The surface area of a pyramid is 540 square inches.

Its base is a square with a side length of 10 inches.

What is the height of one of the triangular faces of the

pyramid? Explain how to find the answer.

Answer:

y=e^x - 4

Step-by-step explanation:

The log functions decrease with increasing x.  The line shown increases as x increases, so it must be one of the two e^x equations.  We can decide which one by calculating which equation povides the correct values to match the two points the curve crosses the y and x axes.

The graph shows the line crossing the y axis at -3 (0,-3)

It shows it crossing the x axis at a little over 1, perhaps 1.4 (1.4,0).  

When x=0, e^0 = 1.  

Look at the point (0,-3):  

We know the e term will be 1 (e^0 = 1), so for y to be -3, we need to subtract 4:  The form e^x - 4  would yield a value for y, when x is 0, of y = 1 - 4 or -3.

Check the other point (1.4,0):

y = e^1.4  is equal to 4.00

y = 4.00 - 4

y = 0

This point is also correct (1.4,0)

The correct equation is y=e^x - 4

Answer:

b = 10

Step-by-step explanation:

Expand the left side and compare the coefficients of like terms

(2x + a)(4x - 1) ← expand using FOIL

= 8x² + 4ax - 2x - a = 8x² + x(4a - 2) - a

Compare coefficients of like terms with

8x² + bx - 3

Then a = 3 ( constant term )

b = 4a - 2 ( coefficients of the x- term )

b = 4(3) - 2 = 12 - 2 = 10

Answer:

b = 10

Step-by-step explanation:

We can break those parenthesis like this

\((2x + a)(4x - 1) \\ = 2x(4x - 1) + a(4x - 1) \\ = 8{x}^{2} - 2x + 4ax - a\)

And then combine the terms end with x we get

\(8 {x}^{2} - 2x + 4ax - a \\ = 8 {x}^{2} + 4ax - 2x - a \\ = 8 {x}^{2} + (4a - 2)x - a\)

Now by comparing 2 expressions, we can see that a is 3, and b = 4a-2 = 12-2 = 10

The option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have a table given that shows the survey asks teachers and students whether they would like the new school mascot to be a pirate or a moose.

The probability of a person that is a student:

P(student) = (75+15)/110 = 0.83

The probability:

P(student|pirate) = 75/80 = 0.93

The probability of both events is different.

Thus, the option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.

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Answer:

the elevators total capacity is 15 passengers.

Answer:

I think the answer is 23

Step-by-step explanation:

Because the pattern is # - 2 - 1 x 2 + 1

That is because 10 is the starting number and 10 - 2 is 8 and 8 - 1 is 7 and 7 x 2 is 14 and 14 + 1 is 15 and then it starts the process all over again with 15 - 2 is 13 and 13 - 1 is 12 and 12 x 2 is 24 and 24 + 1 is 25. And so 25 would be the end of the second round of the pattern. So it would start again with 25 - 2 is 23... and so on and so forth.

Hope this helps!!

Answer:

A. shawn added 4 to both sides of the equation instead of subracting 4

The space curve given by r(t) = 〈sin(t), cos(t/2), 4t〉 intersects the z-axis at the points (0, 0, 0), (0, 0, 8π), and (0, 0, 16π) in the given range.

To determine whether the curve intersects the z-axis, we need to find the values of t for which the z-coordinate of r(t) is equal to zero. Thus, we set the z-coordinate of r(t) equal to zero and solve for t:

4t = 0

t = 0

This means that the curve intersects the z-axis at the point (0, 0, 0).

Next, we need to find the other points where the curve intersects the z-axis in the range 8π ≤ z ≤ 16π. Since the z-coordinate of r(t) is given by 4t, we can solve for t in terms of z:

4t = z

t = z/4

Substituting this value of t into the x-coordinate of r(t), we get:

x = sin(z/4)

To find the points of intersection with the z-axis in the given range, we solve sin(z/4) = 0. This gives us:

z/4 = π, 2π, 3π, ...

z = 4π, 8π, 12π, ...

Out of these values, only the ones in the range 8π ≤ z ≤ 16π are of interest. Thus, the curve intersects the z-axis at z = 8π and z = 16π.

Therefore, the space curve given by r(t) = 〈sin(t), cos(t/2), 4t〉 intersects the z-axis at the points (0, 0, 0), (0, 0, 8π), and (0, 0, 16π) in the given range.

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Either the slope intercept form or the point-slope form can be used to express the equation of a line-, the line's equation is - 3x - 5.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two distinct points on a line can be used to calculate the slope of any line.

The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.

According to our question-

the points are given as

(x1,y1)=0,-5

(x2,y2)=-3,4

m = y2-y2/x2-x2

Hence, the line's equation is - 3x - 5.

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Monique is wrong because 3 1/4 g/cm³ represents the highest density and it is close to the other density values.

In Mathematics and Statistics, an outlier is also known as an anomalous data and it can be defined as a numerical value that is either unusually too large (big) or little (small) in comparison with the overall pattern of the numerical values contained in a data set.

