Solve the problem.
The formula P = 14.7e-0.21x gives the average atmospheric pressure, P, in pounds per square inch, at an altitude x, in miles above sea level. Find the average atmospheric pressure for an altitude of 2.3 miles. Round your answer to the nearest tenth.
A) 9.1 lb/in.²
B) 8.4 lb/in.²
C) 11.0 lb/in.²
D) 7.8 lb/in.²

There are total percentage of 56% of red gumballs and 44% of blue gumballs in 4000 gumball machine.

Percentage is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given,

Total gumballs in the machine = 4000

Red gumballs in the machine = 2240

Blue gumballs in the machine = 1760

Percentage of each gumballs,

Percentage of red gumballs,

Value/Total × 100%

2240/4000 × 100

0.56 × 100

56%

Percentage of blue gumballs,

1760/4000 × 100%

0.44 × 100%

44%

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(Option A) 1/2 - This is a rational number because it is a fraction with both numerator and denominator being integers.

A rational number is any number that can be written as a fraction of two integers (where the denominator is not equal to zero). Examples of rational numbers include:

A rational number can be represented in many different forms. It can be written as a fraction, with both the numerator and denominator being integers, or as a decimal, with the decimal part either terminating or repeating. A rational number can also be written as a mixed number, which is a combination of an integer and a fraction.

Which of the following is a rational number?

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Answer:

114

Step-by-step explanation:

120% of 95 = 1.2 × 95 = 114

The correct option is D .

This is a parabola with domain all real numbers D .

Answer:

3(13/2)+2y=9 the answer is y=-21/4

Hence for miles greater than 45, the Company A will charge less than Company B.

Given:

Jina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

we are asked to find for what mileages will Company A charge less than Company B = ?

from the question we frame  the inequality as:

⇒ 91< 55+0.80m

⇒ 36<0.80m

⇒ 45<m

or

m>45

Check answer

55+45(0.8)=91 check

Hence for miles greater than 45, the Company A will charge less than Company B.

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Proving  that the maximum spanning tree of g contains the widest paths between every pair of vertices .

Suppose now we were to add an edge from the widest path into the spanning tree in a place that it won't cause a cycle.

so every path between our two nodes must contain some edge between two previously unconnected nodes.

The weight of the edge we removed was equal to the width of the original path, and because the path was that every edge in the new path must have had more weight than that edge.

This means that our new spanning tree must have strictly more total weight than the original, which contradicts the definition of the original 'maximum' spanning tree.

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The Equidistant Theorem states that the distance between two points on a line is equal to the sum of the distances from each point to a third point. This theorem is often used to prove the existence of certain geometric shapes, such as triangles and circles.

The Equidistant Theorem is a useful tool for proving the existence of certain geometric shapes. By measuring the distance between two points and then measuring the distance from each point to a third point, the distance between the two points will be equal to the sum of the distances of the two points to the third point.

This theorem is helpful for constructing triangles and circles, as it allows us to quickly and accurately identify the necessary distances between the points. This theorem is also useful for finding the center of a circle, as the center of the circle is always equidistant from its circumference. As a result, the Equidistant Theorem is a fundamental theorem in geometry that is used to prove the existence of certain geometric shapes.

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The equation of the parabola that passes through the points (1,4) and (2,2) would be y = (-4)(x - 1.5)² + 3.

What is a parabola?

A parabola is defined as a collection of points such that the distance to a fixed point (the focus) and a fixed straight line (the directrix) are equal. But it's probably easier to remember it as the U-shaped curved line created when a quadratic is graphed.

To find the equation of the parabola that passes through the points (1,4) and (2,2), we can use the formula for the general form of the equation of a parabola:

y = a(x - h)² + k

where (h,k) is the vertex of the parabola, and a is a nonzero constant that determines the direction and shape of the parabola.

To find the values of a, h, and k that will give us the equation of the parabola that passes through the points (1,4) and (2,2), we can use the following steps:

Find the coordinates of the vertex of the parabola. The vertex of the parabola is the point where the parabola changes direction. In this case, the parabola changes direction at the midpoint of the two given points, which is the point (1.5,3).

Substitute the coordinates of the vertex into the formula for the general form of the equation of a parabola: y = a(x - h)² + k.

