Please help this is the last problem on my homework and I don’t understand how to do it

Answer:

Cross multiply:

2 * 4 = 7 * r

Simplifying

2 * 4 = 7 * r

Multiply 2 * 4

8 = 7 * r

Solving

8 = 7r

Hope this helps.

The standard deviation of the data set is approximately 11.1, rounded to one decimal place.

To calculate the standard deviation of a set of data, we need to follow a few steps. First, we need to find the mean (average) of the data set. Then, we need to subtract the mean from each data point and square the result. We add up all of the squared differences, divide by the number of data points minus one, and take the square root of the result.

So, for the data set 4, 25, 11, 26, 30:

- The mean is (4+25+11+26+30)/5 = 19.2

- The differences between each data point and the mean are:

   - 4-19.2 = -15.2

   - 25-19.2 = 5.8

   - 11-19.2 = -8.2

   - 26-19.2 = 6.8

   - 30-19.2 = 10.8

- Squaring these differences gives:

   - (-15.2)^2 = 231.04

   - 5.8^2 = 33.64

   - (-8.2)^2 = 67.24

   - 6.8^2 = 46.24

   - 10.8^2 = 116.64

- Adding up these squared differences gives 495.96

- Dividing by 4 (the number of data points minus one) gives 123.99

- Taking the square root of 123.99 gives approximately 11.1

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Answer:

• \(x\) = 42°

• \(y\) = 74°  

• \(z\) = 114°

Step-by-step explanation:

To solve these problems, we have to use the triangle sum theorem, which states that "the sum of all the interior angles of a triangle is 180°".

A)

\(x\) + 90° + 48° = 180°

⇒ \(x\)  + 138° = 180°

⇒ \(x\) + 138° - 138° = 180° - 138°      [Subtracting 138° from both sides]

⇒ \(x\) = 42°

B)

The triangle in this question is an isosceles triangle, therefore the two angles at the base of the triangle are equal and have measures of \(y\).

\(y\) + \(y\) + 32° = 180°

⇒ 2\(y\) + 32° = 180°

⇒ 2\(y\) = 180° - 32°

⇒ 2\(y\) = 148°

⇒ \(\frac{2}{2} y\) = \(\frac{148^{\circ}}{2}\)             [Dividing both sides by 2]

⇒ \(y\) = 74°                    

C)

\(z\) + 28° + 38° = 180°

⇒ \(z\) + 66 = 180°

⇒ \(z\)  = 180° - 66°

⇒ \(z\) = 114°

The value of \(z_{\alpha /2}\) that corresponds to a 90% confidence interval is

The confidence level is the likelihood that, if you repeat your experiment or resample the population in the same manner, you will come close to arriving at the same estimate.

The estimate's upper and lower bounds are what make up the confidence interval for a particular level of confidence.

For 90%confidence interval = 0.9

significance level, α = 1 - 0.9 = 0.10

For two tailed test, α/2 = 0.05

using z table

0.0505 = -1.64

0.05 = x

0.0495 = -1.65

solving for x by interpolation

(0.0505 - 0.05) / (0.05 - 0.0495) = (-1.64 - x) / (x - -1.65)

0.0005(x + 1.65) = 0.0005(-1.64 - x)

x + x = -1.64 - 1.65

x = -1.645

from z tables at 90% confidence interval in two tailed test the score is found to be 1.645

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The effective annual rate is the total interest rate that would be earned or paid on an investment or loan, taking into account the effects of compounding over a year.

To calculate the effective annual rate with a monthly compounding interest rate of 5%, we can use the formula:

\[\text{{Effective Annual Rate}} = \left(1 + \frac{{\text{{interest rate}}}}{{\text{{number of compounding periods per year}}}}\right)^{\text{{number of compounding periods per year}}}\]

In this case, the interest rate is 5% (or 0.05) and the number of compounding periods per year is 12 (since it's compounded monthly). Plugging these values into the formula, we get:

\[\text{{Effective Annual Rate}} = \left(1 + \frac{{0.05}}{{12}}\right)^{12}\]

Calculating this gives us an effective annual rate of approximately 0.0512, or 5.12% (rounded to four decimal places). Therefore, the effective annual rate is 0.0512.

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Answer:

try this

Step-by-step explanation:

19 g

Using differentiation and area of a rectangle, the dimensions of the poster with the smallest height are 24 cm x 216 cm.