Based on the line plot for the densities of various rock samples shown in the image attached below, we can logically deduce that Monique is wrong to say 3 1/4 g/cm³ is an outlier.

In conclusion, 3 1/4 g/cm³ represents the highest density, which is still close to the other density values.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

k = 75

Step-by-step explanation:

Let's write down the prime factors of 15 and 375

15 = 3 x 5

375 = 3 x 5 x 5 x 5

So 15 x 375 = 3 x 5 x 3 x 5 x 5 x 5

= (3 x 3) x   (5 x 5 x 5) x 5

This cannot be a perfect cube

However if we multiply this by 3 x 5 x 5 we will get

(3 x 3 x ) x (5 x 5 x 5) x(5 x 5 x 5) which is a perfect cube

Since we are asked to find k such that 15 x 375 x k is a perfect cube

k = 3 x 5 x 5 = 75

ans
k = 75

In this case, the independent groups t-test helps determine if there is a significant difference in the means of the dependent variable between the two independent groups.

The independent groups t-test may be used to analyze the relationship between two variables when:
1. The two variables consist of one continuous dependent variable and one categorical independent variable with two independent groups (levels).
2. The independent groups are not related or matched in any way, meaning that the data in one group does not influence the data in the other group.
3. The assumption of normality and homogeneity of variances for the continuous dependent variable are met within each group.

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In this case, the independent groups t-test helps determine if there is a significant difference in the means of the dependent variable between the two independent groups.

The independent groups t-test may be used to analyze the relationship between two variables when:
1. The two variables consist of one continuous dependent variable and one categorical independent variable with two independent groups (levels).
2. The independent groups are not related or matched in any way, meaning that the data in one group does not influence the data in the other group.
3. The assumption of normality and homogeneity of variances for the continuous dependent variable are met within each group.

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Answer:

d = 16 units

Step-by-step explanation:

(- 8, 8 ) and (8, 8 )

since the y- coordinates of both points are 8 , then the 2 points lie on the same horizontal line.

the distance d between them can be calculated as the absolute value of the difference in the x- coordinates, that is

d = | - 8 - 8 | = | - 16 | = 16 units

or

d = | 8 - (- 8) | = | 8 + 8 | = | 16 | = 16 units

Answer:

25

Step-by-step explanation:

percentage calculator 40 is what percent of 160=25;)

Answer:

40/100×160

Step-by-step explanation:

2/5×160

320/5

64

Answer:

k = -7

Step-by-step explanation:

Let's put the side with the variables on the left.

-k+16-2k-9=28

Now we need to isolate the variable, which is k in this case.

-k+16-2k-9=28

-k-2k+16-9=28

-3k+7=28

(-3k+5) -7 = 28 -7

-3k = 21

k = -21/3

That's your answer:

k = -7

a) The number of occupied units can be expressed as: N = 100 - V

b)  (100 - ((x - 800) / 10)) * x

c) The manager should calculate the critical points of the revenue function and choose the rent value that falls within a practical range.

a. The number of units occupied, N, can be determined by subtracting the number of vacant units from the total number of units. From the given information, we know that each $10 increase in rent corresponds to one additional vacant unit. Let's denote the rent charged as x.

The number of vacant units can be calculated by dividing the increase in rent by $10: V = (x - 800) / 10.

Therefore, the number of occupied units can be expressed as: N = 100 - V.

b. The revenue generated can be found by multiplying the number of units occupied by the rent charged per unit. Let R represent the revenue.

R = N * x

= (100 - V) * x

= (100 - ((x - 800) / 10)) * x

c. To maximize the revenue, we need to find the value of x that maximizes the revenue function R. We can achieve this by finding the critical points of R.

Taking the derivative of R with respect to x and setting it equal to zero:

dR/dx = 0

100 - ((x - 800) / 10) - ((100 - ((x - 800) / 10)) / 10) = 0

Simplifying the equation, we find:

9000 - 90(x - 800) - 100(100 - (x - 800)) = 0

After further simplification, we obtain:

200x - x^2 - 120000 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Plugging in the values a = -1, b = 200, and c = -120000, we can calculate the two potential values for x. The manager should choose the value that falls within a realistic range for rent.

a. The function that gives the number of units occupied N as a function of the rent charged x is N = 100 - ((x - 800) / 10).

b. The function that gives the revenue in dollars R as a function of the rent charged x is R = (100 - ((x - 800) / 10)) * x.

c. To maximize revenue, the manager should calculate the critical points of the revenue function and choose the rent value that falls within a practical range.

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Answer: Is there any answers to choose from

Answer:

-7y - 8x

the person who answered the question before me is buggin

Answer:

1&1/3

Step-by-step explanation:

(y2 - y1) / (x2 - x1)

(8 - 0) / (4 +2)

8/6

1 1/3

The primary role of a control in an experiment is not to prove that a hypothesis is correct but rather to provide a baseline for comparison and ensure the validity and reliability of the experimental results. The statement attributed to Rachel Carson is about the concern regarding pesticides. Among the given categories of thinking (critical, creative, analytical, reflective, logical), there is no single category that is above all others. Each category has its own significance and contributes to different aspects of thinking.

The primary role of a control in an experiment is to provide a standard or baseline against which the experimental group is compared. It helps researchers assess the effect of the independent variable by isolating it from other potential variables. The purpose is not to prove the hypothesis correct but rather to ensure that any observed changes or effects can be attributed to the independent variable and not to other factors.

The statement about pesticides eating and drinking chemicals is attributed to Rachel Carson, who was an influential environmentalist and author known for her book "Silent Spring" which highlighted the harmful effects of pesticides on the environment and human health.

Regarding the categories of thinking, critical, creative, analytical, reflective, and logical thinking are all important and serve different purposes. Critical thinking involves evaluating and analyzing information, creative thinking involves generating new ideas, analytical thinking involves breaking down complex problems, reflective thinking involves introspection and learning from past experiences, and logical thinking involves reasoning and making logical connections. Each category of thinking has its own value and is applicable in different contexts, and there is no single category that can be considered above all others as they are all important in their own right.

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I don't know if you need to solve the x but that what are going to do

Answer: 13/6

Step-by-step explanation:

2x - 3 = 9-4x

2x + 4x = 9 + 4

6x = 13

X= 13/6

Or

X= 2.16

Step-by-step explanation:

that is

sum(2^r) for r=1 to n, plus sum(1/2) for r=1 to n.

and that is

sum(2^r) + n/2 for r=1 to n.

2^r is a geometric sequence with 2 being the common ratio (every new term is created by multiplying the previous term by 2).

and since r is starting at 1, the first term a1 = 2.

the formula for the sum of a finite geometric sequence is

Sn = a1×(1 - r^n) / (1 - r)

with r being the common ratio .

so, in our case

Sn = 2×(1 - 2^n) / (1 - 2)

Sn = (2 - 2^(n+1)) / -1 = 2^(n+1) - 2

and so, in total we get

2^(n+1) - 2 + n/2 = 2^(n+1) + (n - 4)/2

Step-by-step explanation:

-2 x 3/7 = (-2 x 3) /7

= -6/7

Let's see

That's the answer

Answer:

x(x-1)^2

Step-by-step explanation:

x(x^2-2x+1)

x(x-1)(x-1)

(x-1)(x-1)=(x-1)^2

Answer:

width = (21 - 2n) ÷ 2 or 21/2 - n

Step-by-step explanation:

To find Width

let's say width is x

so 2x + 2n = 21

take away 2n from both sides

then 2x = 21 - 2n

Divide both sides by 2 to get x on its own

x = 21 - 2n /2

therefore the width of the rectangle is 21 - 2n /2

Answer:

Option C represents an exponential function

Step-by-step explanation:

Generally, we have an exponential function in the form ;

y = a.b^x

Where in fact, a is not 0

In this case, let us have a as 1 and b as 2

So we have;

for x = -1

y = 2^-1 = 1/2

for x = 0

y = 2^0 = 1

for x = 1

y = 2^1 = 2

for x = 2

y = 2^2 = 4

So the correct choice here is the third option

Answer:

Option (D)

Step-by-step explanation:

Length of the bar EG = 1.6x

If F is a point on the bar such that,

EF + FG = EG

Measure of segment EF = 6

Measure of FG = x

By substituting measures of each side,

6 + x = 1.6x

1.6x - x = 6

0.6x = 6

x = 10

Length of EG = x + 6

                      = 10 + 6

                      = 16 units

Option (D) will be the correct option.

From the given diagram , the length of EG is 16

Given :

From the diagram , we can see that

EF=6, FG=x and EG=1.6x

We know that , EG=EF+FG

\(EG=EF+FG\\1.6x=6+x\\Solve \; for \; x\\1.6x-x=6\\0.6x=6\\divide by \; 0.6\\x=10\)

Now we find out EG

EG=1.6x

Substitute 10 for x

\(EG=1.6x=1.6(10)=16\\\)

EG=16

The length of EG is 16

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Answer:

the price with the offer is going to be 1.59$

Step-by-step explanation:

\( \frac{x}{5.30} = \frac{70}{100} \)

\(100(x) = 70(5.30)\)

\(100(x) = 371\)

\( \frac{100(x)}{100} = \frac{371}{100} \)

\(x = 3.71\)

\(70\% \: \: \: of \: \: \: 5.30 \: \: \: is \: \: \: 3.71\)

\(5.30 - 3.71 = 1.59\)

The number of degrees of freedom is large, then the student's T distribution is close to the normal distribution.

The degrees of freedom is the number of observation in a sample that are free to vary when we estimate the statistical data. Degree of freedom will also indicate the independent piece of information in the data.

Basically, the T distribution or student's distribution is a family's of distribution that look identical to the normal distribution.

So, the number of degrees of the freedom is large then it will closely related to normal distribution.

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