Mr. Oakley class surveyed 200 students about their favorite type of pie. The double bar graph below shows the result of the survey. What is the difference in the total number of students who chose peach pie as their favorite type of pie and the total number of students who chose apple pie? Show all your work. Explain why you did each step.

The missing measures in the triangle are given as follows:

m < F = 111.4º, m < D = 28.6º, f = 35.1.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Considering the triangle in this problem, the relation is given as follows:

sin(D)/18 = sin(40º)/24.2.

Hence the measure of angle D is obtained as follows:

sin(D) = 18 x sine of 40 degrees/24.2

sin(D) = 0.4781

m < D = arcsin(0.4781)

m < D = 28.6º.

The sum of the internal angle measures of a triangle is of 180º, hence the measure of angle F is obtained as follows:

m < F + 40 + 28.6 = 180

m < F = 180 - (40 + 28.6)

m < F = 111.4º

Then the length f is obtained as follows:

sin(111.4º)/f = sin(40º)/24.2

f = 24.2 x sine of 111.4 degrees/sine of 40 degrees

f = 35.1.

More can be learned about the law of sines at https://brainly.com/question/4372174

#SPJ1

The expected number of education majors in the sample is 20.

Since 80 out of 200 freshmen are education majors, the probability of randomly selecting an education major from the population is:

P(edu major) = 80/200 = 0.4

To find the expected number of education majors in a sample of 50 freshmen, we can use the formula for the expected value of a discrete random variable:

E(X) = n x p

Substituting the given values, we get:

E(X) = 50 x 0.4 = 20

Therefore, the expected number of education majors in a sample of 50 freshmen is 20.

More on probability can be found here: https://brainly.com/question/30034780

#SPJ1

Thermal energy and heat transfer principles guide the design of efficient systems, minimizing heat loss and maximizing performance.

It is crucial to take into account a number of aspects that may impact the functionality and efficiency of systems and objects that include thermal energy and heat transmission. You would need to take into account things like the kind and quantity of heat source, the materials utilized, the insulation, and the processes employed for heat transfer, for instance.

Additionally, you would have to think about ways to increase heat transmission effectiveness and reduce heat loss. High thermal conductivity materials may be used, or the system may be designed to have more heat-transfer surface area.

More about the heat transfer link is given below.

https://brainly.com/question/31065010

#SPJ1

Answer:

Step-by-step explanation:

The probability that a person will wait for more than 9 minutes is approximately 0.0912 or 9.12%. This means that out of 100 people, about 9 of them will wait for more than 9 minutes in the line.

We know that,

To solve this problem, we need to use the normal distribution and standardize the variable of interest. We know that the mean waiting time is 5 minutes and the standard deviation is 3 minutes, so we can write: Z = (X - μ) / σ

where X is the waiting time, μ is the mean waiting time (5 minutes), σ is the standard deviation (3 minutes), and Z is the standardized variable.

To find the probability that a person will wait for more than 9 minutes, we need to find the area under the normal curve to the right of 9. We can do this by standardizing 9 using the formula above: Z = (9 - 5) / 3 = 1.33 .

We can use a standard normal table or a calculator to find the probability that Z is greater than 1.33. Using a calculator, we find that this probability is approximately 0.0912.

Learn more about probability here:

brainly.com/question/30034780

#SPJ1

The summation of the given expression is as follows:

17.) = 5

18.) = 1

19.) = 1/2

For question 17.)

The summation of 2k+3 when K= 1

= 2(1)+3

= 2+3

= 5

For question 18.)

The summation of (3/2)^k where k = 0 would be = 1

For question 19.)

The summation of 1/2^k+1 where k = 0

= 1/2^0+1

=1/2^1

=1/2

Learn more about summation here:

https://brainly.com/question/31500549

#SPJ1

There are 560 cubes with edge lengths of 1/2 cm needed to fill the rectangular prism.

The volume of a rectangular prism is found by multiplying its length by its width by its height.

So, the volume of this rectangular prism is:

Volume = length x width x height

Volume = 7 cm x 4 cm x 2 1/2 cm

Volume = 70 cm³/2

Now, we need to find out how many cubes with edge lengths of 1/2 cm can fit into this volume.

The volume of each cube with an edge length of 1/2 cm is:

Volume of cube = edge length x edge length x edge length

Volume of cube = (1/2 cm)³

Volume of cube = 1/8 cm³

To find no. of cubes are needed, we need to divide the volume of the rectangular prism by the volume of each cube:

Number of cubes = (Volume of rectangular prism) / (Volume of each cube)

Number of cubes = (70 cm³/2) / (1/8 cm³)

Number of cubes = (70 cm³/2) x (8/1 cm³)

Number of cubes = 560 cubes

Therefore, 560 cubes with edge lengths of 1/2 cm are needed.

