Find the height of each pyramid.

The probability that a class of 50 has an average midterm mark that is less than 75 is value=0

Average is the mathematics mean, and is calculated by means of adding a group of numbers and then dividing with the aid of the count of these numbers. for instance, the average of 2, three, three, five, 7, and 10 is 30 divided with the aid of 6, that is five.

The common is described as the implied value that is identical to the ratio of the sum of the number of a given set of values to the whole wide variety of values gift within the set.

There are three primary sorts of common: imply, median, and mode. each of those techniques works slightly differently and frequency effects in barely specific regular values. The suggestion is the maximum normally used average. To get the suggested fee, you add up all of the values and divide this total by using the number of values.

The probability that a class of 50 has an average midterm mark that is less than 75

n = 50

P(<75)=P(Z<75)

P(Z<75−786√50)

P(Z<−3.5355)

We will look for the value in the StandardNormal able. We will get the value=0

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The values represent the robot facing east, south, and west are 1, -i, -1.

To offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve : challenge mentally also : to exert (oneself, one's mind, etc.) over such a problem or situation they puzzled their wits to find a solution.

given that,

The robot can only go north, south, east and west.

Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.

Now,

It is provided that the ' i ' represent that robot is facing north.

So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.

Since, the values on y-axis are negative in that direction.

Hence, South will be represented by ' - i ' .

Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.

So, the value that represents East will be 1.

(as it is on the positive x-axis ).

Since, west is in the opposite direction of east.

So, West will be represented by -1.

Hence,The values represent the robot facing east, south, and west are 1, -i, -1.

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Answer:

x = 4

Step-by-step explanation:

These triangles are similar by the AA Similarity Postulate.

12 + 4 = 16

(5x - 2)/12 = 6x/16 (3x/8)

Cross multiply: 8(5x - 2) = 12(3x)

40x - 16 = 36x

4x - 16 = 0

4x = 16

x = 4

Slope-Intercept Form: y = mx + b

---Where m is the slope and b is the y-intercept

Correct Answer: y = -5/4x + 2

---Option A

Hope this helps!

Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.

The surface area of a sphere is simply the total area that covers its outer surface.

The surface area of a sphere is expressed as;

A = 4πr²

Where r is radius and π is pi. ( π = 3.14 )

Given the data in the question;

We substitutes the given values into the equation above.

A = 4πr²

320cm² = 4 × 3.14 × r²

320cm² = 12.56 × r²

r² = 320cm² / 12.56

r² = 25.477707cm²

r = √25.477707cm²

r = 5.05cm

Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.

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Answer:

The radius is 5.05 centimeters.

Hope this helps!

Step-by-step explanation:

Using proportions, the value of y is of 100º.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a circle, the measure of an arc is twice the measure of it's equivalent internal angle. The internal angle is of 50º, hence the measure of the arc, given by y, is found as follows:

y = 2 x 50º = 100º.

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Answer:

a = 3.14

b = 6.28

Step-by-step explanation:

The interval where the function is decreasing is where increasing x values result in decreasing y values. The y values peak at the point (3.14, 2) and decrease until the point (6.28, 0) where the function starts increasing again.

Answer: 4/10, 6/15, 8/20

Hope this helps!

Using proportions, the missing side length in the image below is of 20.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the side lengths are proportional, being related by the rule of three given as follows:

x/10 = 14/7

Applying cross multiplication:

7x = 14 x 10

7x = 140

x = 140/7

x = 20.

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The equation be 38 + 2x - (64 - 2x) = 0 then the value of x = 6.5.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Let the day be x

38 + 2x - (64 - 2x) = 0

Subtract 38 from both sides

38 + 2x - (64 - 2x) - 38 = 0 - 38

Simplifying the above equation, we get

2x - (64 - 2 x) = -38

Expanding the above equation, 2x - (64 - 2x) = 4x - 64

4x - 64 = -38

Add 64 to both sides

4x - 64 + 64 = -38 + 64

Simplify

4x = 26

Divide both sides by 4

[tex]$\frac{4 x}{4}=\frac{26}{4}[/tex]

Simplifying the equation

[tex]$x=\frac{13}{2}[/tex]

The value of x = 6.5.

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For function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

For given question,

We have been given a function k(x, y) = -x² - y² + 4x + 4y

We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

First we find the partial derivative of function k(x, y) with respect to x.

⇒ [tex]k_x=-2x+4[/tex]

Now, we find the partial derivative of function k(x, y) with respect to y.

[tex]\Rightarrow k_y=-2y+4[/tex]

To find the critical point:

consider    [tex]k_x=0[/tex]     and      [tex]k_y=0[/tex]

⇒       -2x + 4 = 0     and    -2y + 4 = 0

⇒          x = 2            and       y = 2

This means, the critical point of function is (2, 2)

We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

Consider k(0, 0)

⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)

⇒ k(0, 0) = 0

Consider k(3, 3)

⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)

⇒ k(3, 3) = -9 - 9 + 12 + 12

⇒ k(3, 3) = -18 + 24

⇒ k(3, 3) = 6

Therefore, for function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

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Answer: 42.99

Step-by-step explanation:

42.988. Since 8 is close to ten and is in the hundredth we round it hence 42.99.

The effective annual yield is 3.04%

What is effective annual yield?

Effective annual yield is the rate of return that considers the frequency of compounding, in other words, the number of times in a year that interest on the balance is compounded.

The easiest way to determine the effective annual yield in this case is to compare the end of the year balance with the initial balance at the start of the year

effective annual yield=(ending balance/initial balance)-1

ending balance=$4,121.66

initial balance=$4000

effective annual yield=($4,121.66/$4000)-1

effective annual yield=3.04%

Another way to determine the effective annual yield is use the below formula which considers that interest rate is 3% compounded monthly, in other words, n, the frequency of compounding is 12

EAR=(1+r/n)^n-1

r=3%

n=12

EAR=(1+3%/12)^12-1

EAR=3.04%

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89% of pebbles weigh more than 2.1 grams.

What is a percentage?

Given,

         Mean = 2.6

           SD = 0.4

As we have to find the percentage of pebbles weighing more than 2.1, we have to find the z-score for 2.1 first.

             [tex]z = \frac{x- mean}{SD}[/tex]

             [tex]z = \frac{2.1 - 2.6}{0.4}[/tex]

             [tex]z = -1.25[/tex]

Now we have to use the z-score table to find the percentage of pebbles weighing less than 2.1

So,

   [tex]P ( x < 1.25 ) = 0.10565[/tex]

This gives us the probability of P(z<-1.25) or P(x<2.1)

To find the probability of pebbles weighing more than 2.1

[tex]P ( x > 2.1 ) = 1 - P( x < 2.1 ) = 1 - 0.10565 = 0.89435[/tex]

Converting into percentage

0.89435 × 100 = 89.435 %

Rounding off to nearest percent   =89%

Therefore, 89% of pebbles weigh more than 2.1 grams.

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Answer:

A=36°

B=54°

C=90°

a=7

b=9.6

c=11.9

Step-by-step explanation:

Upper case A,B,C are angles. B and C are given. Calculate A because the three angles in a triangle add up to 180°. See image.

Lower case a,b, and c are side lengths.

a is given. You need to use trigonometry and a calculator to find b or c or both. Or you can find one and use the Pythagorean Theorem to find the other. See image.

Recall the power series expansions of [tex]\sin(x)[/tex] and [tex]e^x[/tex].

[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1}[/tex]

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{1}{n!} x^n[/tex]

By substituting [tex]3x[/tex] for [tex]x[/tex] in the latter series, we have

[tex]\displaystyle e^{3x} = \sum_{n=0}^\infty \frac{1}{n!} (3x)^n = \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

Then the series expansion of [tex]f(x)[/tex] is

[tex]\displaystyle f(x) = x^3 \sin(x) + e^{3x+2} \\\\ ~~~~~~~~ = x^3 \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2(n+2)} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.

In the question the given function is,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

We know that series representation of sin x and eˣ are:

   ⇒ [tex]e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]

             = [tex]\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Substituting the series representation in the function we get,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

⇒ [tex]f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Hence [tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]  is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².

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Answer:

2

Step-by-step explanation:

Your slope is your change in y over your change in x.  The ordered pair is in the form of (x,y), so you subtract the y's and put that in your numerator (top)and subtract your x's and put that in your denominators (bottom).

2 - (-4) would be your top number.  To subtract a negative number is the same as adding a positive, so 2 - (-4) is the same as 2 +4, so your top number is 6.  

Now, to find the bottom number, you subtract the x's.

5-2 which is 3.

We now have the top and the bottom number

6/3 which is the same as 2.

Answer:

x=14

Step-by-step explanation:

4(x-7)= 14(2)

4x - 28 = 28

4x = 56

x = 14

The dart player throws a dart horizontally at a speed of 24.75 m/s.

In this question,

The horizontal distance traveled by the dart, x = 2.5 m

The dart hits the board 5 cm below the height from which it was thrown.

⇒ 5 cm = 0.05 m

Let the time taken by the dart to hit the board is t.

