A box, in the shape of a square pyramid, has a base side of 9 in. and a height of 15 in. What is the approximate volume of the box when it is 75% full? (Use V=
'Bh, where B is the area
of the base, and h is the height.)

Point A

(-16, 20)

Point B

(-16, -14)

The Distance Formula itself is actually derived from the Pythagorean Theorem which is a

The distance would be 34 units

Using the Fundamental Counting Theorem, it is found that:

a) 1000 combinations are possible.

b) The probability of winning is of 0.001.

c) If you win, the net profit is of $497.

d) The expected value of a $3 bet is of -$2.5.

It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In the context of this problem, three digits that can be repeated are chosen, hence the parameters are:

[tex]n_1 = n_2 = n_3 = 10[/tex]

Hence the number of combinations is:

N = 10³ = 10 x 10 x 10 = 1000.

The order also has to be correct, hence the there is only one winning outcome and the probability is:

p = 1/1000 = 0.001.

You bet $3, and if you win you collect $500, hence the net profit is of:

500 - 3 = $497.

Then the distribution of earnings are as follows:

Hence the expected value is:

E(X) = -3 x 0.999 + 497 x 0.001 = -$2.5.

The problem is given by the image at the end of the answer.

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[tex]-14x^2 \div 3x\implies \cfrac{-14x^2}{3x}\implies -\cfrac{14}{3}\cdot \cfrac{x^2}{x}\implies -\cfrac{14}{3}x[/tex]

9/25

Step-by-step explanation:

students who have either cat or dog =25-3=22

students who have both= 15+16-22= 9

probabillity that a student chosen at random has both= 9/25

Answer:

compression

Step-by-step explanation:

If b>1 then the graph will compress

Answer:

sss

Step-by-step explanation:

Answer:

Step-by-step explanation:

$17.64 for 147 text messages

Therefore 1 text message will cost $17.64 ÷ 147 Text messages = $0.12 per text message

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given polynomials

One of the zeroes is:

STEP 2: Use synthetic division to divide the polynomials

Write the coefficients of the numerator

The last carry-down value is the remainder and it is 0 (zero)

Since the remainder is a zero, hence, x=-5 is a zero

Step 3: Answer question b

To get the factors, the remainder of the division in step 2 is given as:

The remaining factors of f(x) is:

STEP 4: Answer Question c

The complete factorization will give:

STEP 5: Answer question d

The zeroes of f(x) will be:

zeroes are: -5,4,-5

STEP 6: Plot the graph

Given three side lengths form an acute obtuse or a right triangle 17, 21, & 28

Check Right triangle

Not a Right triangle

An obtuse triangle is a triangle with one obtuse angle and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry.

Not an Obtuse triangle

Hence it is acute angle because all angles are less than 90°

The measure of the numbered angles formed by the common transversal to the two parallel lines are;

[tex] \angle 1 = 113^{ \circ} [/tex]

[tex] \angle 2 = 67^{ \circ} [/tex]

[tex] \angle 3 = 67^{ \circ}[/tex]

[tex]\angle 4 = 113^{ \circ} [/tex]

The relationships between the angles are;

The given angle is 113°

According to corresponding angles theorem, we have;

[tex] \angle 1 = 113^{ \circ} [/tex]

[tex]\angle 1 \: and \: \angle 4 [/tex] are vertical angles

According to vertical angles theorem, we have;

[tex]\angle 1 = \angle 4 = 113^{ \circ} [/tex]

[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are same side exterior angles.

According to same side exterior angles theorem, we have;

[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are supplementary angles. Which gives;

[tex] \angle 3 + 113^{ \circ} = 180^{ \circ} [/tex]

[tex] \angle 3 = 180^{ \circ} - 113^{ \circ} = 67^{ \circ}[/tex]

[tex] \angle 2 \: and \: \angle 3 [/tex] are vertical angles, which gives;

[tex] \angle 2 = \angle 3 [/tex] = 67°

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Answer:

I don't know if you can use permutations but

(6P2-6)/6=4 ????

The advantage and disadvantages are sampling.

We have to find the advantages and disadvantages of sampling.

The advantage is:

It provides an opportunity to do data analysis with a lower likelihood of carrying an error.

Researchers can analyze the data that is collected with a smaller margin of error thanks to random sampling. This is permitted since the sampling procedure is governed by predetermined boundaries. The fact that the entire procedure is random ensures that the random sample accurately represents the complete population, which enables the data to offer precise insights into particular topic matters.

The disadvantage is:

No extra information is taken into account.

Although unconscious bias is eliminated by random sampling, deliberate bias remains in the process. Researchers can select areas for random sampling in which they think particular outcomes can be attained to confirm their own bias. The random sampling does not take into account any other information, however sometimes the data collector's supplementary information is retained.

