12 of the students in the art class like to draw animals these 12 students make up 24% of the art class how many students are in the art class

Answer:

Step-by-step explanation:

Answer:

(a) The difference between Kate's IQ and the mean is 21

(b) The z score is 1.4

Step-by-step explanation:

Here is the complete question:

IQ scores have a mean of 100 and a standard deviation of 15. Kate has an IQ of 121. (a) What is the difference between Kate's IQ and the mean (b) Convert Kate's IQ score to a z score.

Step-by-step explanation:

(a) To determine the difference between Kate's IQ and the mean, this can be done by subtracting the mean from Kate's IQ.

Mean = 100

Kate's IQ = 121

Difference between Kate's IQ and the mean = 121 - 100 = 21

Hence, the difference between Kate's IQ and the mean is 21.

(b) To convert Kate's IQ score to a z score,

z score is given by the formula

\(z =\frac{x - \mu}{\sigma}\)

Where \(x\) is the score

\(\mu\) is the mean

and \(\sigma\) is the standard deviation

From the question,

\(x\) = 121

\(\mu\) = 100

\(\sigma\) = 15

Then, the z score is

\(z =\frac{x - \mu}{\sigma}\)

\(z =\frac{121 - 100}{15}\)

\(z =\frac{21}{15}\)

\(z =\frac{7}{5}\)

z = 1.4

Hence, the z score is 1.4.

Answer:

Step-by-step explanation:

For the first bag:

Price of the bag = $12

Number of balls in the bag = 15

Price per ball = Price of the bag / Number of balls

Price per ball for the first bag = $12 / 15 = $0.8

For the second bag:

Price of the bag = $15

Number of balls in the bag = 20

Price per ball = Price of the bag / Number of balls

Price per ball for the second bag = $15 / 20 = $0.75

Comparing the prices per ball, we find that the second bag has a lower price per baseball. Therefore, the second bag offers a better price for individual baseballs compared to the first bag.

Answer:

Step-by-step explanation:

To find out which bag prices individual baseballs lower, we can divide the total cost of each bag by the number of balls in the bag. This will give us the price per ball for each bag.

For the first bag, the price per ball is $12 / 15 = $0.80.

For the second bag, the price per ball is $15 / 20 = $0.75.

Therefore, the second bag prices individual baseballs lower.

Answer:(a) To find the projected population in 2028 (28 years after 2000), we can substitute x = 28 into the equation:

10.0y - 4.55 * 28 = 581

Solving for y, we get:

10.0y = 581 + 4.55 * 28

10.0y = 581 + 127.4

10.0y = 708.4

y = 70.84 million

So, the projected population in 2028 is 70.84 million.

(b) To find the year when the population is predicted to be 67.2 million, we can substitute y = 67.2 and x = the number of years after 2000 into the equation:

10.0y - 4.55x = 581

10.0 * 67.2 - 4.55x = 581

672 - 4.55x = 581

91 = 4.55x

x = 91 / 4.55

x = 20

So, the population is predicted to be 67.2 million 20 years after 2000, or in the year 2020.

Step-by-step explanation:

Answer:

Slope EQUALS: \(-\frac{6}{7}\)

Step-by-step explanation:

y=-x+3

Step-by-step explanation:

y = k/x^2

substitute 8 and 3.5 to get the value of k.

k= 98

are u just looking for k? or the question is missing

Answer:

Step-by-step explanation:

Rounded to the underlined digit, 84.59 becomes 84.6.

Rounding a number means approximating it to a specified place value. In this case, we are rounding 84.59 to the nearest tenth, which is the first digit to the right of the decimal point.

1. Identify the Digit:

Underline the digit in the tenth's place, which is 5 in 84.59.

2. Look at the Next Digit:

The digit immediately to the right of 5 is 9. Since 9 is greater than or equal to 5, we round up the underlined digit.

3. Adjust the Digit: Add 1 to the underlined digit, which becomes

6 (5 + 1 = 6).

4. Replace Other Digits: Keep all the digits to the left of the underlined digit unchanged. Therefore, the 84 remains the same.

5. Final Result: The rounded number is 84.6.

So, when rounding 84.59 to the nearest tenth, we get 84.6. Rounding helps make numbers easier to work with when precision beyond a certain point is not necessary.

Remember that when the digit to the right of the one you're rounding to is 5 or greater, you round up, and when it's less than 5, you round down.

