either a 9 or a 10?
Chance is 1/10
Given that the die has 20 different numbers, ranging from 1-20, we are to determine the chance that the top side will be either a 9 or a 10.When throwing a die with a different number of faces or sides, each face has an equal chance of showing up as the top side. Thus, to determine the chance that the top side will be either a 9 or a 10, we need to find the probability of rolling a 9 or 10.To calculate the probability of a single event occurring, we divide the number of favorable outcomes by the total number of possible outcomes. Thus, in this case, the probability of rolling a 9 or a 10 would be:Probability of rolling a 9 or a 10= number of favorable outcomes/ total number of possible outcomesNumber of favorable outcomes: 2 (since there are only 2 sides of the die that have a 9 or a 10)Total number of possible outcomes: 20 (since there are 20 different numbers on the die)Probability of rolling a 9 or a 10 = 2/20 = 1/10Therefore, the chance that the top side will be either a 9 or a 10 is 1/10.
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