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Answer:

540,000

Step-by-step explanation:

Since you are rounding to the 10,000s place you must look at the 1,000s place to decide what to round to. Since in the 1,000s place is a 1, you will round the number down (1 < 5).

The probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648

We are given:

u= 38,s = 12

We have to find P(29 < x< 44)

Using the z-score formula, we have:

P(29 <x <44) = P(-0.75 < z <0.5)

Using the standard normal table, we have:

P(29 <x<44) = P(-0.75 < z < 0.5) = 0.4648

Therefore, the probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648

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The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.

Let X the random variable that represent the diameters of interest for this case, and for this case we know the following info

Where [tex]$\mu=205$[/tex] and [tex]$\sigma=1.5$[/tex]

Let the probability be

[tex]$P(205-0.3=204.7 < \bar{X} < 205+0.3=205.3)$$[/tex]

For this case they select a sample of n = 79 > 30, so then we have enough evidence to utilize the central limit theorem and the distribution for the sample mean can be approximated with:

[tex]$\bar{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$$[/tex]

To simplify this problem is utilizing the normal standard distribution and the z score given by:

[tex]$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]

To find the z scores for each limit and we got:

[tex]$z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778$$[/tex]

[tex]$z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778$$[/tex]

To find this probability:

P(-1.778 < Z < 1.778) = P(Z < 1.778) - P(Z < -1.778)

simplifying the above equation, we get

= 0.962 - 0.0377

= 0.9243

The interest exists the probability that the mean diameter of the sample shafts would vary from the population mean by more than 0.3 inches utilizing the complement rule we got:

P = 1 - 0.9243 = 0.0757

The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.

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A tall child with an arm span of 120 cm and height of 118 cm was added to the sample used in this study then the correlation will increase whereas the slope stays the same.

Correlation is a relation between two variables, by shifting one independent variable, how the dependent variable will shift, that's the degree of correlation since Correlation can be fitted in any shape or condition. It can be fitted nonlinear, straight or curvy straight, etc whereas slope is related to a straight variety of two variables, it is characterized as the rate of altering of the dependent variable in order with the independent variable. By and large you'll discover equation incline =( y2-y1)/(x2-x1).

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We are given a two-way probability table

Part a)

If one of the vehicles is selected at random, determine the probability that the vehicle is a car.

From the table, we see that the total number of cars are 1441

Also, the total number of vehicles is 2420

Then the probability of selecting a car is

Therefore, the probability that the vehicle was a car is found to be 0.5955

Part b)

If one of the vehicles is selected at random, determine the probability that it used the electronic toll pass, given that it was a car.

This is a conditional probability problem.

The conditional probability is given by

From the table, we see that,

So, the probability is

Therefore, the probability that it used the electronic toll pass, given that it was a car is found to be 0.3727

The probability that the randomly chosen vehicle is a car is  59.54 %.

The probability that the randomly chosen vehicle is a car given that it used the toll pass is  61.94%.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

The probability that the randomly chosen vehicle is a car is the total no of cars divided by the total no. of vehicles which is,

= 1441/2420.

= (1441/2420)×100%.

= 59.54 %.

The probability that the randomly chosen vehicle is a car given that it used the toll pass is the total no. of cars that used the toll pass divided by the no. of vehicles that used the toll pass which is,

= (537/867)×100%.

= 61.94%.

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The amount of paint that must be used from can A and can B is 3.86 liters and 5.14 liters respectively to obtain 9 liters of paint which is half blue and half yellow.

Can A has 9 parts of blue paint and 1 part of yellow paint, this can be expressed in percentage as;

Can A = 90% blue, 10% yellow

Similarly,

Can B = 20% blue, 80% yellow

Now consider an algebraic expression as follows;

A + B = 9 liters

90% A + 20% B = 50% [Blue]

10% A + 80% B = 50% [Yellow]

Resolving;

90% A + 20% B = 10% A + 80% B

80% A = 60% B

Solving the equation, A + B = 9, for one variable;

A + B = 9

B = 9 - A

80% A = 60% (9 - A)

80% A = 540% - 60% A

140% A = 540%

A = 3.86 Liters

Now solving for B;

B = 9 - A

B = 9 - 3.85

B = 5.14 Liters

Therefore 3.86 liters should be used from can A and 5.14 liters should be used from can B.

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4x + 3y = -24 (option D)

To determine the orrect option, we would find the equation of the line.

Equation of line: y = mx + c

m = slope, c = y-intercept

Using the slope formula:

We would use any two points on the graph.

Using points: (-6, 0) and (0, -8)

The y intercept is the point where the line crosses the y axis and the value of x is zero. It crosses the line at y = -8

The equation of line becomes:

y = -4/3 x + (-8)

y = -4/3x - 8

Multiply both sides by 3:

3(y) = 3(-4/3 x) - 3(8)

3y = -4x - 24

3y + 4x = -24

4x + 3y = -24 (option D)

a) We will draw the situation.

b) Considering the theory, the vertex of a parabola is represented in (h,k) where h is the x-coordinate, in this case, if our parabola has an amplitude of x=320feet then h=320/2=160feet, and k is the highest y-coordinate 80 feet. So the equation is:

We have to know the value for a, so we will use a point to replace it in the equation and with that, we will know the value, so in x=0 the y-value is 0 too so:

So the equation is:

c. To know the answer to this question we will have to replace x=280feet with the y value we will know if at the moment the ball can go over the tree or if it would crash into it.

At that point, the ball would be 35 feet up so if it could pass over the tree 5 feet higher.

Using the function rule, the value of g(r +2)  is r-2

Given the function rule g(k) = k-4.

Then g(r + 2)  can be found by replacing k with r+2 in the function g(k):

g(r+2) = r + 2 - 4

           = r - 2

Therefore, g(r+2) gives r - 2 when evaluated using the function rule.

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You have the following equation:

y = 1/2 x

In order to determine what is the constant of proportionality, consider the general fom of proportional relatioship, given by:

y = kx

by comparing the previous equation with y=1/2x, you can notice that k=1/2. Then, the constant of proportionality is k = 1/2

A. 1/2

The reasonable domain and range are 0 ≤ x ≤ 15 and 0 ≤ y ≤ 360 and the domain is continuous

From the question, we have

Gallon gas tank = 15 gallons

This means that the domain is from 0 to 15

This can be represented as 0 ≤ x ≤ 15

For the range, we have

0 * 24 ≤ y ≤ 15 * 24

Evaluate

0 ≤ y ≤ 360

This means that

Range: 0 ≤ y ≤ 360

Lastly, the domain of the situation is continuous

This is so because the gas in the tank can take decimal values

Take for instance, the gas tank can be 13.79 gallons full

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Answer:

Step-by-step explanation:

y = 0.81x + 6.9

residual value = Measured value - Predicted value

Measured value = actual y-coordinate of the point, y

Predicted value = value of y from the equation, y1

residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)

residual value = y - y1

x y        y1                residual (y-y1)

3 9     9.33                    -0.33

6 9     11.76                    -2.76

5 13     10.95                   2.05

7 13    12.57                    0.43

8 16     13.38                    2.62

8 11     13.38                   - 2.38

Sum of residuals:

sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)

B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.

(Though not very accurate as it should have been if the sum of residuals was equal to 0).

A total discrepancy of -0.37 is not too bad.

Answer:Answer:

B. −0.37;

This indicates that the line of best fit is accurate and is an overall good model for prediction.

Step-by-step explanation:

y = 0.81x + 6.9

residual value = Measured value - Predicted value

Measured value = actual y-coordinate of the point, y

Predicted value = value of y from the equation, y1

residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)

residual value = y - y1

x y        y1                residual (y-y1)

3 9     9.33                    -0.33

6 9     11.76                    -2.76

5 13     10.95                   2.05

7 13    12.57                    0.43

8 16     13.38                    2.62

8 11     13.38                   - 2.38

Sum of residuals:

sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)

sum of residuals = -0.37

ANSWER:

B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.

(Though not very accurate as it should have been if the sum of residuals was equal to 0).

A total discrepancy of -0.37 is not too bad.

Answer:

b.

Step-by-step explanation:

No, because -1 is x and -17 is y. if You plug it in, it will look like this:

-17=-1+16

-1+16=15

15 is not equal to -17, so the answer is no, b.

Hope this helps!

Answer:

a.)yes. у=х+16

Answer:

(-1)

Answer: D) -a

Step-by-step explanation:

a+b=0 , add -a for both side

- a + a + b = 0 - a

we cancel (- a + a) and we get

b = 0 - a => b = -a

Answer:

option d -a

if you take a to the opposite side of the equal mark it's sign is going to change since it's positive it's going to be negative on the other side 0 -a = -a

baam answer

Given the equations

x + y = 5----------------------(1)

x - 3y = 3-----------------------(2)

Subtract equation (2) from (1)

x - x -3y - y = 3 - 5

-4y = -2

Divide both -4

Substitute y = 1/2 into equation (1)

x + y = 5

Hence, the solution to the equations is

Starting with the equation:

take the inverse tangent function to both sides of the equation:

Yet another value can be found for this equation to be true since the period of the tangent function is π:

Starting with the equation:

Divide both sides by 7:

Take the inverse tangent to both sides of the equation:

The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:

We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:

Therefore, for each equation we know that:

Starting with the equation:

take the inverse tangent function to both sides of the equation:

Yet another value can be found for this equation to be true since the period of the tangent function is π:

Starting with the equation:

Divide both sides by 7:

Take the inverse tangent to both sides of the equation:

The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:

We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:

Therefore, for each equation we know that: