what is the volume of the pyramid shown below?

Answer: Equivalent

Step-by-step explanation:

There is the same amount of red filling in the boxes in both.

Answer:

a or =

Step-by-step explanation:

5th are like half of ten

(a)To solve the system of equations, x^2 - y^2 = 16 and x^2 - y = 7, we can use substitution or elimination method to find the values of x and y.

(b) To graph the solution set of the system of inequalities, x^2 - y^2 > 7 and x^2 - y < 0, we need to plot the boundaries and shade the appropriate regions based on the given inequalities.

(a)Let's use the substitution method to solve the system of equations:

From the second equation, we can rewrite it as x^2 = y + 7.

Substituting this value of x^2 in the first equation, we get (y + 7) - y^2 = 16.

Rearranging the equation, we have -y^2 + y + 7 - 16 = 0.

Simplifying further, we get -y^2 + y - 9 = 0.

Now, we can solve this quadratic equation for y by factoring or using the quadratic formula.

After finding the values of y, we can substitute them back into the second equation to find the corresponding values of x.

(b)To graph the solution set, we first graph the boundaries of the inequalities. For x^2 - y^2 > 7, we draw the curve of the equation x^2 - y^2 = 7, which represents a hyperbola. For x^2 - y < 0, we graph the curve of the equation x^2 - y = 0, which represents a parabola opening upwards.

Next, we need to determine which regions satisfy the given inequalities. For x^2 - y^2 > 7, the shaded region lies outside the hyperbola. For x^2 - y < 0, the shaded region lies below the parabola.

By combining the shaded regions of both inequalities, we find the solution set of the system of inequalities. It includes the regions outside the hyperbola and below the parabola. We label the corners of the shaded region to indicate the solution set accurately.

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Answer:

Step-by-step explanation:

Given sequence is,

5, 6, 7, .........

Difference in second and first term = 6 - 5 = 1

Difference in third and second term = 7 - 6 = 1

There is a common difference of 1 in each successive term of the given sequence.

Therefore, This is an Arithmetic sequence and the common difference is equal to 1.

Answer:

(-1,1)

Step-by-step explanation:

1.  Rearrange either equation to isolate one of the variables.   Lets use 6x - y = -7 :

6x - y = -7

-y = -7 - 6x

y = 7+6x

2.  Now use this definition of x in the second equation:

5x + y = -4

5x + (7+6x) = -4

11x  = -11

 x = -1

3.  Now use x = -1 in either equation to find y:

   6x - y = -7

  6 (-1) - y = -7

-y = -1

y = 1

The solution is  (-1,1)

See the attached graph.

The ratios of 18/32, 27/48​ do not form a proportion.

The concept that will be used here is ratios. when we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.

The given proportion is 18/32, 27/48​

18/32 = 0.5625

27/48​ = 0.354

Hence they  do not form proportion since they are not equal.

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If we take a simple random sample of size n=500 from a population of size 5,000,000, the variability of our estimate will be  (c) about the same as the variability for a sample  size n=500 from a population of size 50,000,000.

The variability of an estimate primarily depends on the sample size (n) rather than the population size. Since both scenarios have a sample size of 500, the variability will be approximately the same.

The correct answer is (d) slightly greater than the variability for a sample size n = 500 from a population of size 50,000,000. This is because the larger the population size, the smaller the sampling variability. In other words, if we take a sample of the same size from a larger population, there will be more variability due to the increased number of potential outcomes. However, the difference in variability between a population size of 5,000,000 and 50,000,000 is not significant enough to make a substantial impact on the estimate.

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The particular solution for the given differential equation when y(1) = 1 is:
arctan(y) = x + π/4 - 1

The given equation is:
dy/dx = y² + 1

To solve this first-order, nonlinear, ordinary differential equation, we can use the separation of variables method. Here are the steps:

1. Rewrite the equation to separate variables:
dy/(y² + 1) = dx

2. Integrate both sides:
∫(1/(y² + 1)) dy = ∫(1) dx

On the left side, the integral is arctan(y), and on the right side, it's x + C:
arctan(y) = x + C

Now, we'll find the particular solution using the initial condition y(1) = 1:
arctan(1) = 1 + C

Since arctan(1) = π/4, we can solve for C:

π/4 = 1 + C
C = π/4 - 1

So, the particular solution for the given differential equation when y(1) = 1 is:

arctan(y) = x + π/4 - 1

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Answer:

Options (B), (C) and (F) are correct.

Step-by-step explanation:

Properties of a rhombus,

1). All sides of a rhombus are equal in measure.

2). Both the diagonals of a rhombus are the perpendicular.

3). Diagonals bisect the vertex angles.

By these properties of a rhombus,

Option (B): PR is perpendicular to QS.

Option (C): ∠QPR ≅ ∠SPR

Option (F): PQ ≅ QR

Therefore, options (B), (C) and (F) are correct.

Answer:

B, C, F, and E are all correct.

Step-by-step explanation:

Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

Answer:

Option C

Step-by-step explanation:

Given the following question:

Total cost is $725
15% Marcus makes in commission.

In order to find the answer, we have to find 15% of $725 and that number will be the total in commissions he earned that week.

\(\frac{15\times725}{100} =15\times725=10875\div100=108.75\)

Marcus makes "$108.75" or option C in commissions last week.

Hope this helps.

Answer:

Step-by-step explanation:

If J and K are complementary, then J + K = 90. If J is 18 less than K, then:

J = K - 18. Now we have a system. We'll sub in K - 18 for J to the first equation:

K - 18 + K = 90 and

2K - 18 = 90 and

2K = 108 so

K = 54

Now that we know K, we'll sub in to find J:

J + 54 = 90 so

J = 36

The expression √180 * 2√30 is equivalent to the expression 60√6

An equation is an expression that shows the relationship between two numbers and variables.

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given the expression √180 * 2√30

Collecting like terms give:

= 2√(180 * 30)

Simplifying:

= 60√6

The expression √180 * 2√30 is equivalent to the expression 60√6

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Using a system of equations, the price for each type of ticket is as follows:

Student = $7

Adult = $22.

A system of equations is two or more equations solved concurrently.

A system of equations is also described as simultaneous equations because they are solved at the same time.

                 Students      Adults    Total Cost

Mrs. Blake       28                26          $768

Mr. Hurst          31                27           $811

Let the price per student ticket = x

Let the price per adult ticket = y

28x + 26y = 768 ... Equation 1

31x + 27y = 811 ... Equation 2

Subtract Equation 1 from Equation 2

31x + 27y = 811

-

28x + 26y = 768

3x + y = 43

y = 43 - 3x

Substitute y = 43 - 3x in Equation 1:

28x + 26y = 768

28x + 26(43 - 3x) = 768

28x + 1,118 - 78x = 768

-50x = -350

x = 7

Substitue x = 7 in Equation 1:

28x + 26y = 768

28(7) + 26y = 768

196 + 26y = 768

26y = 572

y = 22

Check in Equation 2:

31x + 27y = 811

31(7) + 27(22) = 811

217 + 594 = 811

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To compute for the probability of normal distribution, we need to determine the z-score as z = (X - μ)/ (σ/√n)

Probability is the likelihood that something will happen. Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes

To calculate the average selling price of a product, divide the total revenue earned from the product or service and divide it by the number of products or services sold.

X = value of interest

n = number of sample taken

μ = mean

σ = standard deviation

(σ/√n) = standard error

Given that

μ = mean = $231,600

σ = standard deviation = $38,550

a) What is the probability that a randomly selected home is worth more than $300,000?

At n = 1

P(X > $300,000)

= P(z > ($300,000 - μ)/ (σ/√n))

= P(z > ($300,000 - $231,600)/ ($38,550/√1))

= P(z > 1.774319066)

Using the online z-calculator, we have

P(z > 1.774319066) = 0.038005

b) Take an SRS of 5 homes. What is the probability that the mean price of these homes is more than $300,000?

At n = 5

P(X > $300,000)

= P(z > ($300,000 - μ)/ (σ/√n))

= P(z > ($300,000 - $231,600)/ ($38,550/√5))

= P(z > 3.967498046)

Using the online z-calculator, we have

P(z > 3.967498046) = 0.00004

c) What is the probability that the mean price of an SRS of 75 homes is more than $300,000?

At n = 75

P(X > $300,000)

= P(z > ($300,000 - μ)/ (σ/√n))

= P(z > ($300,000 - $231,600)/ ($38,550/√75))

= P(z > 15.36605386)

Using the online z-calculator, we have

P(z > 15.36605386) = 0

d) Why has the probability decreased so dramatically from part (a) to part (c)?

Notice that the probability decreased dramatically from (a) to (c) because of the number of sample taken. The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.

In this case, notice that the standard error gets smaller due to larger sample size. This means that at greater sample size, we are getting closer to represent the overall population. Thus, at greater sample size, the error with which should occur since we are only doing sampling tends to get smaller. That is why the standard error gets smaller and as a result, the probability is getting closer to its actual value (in this case, the probability gets closer to 0)

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Answer:

\(\rm{-2\)

Step-by-step explanation:

Hi there!

