how do I solve this?​

Answer:

The Z score for $37,000 is 8.49.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean family income is $34,000, with a standard deviation (for the population) of $5,000.

This means that [tex]\mu = 34000, \sigma = 5000[/tex]

Subsample of 200 city residents.

This means that [tex]n = 200, s = \frac{5000}{\sqrt{200}} = 353.55[/tex]

What is the Z score for $37,000 ?

This is Z when X = 37000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{37000 - 34000}{353.55}[/tex]

[tex]Z = 8.49[/tex]

The Z score for $37,000 is 8.49.

Complete Question:

Kyra is framing a square painting with side lengths of (x + 6) inches. The total area of the painting and the frame has a side length of (2x - 5) inches. The material for the frame will cost $0.07 per square inch.

Find the cost of the material for the frame is x = 16.

Answer:

The material cost of the frame is: $17.15

Step-by-step explanation:

Given

[tex]L_1 = (x + 6)\ in[/tex] --- Length of painting

[tex]L_2 = (2x - 6)[/tex] --- Frame and Painting

[tex]Cost = \$0.07[/tex] per square inch

Required

The cost of material of the frame

First, we calculate the area of the frame only

This is the difference between the areas of the frame and painting and the area of the painting

[tex]Area = (L_2)^2 - (L_1)^2[/tex]

[tex]Area = (2x - 5)^2 - (x + 6)^2[/tex]

Substitute 16 for x

[tex]Area = (2*16 - 5)^2 - (16 + 6)^2[/tex]

[tex]Area = (27)^2 - (22)^2[/tex]

[tex]Area = 245\ in^2[/tex]

The cost of the painting is:

[tex]Total\ Cost = Unit\ Cost * Area[/tex]

[tex]Total\ Cost = \$0.07 * 245[/tex]

[tex]Total\ Cost = \$17.15[/tex]

Hence, the material cost of the frame is: $17.15

Answer:

Step-by-step explanation:

Experimental probability is the number of a certain outcome divided by the number of trials, in this case

32/300

0.10666... rounded to nearest thousandth this is

0.107

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

[tex] {f}^{ - 1} (x) = x \: value[/tex]

[tex]f(x) = \sqrt[4]{x} + 6 \\ [/tex]

[tex]x - 6 = \sqrt[4]{x} [/tex]

[tex] {(x - 6)}^{4} = x[/tex]

[tex] {f}^{ - 1}(x) = {(x - 6)}^{4} [/tex]

Answer:

Step-by-step explanation:

y = 3 ^ - sqrt(3)

y = -sqrt(3) * log(3)

Log (3)= 0.47712

- sqrt(3) = - 1.732

y = 0.47712 * -1.732

y = - 0.82637

The y really has no meaning. I just used it so I could get from 1 line to the next.

Look carefully at how that - sqrt(3) was handled. You are not taking the square root of -3.

Based on the arithmetic sequence, the sum of the first 19 terms is 532.

1, 4, 7, 10, 13, 16...

Sn = n/2{2a + (n - 1)d}

= 19/2{2×1 + (19 - 1)3}

= 9.5{2 + (18)3}

= 9.5(2 + 54)

= 9.5(56)

Sn = 532

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Answer:

8

Step-by-step explanation:

Thrice means the same as 3, so 3 × 8 = 24 and when 9 is subtracted from 24 it is equal to 15

Answer:

Step-by-step explanation:

let the number be x

3x-9=15

3x=15+9     add 9 from both sides

3x=24

x=8

Answer:

4 marble lost

Step-by-step explanation:

1/6×24=4

so 4 marble lost

Answer:

1/2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2.36 would need to be at least 2.50 or higher to be rounded to 3 so we round down to 2

hope this helps <3

Answer:

10

Step-by-step explanation:

6^2=36

8^2=64

64+36=100

The square root of 100 is 10

Answer:

[tex]\displaystyle \frac{1}{2}[/tex]

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle (\frac{(2.7 - 0.8) \cdot 2\frac{1}{3}}{(5.2 - 1.4) \div \frac{3}{70}} + 0.125) \div 2\frac{1}{2} + 0.43[/tex]

Step 2: Compute

Answer:

[tex] \frac{11}{12} [/tex]

Can I be brainliest pls

Answer:

X = 2/3

Hope this helps :D

Answer:

Here is what i got x^2+6x^5+15x^4+6x+1

Step-by-step explanation:

^ that mark is for exponents btw. For anyone that is new to this

The Binomial Expansion of  [tex](x+ 1)^6[/tex] is [tex]x^6[/tex] + 6[tex]x^5[/tex]y + 15[tex]x^4[/tex]y² + 20x³y³ + 15x²[tex]y^4[/tex] + 6x[tex]y^5[/tex] + [tex]y^6[/tex].

An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem. A binomial expression is an algebraic expression with two terms that are not the same.

Given:

We have to expand [tex](x+ 1)^6[/tex]

We know the general form of Binomial Expansion

(x + y[tex])^n[/tex] = C(n, 0) [tex]x^ny^0[/tex] + C(n, 1) [tex]x^{n-1}y^1[/tex] +.........+ C(n, n) [tex]x^0y^n[/tex]

Here n= 6

So, the expansion of [tex](x+ 1)^6[/tex] is

= C(6, 0) [tex]x^6y^0[/tex] + C(6, 1)[tex]x^5y^1[/tex] + C(6, 2) [tex]x^4y^2[/tex] + C(6, 3) x³y³ + C(6, 4) x²[tex]y^4[/tex] +  

   C(6, 5) x[tex]y^6[/tex] + C(6, 6) [tex]x^0y^6[/tex]

= [tex]x^6[/tex] + 6[tex]x^5[/tex]y + 15[tex]x^4[/tex]y² + 20x³y³ + 15x²[tex]y^4[/tex] + 6x[tex]y^5[/tex] + [tex]y^6[/tex]

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Answer:

The percentage error is 8%

Step-by-step explanation:

Given

[tex]r = 10cm[/tex]

[tex]\triangle r =0.1cm[/tex]

Required

% error in the surface area

The surface area of a sphere is:

[tex]S = \4\pi r^2[/tex]

Differentiate

[tex]dS \approx 8\pi r\ dr[/tex]

Rewrite as:

[tex]\triangle S =8\pi r \triangle r[/tex] --- This represents the relative error

The percentage error is then calculated as:

[tex]\% Error = \frac{Relative\ Error}{Surface\ Area}[/tex]

[tex]\% Error = \frac{\triangle S}{S} * 100\%[/tex]

[tex]\% Error = \frac{8\pi r \triangle r}{\pi r^2} *100\%[/tex]

[tex]\% Error = \frac{8 \triangle r}{r} * 100\%[/tex]

[tex]\% Error = \frac{8 *0.1}{10} * 100\%[/tex]

[tex]\% Error = \frac{0.8}{10} * 100\%[/tex]

[tex]\% Error = 0.08 * 100\%[/tex]

[tex]\% Error = 8\%[/tex]

Answer:

Step-by-step explanation:

1. A=12

2. A=17.5

3. A=12.5

4. A=21

5. A=9

6. A=10

7. A=10.5

8. A=18

9. A=6

Answer:

Correct option is

D

(0, 0)

Form the graph, we can see that solution is (0,0).

or

The point of intersection of lines y = 3x and x = 3y must satisfies both the equation.

From the options (0,0) satisfies both the equations, hence the point of intersection of given lines is at origin i.e. (0,0).

Answer:

Step-by-step explanation:

At the point of intersection, x+3 = 3x-3

6=2x

x = 3

y = x+3 = 6

Given:

The piece-wise function is:

[tex]F(x)=\begin{cases}4&\text{ if }0\leq x<2\\3&\text{ if }2\leq x<4\\2&\text{ if }4\leq x<6\end{cases}[/tex]

To find:

The domain of the given function.

Solution:

Domain of the a function is the set of those values for which the function is defined. In other words, the set of input values is called domain.

The given function is defined for the intervals [tex]0\leq x<2,2\leq x<4,4\leq <6[/tex]. So, the domain of the given function is

[tex]Domain=\{x|0\leq x<2,2\leq x<4,4\leq <6\}[/tex]

Therefore, the correct option is B.

Answer:

A

Step-by-step explanation:

The design of the survey leads to bias because a nonresponse error was made in this design. This type of sampling only represents those who answered the survey; it does not represent the entire population.

Only 56% of response were received this means the entire population did not participate in the survey only a chuck of them answered the survey. This can lead to a biased result, an assumption.

0.5 is the value of 2.5 by 5.

A division is a process of splitting a specific amount into equal parts.

We need to find the solution when 2.5 divided by 5.

2.5/5

2.5 is the numerator and 5 is the denominator.

5 is the divisor and 2.5 is the dividend.

Zero point five is the value of 2.5 by 5.

0.5 is the value of 2.5 by 5.

Hence, 0.5 is the value of 2.5 by 5.

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Answer:

90 dollars

Step-by-step explanation:

I did maths hghbhhbghfggghggfgy

Answer:

2 product of x & adding it from 3 is equals to 5 ..

Answer:

Carlos born in 1944

Julio born in 1945

Ricky born in 1946

Step-by-step explanation:

x = Carlos age

x+1 = Julio age

x+2 = Ricky age

x + x+1 + x+2 = 129

3x + 3 = 129

3x = 126

x = 42 (Carlos age)

x+1 = 43 (Julio age)

x+2 = 44 (Ricky age)

1990 - 42 = 1944 (year Carlos born)

1990 - 43 = 1945 (year Julio born)

1990 - 44 = 1946 (year Ricky born)

Answer:

B) 103.25

Step-by-step explanation:

Area of rectangle:

A = bh

A = (16)(4)

A = 64

Area of a semi-circle:

r = d/2 = 5

A = (πr²)/2

A = (3.14 * 5²)/2

A = (3.14 * 25)/2

A = (78.5)/2

A = 39.25

Combined:

64 + 39.25 = 103.25

Answer: 103.25

Step-by-step explanation:

area of the rectangle is 4*16= 64

The area of the complete circle is [tex]\pi r^{2}[/tex]

r=d/2

r=10/2

r=5

[tex]25\pi[/tex] is the area of the full circle

[tex]\frac{25\pi }{2}[/tex] is the area of the semi- circle

area of the figure

[tex]64+\frac{25\pi }{2}[/tex]=103.27

Answer:

(0,-3) and (6,0)

Step-by-step explanation:

Now you use two point form to make equation

Y2-Y1/Y-Y1=X2-X1/X-X1

here Y2=0 ,Y1=-3

X2=6 and X1=0  now put in equation to get answer

Answer:

11 cows and 6 ducks

Step-by-step explanation: