Answer:
The first one...............
lisa is on her way home in her car. she has driven 24 miles so far, which is three-fourths of the way home. what is the total length of her drive?
If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.
Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:
24 = (3/4) x
To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:
24 * (4/3) = x
Simplifying, we get:
32 = x
We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.
To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.
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use excel to find the critical value of z for each hypothesis test. (negative values should be indicated by a minus sign. round your answers to 3 decimal places.) (a) 2 percent level of significance, two-tailed test.
The critical value of z for each hypothesis test is 2.326
In this question, we are asked to use Excel to find the critical value of z for each hypothesis test. We are given a 2 percent level of significance for a two-tailed test. To find the critical value, we can use the NORM.S.INV function in Excel. The syntax for this function is =NORM.S.INV(probability).
We can enter the probability as 1 - (alpha / 2) for a two-tailed test, where alpha is the level of significance. We can then round the result to three decimal places.
To find the critical value for a 2 percent level of significance, two-tailed test, we can follow these steps:
Step 1: Calculate the value of alpha
Alpha = 2% = 0.02
Step 2: Calculate
1 - (alpha / 2)1 - (alpha / 2)
= 1 - (0.02 / 2)
= 0.99
Step 3: Use the NORM.S.INV function in Excel=NORM.S.INV(0.99)
This gives us a critical value of z = 2.326.
Therefore, the critical value of z for the hypothesis test with a 2 percent level of significance and a two-tailed test is 2.326.
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what is the inductive hypothesis in a proof by strong induction that every simple polygon with at least three sides can be triangulated?
The pieces are reassembled into a triangulation of the original polygon.
What is inductive hypothesis?In a proof by strong induction, the inductive hypothesis is a statement that assumes the desired property is true for all cases up to some fixed size, and then uses that assumption to prove that the property is also true for the next case.
According to information:For the proof that every simple polygon with at least three sides can be triangulated, the inductive hypothesis would be something like,
"Assume that every simple polygon with up to k sides can be triangulated for some fixed k >= 3."
In other words, we are assuming that the property is true for all polygons with up to k sides, where k is some fixed number greater than or equal to 3.
The proof then proceeds by showing that if the property is true for all polygons with up to k sides, then it must also be true for polygons with k+1 sides. This usually involves breaking the (k+1)-sided polygon into smaller pieces (using a diagonal), each of which has fewer sides and can therefore be triangulated by the inductive hypothesis. Finally, the pieces are reassembled into a triangulation of the original polygon.
By completing this proof, we have shown that the property is true for all simple polygons with at least three sides.
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The expression the quantity secant of x plus 1 end quantity over tangent of x was simplified with the following steps:
Step 1: secant x over tangent x plus 1 over tangent x
Step 2: the quantity 1 over cosine x end quantity over tangent x plus 1 over tangent x
Step 3: the quantity 1 over cosine x end quantity over the quantity sine x over cosine x end quantity plus cosine x over sine x
Step 4: 1 over sine x plus cosine x over sine x
Step 5: cosecant x plus cosine x over sine x
Step 6: cosecant x plus cotangent x
Which identity/formula was used to simplify from step 2 to step 3?
The identity used to simplify from step 4 to step 5 is the definition of the cosecant function cosecant x = 1/sine x.
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Expression is (Number/Variable, Arithmetic Operator, Number/Variable).
For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
= the expression 1/sine x
= 1/sine x + cosine x/sine x
= cosecant x + cosine x/sine x
= cosecant x + cotangent x.
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What is the median for 5, 7, 24, 3, 6, 4, 4, 30, 19
There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.
what is median ?When a dataset is sorted from lowest to highest, the median, a measure of central tendency, reflects the midpoint value of the dataset. The values are first presented from lowest to greatest in order to get the median of a set of data. The median is the middle value when there are an odd number of values. Use the following data set as an example: 5, 7, 24, 3, 6, 4, 4, 30, 19. We first organise the data in order before calculating the median: 3, 4, 4, 5, 6, 7, 19, 24, 30
The dataset contains 9 values, which is strange. The middle value, which is six, is therefore the median.
given
We must first arrange the numbers in ascending order in order to determine the median of the group:
3, 4, 4, 5, 6, 7, 19, 24, 30
The median will be the middle number as there are nine numbers in this collection.
There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.
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scientists tagged 770 pike for a research project about a local lake. later, they trapped 270 pike, of which 21 had tags. to the nearest whole number, what is the best estimate for the pike population?
