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Direct variation equation relating s and t as: S = 0.5t and t=32 when s=16.

What is direct variation equation?

A direct variation equation is a mathematical equation that describes a relationship between two variables that varies proportionally. In other words, if one variable increases or decreases, the other variable also increases or decreases in proportion to it.

Given, S varies directly as t, and S = 8 when t = 16.

Let's find the constant of variation (k) using the given information:

k = S/t = 8/16 = 0.5

So, the constant of variation is 0.5.

Using the constant of variation, we can write a direct variation equation relating s and t as:

S = kt

Substituting k = 0.5 in the above equation, we get:

S = 0.5t

When S = 16, we can find t as follows:

16 = 0.5t

t = 16/0.5

t = 32

Therefore, when S = 16, t = 32.

Therefore, direct variation equation relating s and t as: S = 0.5t and t=32 when s=16.

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The volume of the cone is approximately700π/3 inches³.

What exactly is a cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat, circular base to a point called the apex or vertex. The base can be any shape, but a circular base is the most common. A cone has a curved surface that extends from the base to the apex, and the distance from the apex to the base along a straight line passing through the center of the base is called the height of the cone.

Now,

As the Volume of cone is given by:

V = (1/3)πr²h

where r is the radius of the base, h is the height, and π is the mathematical constant pi.

In this case, we know that the diameter of the base is 20 inches, which means that the radius is 10 inches. We also know that the height is 21 inches. Therefore, we can plug in these values into the formula to find the volume:

V = (1/3)π(10²)(21) = (1/3)π(100)(21) = 700π/3 inches

Therefore, the volume of the cone is approximately700π/3 inches³, expressed in terms of pi and rounded to the nearest cubic inch.

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It would be very surprising to observe a random sample of 30-time intervals between eruptions with a mean of 97 minutes, given the population mean and standard deviation.

Based on the information provided, we know that the mean time between eruptions of Old Faithful is 85 minutes and the standard deviation is 21 minutes. We are also given a sample of 30-time intervals between eruptions, and we want to determine whether it would be surprising to observe a sample mean of 97 minutes.

To answer this question, we need to calculate the standard error of the mean (SEM), which is given by the formula:

SEM = σ / sqrt(n)

where σ is the population standard deviation (21 minutes), and n is the sample size (30). Plugging in the values, we get:

SEM = 21 / sqrt(30) ≈ 3.84

Next, we calculate the z-score for a sample mean of 97 minutes, using the formula:

z = (x - μ) / SEM

where x is the sample mean (97 minutes), μ is the population mean (85 minutes), and SEM is the standard error of the mean (3.84 minutes). Plugging in the values, we get:

z = (97 - 85) / 3.84 ≈ 3.13

Finally, we can look up the probability of observing a z-score of 3.13 or more extreme in a standard normal distribution table (or using a calculator or software). The probability turns out to be very small, less than 0.01.

Therefore, Given the population mean and standard deviation, it would be very unexpected to find a random selection of 30-minute gaps between eruptions with a mean of 97 minutes. This suggests that the sample may not be representative of the population, or there may be some other factors affecting the intervals between eruptions.

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Answer:

The outlier in this graph is (4, 55)

Step-by-step explanation:

Outliers can be seen graphically when we first draw a line of best fit. When we draw the line of best fit it connects through the middle of the string of points near the top of our graph. We can see that any given point on the graph is either on the line of best fit or very close to it. This can be said about all points but one... the point (4,55). This point lies far away from the line we've created and can be identified as an outlier for this reason.

E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .

To calculate the variance of y, follow these steps:

Recall that for a Poisson distribution, the mean (first moment) is equal to the variance. So, if the first moment of x is less

than the first moment of y by 8, we can write: E(x) = E(y) - 8.

We are also given that the second moment of x is 60% of the second moment of y:

[tex]E(x^2) = 0.6 × E(y^2).[/tex]

Recall that for a Poisson distribution, the second moment is given by [tex]E(X^2) = E(X)² + E(X)[/tex]. Thus, we can write equations

for x and y using this relationship: [tex]E(x^2) = E(x)² + E(x) and E(y^2) = E(y)² + E(y).[/tex]

Plug the expressions from step 1 into the equation from  [tex]E(x^2) = (E(y) - 8)² + (E(y) - 8).[/tex]

Plug the expressions from step 2 into the equation from[tex]0.6 × E(y^2) = (E(y) - 8)² + (E(y) - 8).[/tex]

Solve for [tex]E(y^2)[/tex] from the equation in  [tex]E(y^2) = (10/6) × ((E(y) - 8)² + (E(y) - 8)).[/tex]

Substitute [tex]E(y^2)[/tex] back into the equation for the second moment of y from [tex]E(y^2) = E(y)² + E(y).[/tex]

Solve for E(y) from the equation in

Since E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .

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Therefore, the prism's base can be either 9 x 9 inches, 6 x 6 inches, or

4 x 4 inches in size.

.

The amount of space that an object's surface takes up in total is measured by its surface area. It is usually expressed in square units, such as square inches or square metres.The surface area of a three-dimensional object can be determined by adding up the areas of all of its faces.

For instance, the surface area of a rectangular prism can be calculated using the formula below:

A = lw + lh + lw

The formula SA = 2lw + 2lh + 2wh, where l is the prism's length, w is its width, and h is its height, determines the surface area of a rectangular prism. Inputting the values provided yields:

306 is equal to 2l + 2(24) + 2(24) + 48

306 - 48l = 2w(l+24) 153 - 24

l = wl + 48w 153 - 48w = l(w+24) 153 - 24l - 48w = wl

We can identify all potential values of l and w that meet this equation because they are both whole numbers. Since it is a rectangular prism with a square base, we know that l > w. Given that the surface area cannot be more than 306, we also know that l(w+24) 153. We may therefore begin by identifying all variables of (153-48w) bigger than w.and equal to or less than 12 (since w cannot be greater than 12). We get:

W=1, L=9, L=2, L=6, and L=3

Therefore, the prism's base can be either 9 x 9 inches, 6 x 6 inches, or 4 x 4 inches in size.

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Answer:

Step-by-step explanation:

You want the mass of cashews and pecans in a box that sells for $136 if there are 3 fewer kg of cashews at $11.25 per kg than of pecans at $13 per kg.

Let c represent the mass of cashews in kg. Then (c+3) is the mass of pecans. The total value of the mix is ...

  11.25c +13(c +3) = 136

Simplifying the equation gives ...

  24.25c +39 = 136

  24.25c = 97

  c = 4

The mix should contain 4 kg of cashews and 7 kg of pecans.

The explicit rule is 2000 + 3500n

The salesperson has earned $33500 after 9 months since starting the job.

What is Linear Equation?

A linear equation is a mathematical equation that involves two variables and forms a straight line when graphed. It can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.

The explicit rule for the amount of money the salesperson has earned since starting the job can be given by:

Earnings = 2000 + 3500n

Where n represents the number of months since the salesperson started the job.

To find out how much money the salesperson has earned after 9 months, we can substitute n = 9 in the above formula:

Earnings = 2000 + 3500(9)

= 2000 + 31500

= $33500

Therefore, the salesperson has earned $33500 after 9 months since starting the job.

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The amount Mariano must make from his job is

$2,500 ($12,500 * 0.2) =  $2500.

A number can be divided by five or multiplied by 0.2 to determine 20% of that amount.

Mariano, for instance, would have to pay $12,500 ($15,000 - $800 - $1,700)

if he had to pay $15,000 for a year of classes at the University of Texas at Brownsville but had also been awarded a grant for $800 and a scholarship for $1,700.

We can divide $12,500 by 5 or multiply it by 0.2 to calculate how much he must make from his employment to cover 20% of the remaining expenses.

The amount Mariano must make from his job is

$2,500 ($12,500 * 0.2) =  $2500.

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The parameter of interest is the difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer.

The difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer.

This parameter represents the average difference in reaction times between the two groups - those who did not drink beer and those who drank two cans of beer. It is a measure of the effect that drinking two cans of beer has on reaction times, and it is the focus of the hypothesis test being conducted.

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The statement cannot be determined from the graph, the reason is that the graph shows only the chances of survivals of Albertosaurus and it does not define the life span of the Albertosaurus.

When we carefully asses the graph, according to the information provided, the mortality rate of Albertosaurus dinosaurs between 25% and 50% of their maximum life span was significantly higher than the mortality rate of dinosaurs who lived to 75% of their maximum life span. This conclusion cannot be inferred from the graph because it only depicts the possibilities of survival for Albertosaurus and does not specify how long they lived.