Learn more about the rectangular prism here:

https://brainly.com/question/3160281

#SPJ1

The  line integral of F around the perimeter of the rectangle with corners (3,0),(3,2),(-3,2),(-3,0) traversed in that order is -333.06456

The F can be rewritten as

F(x,y)  = [6(x+y) , 6sin(y)

The path C on which we are going to evaluate the integral is

Both lines will be solid lines and the intersection of the point will be at (1/3, 1).

Given that:

y ≥ −3x + 2

y ≥ 3x

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The region above the line y ≥ −3x + 2 is considered.

The region above the line y ≥ 3x is considered.

And both lines will be solid lines and the intersection of the point will be at (1/3, 1).

The graph is given below.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ1

The measure of the arc length AB is 16π/15 centimeters.

Since,

An arc length is simply the distance between two points along a section of a curve.

We know that;

The arc length is expressed as:

s = 2πr × (θ/360°)

Where s is the arc length, r is the radius, θ is the angle and π is constant pi.

Given that:

Radius r = 3cm

Angle θ = 64 degree

Arc length s = ?

Now, Plug the values into the above formula

s = 2πr × (θ/360°)

s = 2 × π × 3cm × ( 64°/360°)

s = 16π/15 cm

Therefore, the arc length is 16π/15 cm.

Learn more about arc length here:

brainly.com/question/16403495

#SPJ1

The length of the arc of a circle of radius 12 is 37.68.

The arc of a circle is defined as the part or segment of the circumference of a circle.

To calculate the arc of the circle, we the formula below.

Formula:

Where:

From the question,

Given:

Note: 360° = 2π radian

Substitute these values into equation 1

Hence, the length of the arc is 37.68.

Learn more about arc here: https://brainly.com/question/28108430

#SPJ1

The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.

The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.

The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.

Therefore, the probability of the friend being between 10 and 30 minutes late is:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

To know more about probability follow

https://brainly.com/question/27077702

#SPJ1

Answer:

The silver will cost $1908.5125 to make one solid sphere

Step-by-step explanation:

The formula for the volume of a sphere is:

V = (4/3)πr^3

where r is the radius of the sphere.

Substituting the given value for the radius:

V = (4/3)π(4.5 cm)^3

= (4/3)(3.14)(91.125 cm^3)

= 381.7025 cm^3

The cost of the silver can be calculated by multiplying the volume by the cost per cm^3:

Cost = 381.7025 cm^3 × $5.00/cm^3

= $1908.5125

Step-by-step explanation:

dependingon h o w m a n y bedrooms that are added to the

apartment, an additional $150will be added to $850.

The record long jump is 8 inches short of 10 yards.

First, we need to convert 10 yards to inches. Since 1 yard = 3 feet and 1 foot = 12 inches, we have:

10 yards = 30 feet

= 30 x 12 inches

= 360 inches

To find how many inches short of 10 yards the long jump is, we can subtract the length of the long jump from 360 inches:

360 inches - 29 feet 4 inches

= 360 inches - (29 x 12 + 4) inches

= 360 inches - 352 inches

= 8 inches

To learn more about multiplication;

https://brainly.com/question/19634536

#SPJ1

a. A translation on a coordinate plane involves moving every point on the plane a certain distance in a particular direction without distrupting their orientation. The shape and size of the figure do not change, only that the position shifts.

b. If the translation is moving 3 units to the right, it is affecting the x-coordinate. Basically, the x-coordinate of each point on the plane is increased by 3 units, while the y-coordinate remains the same.

c. If the translation is moving 8 units down, it is affecting the y-coordinate. Basically, the y-coordinate of each point on the plane is decreased by 8 units, while the x-coordinate remains the same.

learn more about translation: https://brainly.com/question/1574635

#SPJ1

Based on the percentage of blue paint to red paint, Bo's purple paint will be bluer.

The percentage refers to the quotient of one value (proportion of blue paints) compared to another (the sum of blue and red paints).

Percentages are ratios expressed over 100.

                           Blue     Red   Ratio (%) of Blue to Red

Bo's paints            3          4       3:4 = 43% (3/7 x 100)

Sum of ratios = 7

Latanya's paints   2          3       2:3 = 40% (2/5 x 100)

Sum of ratios = 5

Thus, based on the ratios or percentages of to red paints, Bo's purple paint will be bluer than Latanya's.

Learn more about ratios at https://brainly.com/question/12024093.

#SPJ1

The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.

We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.

We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;

Now solving for p,

2 (p+ 7) = 4 - 8

Open the bracket,

2p+ 14 = 4 - 8

Combine the like terms,

2p = -4 - 14

2p = -18

p = -18/2 = -9

Therefore, the equation has only one solution which is -9.

Learn more about solving equations here:

brainly.com/question/13072448

#SPJ1

The distance between Alberto and the base of the building is  93.4ft

We can view this as a right triangle, such that one cathetus (opposite to the known angle) measures:

40ft - 6ft = 34ft

And the known angle is 70°, we want to get the other leg of the right triangle, so we can use the tangent trigonometric relation which is:

tan(angle) = (opposite cathetus)/(adjacent cathetus)

Replacing the things that we know we get:

tan(70) = x/34ft

tan(70)*34ft = x = 93.4ft

That is the distance.