The best estimate for the pike population is 9860, rounded to the nearest whole number.
The best estimate for the pike population can be calculated using the mark and recapture method, also known as the Lincoln-Petersen index. According to this method, the population estimate is given by:
N = (M * C) / R
Where:
N = Population estimate
M = Number of individuals in the first sample
C = Number of individuals in the second sample
R = Number of individuals in the second sample that were tagged in the first sample
Substituting the given values, we get:
N = (770 * 270) / 21
N = 9860
The method used to estimate the pike population is the mark and recapture method, also known as the Lincoln-Petersen index. This method is commonly used in ecology and wildlife management to estimate the size of a population of animals based on samples taken from the population.
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Factor 64v+8w. ASAPPP PLSS
Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran
Step-by-step explanation:
Aright cone has radius 5 ft and slant height 9 ft. The radius and slant height are both multipliedby 1/2. Which of the following correctly describes the effect on the surface area?a. The surface area is multiplied by 4b. The surface area is multiplied by 1/2.c. The surface area is multiplied by 2d. The surface area is multiplied by 1/4
The effect on the surface area is best described by the statement "the surface area is multiplied by 1/4." The correct option is D.
Given that the radius of a right cone is 5 ft and the slant height is 9 ft. If the radius and slant height of the cone are both multiplied by 1/2, then the new radius of the cone will be:5 × (1/2) = 2.5 ft
New slant height of the cone will be:9 × (1/2) = 4.5 ft. The surface area of a cone can be given by the formula:
S = πrl + πr² Where r is the radius of the base, l is the slant height of the cone, and π is a constant (3.14). The surface area of the original cone can be calculated as:
S1 = π × 5 × 9 + π × 5² = 141.37 ft². Now, if we multiply the radius and slant height by 1/2, the new surface area of the cone will be:S2 = π × 2.5 × 4.5 + π × 2.5² = 17.67 ft².
Therefore, the ratio of the new surface area to the original surface area will be:S2/S1 = 17.67/141.37 = 0.125Thus, the new surface area is 1/8th (0.125) of the original surface area or multiplied by 1/8th (1/2 × 1/4). So, the surface area is multiplied by 1/4.
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job elimination in the past year, of businesses have eliminated jobs. if businesses are selected at random, find the probability that at least have eliminated jobs during the last year. round your answer to at least three decimal places. do not round your intermediate calculations.
The probability that at least 5 have eliminated jobs during the last year is 0.002965.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
n = 9
p = probability of businesses have eliminated jobs = 0.13
X = Number of businesses have eliminated jobs ~
Binomial( n= 9 , p = 0.13)
[tex]P(X \geq 5)[/tex]
[tex]P(X \geq 5) = 1-P( X < 5)[/tex]
[tex]P(X \geq 5) = 1-P( X \leq 4)[/tex]
Use following Excel command:
=1-BINOM.DIST(x, n, p, cumulative)
=1-BINOM.DIST(4,9,0.13,TRUE)
=0.0029649
=0.002965
Thus
[tex]\mathbf{{P(X \geq 5) =0.002965}}[/tex].
Therefore, probability that at least 5 have eliminated jobs during the last year is 0.002965.
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Complete question';
Job Elimination in the past year, 13% of businesses have eliminated jobs. If 9 businesses are selected at random, find the probability that at least 5 have eliminated jobs during the last year. Round the answer to at least four decimal places P(at least 5 have eliminated jobs during the last year) X
Solve 2x2 + 26 = 0 to identify the roots.
Help please it’s urgent
By function, The fact that this number is 1/2 indicates the half-life of the substance is 1 year.
How would you define a function in plain English?
A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output.
Every function has an associated domain, codomain, or range. A mathematical function is a rule that, given the values of one or more independent variables and the dependent variable, determines the value of the dependent variable.
300 represents the initial amount of the substance, the amount present at t=0.
0.5 is the fraction of substance remaining at the end of each year. The fact that this number is 1/2 indicates the half-life of the substance is 1 year.
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d. if a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an mba degree (to decimals)?
0.4
The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.
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What is the length of one side of the fenced-in garden? 12 ft 15 ft 21 ft 108 ft
Answer:
B. 15
Step-by-step explanation:
its right on edge
in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, brad has scored 87 , 89 , and 78 on the first three. what range of scores on the fourth test will give brad a c for the semester (an average between 70 and 79 , inclusive)?
Brad needs to score between 72 and 79 on the fourth test in order to get a C for the semester.
