The probability is approximately 0.129 or 12.9%.
Describe probability ?Probability can also be used to describe more complex events, such as the likelihood of a stock price increasing by a certain amount in a given period of time, or the probability of a medical treatment being effective for a certain disease.
To calculate the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag, we need to use the binomial probability formula:
P(X >= 48) = 1 - P(X < 48)
Where
X is the number of orange Stattles in a 14 ounce bag
P(X < 48) is the probability of getting less than 48 orange Stattles in a 14 ounce bag
To calculate P(X < 48), we need to use the binomial probability formula:
[tex]P(X = x) = (nCx) * p^x * q^{(n-x)[/tex]
Where
n is the number of Stattles in a 14 ounce bag (we don't know this value)
x is the number of orange Stattles in a 14 ounce bag (we want to find the probability of getting less than 48)
p is the probability of getting an orange Stattle (0.4)
q is the probability of getting a non-orange Stattle (0.6)
nCx is the binomial coefficient
nCx is the binomial coefficient, which can be calculated using the formula:
nCx = n! / (x! * (n-x)!)
where ! denotes the factorial function.
We can use a cumulative binomial distribution table or a binomial calculator to find the probability of getting less than 48 orange Stattles in a 14 ounce bag. For example, using an online calculator, we find that:
P(X < 48) = 0.871
Therefore, the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag is:
P(X >= 48) = 1 - P(X < 48) = 1 - 0.871 = 0.129
So, the probability is approximately 0.129 or 12.9%.
To know more about binomial visit :
brainly.com/question/24756209
#SPJ1
Let h = height. Write an
inequality to show that a child must be at least 48 inches tall to ride the rollercoaster.
Answer:
h [tex]\ge[/tex] 48
Step-by-step explanation:
This inequality states that the height h, must be either equal to 48 to greater than 48.
The mean score of the students in Dr. Battle’s math class on the most recent quiz was 78 points with a standard deviation of 6 points. If these scores can be modeled using a normal distribution, which percentage best represents the number of students with quiz scores between 72 and 90 points?
Approximate Percentages of Data in a Normal Distribution:
• 68% of the data lie within 1 standard deviation of the mean.
• 95% of the data lie within 2 standard deviations of the mean.
• 99.7% of the data lie within 3 standard deviations of the mean.
Responses
A.68.0%
B.81.5%
C.95.0%
D.97.5%
The percentage of students with quiz scores between 72 and 90 points would be 81.5%.
What is standard deviations?Standard deviations is a statistical measure of the spread of data points around the mean in a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Standard deviations are used to measure the uncertainty of a statistic or the variability of a population or sample of observations.
This answer is correct because the data is being modeled using a normal distribution. This means that the quiz scores can be described as a bell-shaped curve, with the mean score of 78 points being the highest peak. The 68% of the data that lies within 1 standard deviation of the mean would be between 72 and 90 points, which is the range specified in the question, so the answer is 81.5%. This is because 68% of the data lies within 1 standard deviation of the mean and 13.5% of the data lies within the second standard deviation of the mean. The sum of these two figures (68% + 13.5%) is 81.5%. Therefore, the percentage of students with quiz scores between 72 and 90 points would be 81.5%.
To know more about standard deviations click-
https://brainly.com/question/475676
#SPJ1
Probability and Stats: Suppose a group of research proposals was evaluated by a panel of experts to decide whether or not they were worthy of funding. When these same proposals were submitted to a second independent panel of experts, the decision to fund was reverse in 74 % of the cases. If the probability that a proposal is judged worth of funding by the first panel is 22 %, what is the probability that a worthy proposal is disapproved by both panels?
Answer: Let's define the events:
A: a proposal is judged worthy of funding by the first panel
B: the decision to fund a proposal is reversed by the second panel
We want to find the probability of the intersection of events A and B (i.e., a worthy proposal is disapproved by both panels). We can use the formula:
P(A and B) = P(B|A) * P(A)
We know that P(A) = 0.22 (the probability that a proposal is judged worthy of funding by the first panel). We also know that when a proposal is judged worthy of funding by the first panel, the probability that the decision to fund is reversed by the second panel is 0.74 (i.e., P(B|A) = 0.74).