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Bank B will cost him R3205 MORE.

He must go with Bank A.

Answer:

Step-by-step explanation:

Answer:

we reject H₀

We have enough evidence to claim that people in the sample are significantly  more satisfied than others in general population at 95 % of CI

Step-by-step explanation:

Population mean    μ₀  = 20

Sample data   18  23  24 44  19 27 23 26 25

Then:

Sample mean      μ   =  25,44

Sample standard deviation     s = 7,14

Sample size     n  =  9

Hypoyhesis test:

Null hypothesis                                H₀              μ   =   μ₀

Alternative hypothesis                   Hₐ               μ   >   μ₀

Significance level    α  = 0,05    CI = 95 %

We must develop a  t-student one-tail test  ( to the right ) as follows

t(c)  =  ??

degree of freedom    df = n - 1         df =  8      and    α = 0,05

Then from t-student table    t(c)  =  1, 8595

To calculate   t(s)  =  (  μ  -  μ₀  ) / s/√n

t(s)  =  ( 25,44  -  20 ) * √9 / 7,14

t(s)  = 5,44*3 / 7,14

t(s)  = 2,29

Comparing   t(c) and  t(s)

t(s)  >  t(c)

Then t(s) is in the rejection region   we reject H₀

We have enough evidence to claim that people in the sample are significantly  more satisfied than others in general population at 95 % of CI

Answer:

x=17

Hope it helps;)

Step-by-step explanation:

Subtract 8 from both sides of the equation

-x+8=9

-x+8-8=9-8

Simplify

Subtract the numbers

x= -17

Divide both sides of the equation by the same term

x= 17

-x/-1= -17/-1

Simplify

Cancel terms that are both in the numerator and denominator

Divide the numbers

x = 17

multiply total area by fraction painted.

76 1/2 x 2/3 = 153/2 x 2/3 = 306/6 = 51 square feet

he panted 51 square feet

76 1/2 - 51 = 25 1/2 square feet left

Since E is the midpoint of DF, DE and EF are two halves of DF. First, let's write down what we know.

DE = 3x + 4

EF = 5x - 2

DE = EF

DE + EF = DF

Now, let's plug our values for DE and EF into our first expression.

3x + 4 = 5x -2

Add 2 to both sides and subtract 3x from both sides.

6 = 2x

Divide both sides by 2

3 = x

Let's plug 3 in for x into DE.

DE = 3x + 4 = 3(3) + 4 = 9 + 4 = 13

DE = EF = 13

We can plug 13 in for DE and EF to get DF

DF = DE + EF = 13 + 13 = 26

Answer:

79.5 feet

Step-by-step explanation:

5.3 per minute can also be written as the ratio 5.3:1. so if we have x:15, we can see that we've multiplied the right side by 15 so we have to do the same to the other side. 15 times 5.3 is 79.5. so thats your answer.

i hope this helps :))

The integer that explained the depth of the hole after 15 minutes is 79.5 feet.

Given that,

So, the integer that explained the depth of the hole after 15 minutes is

\(= Rate \times time \\\\= 5.3 \times 15\\= 79.5\ feet\)

Therefore we can conclude that the integer that explained the depth of the hole after 15 minutes is 79.5 feet.

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Using it's concept, it is found that there is a 0.0333 = 3.33% probability of choosing a B not replacing it and then choosing a vowel.

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

The word basketball has 10 letters.

Thus, the probability of choosing a B not replacing it and then choosing a vowel is given by:

\(P(A \cap B) = P(A)P(B|A) = 0.1 \times 0.3333 = 0.0333\)

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Answer: 2/45

The question asks for choosing the letter B, which we know that there is two of in basketball, so 2/10, and then we multiply it by the amount of vowels, which is 2/9, and when we multiply we get 4/90 which can be simplified to 2/45.

Answer:

2/15 or 0.13

Step-by-step explanation:

first you multiply 2/3 and 1/5 which gets you 2/15

Answer:

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

Find the differences in the sequence  -11, -7, -3, 1, ...

The difference is common, so the sequence is an AP.

The nth term is:

Find the 52nd term:

Find the 52nd term using the given formula:

Find the previous term:

Find the common difference:

Answer:

\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)

\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Given sequence:

To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.

\(a_4-a_3=1-(-3)=4\)

\(a_3-a_2=-3-(-7)=4\)

\(a_2-a_1=-7-(-11)=4\)

As the differences are constant, the sequence is arithmetic, with common difference, d = 4.