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Answer:

To find the slope between two points (x1, y1) and (x2, y2), we use the formula:

slope = (y2 - y1) / (x2 - x1)

Using the given points P(-11, -24) and Q(21, 40), we can substitute the values into the formula:

slope = (40 - (-24)) / (21 - (-11))

slope = 64 / 32

Therefore, the slope between points P(-11, -24) and Q(21, 40) is 2.

Answer:

2

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 40 - -24)/(21 - -11)

    = ( 40+24)/(21+11)

    = 64/32

    = 2

Answer:

the final answer is 80800 exactly

Answer: $80 880 US$

Step-by-step explanation:

Add all up

Answer:

There are 20 students. Of those 20 students, 4 knew 15 capitals. We have:

4/20 = 20/100 = 20% of the students knew 15 capitals.

The area of a triangle whose sides have lengths √70,√70,√and 28 is 10.45.

What is the area of the triangle?

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The area of the triangle is defined as the product of half the base and the height of the triangle.

The area of the triangle =  (0.5)x b x h

Length of its base = b units

Its height = h units long,

Given;

The sides of the triangle √70,√70,√28

Now,

H²=70-28/4

H²=70-7

H=7.9

[tex]Area= b *\frac{ h}{2}[/tex]

[tex]=\sqrt{28}\frac{7.9}{2}[/tex]

=10.45

Therefore, the area of the triangle will be 10.45.

The complete question is-

What is the area of a triangle whose sides have length √{70},√{70}, and √{28} ?

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The least number of packs of nails Jess needs to buy is 1.

To find the least number of packs of nails Jess needs to buy, we need to find the lowest common multiple (LCM) of the pack sizes of hammers and nails.
Step 1: Identify the numbers
Hammers come in packs of 3, and nails come in packs of 6.
Step 2: Find the LCM of 3 and 6
List the multiples of each number:
Multiples of 3: 3, 6, 9, 12, ...
Multiples of 6: 6, 12, 18, 24, ...
The lowest common multiple of 3 and 6 is 6.
Step 3: Determine the number of packs of nails.

Since the LCM is 6 and nails come in packs of 6, Jess needs to buy 1 pack of nails to have the same number of each item.

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Answer:

x = 122

Step-by-step explanation:

the measure of the chord- chord angle 125° is half the sum of the arcs intercepted by the angle and its vertical angle, that is

125 = [tex]\frac{1}{2}[/tex] (x + 6 + x) ← multiply both sides by 2 to clear the fraction

250 = 2x + 6 ( subtract 6 from both sides )

244 = 2x ( divide both sides by 2 )

122 = x

Answer:mason must need 33.6 m of materail to make  8 curtains.

so he need to 17.6m of material

Step-by-step explanation:

To find the third side length, we can use the fact that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. So we can write: (z + 13) + (2z + 6) > third side Simplifying the left side, we get: 3z + 19 > third side Now we also know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can write: (z + 13) + (2z + 6) + third side = 8z + 11 Simplifying this equation, we get: 3z + 19 + third side = 8z + 11 Subtracting 3z + 19 from both sides, we get: third side = 5z - 8 Therefore, the

To given expression |x + 3| simplifies solution is x + 3.

What is expression?

In mathematics, an expression is a combination of symbols, numbers, and operators that represent a quantity or a mathematical relationship. It can be a single number or a combination of numbers, variables, and operators that can be evaluated to give a numerical result.

If x > 2, then the expression |x + 3| can be simplified as follows:

|x + 3| = x + 3

since x + 3 is already non-negative when x > 2.

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Answer:

the solution for x is (53 - b)/a.

Answer:

Therefore, the staff should order 320 blue bags, 360 black bags, and 120 gray bags.

Step-by-step explanation:

To determine how many bags of each color to order, we need to estimate the proportion of students who prefer each color based on the sample of 120 students. We can then use these proportions to predict the number of bags of each color needed for all 800 students. Here's how we can do it:

Determine the number of students in the sample who prefer each color:

Let B be the number of students who prefer blue

Let K be the number of students who prefer black

Let G be the number of students who prefer gray

Based on the sample of 120 students, we know:

B + K + G = 120

Estimate the proportion of students who prefer each color:

The proportion of students who prefer each color in the sample is:

p(B) = B/120

p(K) = K/120

p(G) = G/120

Predict the number of bags of each color needed for all 800 students:

The predicted number of bags of each color needed for all 800 students is:

Bags of blue = p(B) * 800

Bags of black = p(K) * 800

Bags of gray = p(G) * 800

So, using the sample results, we get:

Bags of blue = (48/120) * 800 = 320

Bags of black = (54/120) * 800 = 360

Bags of gray = (18/120) * 800 = 120

The first, second, and third one.