Plugging in these values, we get:
P(A and B) = 0.74 * 0.22 = 0.1628
Therefore, the probability that a worthy proposal is disapproved by both panels is 0.1628, or approximately 16.28%.
Step-by-step explanation:
Answer the following questions on the basis of the following three sets of data for the country of North Vaudeville:
(A)
Price Level
110
100
95
90
Real GDP
(A)
275
250
225
200
The data in
Price
Level
(B)
100
100
100
100
Real GDP
(B)
200
225
250
275
Price
Level
(C)
110
100
95
90
Real GDP
(C)
225
225
225
225
a. Which set of data illustrates aggregate supply in the immediate short run in North Vaudeville?
The data in B
The short run?
The long run?
The data in C
b. Assuming no change in hours of work, if real output per hour of work increases by 10 percent, what will be the new levels of real
GDP in the right column of A?
Instructions: Enter your answers rounded to the nearest whole number.
At a price level of 110:
At a price level of 100:
At a price level of 95: [
At a price level of 90:
The solutions are given below.
What is GDP?Gross domestic product is a monetary measure of the market value or the market value of all the final goods and services produced and sold in a specific time period by a country or countries, generally "without double counting the intermediate goods and services used up to produce them".
here, we have,
1a. We can see immediate short run aggregate supply in North vaudeville in column A. This is because the price is fixed while output increases
1b. We can see short run aggregate supply in North vaudeville in column c. This is because output increases with price increase.
1c we can see long run aggregate supply in North vaudeville in column B. This is because output is constant with price increase.
Assuming output per hour of work decreases by 25% for column C then for each price, output is:
2A. Given price P= 110, output is 285(1-0.25) = 213.75
2B. Given price P = 100, output is 260(1-0.25) = 195
2C. Given price P = 95, output is 235(1-0.25) = 176.25
2D. Given price P = 90, output is 210(1-0.25) = 157.50
3. The new data from question 2 reflects a decrease in aggregate supply.
To learn more on GDP click:
https://brainly.com/question/30737857
#SPJ1
3. The coordinates of the vertices of quadrilateral LOVE are L (-2, -1), O (2, 1), V (5, 0), and E (-1, -3). Grace states that quadrilateral LOVE is a parallelogram. Is Grace correct? Support your answer and show all your work.
The given vertices don't form parallelograms.
What is parallelogram:A parallelogram is a quadrilateral with two pairs of parallel sides. In other words, opposite sides of a parallelogram are parallel and have the same length. Examples of parallelograms include rectangles, rhombuses, and squares.
Here we have
The coordinates of the vertices of quadrilateral LOVE are L (-2, -1), O(2, 1), V (5, 0), and E (-1, -3).
Using the distance formula we can find the lengths of the sides as follows
From L (-2, -1) and O(2, 1),
=> LO = √[ (2 + 2)² + (1 + 1)² ] = √20
From O(2, 1) and V (5, 0)
=> OV = √[ (5 - 2)² + (0 + 1)² ] = √10 d = √(x2 - x1)^2 + (y2 - y1)^2)
From V (5, 0) and E (-1, -3)
=> VE = √[(-1 - 5)² + (-3 - 0)²] = √45
From L (-2, -1) and E (-1, -3)
=> LE = √[(-1 +2 )² + (-3 + 1)²] = √5
Here LO ≠ OV ≠ VE ≠ LE
Therefore,
The given vertices don't form parallelograms.
Learn more about Parallelograms at
https://brainly.com/question/29147156
#SPJ1
PLEASE HELP The toll to cross a bridge is $1.25. If $72.50
was collected at a toll booth in one hour,
how many cars went through the booth? How would you put that in an equation with the letter C?
The answer to this question is as follows The formula for the letter C is: equation $1.25C = $72.50
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
Let C represent the volume of vehicles that passed through the booth.
As $1.25 is the amount collected per vehicle, the following equation represents the total amount collected:
Total = $1.25 plus C
Also, we are aware that $72.50 was collected in one hour, allowing us to create another equation:
$72.50 = $1.25 × C
We may divide both sides by $1.25 to find C:
C = $72.50 ÷ $1.25
C = 58
58 vehicles passed through the booth as a result.