The explicit formula for an arithmetic sequence is:

\(\boxed{a_n=a+(n-1)d}\)

where:

To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:

\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)

Therefore, the 52nd term is a₅₂ = 193.

\(\hrulefill\)

Given explicit formula for an arithmetic sequence:

\(a_n=-30-4n\)

To find the common difference, we need to compare it with the explicit formula for the nth term:

\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)

The coefficient of the n-term is -4, therefore, the common difference is d = -4.

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)

Therefore, the 52nd term is a₅₂ = -238.

The within-group sum of squares is 58250.44

The degrees of freedom are given as 355

The estimate of the within-groups variance is 164.0657

Variance, as a statistical measure, evaluates the level of variability or dispersion contained in a dataset by inspecting how distant each value in a set is from the mean of that same set.

If there is a higher variance, it signals that data points are more widely distributed and further removed from the mean, whereas if there is a lower variance, one can assume that they are primarily clustered more closely around the mean.

To obtain the variance value, one must determine an average signal-to-noise ratio for each squared difference derived from every respective value taken away from the arithmetic mean. It is no exaggeration to say that variance is progressively employed across diverse subject areas including finance, engineering, and science.

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Answer:

120 degress

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

The coefficient of x^7 when the expression is expanded by the binomial theorem (3x + 4)^10 is 16,796,160.

In the given question, we have to find the coefficient of the given term when the expression is expanded by the binomial theorem.

The given expression is (3x + 4)^10 coefficient of x^7.

The binomial expression

\((x+y)^n = x^n+^nC_{1}x^{n-1}y^1+^nC_{2}x^{n-2}y^2+\dots\dots+^nC_{k}x^{n-k}y^k+\dots\dots +y^n\)

where \(^nC_{k}=\frac{n!}{k!{(n-k)!}}\)

coefficient of x^7

T(4) = T(3+1)

T(4) = \(^{10}C_{3}(3x)^{10-3}(4)^3\)

Solving

T(4) = \(\frac{10!}{3!(10-3)!}\cdot(3x)^{7}\cdot64\)

T(4) = \(\frac{10!}{3!7!}\cdot2187x^{7}\cdot64\)

T(4) = \(\frac{10\times8\times7!}{3\times2\times1\times7!}\cdot2187x^{7}\cdot64\)

T(4) = 16,796,160 x^7

The coefficient of x^7 when the expression is expanded by the binomial theorem (3x + 4)^10 is 16,796,160.

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The X variables have an overall correlation of 0. VIF, or Variance Inflationary Factor, measures the

Regression analysis's level of multicollinearity is gauged by a variance inflation factor, or VIF. When several independent variables in some kind of a model with multiple regression correlate with one another, this is known as multicollinearity. The regression findings may be significantly impacted by this.

Greater correlation between the variable and other variables is indicated by a higher value. With values of Ten or more being considered very high, values greater than 4 or 5 are occasionally considered to be moderate to high.

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Answer:

2. 1/24 tablespoons

3. Approximately 29 salt shakers

Step-by-step explanation:

2. The child needs to take 1/6 tablespoons of medicines in 4 equal doses. One dose would therefore be 1/6 divided by 4.

= 1/6 ÷ 4

= 1/6 * 1/4

= 1/24 tablespoons of medicine

3. One cup salt shaker takes 5/6 cups to be filled. Assume the number of salt shakers that can be filled by cups is x.

5/6* x = 24

x = 24 ÷ 5/6

x =  28.8 salt shakers

= Approximately 29 salt shakers

The expression when evaluated is 4√2x

From the question, we have the following parameters that can be used in our computation:

√32x

Express 32 as the product of 16 and 2

So, we have

√32x = √(16 * 2x)

Take the LCM of 16

So, we have the following representation

√32x = 4√2x

Hence, the solution is 4√2x

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The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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The amount of change that the customer will be given when payment is made with a $20 bill would be = $7.15. That is option G.

The total number of items purchased by the customer = 10

The cost for 5 items = $1.60× 5 = $8

The cost of 3 items = $1.25×3 = $3.75

The cost of 2 items = $0.55×2 = $1.1

The total cost = 8+3.75+1.1 = $12.85

Therefore, the change of the customer when $20 bill is used = 20-12.85

= $7.15.

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