The Perimeter of the rectangle shaped field is 16x+32 unit.

What exactly is a rectangle?

A rectangle is a four-sided, two-dimensional geometric object with four right angles (90-degree angles) and opposing parallel and equal-length sides. Rectangles are classified as a type of quadrilateral, which is any four-sided polygon.

The opposite sides of a rectangle are also congruent, meaning that they have the same length, and all four angles are congruent, meaning that they have the same measure of 90 degrees. The area of a rectangle can be calculated by multiplying the length and width of the rectangle, while the perimeter can be calculated by adding the lengths of all four sides.

Now,

Given rectangular field has

length = 5x+10

Breadth = 3x+6

As we know Perimeter of a rectangle = 2(L+B)

P=2*(5x+10+3x+6)

P=2(8x+16)

P=16x+32

Hence,

          The Perimeter of the field is 16x+32.

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The area of triangle in given figure is = 60 cm²

A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane.The sum of the interior angles of a triangle is always 180 degrees, and the length of each side can be determined by the application of the Pythagorean theorem or other trigonometric functions, depending on the given information. Triangles can also be classified based on the size of their angles and the lengths of their sides, which give rise to various types of triangle such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.

According to quesrtion

Given height = 3cm

Base = 10cm

if the height is quadrupled then height = 4 × 3 = 12cm

Area = 1/2 × base × height

= 1/2 × 70 × 12

to solve this we get

Area = 60cm²

So, the area of this triangle is 60cm²

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The probability that the amount dispensed per box will have to be increased is 0.

To answer this question, we need to know the target amount that should be distributed per carton.

Assuming that the target amount is also 1 pound, we can use the concept of the normal distribution to estimate the likelihood that we will have to increase the amount distributed per case.

hence the probability of having to increase the amount is 0.

z = (target volume - mean) / standard deviation

z = (1 - 1) / 0.2

z = 0

A Z-score of 0 indicates that the target volume is equal to the mean. A standard normal distribution table or calculator can be used to find the probability that the amount should be increased.

However, the target amount is equal to the mean value,

In summary, without knowing the target amount to be dispensed in each case, it is not possible to determine the potential for volume increases.

If the target amount is to be £1 and the mean and standard deviation is also £1 and 0.2 respectively, then the probability of having to increase the amount is 0.

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The range of the depths of the 10 artifacts is 18.5 inches.

The range in statistics is a measure of variability, which represents the difference between the largest and smallest values in a data set. To calculate the range, we simply subtract the smallest value from the largest value. In this case, the largest value is 38.5 inches, and the smallest value is 20.7 inches.

Therefore, the range of the depths of the artifacts in the remote area is:

Range = 38.5 - 20.7

Range = 17.8

So the range of depths is 17.8 inches. This tells us that there is quite a bit of variability in the depths at which the artifacts were found. The smallest depth was 20.7 inches, while the largest depth was 38.5 inches.

This information could be useful for archaeologists or other researchers who are interested in understanding the distribution of artifacts in the area, as well as the possible reasons for why some artifacts were found at certain depths while others were found at different depths.

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Answer:

AB = 6.71 to nearest hundredth.

Step-by-step explanation:

To get from A to B we move 3 units to the right then 6 units up.

This form a right angled triangle so we use Pythagoras theorem:

AB^2 = 3^2 + 6^2

         =  9 + 36

         = 45

So AB = √45

           = 3√5  = 6.7082

The chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.

A statistics teacher wants to know if the student birth month is distributed equally across all months. He uses school records to determine the birth month of all the students at the school and calculates a chi-square statistic to test this hypothesis.

This is not an appropriate use of a chi-square goodness-of-fit test because chi-square goodness-of-fit tests are used to compare the distribution of categorical data to a theoretical distribution.

The chi-square goodness-of-fit test compares observed frequencies of categorical data to expected frequencies based on a theoretical distribution. It is used to determine if a sample of data comes from a specific population or not.

In this case, the teacher is not comparing observed frequencies to expected frequencies, but instead is testing the hypothesis that the distribution of student birth months is equal across all months.

This is not a proper use of a chi-square goodness-of-fit test because the hypothesis being tested is not related to the expected frequencies of a categorical variable. Therefore, the chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.

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Answer:

187,550,190

Step-by-step explanation: