? answer thissssss and ​

since the diameter is 14, then its radius is half that or 7.

\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=7 \end{cases}\implies SA=4\pi (7)^2\implies SA=196\pi\)

Calista's grade on her last assignment is 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

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Answer:

£131.88 or 13188 pence

Step-by-step explanation:

1 unit = 14p

942 units = 942 x 14

942 units = 13188p

£1 = 100p

13188 ÷ 100 = £131.88

Hope this helps!

Answer:

His economics grade had a higher z-score, so you performed better relative to the class average in economics.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In which class did you perform better relative to the class average?

In whichever class you had the higher z-score.

Statistics:

Scored 65, mean 60, standard deviation 6. So \(X = 65, \mu = 60, \sigma = 6\)

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{65 - 60}{6}\)

\(Z = 0.83\)

Economics:

Scored 78, Mean 75, Standard deviation 2.5. So \(X = 78, \mu = 75, \sigma = 2.5\)

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{78 - 75}{2.5}\)

\(Z = 1.2\)

His economics grade had a higher z-score, so you performed better relative to the class average in economics.

g(8x-3)=x

have a good day

Answer:

151.9 or 15.2

Step-by-step explanation:

Answer: 2/90 = 1/45

Step-by-step explanation:

a) These are the four solutions to the equation z⁴ = 1. We can plot these solutions on an Argand diagram by marking points at (1, 0), (0, 1), (-1, 0), and (0, -1).

b) These are the three solutions to the equation z³ = 8. We can plot these solutions on an Argand diagram by marking points at (2, 0), (-1, √3), and (-1, -√3).

c) These are the three solutions to the equation z³ = i. We can plot these solutions on an Argand diagram by marking points at (1, 0), (-1/2, √3/2), and (-1/2, -√3/2).

a) To find all solutions to the equation z⁴ = 1, we can use De Moivre's theorem:

z⁴ = 1 = cos(0) + i sin(0)

We can rewrite this in polar form as:

z = cos(0/4 + 2kπ/4) + i sin(0/4 + 2kπ/4)

where k = 0, 1, 2, 3.

Simplifying the expression for z, we get:

z = cos(kπ/2) + i sin(kπ/2)

For k = 0, we get z = 1.

For k = 1, we get z = i.

For k = 2, we get z = -1.

For k = 3, we get z = -i.

These are the four solutions to the equation z⁴ = 1. We can plot these solutions on an Argand diagram by marking points at (1, 0), (0, 1), (-1, 0), and (0, -1).

b) To find all solutions to the equation z³ = 8, we can use De Moivre's theorem:

z³ = 8 = 8(cos(0) + i sin(0))

We can rewrite this in polar form as:

z = 2(cos(0/3 + 2kπ/3) + i sin(0/3 + 2kπ/3))

where k = 0, 1, 2.

Simplifying the expression for z, we get:

z = 2(cos(kπ/3) + i sin(kπ/3))

For k = 0, we get z = 2.

For k = 1, we get z = -1 + i√3.

For k = 2, we get z = -1 - i√3.

These are the three solutions to the equation z³ = 8. We can plot these solutions on an Argand diagram by marking points at (2, 0), (-1, √3), and (-1, -√3).

c) To find all solutions to the equation z³ = i, we can use De Moivre's theorem:

z³ = i = cos(π/2) + i sin(π/2)

We can rewrite this in polar form as:

z = (cos(π/6 + 2kπ/3) + i sin(π/6 + 2kπ/3))

where k = 0, 1, 2.

Simplifying the expression for z, we get:

z = cos(kπ/3) + i sin(kπ/3)

For k = 0, we get z = 1.

For k = 1, we get z = (-1 + i√3)/2.

For k = 2, we get z = (-1 - i√3)/2.

These are the three solutions to the equation z³ = i. We can plot these solutions on an Argand diagram by marking points at (1, 0), (-1/2, √3/2), and (-1/2, -√3/2).


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Answer:

17

Step-by-step explanation:

∠CDE is a 90 degree's, and it splits, because ∠CZB said that it is 39 degrees, thus meaning that the degree of ∠BZD=51, and x=17, because 17*3=51.

I know this will be helpful to you  

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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The amount after 1 year is $7280 and the amount after two year is $8153.

Given that $6500 is placed in an account that pays 12% interest compounded each year.