Let x = width of printed material

Total width = printed material width + left margin + right margin

Total width = x + 8 + 8 = x + 16 cm

Total height = printed material height + top margin + bottom margin

Total height = 1536/x + 12 + 12 = 1536/x + 24 cm

The total area of the poster is the product of the width and height:

Total area = Total width * Total height

1536 = (x + 16) * (1536/x + 24)

To find the dimensions of the poster with the smallest height, we can find the minimum value of the total height. To do this, we can differentiate the equation with respect to x and set it to zero:

d(Total height)/dx = 0

Differentiating the equation and simplifying, we get:

1536/x² - 24 = 0

Rearranging the equation, we have:

1536/x² = 24

Solving for x, we find:

x² = 1536/24

x² = 64

x = 8 cm

Substituting this value back into the equations for total width and total height, we can find the dimensions of the poster:

Total width = x + 16 = 8 + 16 = 24 cm

Total height = 1536/x + 24 = 1536/8 + 24 = 192 + 24 = 216 cm

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Answer:

6 is the answer. Hope this helps you! Stay blessed .

Answer:

3

Step-by-step explanation:

1/2*b*h

1/2*2*3=3

Area=3

Hope this helps!

If not, I am sorry.

Answer:

sin²x+2cos y is approximately 1.328.

Step-by-step explanation:

To find the value of sin²x+2cos y, we first need to know the values of sin(x) and cos(y).

Given x = 34°, we can use a calculator to find that sin(x) is approximately 0.5592. Given y = 51°, we can use a calculator to find that cos(y) is approximately 0.6235.

Now we can substitute these values into the expression sin²x+2cos y to get:

sin²x+2cos y = (0.5592)^2 + 2(0.6235) ≈ 1.328

Therefore, sin²x+2cos y is approximately 1.328.

Answer:

the variable is k

Step-by-step explanation: Hope this helps btw can i have brianliest?

The required inequality that represents all possible values of the total length of rope x, in centimeters, needed for the parachute is  270 ≤ x ≤ 280. Option A is correct.

Given that,
18 different ropes are used in a parachute design. Each rope piece must be no longer than 280 centimeters and no shorter than 270 cm. It is necessary to establish which inequality encompasses all feasible values of the entire length of rope x, in centimeters, required for the parachute.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Consider the length of the rope be x,
accoding to the question,
Length of the rope at least 270 centimeters and a maximum of 280 centimeters. So,
X should be,
270 ≤ x ≤ 280.

Thus, the required inequality that represents all possible values of the total length of rope x, in centimeters, needed for the parachute is  270 ≤ x ≤ 280. Option A is correct.

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Answer:

2 out of 15 chance its green

Step-by-step explanation:

there's 15 marbles in total and 2 are green

Answer:

4z-12

Step-by-step explanation:

the perimeter is the sum of all sides

so

\(P=(z+3)+(z-9)+(z+3)+(z-9)\\\\P=z+3+z-9+z+3+z-9\\\\P=4z+6-18\\\\P=4z-12\)

Answer:

24

Step-by-step explanation:

5^2-(-3)^0

=25-(-3)^0

=25-3^0

=25-1

24

To complete the blank, the answer will be represented as: 9 × \(1 \frac{4}{5} \) is greater than \(1 \frac{4}{5} \).

We need to convert the number on Left Hand Side and Right Hand Side from mixed fraction to fraction.

LHS = 9 × ((5×1)+4)/5

Solving the brackets

LHS = 9 × (9/5)

Multiply the numbers

LHS = 81/5

Converting the numbers on RHS

RHS = ((5×1)+4)/5

RHS = 9/5

We see that number of LHS is greater than RHS, hence, greater than will be the correct option.

Alternatively, we do not to solve the numbers. As both LHS and RHS contain same mixed fraction, with extra presence of 9 on LHS with multiplication sign. It simply increases the value of LHS number and hence it will be greater.

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The store should have 445 picks remaining, not 450 as estimated by the manager. To determine if the store manager's estimate is reasonable, let's analyze the situation.

The store initially has 500 guitar picks. They order 15 boxes, and each box contains 9 picks. So the total number of picks they receive from the order is:

15 boxes * 9 picks/box = 135 picks

Next, the store sells 19 boxes, with each box containing 10 picks. Therefore, the total number of picks sold is:

19 boxes * 10 picks/box = 190 picks

To find the remaining number of picks, we can subtract the sold picks from the received picks:

Total remaining picks = Initial picks + Received picks - Sold picks

Total remaining picks = 500 + 135 - 190 = 445 picks

According to the calculations, the store should have 445 picks remaining, not 450 as estimated by the manager.