\(\rm{-4(t+4)=-8t-24}\)

\(\rm{-4t-16=-8t-24\)

\(\rm{-4t+8t=-24+16\)

\(\rm{4t=-8\)

\(\rm{-2\)

Thus, \(-2\) is our final answer.

Hope it helps! Enjoy your day!

\(\bold{GazingAtTheStars}\)

solve for t:

-4(t+4)=-8t-24

t = -2

\( \red \rightarrow \)-4(t+4) = -8t-24

\( \green \rightarrow\)-4t-16 = -8t-24

\( \orange \rightarrow\)-4t+8t = -24+16

\( \blue \rightarrow \: \)4t = -8

\( \pink \rightarrow\)t = -8/4

\( \tt{ \boxed {t = - 2}}\)

Answer:

615.44 in²

Step-by-step explanation:

The shape of Captain America's shield = Circular

The area of a circle = πr²

The radius of the whole shield = 14 inches.

The first ring = Red ring

Hence, the area of the red ring =

π = 3.14

3.14 × 14²

= 615.44 in²

The area of the space he needs to paint red is 615.44 in²

The percentage of the students at the university which are foreign are 25% by conditional probability formula.

According to the question,  10% of all college students are foreign students who also smoke and it is also known that 40% of all foreign college students smoke.

We use the conditional probability formula to solve this question.

Let foreign students be denoted as F

Let students smoking be denoted as S

We know that 10% of all college students are foreign students who also smoke this means

P(F ∩ S) = 0.1

and 40% of all foreign college students smoke which means

P(S/F) = 0.4

So, the percentage of the students at this university who are foreign can be calculated as  

\(P(F) = \frac{0.1}{0.4}\) = 0.25

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Answer:

1

Step-by-step explanation:

I assume you mean slope

(-3-(-8))/(2-(-3))=5/5=1

The sum of probabilities is equal to 1, so the probabilities are correctly normalized.

To perform the tasks using R, first, make sure you have R and RStudio installed on your computer. Then, follow these steps:

Step 1: Enter the data into R.

# Enter the data

x <- c(1, 2, 3, 4)

f_x <- c(0.2, 0.5, 0.2, 0.1)

Step 2: Plot the probability mass function (PMF).

# Plot the probability mass function

plot(x, f_x, type = "h", lwd = 10, col = "blue", xlab = "X", ylab = "P(X)", main = "Probability Mass Function")

Step 3: Verify that the probabilities add up to 1.

# Verify that the probabilities add up to 1

sum_probabilities <- sum(f_x)

print(paste("Sum of probabilities: ", sum_probabilities))

Step 4: Calculate the cumulative distribution function (CDF) and plot it.

# Calculate the cumulative distribution function

cdf <- cumsum(f_x)

# Plot the cumulative distribution function

plot(x, cdf, type = "s", lwd = 3, col = "red", xlab = "X", ylab = "F(X)", main = "Cumulative Distribution Function")

Sum of probabilities = 0.2 + 0.5 + 0.2 + 0.1 = 1

The sum of probabilities is equal to 1, so the probabilities are correctly normalized.

Make sure to execute each step in the RStudio console or script. The plots will appear in separate windows, and the sum of probabilities will be displayed in the console. The PMF plot will show vertical lines with heights corresponding to the probabilities, and the CDF plot will show a step function.

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Answer:

E

Step-by-step explanation:

=√9pr / (pr)^-3/2

=3√(pr) × (pr)^3/2

= 3p²r²

Answer:

E. 3p²r²

Step-by-step explanation:

√9pr / (pr)^-3/2=

3(pr)^1/2*(pr)^3/2=

3(pr)^(1/2+3/2)=

3(pr)^2=3p^2r^2

Answer:

Mean:  The sum of all data values divided by the total number of data values.

Median: The middle value when all data values are placed in order of size.  If there is an even number of data values, the median is the mean of the middle two values.

Mode: The most frequently occurring data value.

-------------------------------------------------------------------------------------------------

Question 3

\(\textsf{Mean}=\dfrac{69 + 70 + 71 + 73 + 74 + 75 + 76 + 76 + 76 + 86}{10}=74.6\)

Ordered data values:  69, 70, 71, 73, 74, 75, 76, 76, 76, 86

Median = (74 + 75) / 2 = 74.5

Mode = 76

-------------------------------------------------------------------------------------------------

Question 4

\(\textsf{Mean}=\dfrac{3 + 5 + 5 + 5 + 6 + 6 + 7 + 8 + 8}{9}=5.9\: \sf (nearest \:tenth)\)

Ordered data values:  3, 5, 5, 5, 6, 6, 7, 8, 8

Median = 6

Mode = 5

-------------------------------------------------------------------------------------------------

Question 5

\(\begin{aligned}\textsf{Mean} & =\dfrac{11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 16 + 16 + 17 + 18 + 19 + 20 + 23}{15}\\ & =15.5 \: \sf (nearest\:tenth)\end{aligned}\)

Ordered data values:  11, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 18, 19, 20, 23

Median = 15

Mode = 12, 13, 14, 16

Answer:

see explanation

Step-by-step explanation:

the mean is calculated as

mean = \(\frac{sum}{count}\)

the median is the middle value of a set of data. If there is no exact middle value then it is the average of the values on either side of the middle.

the mode is the value that occurs most often in the data set

A data set can have more than 1 mode

------------------------------------------------------------------------

(3)

(a)

mean = \(\frac{74+73+75+76+71+69+70+76+76+86}{10}\) = \(\frac{746}{10}\) = 74.6

(b)

Arrange the data in ascending order

 69  70  71  73  74  75  76  76  76  86

                              ↑ middle

median = (74 + 75) ÷ 2 = 149 ÷ 2 = 74.5

(c)

mode = 76

(4)

(a)

mean = \(\frac{6+8+8+5+6+7+5+3+5}{9}\) = \(\frac{53}{9}\) ≈ 5.9 ( to 1 dec. place )

(b)

3  5  5  5  6  6  7  8  8

                 ↑ middle

median = 6

(c)

mode = 5

(5)

(a)

mean = \(\frac{12+13+18+23+14+17+14+16+13+16+15+19+11+20+12}{15}\) = \(\frac{233}{15}\)  ≈ 15.5 ( to 1 dp )

(b)

11  12  12 13  13  14  14  15  16  16  17  18  19  20  23

                                      ↑ middle

median = 15

(c)

the mode is multimodal

modes are 12, 13, 14, 16

Answer:

The answer is option D.

Equation of a line is y = mx + c

m = slope

c = intercept on y axis

y-4= -2/3 (x-6)

y = -2/3x + 4 + 4

y = -2/3x + 8

From the above equation

m= -2/3

Since the lines are perpendicular the slope of the line is the negative inverse of the original line.

so m = 3/2

Equation of the line using point (-2 , -2) is

y + 2 = 3/2(x+2)

y = 3/2x + 3 - 2

y = 3/2x + 1

That's the last option

Hope this helps

The linear equation with the given characteristics is given by:

\(y = \frac{3}{2}x + 1\)

It is given by:

y = mx + b.

In which:

When two lines are perpendicular, the multiplication of their slopes is -1, hence:

\(-\frac{2}{3}m = -1\)

\(2m = 3\)

\(m = \frac{3}{2}\)

Then:

\(y = \frac{3}{2}x + b\)

It passes through the point (-2, -2), hence:

\(-2 = \frac{3}{2}(-2) + b\)

\(-3 + b = -2\)

\(b = 1\)

Hence, the equation is:

\(y = \frac{3}{2}x + 1\)

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The point  (6, -2) lie on the given line segment y= 1/2x-5.

A point denotes exact location on any surface,

and the collection of points in the definite pattern is called line.

So, every line itself have infinite points.

Given point = (6, -2)

Hence, the given line = y= 1/2x-5

So, to find whether any point is on the line or not,

we have to put the point on line.

If it satisfies it will lie on line segment.

If not it will not pass through given line segment.

y= 1/2x-5

Putting x= 6 and y= -2

-2 = 3- 5

Hence, -2 = -2

Hence the (6, -2) lie on the given line segment y= 1/2x-5

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The explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have given:

\(\rm a_n=3+a_n_-_1\) and

\(\rm a_1=5\)

\(\rm a_n-a_n_-_1= 3\)

The above expression represents the common ratio:

d = 3

First term:

a = 5

The explicit rule for the arithmetic sequence:

a(n) = 5 + (n - 1)3

a(n) = 3n + 2

Thus, the explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

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Answer:

The correct answer is C. 20 in. To calculate the area of the triangle, we can use the formula A = 1/2 bh. The base of the triangle is 10 in and the height is 8 in, so the area is 1/2 x 10 x 8 = 40 in^2. Since the triangle is a right triangle, the area is half of 40 in^2, which is 20 in^2

To find the box to the top left, we can multiple the sides like rectangles. To find the top left box, we can multiply -1 and 0.5y to get -0.5y.

To find the box on the bottom right, we can multiply the sides like rectangles again. To find the bottom right box, we can multiply 24x and 3 to get 72x.