Substitute the coordinates of one of the given points into the equation to find the value of a. For example, if we substitute the coordinates of the point (1,4) into the equation, we get:

4 = a(1 - 1.5)² + 3

4 - 3 = a(-0.5)²

1 = a(-0.25)

a = -4

Substitute the values of a, h, and k into the formula for the general form of the equation of a parabola to find the equation of the parabola that passes through the points (1,4) and (2,2):

y = (-4)(x - 1.5)² + 3

Hence, the equation of the parabola that passes through the points (1,4) and (2,2) would be y = (-4)(x - 1.5)² + 3.

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Volume of the solid (when squares divided into 4 equal parts in the lower left hand corners) = 318 cubic units.

Step-by-step explanation:

Paraboloid z=81-x2 -y2

The lower left hand corners of the squares are(0,0)(1,0)(0,1) and (1,1).

Then the volume can be estimated as,

Volume ≈ΔA [f(0,0)+f(1,0)+f(0,1)+f(1,1)]

            = 1[81+79+80+78]=318 cubic units.

b.) estimate the volume by dividing R into 4 equal squares and choosing the sample points to lie in the upper right hand corners.

Volume of the solid (when squares divided into 4 equal parts in the upper right hand corners) = 294 cubic units.

Paraboloid z=81-x2 -y2

The upper right hand corners of the squares are(1,1)(2,1)(1,2) and (2,2).

Then the volume can be estimated as,

Volume ≈ΔA [f(1,1)+f(2,1)+f(1,2)+f(2,2)]

            = 1(78+69+75+72)=294 cubic units

c.) what is the average of the two answers from a and b

Average of part a and b answer = (318+294)/2 = 712/2=306 cubic units

d.) using iterated integrals compute the exact value of the volume.

0202(81-x2 -y2) dy dx = 02[81y-x2y-⅓ y3]02 dx

                              = 02[162-2x2-8/3] dx

        = [162x-2x3/3-8/3 x]20

                              =644-16/3-16/3

                              = 644 cubic units.

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Answer:

The absolute value parent function is represented by the function F(x) = |x|. This function takes any real number as input and returns the absolute value of that number as output. For example, F(5) = |5| = 5, and F(-3) = |-3| = 3. The other functions you have listed are not absolute value functions.

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is C because 65 is a one Time thing and 30x means every month u rent it times the money.

The line chart can be created using insert tab and then click line symbol in charts group.

Line chart is a type of chart with line visualization to show information of changing values over time.

Insert tab is tab in excel to insert object, symbol, chart, etc.

To create line chart,

I'm attaching a image for microsoft excel 365 version, your excel version may be different, but the line chart is still in the insert tab.

Thus, to create the line chart use insert tab and in chart group click line symbol.

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Answer:

b

Step-by-step explanation:

did the math?

8 is the best estimate of [tex]8\frac{1}{8}[/tex].

In simple words, the ratio of the two numbers is called a fraction.

Mixed fraction is a form of a fraction which is defined as the ones having a fraction and a whole number.

For example, 2 (1/3) is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Step 1: Multiply the denominator with the whole number,

i.e. Multiply 8 with 8 in the given example, 8(1/8).

                                            8× 8  =64

Step 2: Add the numerator of the Fraction to the result in step 1. i.e.,             Add                                      1+ 64=65.

Step 3: Keep the Denominator same i.e. 8.

Step 4: The Improper fraction obtained is: 65/8.

Given number can be denoted as 8+[tex]\frac{1}{8}[/tex] = 8+0.15 = 8.15

So the number is nearest to 8 itself.

i.e. 8 is the best estimate.

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Answer:

  73.3%

Step-by-step explanation:

You want to know the percentage adopted when 4 of 15 were not adopted.

The percentage can be found by multiplying the fraction by 100%. The fraction of dogs adopted was 11 out of 15, or 11/15. The percentage is ...

  11/15 × 100% ≈ 73.3%

About 73.3% of the dogs were adopted.

Given the following sample of three data points: 3, 6, 9, calculate the (estimated) standard error for the sample mean. Round to 3 decimal places.

s = √((3 - 8)² + (6 - 8)² + (9 - 8)²) / (3 - 1) = 4

2. Calculate the standard error of the sample mean:

SE = s / √n = 4 / √3 = 2.45

3. Round the standard error to three decimal places:

SE = 0.567

The standard error of the sample mean can be calculated by first finding the standard deviation of the sample (s). This is done by taking the sum of the squared differences between each data point and the mean, divided by the number of data points minus one. In this case, the standard deviation is 4. The standard error is then calculated by dividing the standard deviation by the square root of the number of data points, which is 3. The result is 2.45, which can be rounded to 0.567.

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The given function models the amount in the account after t years is true.

What is compounded quarterly?

The process of calculating the interest earned quarterly on a fixed deposit or investment, computed based on the principal amount plus the interest earned for previous periods, is known as quarterly compounding.

Given:

Albert deposits $3250 in an account that earns 4.3% interest compounded quarterly.

P = $3250

r = 4.3% = 0.043

n = 4

t = t years

So, the function models the amount in the account after t years is,

[tex]A = P(1+\frac{r}{n})^n^t\\ A = 3250(1+\frac{0.043}{4})^4^t[/tex]

This equation is same as the given equation.

Hence, the given function models the amount in the account after t years is true.

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Complete question:

Complete question is attached below.

The volume of the cube with a side edge of 3 inches will be 27 cubic inches.

Suppose that: The side length of the considered cube is L units. Then, we get:

Volume of that cube = L³ cubic units.

Terrance has a shape that actions 3 inches long along each side.

The edge length of the cube is 3 inches. Then the volume of the cube  will be given as,

V = (3)³

V = 27 cubic inches

The volume of the cube with a side edge of 3 inches will be 27 cubic inches.

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The correct answer is (B) 99.73%..

For a process in control, we expect 99.73% of the points on a process control chart to fall within the upper control limit (UCL) and the lower control limit (LCL).

A process control chart is a tool used in statistics and quality control to monitor and analyze a process over time. It consists of a line graph that plots the measured values of a process variable, such as the temperature or weight of a product, over time. The UCL and LCL are horizontal lines that are drawn on the graph at a predetermined distance above and below the average value of the process variable.

The expected percentage of points within the UCL and LCL is determined by the chosen level of statistical significance and the distribution of the process variable. In this case, the expected percentage of points within the UCL and LCL is 99.73%.

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Complete Question:

For process in control, we expect Pfo of the points on process control chart to fall within the UCL and the LCL:

A)0.27

B)99.73

C)100

The students should draw the conclusion that the data might have been caused by the genetic connection if the null hypothesis is rejected.

Given information;

The students determine a crucial value of 7.82 and compare it to a chi-squared value of 92.86.

Which of the following results in the chi-square goodness-of-fit test being most complete?

The null hypothesis can be rejected, and the students should conclude that the data may have resulted from the genetic linkage.

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Therefore the solution of the equations could be the result of using substitution is 2[tex]y^{2}[/tex]-6 -y=0

In English, an equation is defined as a properly written formula that consists of two expressions joined by an equals sign, while cognates of the word in other languages may have slightly different meanings. For instance, in French, the word "équation" means "thing with one or more variables."

Given two equations are

x=[tex]y^{2}[/tex]-1 and 2x-y=4

We must select an equation from the list of possibilities that may be obtained by utilizing substitution to resolve the problem.

We substitute x in terms of y because the supplied equation is in terms of y.

From 2x-y=4

x=4+y/2

Substitute x=4+y/2   in other equation

We get,

=> x=[tex]y^{2}[/tex]-1

=> 4+y/2 =[tex]y^{2}[/tex]-1

=>4+y=2[tex]y^{2}[/tex]-2

=>2[tex]y^{2}[/tex]-6 -y=0

Therefore the solution of the equations could be the result of using substitution is 2[tex]y^{2}[/tex]-6 -y=0

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The required total cost of all the purchases is $7,930.00. Option C is correct.

Given that,
Al Roy bought five bonds of Jort Co. 11 3/4 at 93.25% and four bonds of Inst. System 12x08 for 81.125%, the commission on the bonds is $2.50 per bond.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Total bond = 4 + 5 = 9

Face value of a bond = $1000
Total cost = $1000 × 0.9325 × 5 + $1000 × 0.81125 × 4 + 2.50 × 9

Total cost = $7,930.00

Thus, The required total cost of all the purchases is $7,930.00. Option C is correct.

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The number of tickets that will be sold is 5560.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

Ticket sales for Six Flags White Water totaled $94,520 this summer.

Tickets for the water park cost $17 each.

The number of tickets sold will be = 94520/17 = 5560.

Hence, the number of tickets that will be sold is 5560.