The time taken can be calculated using the Newton's second law of motion,

[tex]y = ut+\frac{1}{2}at^{2}[/tex]

Put, u = 0, a = -g and g = 9.8

On substituting the above values, we get

⇒ [tex]-0.05 = 0-\frac{1}{2}(9.8)t^{2}[/tex]

⇒ [tex]0.05(\frac{2}{9.8}) = t^{2}[/tex]

⇒ [tex]t^{2} =0.0102[/tex]

⇒ [tex]t=\sqrt{0.0102}[/tex]

⇒ t = 0.1010 s

Now, the velocity (speed) can be calculated as

displacement = speed × time

⇒ 2.5 = speed × 0.1010

⇒ speed = [tex]\frac{2.5}{0.1010}[/tex]

⇒ speed = 24.7524 m/s

Hence we can conclude that the dart player throws a dart horizontally at a speed of 24.75 m/s.

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Using it's concept, the probability that exactly two of the dice show a 1 and exactly two of the dice show a 2 is: 10/243.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

One of the six numbers is of 1, and also one out of six is 2. The other two trials can be any of the other 4 numbers, hence the probability for the six rolls has the following format:

p = (1/6)² x (1/6)² x (4/6)²

This considers just one order, while there are six rolls, hence there are 6! possible orders, hence the probability is:

p = 6! x (1/6)² x (1/6)² x (4/6)² = 120 x 16/46656 = 10/243.

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Answer:

3x + 4y + 2z = 435

Step-by-step explanation:

let x represent soccer

hence playing soccer three times = 3 × x = 3x

let y represent swimming

hence swimming four times = 4 × y = 4y

let z represent piano

hence playing piano twice = 2 × z = 2z

Victoria spends a total of 435mins doing these three activities every week,

3x + 4y + 2z = 435

Check the picture below.

Answer:

160

Step-by-step explanation:

I multiplied the amount of each item to get to the answer:

- 8 shirts

- 4 pairs of pants

- 5 pairs of shoes

8 x 4 x 5 = 32 x 5

32 x 5 = 160

hope this helps!

The equivalent expression of the expression is 128x^5y^6/2x^7y^5

The expression is given as:

128x^5y^6/2x^7y^5

Divide 128 by 2

64x^5y^6/x^7y^5

Apply the law of indices

64y^(6-5)/x^(7-5)

Evaluate the differences

64y/x^2

Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5

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Answer: someone already answered this check the link out

Step-by-step explanation. https://brainly.com/question/11711784

8 Guidelines for Critically Evaluating a Statistical Study

1. Identify the Goal, Population, and Type of Study

2. Consider the Source

3. Examine the Sampling Method

4. Look for Problems in Defining or Measuring the Variables of

Interest

5. Watch Out for Confounding Variables

6. Consider the Setting and Wording of Any Survey

7. Check That Results Are Fairly Represented in Graphics or

Concluding Statements

8. Stand Back and Consider the Conclusions

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Considering the equation of the parabola, the directrix is: x = 1.

The equation of an horizontal parabola, of vertex (h,k), is given by:

(y - k)² = 4p(x - h).

The directrix is at x = h - p.

For this problem, the equation is:

(y + 3)² = 8(x - 3).

The relevant coefficients for this problem are:

4p = 8 -> p = 2, h = 3.

Hence the directrix is:

x = h - p = 3 - 2 = 1.

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The equation of the parabola whose equation [tex](y + 3)^3 = 8(x - 3).[/tex], the directrix exists x = 1.

The equation of a horizontal parabola, of vertex (h, k), exists given by:

(y - k)² = 4p(x - h).

The directrix exists at x = h - p.

For this problem, the equation exists:

[tex](y + 3)^3 = 8(x - 3).[/tex]

The appropriate coefficients for this problem exist:

4p = 8

p = 8/4 = 2 and h = 3.

Hence the directrix exists:

x = h - p = 3 - 2 = 1.

Therefore, the directrix exists at x = 1.

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The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

What is an equation?

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

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 8):

8 = ab⁰

a = 8

At point (1, 32):

32 = 8b

b = 4

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

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The option that explains the point (1, 1400) is (c) the person surveyed took a day trip

From the graph, we have the following representations:

The point (1,1400) implies that

x = 1 and y = 1400

This means that

The number of days on vacation is 1 and the total cost of vacation is 1400

Hence, the option that explains the point (1, 1400) is (c) the person surveyed took a day trip

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We can comment that the maximum value of the given data is 0.2, maximum value is 42. The interquartile range is 15 to 37, first and third quartile values are 15 and 37 respectively. It can also be inferred from the box plot that there are no outliers. The median of the given data, as shown in the box plot, is 28.

What is a box plot?

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box. The five-number summary of a box plot includes the following:

It also tells if there are any outliers in the data.

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