The formula for the letter C is:
$1.25C = $72.50
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Use all the numbers below and use addition, subtraction, multiplication and/or division, and find an expression that
equals the target number. The target number is -2. The numbers provided are -1, -3, -5, -7, and -2
Answer: One possible expression that equals the target number (-2) using the given numbers (-1, -3, -5, -7, and -2) and basic arithmetic operations (+, -, *, /) is:
-3 * (-5) + (-7) - (-2) / (-1) = -2
Explanation:
-3 * (-5) = 15 (multiplication of -3 and -5 gives +15)
-7 - (-2) = -5 (subtracting a negative is the same as adding a positive, so -7 - (-2) = -7 + 2 = -5)
-2 / (-1) = 2 (dividing a negative number by a negative number gives a positive result, so -2 / (-1) = 2)
Therefore, 15 + (-5) + 2 = -2
Step-by-step explanation:
Describe how to solve 3-7n=27
Answer:
n = -24/7
Step-by-step explanation:
3 -7n = 27
-7n = 24 Subtract 3 from both sides
n = -24/7 Divided by -7 both sides
So, the answer is n = -24/7
Answer:
Below
Step-by-step explanation:
Subtract 3 from both sides of the equation THEN divide both sides of the equation by - 7
RIDDLE: Why was the Mathematician Late for Work?
Directions: Find the slope between each pair of points Show all work on a separate sheet of paper. After completing each set, find matching answers. One will have a letter and the other a number. Write the letter in the matching numbered box at the bottom of the page.
SET 2
T. (7, 5) and (10, 9) ______________ 16. (-5, -2) and (9,2)__________
B. (-8, 2) and (-5, -4) ______________ 8. (-10, -6) and (2, -8) _________
H. (2, -2) and (-4, -1) ______________ 3. (-2, 1) and (-8, -7) ___________
S. (-4, 9) and (-11, 7) ______________ 5. (-4, -2) and (-3, 3) ___________
O. (5, -1) and (4, -6) ______________ 14. (-2, -4) and (-7, 6) ___________
SET 3
K. (1, -3) and (2, -3) ______________ 9. (8, -1) and (6, -4) ___________
R. (3, 0) and (-3, 5) ______________ 1. (-11, -6) and (-8, -5) ___________
E. (12, 4) and (8, -2) ______________ 15. (-5, 4) and (-5, 3) ___________
U. (7, -3) and (7, -9) ______________ 12. (-2, -3) and (-5, 9) ___________
O. (3, 1) and (2, 5) ______________ 6. (-3, 8) and (7, 8) ______________
H. (-1, -6) and (-7, -8) ______________ 10. (-5, 3) and (7, -7) __________
TAKE YOUR TIME!!! THIS IS 60 POINTS!
The slopes of the points are computed below
How to determine the slopes of the pointsThe slope of any two points is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Using the above as a guide, we have the following slopes in set 2
T. Slope = (9-5)/(10-7) = 4/316. Slope = (2-(-2))/(9-(-5)) = 2/7B. Slope = (-4-2)/(-5-(-8)) = -28. Slope = (-8-(-6))/(2-(-10)) = -1/6H. Slope = (-1-(-2))/(-4-2) = -1/63. Slope = (-7-1)/(-8-(-2)) = 4/3S. Slope = (7-9)/(-11-(-4)) = 2/75. Slope = (3-(-2))/(-3-(-4)) = 5O. Slope = (-6-(-1))/(4-5) = 514. Slope = (6-(-4))/(-7-(-2)) = -2For set 3, we have the following slope values
K. Slope = (-3-(-3))/(2-1) = 09. Slope = (-4-(-1))/(6-8) = 3/2R. Slope = (5-0)/(-3-3) = -5/61. Slope = (-5-(-6))/(-8-(-11)) = 1/3E. Slope = (-2-4)/(8-12) = 3/215. The slope is undefined U. The slope is undefined 12. Slope = (9-(-3))/(-5-(-2)) = -4O. Slope = (5-1)/(2-3) = -46. Slope = (8-8)/(7-(-3)) = 0H. Slope = (-8-(-6))/(-7-(-1)) = 1/310. Slope = (-7 - 3)/(7 - (-5)) = -5/6Read more about slope at
https://brainly.com/question/29135291
#SPJ1
Homework: 1. The cost of 4 cartons of milk is $12. What's the unit price? Ratio $12:4 cartons of milk
If f(x) = Sin3x+x , verify that f(-x)=-f(x).
Answer:
True
Step-by-step explanation:
Given a function:
[tex]\displaystyle{f(x)=\sin 3x + x}[/tex]
Verify that f(-x) = -f(x) by substitution -- therefore:
[tex]\displaystyle{f(-x) = -f(x)}\\\\\displaystyle{\sin 3\left(-x\right)+\left(-x\right) = -\left(\sin 3x + x\right)}\\\\\displaystyle{\sin \left(-3x\right) - x = -\sin 3x - x}\\\\\displaystyle{-\sin 3x - x = -\sin 3x - x}[/tex]
Both sides are equal, hence f(-x) = -f(x).
honestly just need some help
Answer:
B
Step-by-step explanation:
The dashed lines are problem asymptotes, where the denominator is 0. It's showing those at x = 0 and x = 4. Plug in 0 to answer B and you get
(0)(0-4) and that equals 0
Plugging in 4, you get
(4)(4-4) = 4(0) and that also equals 0
0 is what creates that space in the function and disconnects it
Find all the missing angles in the diagram below. Explain how you used two different angle theories to find at least two missing angles.
The measures of the angles in the parallel lines is
m∠a = 97°
m∠b = 15°
m∠c = 68°
m∠d = 68°
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the two parallel lines be represented as l and m
Now , the transversal line is t
The measure of m∠a = 97° ( corresponding angles )
The measure of m∠d = 180° - 112° ( angles in a straight line = 180° )
So , the measure of m∠d = 68°
The measure of m∠c = measure of m∠d ( alternate interior angles )
So , the measure of m∠c = 68°
From the triangle formed by the intersection of lines ,
The measure of m∠b = 180° - ( a + d ) ( angles of a triangle = 180° )
So , the measure of m∠b = 180° - ( 97° + 68° )
The measure of m∠b = 15°
Hence , the measures of angles are solved
To learn more about parallel lines cut by transversal click :
https://brainly.com/question/28182928
#SPJ1
Explain how to identify the major and minor axes of an ellipse are by looking at both the graph and the equation.
In the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.
What is ellipse?An ellipse is a geometric shape that is a type of curve. In mathematics, an ellipse is defined as a set of points in a plane, such that the sum of the distances between any point on the curve and two fixed points is a constant which is known as foci.
To identify the major and minor axes of an ellipse, you can use both the graph and the equation of the ellipse.
Identify the major and minor axes using the graph: The major axis is the longest diameter of the ellipse, which passes through the center and touches the curve at two points called the vertices. The minor axis is the shortest diameter of the ellipse, which also passes through the center and touches the curve at two points called the co-vertices. On the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.
Identify the major and minor axes using the equation: The equation of an ellipse can be written in the standard form:
[tex]\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1[/tex]
where the ellipse's center is (h, k), the semi-major axis' length is a, and the semi-minor axis' length is b. The semi-major axis is half the length of the major axis, while the semi-minor axis is half the length of the minor axis. Therefore, you can identify the major and minor axes by looking at the denominators of the terms that contain x and y in the equation. The larger denominator corresponds to the semi-major axis, while the smaller denominator corresponds to the semi-minor axis.
To know more about graph, Visit:
https://brainly.com/question/401878
#SPJ1
Class A: 87, 93, 96, 88, 92, 90, 100, 93, 91, 96
Class B: 72, 69, 54, 66, 63, 74, 59, 64, 70, 68
1. Find the mean, median, and mode for class A
Mean
Median
Mode
2. Find the mean, median, and mode for class B
Mean
Median
Mode
Answer:
Class A: 87, 93, 96, 88, 92, 90, 100, 93, 91, 96
Mean: 92.6
Median: 92.5
Mode: 93 and 96
Class B: 72, 69, 54, 66, 63, 74, 59, 64, 70, 68
Mean: 65.9
Median: 67
Mode: No mode or 0
Step-by-step explanation:
You're welcome.
I need help with this please help me
The measure of the angle ∠ADB of the parallelogram is m∠ADB = 49°
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be represented a ABCD
Now , the measure of ∠ACB = ( 13x - 16 )°
The measure of ∠ACB = ( 9x + 4 )°
And , the measures of the angles ∠ACB = measure of ∠ACB
On simplifying , we get
13x - 16 = 9x + 4
On simplifying , we get
4x = 20
Divide by 4 on both sides , we get
x = 5
So , the measure of m∠ACB = ( 9 ( 5 ) + 4 ) = 49°
The measure of m∠ADB = measure of m∠ACB ( alternate angles )
So , the measure of m∠ADB = 49°
Hence , the angles of the parallelogram are solved
To learn more about parallelogram click :
https://brainly.com/question/23488153
#SPJ1
A store manager instructs some new trainees that a ladder priced at $21 winds up costing a customer $22.05 once the sales tax is included. What is the sales tax percentage?
Answer:
0.05%
Step-by-step explanation:
Qashley has 85 cents.
Noah has 50 cents, and his mother gives him 3
quarters. How much money does Noah have?
Answer: $1.25
Step-by-step explanation: Noah has $1.25 because since Noah has 50 cents, and you add on another 75, you get $1.50
Answer:
Noah has 50 cents initially and his mother gives him 3 quarters, which is 75 cents (3 quarters x 25 cents/quarter).
Therefore, in total, Noah has 50 cents + 75 cents = 125 cents.
In dollars, that is $1.25.
You work for a pet-grooming service. You record the number of animals you groomed each day over a 10-day period: 7, 10, 8, 9, 7, 11, 8, 6, 7, and 9. You state that the typical number of animals that you can groom is the mean of 8.2 animals per day.
Does this measure of central tendency describe the data well?
Yes, because the mean always describes data well.
Yes, because there are no outliers to skew the data.
No, because it is not possible to groom 0.2 of an animal.
No, because the most common number of dogs groomed is 7.
Yes, because half of the time, it is possible to groom more than 8.2 and half the time less than 8.2.
No because it is not possible to groom 0.2 of an animal.
What is median ?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, the median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the center of a sequence to determine its value.
To support this, we can also calculate the median and mode of the data set to see if they are close to the mean. The median is the middle value of the sorted data set, which is 8 in this case, and the mode is the most common value, which is also 7 and 8 in this data set. So, the mean, median, and mode are all relatively close to each other, indicating that the data is roughly symmetric around the center.
Based on the given data, the mean of 8.2 animals per day can be considered as a reasonable measure of central tendency.
Hence the answer is No because it is not possible to groom 0.2 of an animal.
Learn more about median, by the following link
https://brainly.com/question/14532771
#SPJ1
Answer:
Yes, because there is no outliers to skew the data.
Step-by-step explanation:
I did the quiz
i can’t get this question
Answer:
19
y = 6x - 11 it says the input is 5 so you input 5 as x
y = 6(5) - 11
y = 30 - 11
y = 19
Suppose you are a (junk) bond broker who buys only bonds that have a 50% chance of default. You want a portfolio with at least five bonds that do not default. You can dispose of the other bonds in the portfolio with no great loss. What is the smallest number of bonds you should buy if you want to be at least 97% sure that five or more bonds will not default?
Answer:
We should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.
Step-by-step explanation:
This problem can be solved using the binomial distribution, which can tell us the probability of getting a certain number of successes in a given number of trials, each with a certain probability of success. In this case, the trials are the bonds, the probability of success is 50% (the chance that a bond will not default), and we want to know how many bonds we need to buy to have at least a 97% chance of getting 5 or more successes.
Let X be the number of bonds that do not default. We want to find the smallest value of n (the total number of bonds we buy) such that P(X ≥ 5) ≥ 0.97.
Using the binomial distribution, we can calculate that the probability of getting exactly k successes out of n trials with a probability p of success is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n without regard to order.
To find P(X ≥ 5), we can calculate the probabilities of getting 5, 6, 7, 8, 9, or 10 successes and add them up:
P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
We want this probability to be at least 0.97, so we can set up the following inequality:
P(X ≥ 5) ≥ 0.97
P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) ≥ 0.97
We can then use a spreadsheet or a binomial probability table to find the smallest value of n that satisfies this inequality. For example, using Excel's BINOM.DIST function, we can enter the following formula in a cell:
=BINOM.DIST(4,n,0.5,TRUE) + BINOM.DIST(5,n,0.5,TRUE) + BINOM.DIST(6,n,0.5,TRUE) + BINOM.DIST(7,n,0.5,TRUE) + BINOM.DIST(8,n,0.5,TRUE) + BINOM.DIST(9,n,0.5,TRUE) + BINOM.DIST(10,n,0.5,TRUE)
where n is the number of bonds we want to buy, and TRUE indicates that we want to calculate the cumulative distribution function (CDF) up to the given value of k.
We can then use Excel's Goal Seek tool to find the smallest value of n that makes this formula equal to 0.97. For example, if we set the target value to 0.97 and the "Set cell" to the formula cell, and we vary the "To value" of n, Goal Seek finds that the smallest value of n that satisfies the inequality is 19. Therefore, we should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.
Identify the inequality graphed on the number line.
The answer should be: x [tex]\geq[/tex] -10
7.All angles are right angles. Solve for x in the given Rectangle. 5 in x = x. 12 in
8. it says AC not AS
The length of the diagonal of the rectangle is AC = 17.69 units
What is the diagonal of a rectangle?The diagonal of a rectangle is calculated by the formula
From the Pythagoras Theorem , The hypotenuse² = base² + height² , and
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
Given data ,
Let the rectangle be represented as ABCD
Now , the measure of side AB = 12 units
The measure of side BC = 13 units
Let the length be BC and the width be AB
where the diagonal of the rectangle is AC
Now , Diagonal of a Rectangle = √ ( Length )² + ( Width )²
On simplifying , we get
The diagonal of the rectangle AC = √ ( 12 )² + ( 13 )²
The diagonal of the rectangle AC = √ ( 144 + 169 )
The diagonal of the rectangle AC = √313
The diagonal of the rectangle AC = 17.69 units
Hence , the diagonal of the rectangle is 17.69 units
To learn more about diagonal of the rectangle click :
https://brainly.com/question/13583275
#SPJ1
A forgetful farmer is in trouble! He cannot remember how many pigs and how many ducks he has! He knows that altogether he has 28 animals and combined they have 72 legs. Help this poor guy out! How many pigs does he have? How many ducks does he have?
The number of ducks in a farm are 20 and the number of pigs in a farm are 8.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, in a farm there are 28 animals and combined they have 72 legs.
Let the number of pigs be p and let the number of ducks be d.
Here, p+d=28 ------(i)
4p+2d=72 -------(ii)
From equation (i), p=28-d
Substitute p=28-d in equation (ii), we get
4(28-d)+2d=72
112-4d+2d=72
112-72=2d
d=20
Substitute d=20 in equation(i), we get
p+20=28
p=8
Therefore, the number of ducks in a farm are 20 and the number of pigs in a farm are 8.
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
#SPJ1
Pls help i don’t know how to do this
Answer:
Step-by-step explanation:
y = √24²+32² = √1600 = 40
find base angle Ф on the right:
Ф = sin⁻¹(32/40) = 53.13
find other base angle (sum of interior angles of a Δ is 180):
180 - 90 - 53.13 = 36.87
now you can use the Law of Sines to find z, x:
40/sin36.87 = z/sin53.13 = (x+24)/sin90
z = 40(sin53.13)/sin36.87 = 53.33
sin36.87(x+24) = 40(sin90)
x+24 = 40/sin36.87 = 66.66
x = 66.67 - 24 = 42.67
double check the answers:
y² + z² = (x+24)²
40² + 53.33² = (42.67 + 24)²
1600 + 2892 = 4444
4444 = 4444 answers are correct!
The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = -logx where x represents the concentration of the hydrogen ions in the solution in moles per liter. Find the hydrogen ion concentration of the pH=5.4
Answer:The easiest way to do this is to just raise 10 to the negative value of the pH. Thus, in this case hydrogen ion concentration would be 1x10-2.4. However, one doesn't usually leave it that way, so you put it in to the more conventional form as
3.98x10-3 and this would be the hydrogen ion concentration. If you take the negative log of this number (pH) you will get 2.4
Explain why the following function F : [tex]R^{2}[/tex]⇒[tex]R^{2}[/tex] is not a linear transformation:
F([tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]) = x[tex]\left[\begin{array}{ccc}1\\3\end{array}\right][/tex] + 8[tex]\left[\begin{array}{ccc}1\\x+y\end{array}\right][/tex]
The function F: R²⇒R²
where, [tex]F([/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex][tex])[/tex] [tex]= x[/tex][tex]\left[\begin{array}{ccc}1\\3\\\end{array}\right][/tex] [tex]+ 8[/tex] [tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex], is not a linear transformation, as the y-intercept of the given function is not zero, so, we can say that, given function is not a linear transformation.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
the function is defined as, F: R²⇒R²
where,[tex]F([/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex][tex])[/tex] [tex]= x[/tex][tex]\left[\begin{array}{ccc}1\\3\\\end{array}\right][/tex] [tex]+ 8[/tex] [tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex]
so, here, the y-intercept of the function is, [tex]8[/tex][tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex]
now, we know that, [tex]8[/tex][tex]\left[\begin{array}{ccc}1\\x+y\\\end{array}\right][/tex] ≠ 0
so, the y-intercept is not zero.
again, we have,
now, we know that,
A single variable function f(x)=ax+b is not a linear transformation unless its y-intercept b is zero.
we have that,
the given function doesn't have y-intercept = 0.
so, we get, given function is not a linear transformation.
Hence, The solution is, as the y-intercept of the given function is not zero, so, we can say that, given function is not a linear transformation.
To learn more on function click:
brainly.com/question/21145944
#SPJ1
Ninety percent of juniors in high school have their driver’s license. If Eagle Mountain High has 576 juniors with a driver’s license, then
how many juniors are enrolled?
There are 640 juniors enrolled in Eagle Mountain High school.
Define the term Percentage?Percentage can be define as the way of shown a number as a fraction of 100. The word "percent" comes from the Latin per centum, which means "by the hundred." Percentages are commonly used to represent proportions or rates, and they are denoted using the symbol "%".
Let's denote the total number of juniors in the high school as "x".
From the problem, we know that 90% of the juniors have a driver's license. We can express this as:
0.9x = 576
To solve for x, we can divide both sides by 0.9:
x = 576 / 0.9
x = 640
Therefore, there are 640 juniors enrolled in Eagle Mountain High school.
To know more about fraction, visit:
https://brainly.com/question/30154928
#SPJ1
The scale drawing has a scale of 1 inch:9yards. What is the total area of the composite figure.
The figure is a right triangle with a height of 6 in and the height of 6 inches. The rectangle has a length of 7 inches and a width of 6 inches.
How do you solve?
The total area of the composite figure is 107/216 square yards.
What is Area?
Area is a measure of the size of a two-dimensional shape or surface. It is the amount of space inside the boundaries of a flat object, measured in square units such as square meters, square feet, or square inches.
To find the total area of the composite figure, we need to first convert the dimensions from inches to yards, since the given scale is in inches per yards.
Since 1 yard is equal to 3 feet, which is equal to 36 inches, we have:
The height of the triangle is 6/36 = 1/6 yards.
The base of the triangle is 9 times the height, which is 9/6 = 3/2 yards.
The length of the rectangle is 7/9 yards.
The width of the rectangle is 6/9 = 2/3 yards.
The area of the triangle is:
(1/2) x (1/6) x (3/2) = 1/8 square yards.
The area of the rectangle is:
(7/9) x (2/3) = 14/27 square yards.
Therefore, the total area of the composite figure is:
1/8 + 14/27 = 107/216 square yards.
To learn more about Area from the given link
https://brainly.com/question/25292087
#SPJ1
the sides of a rectangle are -x + 18 and x + 4.what is the area?
Answer:
The area of a rectangle is given by the product of its length and width. In this case, the length of the rectangle is -x + 18, and the width is x + 4. So, the area is:
Area = (length) x (width)
= (-x + 18) x (x + 4)
= -x^2 + 14x + 72
Therefore, the area of the rectangle is -x^2 + 14x + 72.