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Change the equation into slope intercept from .identify the slope and y intercept of the equation

Y= mx  +b

2x+3y=1470

Subtracting -2x on both sides,

2x+3y-2x=1470-2x

3y=1470-2x

Divided by 3 on both sides

3y/3=1470/3-2x/3

Y=490-2/3x

Y= -2/3x+490..(1)

we know that,

y=mx +b

with the help of equation (1)draw a graph

we will start from (0,490)and then we will move 2 steps down and 3 step right.

F(x)=-2/3x+490

The graph represent how many graph and sandwich whield,

x=600

put the value of equation (1)

y= -2/3×600+490

y= -400+490

y=90

(600,90)

So these all represent correct things’

1200+270=1470

If you take the x-axis and take the y-axis of any point at that point, the x-axis and the y-axis, when calculating the profit, subtract 0 from 1 4, so it's not. Represents profit Represents the number of sandwiches and reps sold, from which profit is calculated to be 1470.

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Therefore the solution to the given problem is  the each of the congruent base angles is 70°

In Euclidean geometry, an angle is the figure generated by two rays, called the sides of the angle, sharing a common termination, called the vertex of the angle. Angles created by two rays are in the plane where the rays are located. The intersection of two planes also forms angles. We refer to these as dihedral angles.

Here,

As the triangle is an isosceles triangle therefore it will have 2 same angles

thus,

Sum of the 3 angles of a triangle=180°

Vertex angle =40°

Sum of two congruent angles=180°–40°=140°

Measure of each base angle=70°

Therefore the each of the congruent base angles is 70°

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The image of the point after the transformation D₂,₀ T₋₄,₋₅ is (-6, -15)

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The coordinates of the point are given as

(-1, -3)

The transformation is given as D2 0 T-4,-5

This transformation, when properly expressed is

D₂,₀ T₋₄,₋₅

This represents

As mentioned above,

D₂,₀ T₋₄,₋₅

Mathematically, we have

(x, y) ⇒ (2x - 4, 2y - 5)

Substitute (-1, -3) in (x, y) ⇒ (2x - 4, 2y - 5)

So, we have

(x, y) ⇒ (2(-1) - 4, 2(-5) - 5)

Evaluate

(x, y) ⇒ (-6, -15)

Hence, the coordinates of the image are (-6, -15)

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The circumference of the circle with radius 17 millimeter is 106.76 millimeter

The radius of the circle = 17 millimeter

The circumference of the circle is defined as the linear distance around the circle

The radius of the circle is the distance between the center of the circle to the any point of the circumference.

The circumference of the circle = 2 × π × r

Where r is the radius of the circle

The value of the π = 3.14

Substitute the values in the equation

The circumference of the circle = 2 × 3.14 × 17

Multiply the numbers

= 106.76 millimeter

Therefore, the circumference of the circle is 106.76 millimeter

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The equality property that is used to prove the statement is the addition property of the equality.

Let's start with the general equation

A = B

That we assume is a true equation.

There is a property called the addition property of the equality, it says that we can add the same number in both sides of the equation.

Then if we add a number C in both sides, we will get:

A + C= B + C

And that equation is still true.

Ok, let's go to our equation:

x - 2 = 9

We can add the same number in both sides which is 2, then we get:

x - 2 + 2 = 9 + 2

x = 11

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Answer:

Step-by-step explanation:

To solve this problem, we need to divide 3/10 gallons by 1 gallon, which is equal to 4 quarts.

First, let's convert the fraction 3/10 to a decimal by dividing the numerator by the denominator: 3 / 10 = 0.3

Then, we can divide 0.3 gallons by 1 gallon to get the equivalent number of gallons in quarts: 0.3 gallons / 1 gallon = 0.75 quarts

Since 1 quart is equal to 0.25 gallons, 0.75 quarts is equivalent to 3/4 of a gallon.

Finally, we can add the number of quarts given in the problem (11 quarts) to the number of quarts equivalent to the number of gallons (3/4 of a gallon, or 3 quarts). This gives us a total of 14 quarts, which is equivalent to 3 and 1/2 gallons.

Therefore, the final answer is 3 gallons and 11 quarts.

The vertex of the function g(x) = |x - 8| + 6 is (8, 6)

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

g(x) = |x - 8| + 6

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

This means that the vertex is

Vertex = (8, 6)

Remove the x value

y = 6

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

y ≥ 6

So, the range is y ≥ 6

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