However, it's important to note that we are working with whole numbers, so there might be some rounding involved in the manager's estimate. It's possible that the manager rounded up to 450 for simplicity or other reasons.

Given the small discrepancy of 5 picks between the calculated value and the manager's estimate, it is reasonable to conclude that the manager's estimate is close enough to the actual number of picks. The discrepancy could be due to rounding or a small counting error. It's unlikely to have a significant impact on the store's operations or inventory management.

In summary, while the manager's estimate of 450 guitar picks may not be exactly accurate, it is reasonably close to the actual remaining number of picks based on the given information.

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The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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The rate of water flow over the waterfall is approximately 3,817.41 tons of water per day.

To convert the volume from cubic feet to tons, we need to divide the given rate of water flow (2.09 × 10^5 cubic feet per second) by the conversion factor of 1 cubic foot = 7.48052 × 10^(-4) tons.

Next, to convert the weight from pounds to tons, we multiply the volume (in tons) by the weight of one cubic foot of water, which is 62.4 pounds per cubic foot. The conversion factor is 1 pound = 2.20462 × 10^(-3) tons.

Finally, to calculate the rate of water flow in tons per day, we multiply the rate of water flow in tons per second by the number of seconds in a day (24 hours × 60 minutes × 60 seconds).

Performing the calculations, we find the rate of water flow in tons of water per day to be approximately 3,817.41 tons.

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Step-by-step explanation:

A whole clock is 360 degrees

1/12 of 360 degrees  is      30 degrees

Answer:

0.0045 km or 4.5×10^-3 km

Step-by-step explanation:

Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

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Answer:

The responses to these question can be described as follows:

Step-by-step explanation:

Please find the complete question in the attached file.

For the random condition:

If other regular fees have been chosen at random, I'd claim I'm satisfactory.

State of autonomy:

Truly content, since the 44 daily fees represent less than 10% of the total population of daily payments, the community must have more than 440 daily fees.

In the  Normal Condition:

Since the sample size of 44 is 30 or more, the distribution of the sample means is roughly Normal (as per the total probability theorem).

Answer: Rectangualr prism

Pls give brainliest

It will fold into a rectangular prism. Four out of the six shapes there in the cutout are rectangular, while the other two are squares. Since four of them are rectangular, we can infer, or discover, that the shape that the cutout will be folded into is a rectangular prism.

Answer:

\(\pi = \)

236+453

Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

The wavelength of the wave can be calculated as λ = 2π/k = 54.6 cm, and the frequency as f = ω/(2π) = 95.5 Hz.

The given wave 23 This represents a transverse wave, where y is the displacement of the wave from its equilibrium position at a given point x and time t.

The wave is a cosine function of the difference between the fraction of the distance x traveled by the wave and the fraction of the time t elapsed. The wave number k = 2π/l and the angular frequency ω = 2π/τ can be obtained from the wave equation.

The wavelength of the wave can be calculated as λ = 2π/k = 54.6 cm, and the frequency as f = ω/(2π) = 95.5 Hz. which represents the maximum displacement of the wave from its equilibrium position.

The period of the wave can be calculated as T = 1/f = 0.0105 s, which is the time taken by the wave to complete one cycle.

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Answer:

The answer to the problem is 6

Answer:

14

Step-by-step explanation:

10000 = 5000\((1.05)^{t}\)

2 =  \((1.05)^{t}\)

ln(2) = t ln(1.05)

t = ln(2)/ln(1.05)

\(\frac{\ln \left(2\right)}{\ln \left(1.05\right)}=14.20669\dots\)

For $5000 invested at 5% p.a. compound interest with yearly rests to double in value, The time will be 14 years. So, option D is correct.

If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually,

then the final amount after 't' years would be:

\(a = p(1 + \dfrac{r}{n})^{nt}\)

For $5000 invested at 5% p.a. compound interest with yearly

rests to double in value, we need to find the time.

So,

\(a = p(1 + \dfrac{r}{n})^{nt}\)

\(10000 = 5000(0.05)^t\\\dfrac{10000 }{5000} = (0.05)^t\\2 = (0.05)^t\\ln(2) = t ln(1.05)\\t = \dfrac{ln(2)}{ln(1.05)}\\\\t = 14.21\)

Hence, The time will be 14 years. So, option D is correct.

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