Compounding is the addition of interest to the principal of a loan or deposit, or in other words, interest on principal plus interest.

Compounded interest=12%

Principal amount=$6500

Time period = 1 year

\(A=P\left(1+\frac{r}{n}\right)^{nt}\)

where P is Principle amount, r is annual interest, n is number of times the interest compounded monthly, t is number of years

Here P=6500, r=12%, n=1, t=1

Substitute these values in the formula, we get

A=6500(1+(0.12/1))¹⁽¹⁾

A=6500(1+0.12)¹

A=6500×1.12

A=7280

Now we have to calculate for two years.

That is if n=2 , then

A=6500(1+(0.12/1))¹⁽²⁾

A=6500(1+0.12)

A=6500×1.2544

A=8153.6

Hence, the amount for one year and two year when $6500 is placed in an account that pays 12% interest compounded is $7280 and $8153.60.

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Answer:

100 minutes

Step-by-step explanation:

subtract 14h10 from 15h00

this will equal 50

then add the remaining 50minutes from 15h00

The Distance will be  5.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

Let point (7,5) be A and point (4,9) be B

Distance formula =

Ab  = √(x1- x2) ² + (y1 -y2) ²

Then Distance AB will be

Ab  = √(7-4) ² + (5 -9) ²

= √ 3² + 4²

= √ 9 + 16

= 5

Hence the distance  will be 5.

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The points \((7,5)\)  \((4,9)\) are separated by a distance of \(5\) units.

The distance between the two points is given by the length of the segment between them.

The Distance Formula is a helpful tool for figuring out how far apart two points are when they are arbitrarily represented on a coordinate plane as points A\((x_{1},y_{1})\) and B\((x_{2},y_{2})\).

The Pythagorean Theorem is essentially the source of the Distance Formula. Calculating the right triangle's hypotenuse's length is the fundamental purpose of the distance formula.

Use the distance formula to get the distance between two places.

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

In the posted query,

\((x_{1},y_{1})=(7,5)\\\\(x_{2},y_{2})=(4,9)\)

Distance formula,

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

\(d = \sqrt{ (4-7)^{2} +(9-5)^{2} }\)

\(d = \sqrt{ (-3)^{2} +(4)^{2} }\)

\(d = \sqrt{ 9+16 }\)

\(d = \sqrt{ 25 }\)

\(d = 5\)

Therefore, the points \((7,5)\)  \((4,9)\) are at a distance of \(5\) units.

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Answer:

(1,3)

Step-by-step explanation:

3 > -2(1)+ 3 < 4

3 > -2 + 3 < 4

3 > 1 < 4

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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Answer:

Option (4)

Step-by-step explanation:

Each value of x maps onto only one value of y, so it is a function.

Answer:

7.19 per pair

Step-by-step explanation:

Take the total cost and divide by the number of pairs of gloves

$21.57/3 pairs

7.19 per pair

Answer:

$7.19

Step-by-step explanation;

The collective price of the gloves of 21.57. Assuming there is no additional cost for packaging, one will simply have to divide the collective price of the gloves by the amount of gloves to find the unit price of the gloves.

21.57 / 3 = 7.19

Answer:

C

Step-by-step explanation:

7 - 2 = 5

11 - 3(2)

11 - 6 = 5

4(2) - 3

8 - 3 = 5

C is the only one that doesn't equal 5

Answer:

x = 48°

Step-by-step explanation:

Complementary angles

Angles that sum to 90°.

Vertical Angle Theorem

When two straight lines intersect, the vertical angles are congruent (equal).

Therefore, angle x is equal to the angle that is complementary to 42°.

To find x, subtract 42° from 90°:

⇒ x = 90° - 42°

⇒ x = 48°

Answer:

We conclude that the true average percentage of Silicon Dioxide is smaller than 5.5.

Step-by-step explanation:

We are given that the desired percentage of Silicon Dioxide (SiO2) in a certain type of aluminous cement is 5.5.

16 independently obtained samples are analyzed and a sample mean of 5.25 was obtained. Suppose that the percentage of SiO2 in a sample is normally distributed with a sigma of 0.3.

Let \(\mu\) = true average percentage of Silicon Dioxide.

