If the base of a rectangle is 12 inches and the area is 72 inches, then what is the height?​

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The perimeter of each tile Mei uses is 20 units.

The distance or length of any line on the graph,

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

where,

d = distance or the length of the line between point 1 and 2,

(x₁ , y₁) = coordinate of point 1,

(x₂ , y₂) = coordinate of point 2,

The distance between two points on a graph is found using the formula,

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Now, the length between the following points can be found using the above formula.

The length fo the sides of the polygons are:

Now, the perimeter of the polygon can be written as,

\(\rm \text{Perimeter of the polygon} = 5+5+5+5 = 20\ units\)

Hence, the perimeter of each tile Mei uses is 20 units.

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Answer:

Step 2

Step-by-step explanation:

Mario made a mistake in Step 2 when substracting \(\frac{1}{3}\) from \(\frac{4}{3}\). When substracting his result ended up being \(\frac{2}{3}\) but it is actually....

\(\frac{4}{3} - \frac{1}{3} = \frac{4-1}{3} = \frac{3}{3} = 1\)

so the right answer is \(q = 1\)

The exponential function that would give the population after t years is given by:

\(P(t) = 100 \times 2^{\frac{t}{9}}\)

An exponential function is modeled by:

\(y = ab^{\frac{x}{n}}\)

In which:

Considering that the population starts with 100 individuals and doubles every 9 years, the parameters are given as follows:

a = 100, b = 2, n = 9.

Hence the function is given by:

\(P(t) = 100 \times 2^{\frac{t}{9}}\)

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Answer:100 x 2 t/9

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

CORRECT ME IF IM WRONG 735 - 589 is 146 so you just figure out that 20% of 735 is 588 = and thats the closest you will get to it

Answer:

21

Step-by-step explanation:

First at all you replaced:

8(5) + 5 - 2(12)

40 + 5 -24

21

Answer:

4/3

Step-by-step explanation:

GH =√90²-72²=

√8100-5184=

√2916= 54

so, tan (H) = 72/54 = 4/3

⁴/3 is a required answer.

Answer:

Solution given:

FG=72

FH=90

By using Pythagoras law

GH=\(\sqrt{90²-72²}=54\)

Step-by-step explanation:

we have

Tan H=\( \frac{opposite}{adjacent}\)

\(TanH=\frac{GF}{GH}=\frac{72}{54}=\frac{4}{3}\)

Answer:

7.75

Step-by-step explanation:

By Geometric mean property:

\( GH = \sqrt {a \times b} \)

\( GH = \sqrt {3 \times 20} \)

\( GH = \sqrt {60} \)

\( GH = 7.74596669\)

\( GH \approx 7.75\)

Answer:

22.2

Step-by-step explanation:

Answer:

Answer A

Step-by-step explanation:

Below sea level = -x

Above sea level = x

Just read it carefully

Answer:

b

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

Parameter= whole population

Sample statistic= outcome of part of population surveyed

The concept which is the main idea of estimating a population​ proportion is

C. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.

The concept stated in option C is not a main idea of estimating a population proportion.

Estimating a population proportion involves inferential statistics, which is concerned with making inferences or drawing conclusions about a population based on information from a sample. In this context, descriptive statistics refers to methods that summarize and describe the characteristics of a sample or population, such as measures of central tendency and variability.

The main ideas of estimating a population proportion include:

A. The sample proportion is the best point estimate of the population proportion: When estimating a population proportion, the sample proportion (the proportion observed in the sample) is commonly used as the point estimate for the population proportion. This is because it provides an unbiased estimate of the unknown population proportion.

B. Knowing the sample size necessary to estimate a population proportion is important: The sample size plays a crucial role in estimating a population proportion. A larger sample size generally leads to a more precise estimate with a smaller margin of error. Determining an appropriate sample size is essential to ensure the desired level of confidence and accuracy in the estimate.

D. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion: Constructing a confidence interval is a common method to estimate the true value of a population proportion. By using the sample proportion along with the standard error and a chosen level of confidence, a range of values is calculated within which the true population proportion is likely to fall.

In contrast, option C refers to using a sample statistic to estimate the population proportion by utilizing descriptive statistics. However, estimating a population proportion typically involves inferential statistics rather than descriptive statistics.

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Step-by-step explanation:

because you need 2 numbers that

(+)=7

and

(x)=8

no 2 whole numbers work

it will have to be decimals

so you can't factorise

so you have to use the quadratic formula

hope this helps :)

Answer:

Step-by-step explanation:

if a quadratic of this form can be factorised the factors are

(x + a)(x + b).

In this case a*b would be = + 8 and a + b would be + 7.

There are no integer values which will give these 2 results so x^2 + 7x + 8 cannot be factorised.

An example of a quadratic that can be factories is x^2 + 8x + 7,

because ab = 7 *1 and a + b = 7 + 1 = 8 so the factors are:

(x + 1)(x + 7).

Answer:

Step-by-step explanation:

f(x) = ln x

g(x) = - f(x - 4)

g(x) = - ln (x - 4)

g(5) = - ln (5 - 4) = - ln 1 = 0

Answer:

The interest rate is 6.5%.

Step-by-step explanation:

Substitute the values in to the formula, I = Prt:
\(546 = (1200)(r)(7)\)

Solve for r by isolating:
\(r = \frac{546}{8400}\)

Simplify:
\(\frac{546}{8400} = 0.065\)

The algebraic representation of (x,y)-> (5x, 5y) represents transformation of  dilate by a scale factor of 5.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The x and y coordinates of the original figure are multiplied by the scale factor to discover spots on the dilated image when a dilation in the coordinate plane has the origin as the centre of dilation. The algebraic representation of the dilation is (x, y) for scale factor k. (kx, ky). K > 1 for enlargements.