To explain why this is so, we need to first understand how the grade for the semester is calculated.Since the final course grade depends entirely on the average of four equally weighted 100-point tests, this means that each test will count for 25% of Brad’s final grade. Therefore, Brad needs to get an average score of 70-79 (inclusive) on the four tests combined in order to get a C for the semester.
In order to calculate what range of scores Brad needs to get on the fourth test in order to get a C for the semester, we need to look at the scores he has already obtained on the first three tests. Brad has scored 87, 89 and 78 on the first three tests. This gives him a total score of 254 (87+89+78=254). This means that Brad needs to get a score of between 70 and 79 on the fourth test in order to reach a total score of between 280-309 (inclusive), which will result in an average score of between 70-79 (inclusive), and give Brad a C for the semester.
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pls help!!!
a jar contains 8 red marbles numbered 1 to 8 and 4 blue marbles numbered 1 to 4. A marble is drawn at random from the jar. Find the probability of the given event.
a) the marble is red:
b) the marble is odd numbered:
c) the marble is red or odd numbered:
d) the marble is blue or even numbered
Answer:
Step-by-step explanation:
I would say A is the answer! :) It's the only problem that matches up.
a person rolls a standard six-sided die 6 6 times. in how many ways can he get 3 3 fives, 2 2 sixes, and 1 1 two?
The person can get 3 fives, 2 sixes, and 1 two in 336 ways.
To find the number of ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die, we can use the formula for combinations with repetition:
[tex]C(n + k - 1, k) = C(6 + 3 - 1, 3) * C(3 + 2 - 1, 2) * C(1 + 1 - 1, 1)[/tex]
where n is the number of possible outcomes (in this case, 6), k is the number of choices to make (in this case, 3 for fives, 2 for sixes, and 1 for twos), and C(n + k - 1, k) represents the number of combinations with repetition.
Using this formula, we can calculate:
[tex]C(8, 3) * C(4, 2) * C(1, 1) = 56 * 6 * 1 = 336[/tex]
Therefore, there are 336 ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die.
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A right rectangular prism is 3 in by 4.75 in by 20.5 in. what is the total surface area of the prism? 151.5 in2 173.125 in2 317.75 in2 346.25 in2
The rectangular prism is 3 inches by 4.75 inches by 20.5 inches, has a total surface area of 346.25 in².
We need to find the surface area of an object, the surface area of a solid three-dimensional object is the area of the boundary surface of the object and its surroundings, therefore:
The dimensions of the rectangular prism will be as follows:
Let the length of the rectangular prism = 3 inches
Let the width of the prism = 4.75 inches
Let the height of the prism = 20.5 inches
Therefore, the surface area, A, of a rectangular prism can be found using the formula:
A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width
Therefore, the surface area of the rectangular prism in the question is found as follows:
Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25
The total surface area of the rectangular prism is 346.25 in².
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Answer:
346.25
Step-by-step explanation:
took the test :)
Landon owns 16 baseball cards, which is 4 times as many as Phillip owns. The equation 4p = 16 represents this situation where p is the number of baseball cards Phillip owns. Which number line represents the solution to the equation?
The number line :0-------------4-------------10 represents the solution to the equation.
What Is an integer?
An integer is a whole number that can be positive, negative, or zero. In other words, integers are numbers that can be written without fractions or decimals.
Examples of integers are: -3, -2, -1, 0, 1, 2, 3, and so on.
The equation 4p = 16 represents the number of baseball cards owned by Phillip, where p is the number of baseball cards owned by him.
To solve for p, we can divide both sides of the equation by 4:
4p/4 = 16/4
p = 4
Therefore, Phillip owns 4 baseball cards.
Now we need to represent this solution on a number line. We can draw a number line with 0 on the left and 10 on the right, marking every integer in between. Then we can place a dot at the point corresponding to the number 4, which represents the number of baseball cards owned by Phillip.
Therefore the number line :
0-------------4-------------10
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A car uses 50 litres of fuel to complete a 400kmalong a high way. How far will it work if it uses 20 litres
Answer:
[tex]\huge\boxed{\sf 160 \ km}[/tex]
Step-by-step explanation:
Given that,
50 liters = 400 km
Using unitary method.