So, Null Hypothesis, \(H_0\) : \(\mu\) \(\geq\) 5.5     {means that the true average is greater than or equal to 5.5}

Alternate Hypothesis, \(H_A\) : \(\mu\) < 5.5     {means that the true average is smaller than 5.5}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                            T.S. =  \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\)  ~ N(0,1)

where, \(\bar X\) = sample mean percentage of Silicon Dioxide = 5.25

            σ = population standard deviation = 0.3

            n = sample size = 16

So, the test statistics  =  \(\frac{5.25-5.5}{\frac{0.3}{\sqrt{16} } }\)

                                      =  -3.33

The value of z test statistics is -3.33.

Now, the P-value of the test statistics is given by;

                P-value = P(Z < -3.33) = 1 - P(Z \(\leq\) 3.33)

                              = 1 - 0.9996 = 0.0004

Since, the P-value of the test statistics is less than the level of significance as 0.0004 < 0.01, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true average percentage of Silicon Dioxide is smaller than 5.5.

Answer:

The true average percentage of Silicon Dioxide (SiO2) is less than 5.5.

Step-by-step explanation:

In this case we need to test whether the true average percentage of Silicon Dioxide (SiO2) in a certain type of aluminous cement is smaller than 5.5.

The hypothesis can be defined as follows:

H₀: The true average percentage of Silicon Dioxide (SiO2) is 5.5, i.e. μ = 5.5.

Hₐ: The true average percentage of Silicon Dioxide (SiO2) is less than 5.5, i.e. μ < 5.5.

The information provided is:

\(\bar x=5.25\\\sigma=0.30\\n=16\\\alpha =0.01\)  

As the population standard deviation is provided, we will use a z-test for single mean.

Compute the test statistic value as follows:

 \(z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{5.25-5.5}{0.30/\sqrt{16}}=-3.33\)

The test statistic value is -3.33.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

\(p-value=P(Z<-3.33)=0.00043\)  

*Use a z-table for the probability.

The p-value of the test is 0.00043.

p-value = 0.00043 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Thus, it can be concluded that the true average percentage of Silicon Dioxide (SiO2) is less than 5.5.

Answer: 84 salads.

Step-by-step explanation: Assuming that this is Sequences, Probabilities, and Conics, then the number of salads that you can make with the ingredients is 84. Let's see why.

7*6*4*2 = 336, but you need four ingredients to make the salad, so 336/4 = 84, thus 84 salads you can make.

For probability, to find all options of something, multiply every option by its outcomes. For example, a coin. There are 2 sides to a coin so lets say you flip it 3 times. 2×2×2 is 8. There are 8 combos you can get.

You can apply that here as well. 7 lettuce × 6 tomatoes × 2 cucumbers × 4 peppers = 336 options. Then /4 to get 84 salads.

Answer:

Animals eat plants, and when they do, they obtain the carbon. Later, they release that carbon by means of respiration. Fungus, Bacteria, Algae and other microorganisms create carbon when they decompose dead plants and animals.

Step-by-step explanation:

hope this helps

Answer:

0.259 or 25% or 1/4

and i couldnt figure out b sorry

Step-by-step explanation:

a) The proportion of Americans over 40 who smoke will be 7.075.

b) The population proportion of Americans over 47 who smoke will be 227.2.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

a) A sample of 1089 Americans over 40 is drawn.

And, Of these people, 806 don't smoke.

b) A sample of 861 Americans over 47 is drawn.

And, Of these people, 577 don't smoke.

Here,

a) A sample of 1089 Americans over 40 is drawn.

And, Of these people, 806 don't smoke.

So, The proportion of Americans over 40 who smoke = 1089 - 806 / 40

                                                                                   = 283 / 40

                                                                                   = 7.075

b) A sample of 861 Americans over 47 is drawn.

And, Of these people, 577 don't smoke.

So, the 80% confidence interval for the population proportion of Americans over 47 who smoke = 80% of (861 - 577)

                                                 = 80% × 284

                                                 = 80/100 × 284

                                                 = 227.2

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9514 1404 393

Answer:

  61

Step-by-step explanation:

75 = 10×7 +5

500 = 71×7 +3

All the multiples of 7 between the 10th and the 71st (including the 71st, but not the 10th) are numbers in the range that are divisible by 7.

61 numbers in the interval [75, 500] are divisible by 7.

Answer:

20% increase

Step-by-step explanation:

((540 - 450) / 450) * 100

(90 / 450) * 100

0.2 * 100

= 20% change (increase)

Hope this helps!!

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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Answer:

44

Step-by-step explanation:

edge

The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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