Learn more about right triangles at:

https://brainly.com/question/2217700

#SPJ1

If he business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written, checkbook balance after checks and deposit are processed is $6613.25.

To find the checkbook balance, we need to add up the initial balance, subtract the amounts of the written checks, and add the deposit made by the store manager.

Starting with the initial balance of $7349.44, we subtract the amount of the first check for $1349.67, leaving a balance of $6000.77. Then we subtract the second check for $344.12, leaving a balance of $5656.65.

Finally, we add the deposit made by the store manager for $956.60, which gives us a final balance of $6613.25.

To learn more about balance click on,

https://brainly.com/question/29193732

#SPJ1

The lines intercept at the point (3, 9), and:

A system of linear equations can have one solution, no solutions, and infinite solutions, these are the only options.

If we have an equation system, the solutions are the spots where the graphs of the equations intersect.

We know that the solution of the system of linear equations is (3, 9), which signifies that the linear equations intersect at that location.

Can  we have more than one solutions?

Yes, you can have

These are the 3 options.

Learn more about systems of equations:

https://brainly.com/question/24065247

#SPJ1

0≤x≤6 best describes the domain of the function.

The domain of a function describes the set of all possible input values.

In this case, the input variable is x, which represents the time in hours.

Since the horse runs for 6 hours, it is not possible for x to be greater than 6.

Additionally, x cannot be negative or zero, since time cannot be negative or zero.

Therefore, the domain of the function is 0 ≤ x ≤ 6.

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ1

The relative frequency of "tails" when the companions coalesce their results is close to 0.524.

In order to ascertain the relative frequency of "tails" when the friends amalgamate their outcomes, one must accumulate the amount of tails, then divide that sum by the entirety of trials:

Relative frequency of "tails" = total number of tails / cumulative number of trials

= 129 / (117 + 129)

= 129 / 246

≈ 0.524

Consequently, the relative frequency of "tails" when the companions coalesce their results is close to 0.524.

Learn more about frequency on

https://brainly.com/question/254161

#SPJ1

The graph of the population equation is on the image at the end.

Here we know that the function p(h) models the population of bacteria as the function of h, the number of hours.

And we can write this as the exponential function:

p(h) = 150*(3)^h

The graph of this will be an exponential that starts at 150 and triples for each increase in the horizontal variable, then the graph of this will be like the one you can see at the end of the answer.

Learn more about exponential functions at.

https://brainly.com/question/2456547

#SPJ1

A feasible solution to minimizing turbidity value is through the use of an iterative technique, entailing either gradient descent method or simulated annealing method.

The stopping criterion for this approach would be at 0.1 percent.  It involves sequentially determining water turbidity dependent on the coagulant dosages used in adjustment procedures based on preceding calculated values.

By further implementing this process until the specified percentage average is met, ease and accuracy in assessing turbidity levels are achievable.

Learn more about turbidity on

https://brainly.com/question/26612834

#SPJ1

The value of the number is 18. Option A

To determine the product of the expression, we need to consider that;

Algebraic expressions are described as those mathematical expressions that are composed of terms, their coefficients, the variables and the factors and constant values.

These expressions are also made up of mathematical operations. These operations are;

From the information given, we have that;

The product of six and a number is 108

Let the number be x, we have;

6x = 108

Divide sides by the coefficient

x = 18

Learn about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

Answer:

15456

Step-by-step explanation:

My work is attached to this answer

The average rate of change of the height of the rocket is 11.25/(a - 1)

From the question, we have the following parameters that can be used in our computation:

h(1) = 23 meters and h(a) = 34.25 meters.

The average rate of change of the height of the rocket is

Rate = Change in height /Time

So, we have

Rate = (34.25 - 23)/(a - 1)

Evaluate

Rate = 11.25/(a - 1)

Hence, the rate = 11.25/(a - 1)

Read more about average rate of change at

https://brainly.com/question/17131025

#SPJ1

Complete question

Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.

Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.

What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second

The possible shapes of the fencing are a parallelogram and a rectangle.

Given that, a worker fences in a construction site using four pieces of fencing that have lengths of 20, yards 16, yards, 20 yards, and 16 yards.

We need to tell possible four-sided shapes that the worker can enclose with the fencing.

So, we can see that, the pair of sides are equal,

Which is condition in a parallelogram and a rectangle.

Hence, the possible shapes of the fencing are a parallelogram and a rectangle.

Learn more about quadrilaterals, click;

https://brainly.com/question/13805601

#SPJ1

Answer:

The sample space describing all possible outcomes is:

{H1, H2, H3, H4, T1, T2, T3, T4}

The outcomes for the event that the coin toss is heads are:

{H1, H2, H3, H4}

Step-by-step explanation:

If it pertains to using the format H1 to mean that the coin toss is heads and the number chosen is 1.