Given,

The algebraic representation of (x,y)-> (5x, 5y) represent transformation given below:

(B) dilate by a scale factor of 5

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Answer:

The first one 10 units would be the perimenter of the tenth figure.

Answer: the answer is 9/2

To find out how much the Guilderian trader must pay for the same 50 flop barrel of pickles, we need to calculate the cost per gulp and then multiply it by the number of gulps in the barrel.

Given that the Guilderian trader initially exchanged 25 gulps for the 50 flop barrel of pickles, we can determine the cost per gulp by dividing the total cost (50 flops) by the number of gulps (25).  Cost per gulp = 50 flops / 25 gulps = 2 flops/gulp . Since the gulp depreciates to 0.5 flops per gulp, the Guilderian trader must pay 0.5 flops per gulp for the same barrel of pickles.

Therefore, the Guilderian trader must pay 0.5 flops/gulp * 25 gulps = 12.5 flops for the 50 flop barrel of pickles. For the Florish trader, we need to calculate the cost per flop and then multiply it by the number of flops in the crate.

Given that the Florish trader initially exchanged 40 flops for the 20 gulp crate of apples, we can determine the cost per flop by dividing the total cost (40 flops) by the number of flops (20).

Cost per flop = 40 flops / 20 flops

= 2 flops/flop .

Therefore, the Florish trader must pay 2 flops per flop for the same crate of apples.

The Guilderian trader must pay 12.5 flops for the same 50 flop barrel of pickles, and the Florish trader must pay 2 flops for the same 20 gulp crate of apples.

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Answer:

infinitely many solutions

Step-by-step explanation:

Reduce the second equation by dividing all three terms by 3:  y + 1 = 2x.  Then compare this result to the first equation 2x - y = 1.  Noe that these two equations are identical.  Thus, the two lines coincide.  There are "infinitely many solutions."

On solving the expression 2s the value for new amount in Fiona's bank is obtained as $320.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The amount of money in Fiona's savings account s = $160.

The amount is double.

So the expression will be -

New amount = 2 × s

New amount = 2s

Substitute the value in the expression -

New amount = 2 × 160

New amount = 320

Therefore, the new amount is $320.

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Answer:

y=1/2x-3.5

Step-by-step explanation:

The slope is 1/2, plug that in for m in the base equation (y=mx+b) as well as your y intercept, which is b, which in this case is -3.5

The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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Answers:

==================================================

Explanation:

For problems 1 and 2, we just multiply the base and height. This is the same as multiplying the length and width.

So in problem 1 we have 10*12 = 120 square feet. In problem 2 we have 6*10 = 60 square inches.

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

Problem 3 follows the same idea, but we do a bit more work. The area of the garden is 5*12 = 60 square feet.

Let's say x is the number of bags needed.

1 bag covers 6 square feet

2 bags cover 12 square feet

and so on

x of those bags cover 6x square feet. The x is just a placeholder for a number. Specifically, a positive whole number.

The expression 6x represents how much area that can be covered by x bags. We want to cover 60 square feet.

The equation we need to solve is 6x = 60. Doing so leads to x = 10 after dividing both sides by 6.

So this means Travis needs 10 bags.

dimensions of the poster with margin are L  =  12 in and h  = 24 in

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.

Rectangle area equals length times width.

Let call length of printed area of the poster be " x "  and  height of printed area of the poster be " y ".

Area of the poster = length and height

200 = x*y  

y = 200/x

We also know that dimensions of the poster with margin is:

L  =  x + 2   in  and     H  =  y + 4 in

Therefore area of the poster is:

A(p)  = ( x + 2 ) * ( y + 4 )

And area as function of x is:

A(x)  =   ( x + 2 ) * ( 200/x + 4 )

A(x)  =  200 + 4*x + 400 /x  + 8

Taking derivatives on both sides of the equation we have:

A´(x)  =  4 - 400/x²

By taking A´(x)  = 0

4 - 400/x² = 0 ⇒ 4*x² - 400 = 0

x² = 400 / 4

x² = 100

x = 10 in

and y = 200/x ⇒ y = 20

The second derivative A´´(x) = 400/x4 which is > 0

there is a minimum for the function at the point x = 10

As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are

L  = x  +  2   =   10  + 2  =  12 in   and

h = y  +  4   =   20  + 4  =  24  in

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Answer:

hope that helps you out.

Answer:

A. \(\frac{2}{5}\)

B. \(\frac{1}{10}\)

Step-by-step explanation:

A. There are 20 students. Picking 8 out of 20 is \(\frac{2}{5}\) chance.

B. There are 20 students. Picking 2 out of 20 is \(\frac{1}{10}\)

Answers:

Step-by-step explanation:

Easy, just add the girls together to get 8. Put that over 20, then simplify:

8/20 = 4/10 = 2/5

Left handed girls = 2/20 = 1/10

I'm always happy to help :)

Answer:

So, we will be using point-slope form to construct this equation.

Point-slope form's general formula is as follows:

Y - Y1 = m( X - X1)

M is the slope,

Y₁ is the Y-coordinate of the point

X₁ is the X- coordinate of the point.

So, our slope is 3 (since the equation is given in slope-intercept form)

Our Y₁ is 7 and out X₁ is 4    

So, now we just plug our numbers into the equation.

There's your equation.

Y - 7 = 3( X - 4).

Hope this helps!