Divide both sides by 5050/50 liter = 400/50 km
1 liter = 8 km
Multiply both sides by 201 × 20 liter = 8 × 20 km
20 liters = 160 km[tex]\rule[225]{225}{2}[/tex]
Sin^2(45+A)+sin^2(45-A)=1
Prove it
Answer:
Step-by-step explanation:
Setting A=45, we see that it is not true. However, you might find the following revealing:
sin2(45+A)=(sin45cosA+cos45sinA)2=12(1+2cosAsinA)
sin2(45−A)=(sin45cosA−cos45sinA)2=12(1−2cosAsinA)
Now, stare.
1.6.1) Does the relationship in the table represents direct or inverse/indirect proportion?
1.6.2) Determine the value of a.
1.6.3) Determine the distance a car will travel using the first two values in the table.
Answer:
1.6.1) Inversely proportional
1.6.2) 0.6h
1.6.3) 120km
Step-by-step explanation:
1.6.1)
Inversely proportional relationships are in the form of [tex]y=k/x[/tex]
[tex]y=time=t[/tex]
[tex]x=speed=v[/tex]
If we the relationship is inversely proportional, [tex]k[/tex] must be constant for all values.
[tex]yx=k[/tex]
So we just have to check the value of [tex]yx[/tex] in all cases.
[tex]20*3=60\\50*1.2=60\\80*0.75=60[/tex]
Hence relation is inversely proportional.
1.6.2)
[tex]k=60, x=100, y=k/x\\[/tex]
∴[tex]y=60/100[/tex] ⇒[tex]y=0.6[/tex]
1.6.3)
Distance formula:
[tex]v=s/t\\v*t=s\\s=(20*3) + (50*1.2)\\s=60 + 60\\s=120[/tex]
what is the area beyond the z-score in the tail for a z-score of .63? group of answer choices 0.2357 -.2643 0.2643 -.2357
The area beyond the z-score in the tail for a z-score of .63 is 0.2643. This means that there is a 26.43% chance that a sample is at least as extreme as the z-score of .63.
To understand this concept, it is important to first have a basic understanding of the z-score and the normal distribution. A z-score is the number of standard deviations away from the mean of a normal distribution. It is also referred to as a standard score. It is a measure of how far a sample is from the mean. For a given sample, the higher the z-score, the farther away it is from the mean.
When looking at the normal distribution, the area of the tail is the area beyond the z-score. This means that the area of the tail is the area of the distribution that is beyond the z-score of the given sample. In other words, it is the area of the distribution that is farther away from the mean than the z-score. For example, for a z-score of .63, the area of the tail is the area of the distribution that is farther away from the mean that .63 standard deviations.
When finding the area beyond the z-score, it is important to understand that it is divided into two parts, the area in the left tail and the area in the right tail. The area in the left tail is the area beyond the z-score in the direction of the negative standard deviations. This means that it is the area of the distribution that is farther away from the mean than the negative z-score. The area in the right tail is the area beyond the z-score in the direction of the positive standard deviations. This means that it is the area of the distribution that is farther away from the mean than the positive z-score.
For the given z-score of .63, the area beyond the z-score in the tail is 0.2643. This means that there is a 26.43% chance that a sample is at least as extreme as the z-score of .63. This area is divided into the areas in the left tail of -.2643 and the area in the right tail of 0.2357.
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In the last basketball game, Elena scored 2 more than one fourth of herteam's total points.
Part A: Let n represent the number of points Elena's team scored.
Write an expression for the number of points Elena scored.
Part B: The team scored 40 points. How many points did Elena
score?
[tex]E = 2 + \dfrac{1}{4} \ \text{n}[/tex]
[tex]n = 40[/tex]
[tex]E = 2 + \dfrac{1}{4} (40)[/tex]
[tex]E= 2 + 10[/tex]
[tex]E = 12[/tex]
Elena scored 12 points
in the past year, 13% of businesses have eliminated jobs. if 5 businesses are selected at random, find the probability that at least 3 have eliminated jobs during the last year. round your answer to at least three decimal places. do not round your intermediate calculations.
The probability that at least 3 out of 5 businesses have eliminated jobs in the past year is 0.0556.
To find the probability that at least 3 out of 5 businesses have eliminated jobs, we can use the binomial probability formula:
P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)
where X is the number of businesses out of 5 that have eliminated jobs, and P(X = k) is the probability of exactly k businesses out of 5 eliminating jobs.
Using the binomial probability formula, we can calculate the probabilities for each possible value of X:
P(X = 3) = (5 choose 3) x (0.13)³ x (0.87)² = 0.0519
P(X = 4) = (5 choose 4) x (0.13)⁴ x (0.87)¹ = 0.0036
P(X = 5) = (5 choose 5) x (0.13)⁵ x (0.87)⁰ = 0.0001
where (n choose k) represents the number of ways to choose k items from a set of n items, and can be calculated using the formula:
(n choose k) = n! / (k! * (n - k)!)
where n! represents the factorial of n.
Now we can add up these probabilities to get the probability of at least 3 out of 5 businesses having eliminated jobs:
P(X >= 3) = 0.0519 + 0.0036 + 0.0001 = 0.0556
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Isabella rents an apartment for $1,500 a month and has a year's lease. she owns a car that is worth $16,700. she has a savings account of $4,950 and a credit card balance of $925. what is her net worth?
Isabella's net worth is $2,725.
We know that the net worth is nothing but a measure of an individual's financial standing at a given point in time.
Here, to calculate the net worth, we need to add up all of the assets and subtract all of her liabilities:
We can see that,
Assets
Car worth: $16,700
Savings account: $4,950
So, the total assets worth:
$16,700 + $4,950 = $21,650
Now liabilities:
Credit card balance: $925
And the rent for the remainder of the lease:
$1,500 x 12 = $18,000 for year
So, the total liabilities would be:
$925 + $18,000 = $18,925
Hence her net worth would be:
21,650 - 18,925 = 2,725 dollars
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The median is greater than the mean, and the majority of the data points are to the left of the mean. the median is greater than the mean, and the majority of the data points are to the right of the mean. the mean is greater than the median, and the majority of the data points are to the left of the mean. the mean is greater than the median, and the majority of the data points are to the right of the mean.
The option that describes the probability distribution is option (A) The mean is greater than the median, and the majority of the data points are to the left of the mean.
To find the mean of the probability distribution, we can use the formula:
mean = Σ(xi × pi)
where xi is the value of the random variable and pi is the corresponding probability.
Using this formula, we get:
mean = (1 × 0.75) + (2 × 0.1) + (3 × 0.1) + (4 × 0.05) + (5 × 0)
= 0.75 + 0.2 + 0.15 + 0.2
= 1.3
To find the median, we need to arrange the values in increasing order of x and then find the middle value.
Arranging the values in increasing order of x, we get:
x = 1, 2, 3, 4, 5
p(x) = 0.75, 0.1, 0.1, 0.05, 0
The median is the middle value, which is 3 in this case.
Therefore, the mean is 1.3 and the median is 3.
Since the mean is greater than the median, we can eliminate options C and D.
To determine whether the majority of the data points are to the left or right of the mean, we can examine the shape of the distribution.
Since the probability of x=1 is much higher than the other values, the distribution is skewed to the left. This means that the majority of the data points are to the left of the mean.
Therefore, the correct option is (A) The mean is greater than the median, and the majority of the data points are to the left of the mean.
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The given question is incomplete, the complete question is:
Which of the following describes the probability distribution below?
A.) The mean is greater than the median, and the majority of the data points are to the left of the mean.
B.) The mean is greater than the median, and the majority of the data points are to the right of the mean.
C.) The median is greater than the mean, and the majority of the data points are to the left of the mean.
D.) The median is greater than the mean, and the majority of the data points are to the right of the mean.
Small pizzas at Ponnie's Pizza are cut into 6 pieces. The circumference of a small pizza is 12π inches. A large pizza is cut into 8 pieces. The diameter of a large pizza is 16 inches.
Joannie eats 2 slices of a small pizza. Mark eats 5 slices of a large pizza.
How many times greater are the square inches of pizza that Mark ate than the square inches of pizza that Joannie ate?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
Mark ate 3.3 times the square inches of pizza than Joannie ate.
Step-by-step explanation:
Small pizzaThe formula for the circumference of a circle is C = 2πr (where r is the radius). If the circumference of a small pizza is 12π inches, then its radius is:
[tex]\implies \sf Radius_{small\;pizza}=\dfrac{circumference}{2\pi}=\dfrac{12\pi}{2\pi}=6\;inches[/tex]
The formula for the area of a circle is A = πr² (where r is the radius).
Therefore, the area of a small pizza is:
[tex]\implies \sf Area_{small\;pizza}=\pi \cdot 6^2=36\pi \; in^2[/tex]
If the small pizzas are cut into 6 congruent pieces, the area of one slice of small pizza is:
[tex]\begin{aligned}\implies \sf Area_{small\;slice}&=\sf \dfrac{Area_{small\;pizza}}{6}\\\\&=\dfrac{36 \pi}{6}\\\\&=6 \pi \; \sf in^2\end{aligned}[/tex]
Therefore, the area of one slice of small pizza is 6π square inches.
[tex]\hrulefill[/tex]
Large pizzaThe diameter of a circle is twice its radius.
If the diameter of a large pizza is 16 inches then its radius is:
[tex]\implies \sf Radius_{large\;pizza}=\dfrac{diameter}{2}=\dfrac{16}{2}=8\;inches[/tex]
The formula for the area of a circle is A = πr² (where r is the radius).
Therefore, the area of a large pizza is:
[tex]\implies \sf Area_{large\;pizza}=\pi \cdot 8^2=64 \pi \; in^2[/tex]
If the large pizzas are cut into 8 congruent pieces, the area of one slice of large pizza is:
[tex]\begin{aligned}\implies \sf Area_{large\;slice}&=\sf \dfrac{Area_{large\;pizza}}{8}\\\\&=\dfrac{64 \pi}{8}\\\\&=8 \pi \; \sf in^2\end{aligned}[/tex]
Therefore, the area of one slice of large pizza is 8π square inches.
[tex]\hrulefill[/tex]
If Joannie eats 2 slices of small pizza, the square inches of pizza she ate is:
[tex]\implies \sf Joannie=2 \times 6 \pi = 12 \pi\;in^2[/tex]
If Mark eats 5 slices of large pizza, the square inches of pizza he ate is:
[tex]\implies \sf Mark =5 \times 8 \pi = 40\pi\;in^2[/tex]
To calculate how many times greater are the square inches of pizza that Mark ate than the square inches of pizza that Joannie ate, divide the area Mark ate by the area Joannie ate:
[tex]\implies \sf \dfrac{40 \pi}{12 \pi} = \dfrac{10}{3}=3.3\;(nearest\;tenth)[/tex]
Therefore, Mark ate 3.3 times the square inches of pizza than Joannie ate.
The S.S of the two equations : X+2y =5, and 2x+ky=3 in RxR equals phi then k=?
The value of k such that the solution set of the system is empty is any value of k that is not equal to 4.
What is equation?A mathematical statement that expresses the equivalence of two numbers or expressions is known as an equation. It has two sides, the left-hand side (LHS) and the right-hand side (RHS), which are equal and are divided by the equal symbol (=). Variables, constants, and mathematical operations like addition, subtraction, multiplication, and division can all be found in an equation.
To find the value of k such that the solution set of the system of equations X + 2y = 5 and 2x + ky = 3 is the empty set (i.e., the intersection of their solution sets is the empty set), we can use the determinant of the coefficient matrix.
The coefficient matrix for the system is:
| 1 2 |
| 2 k |
The determinant of this matrix is:
[tex]det(| 1 2 |[/tex]
| 2 k |) = (1)(k) - (2)(2) = k - 4
For the solution set of the system to be empty, the determinant must be non-zero, since a zero determinant would indicate that the coefficient matrix is singular and therefore the system has no unique solution.
So, we need to solve the equation k - 4 ≠ 0 for k:
k - 4 ≠ 0
k ≠ 4
To know more about equation:
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Which polynomial is in standard form?
A) 2+x+ 5x²-x³ + 2x4
B) x + 5x³ + 6x² + x - 2
C) 2x + 3x² - 4x³ + 3x² + 2
D) 4x³ + 5x² + 6x6 +7x4-2
Answer:
Step-by-step explanation:
Option A) 2+x+ 5x²-x³ + 2x4 is not in standard form because the terms are not arranged in descending order of exponents.
Option B) x + 5x³ + 6x² + x - 2 also, is not in standard form because like terms are not combined and the terms are not arranged in descending order of exponents.
Option C) 2x + 3x² - 4x³ + 3x² + 2 can be simplified to get: -4x³ + 6x² + 2x + 2. This is not in standard form because the terms are not arranged in descending order of exponents.
Option D) 4x³ + 5x² + 6x6 +7x4-2 can be simplified to get: 6x6 +7x4 + 4x³ + 5x² - 2. This is in standard form because the terms are arranged in descending order of exponents.
Therefore, the polynomial in standard form is option D) 6x6 +7x4 + 4x³ + 5x² - 2.
In the diagram below, what is the measure of angle x?
Answer: C - 105
Step-by-step explanation:
75+75=150
360-150=210
210/2=105