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Answer:

[tex]16^2-(\dfrac{x}{2})^2=(16+\dfrac{x}{2})(16-\dfrac{x}{2})[/tex]

Step-by-step explanation:

The given expression is : [tex]256-\dfrac{x^2}{4}[/tex].

We need to factorize it.

We know that, 16² = 256

So,

[tex]256-\dfrac{x^2}{4}=(16)^2-(\dfrac{x}{2})^2[/tex]

We know that, [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]16^2-(\dfrac{x}{2})^2=(16+\dfrac{x}{2})(16-\dfrac{x}{2})[/tex]

Hence, this is the required solution.

Answer:

add to 180, equal, add to 180, equal

Step-by-step explanation:

<1 + <2 = 180

<1 = <3

<3 + <4 = 180

<2 = <4

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

So

[tex]\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485[/tex]

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

So

[tex]\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314[/tex]

Distribution of the difference:

Mean:

[tex]\mu = \mu_A - \mu_B = 36 - 42 = -6[/tex]

Standard error:

[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142[/tex]

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = zs = 1.96*1.4142 = 2.77[/tex]

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Apply sum rule:

- 2dx + (x^2 +3x) 6/5dx = x^3dx

2dx = 2x

(x^2 + 3x) 6/5dx = 6/5 (x^3/3 + 3x^2/2)

x^3dx = x^4/4

-2x + 6/5 (x^3/3 + 3x^2/2) - x^4/4

Add constant

-2x + 6/5 (x^3/3 + 3x^2/2) - x^4/4 + c

Answer:

Step-by-step explanation:

Which means that Nolan took 100 seconds. This is all from Khan Academy so it's correct!!

Answer:

12

Step-by-step explanation:

4+4+4=12 :)

Answer:12

Step-by-step explanation:

Answer:

x=2^-y

A

Step-by-step explanation:

x | y

1 | 0

2 | -1

4 | -2

Answer:

≈ 634

Step-by-step explanation:

n = 847(1 * .07)^4

n = 847(0.93)^4

n = 633.60005247

n ≈ 634

Given:

In ΔPQR, the measure of ∠R=90°, QP = 85, RQ = 13, and PR = 84.

To find:

The cosecant of ∠P.

Solution:

In a right angle triangle,

[tex]\text{cosec}\theta =\dfrac{Hypotenuse}{Perpendicular}[/tex]

It is also written as:

[tex]\text{cosec}\theta =\dfrac{Hypotenuse}{Opposite}[/tex]

In triangle PQR, QP is the hypotenuse because ∠R=90°.

[tex]\text{cosec}P =\dfrac{QP}{RQ}[/tex]

[tex]\text{cosec}P =\dfrac{85}{13}[/tex]

Therefore, the required trigonometric ratio is [tex]\text{cosec}P =\dfrac{85}{13}[/tex].

Answer:

Part A: D   Part B: B

Step-by-step explanation:

This question is so free

Answer:

Did u get the answers ?

Step-by-step explanation:

I need help lol

Answer: A: -4 B:-29

Step-by-step explanation:

Answer:

x-2 is factor so 2 is zero of f(x) =x^4-3x^3+ax^2-16x+20

Step-by-step explanation:

2^4-3×2^3+a×2^2-16×2+20

solve this Answer is come.THANK YOU.

If (x - 2) is a factor of the polynomial f(x) = x⁴ -3x³ + ax² -16x + 20.

Then the value of a is -17.

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

A polynomial,

x⁴ -3x³ + ax² -16x + 20.

If x - 2 is a factor the x = 2 is the zeros of the polynomial.

When x = 2,

then,

x⁴ -3x³ + ax² -16x + 20 = 0

2⁴ -3(2)³ + a(2)² -16(2) + 20 =0

48 + 20 + 4a = 0

4a = -68

a = -17

Therefore, the value of a is -17.

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Answer:17.5

Step-by-step explanation:

Our output value is 250

We represent the unknown value wit “x”

250= 100%

x= 7%

By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

250/x = 100%/7%

Again, the reciprocal of both sides gives

x/250= 7/100

X= 17.5

17.5=7% of 250

Answer:

169 Pounds

Step-by-step explanation:

...

Answer:

y = 4x -1

Step-by-step explanation:

You use the equation y = mx + b

m is the slope, so you just substitute 4 for m, and b is the y-intercept, so you substitute -1 for b

Answer:

The interval (162, 188)would represent the middle 68% of the scores of all the games that Rashaad bowls.

Step-by-step explanation:

As per the  empirical rule of normal distribution, for any normally distributed curve, the values lie between the extreme values i.e  

(μ - σ) and (μ + σ).

Given  

μ  = 175

σ = 13

(μ - σ) = 175 -13 = 162

(μ + σ) = 175 + 13 = 188

Hence the required interval is 162, 188

Answer:

11.25

Step-by-step explanation:

15x3/4=45/4=11.25pounds

Answer:

The five odd numbers are:

23, 25, 27, 29, and 31

Step-by-step explanation:

A random odd number is written as:

2*n + 1

Where n is an integer.

Then 5 consecutive odd numbers will be:

2*n + 1

2*(n + 1) + 1

2*(n + 2) + 1

2*(n + 3) + 1

2*(n + 4) + 1

Now we want that the sum of the first 3 numbers to be 15 greater than the sum of the two last numbers, then:

(2*n + 1) + (2*(n + 1) + 1) + (2*(n + 2) + 1) = 15 + (2*(n + 3) + 1) + (2*(n + 4) + 1)

Now we just need to solve this for n:

(2*n + 1) + (2*n + 3) + (2*n + 5) = 15 + (2*n + 7) + (2*n + 9)

6*n + 9 = (15 + 7 + 9) + 4*n

6*n - 4*n = 15 + 7 + 9 - 9

2*n = 15 + 7 = 22

n = 22/2 = 11

Then the five numbers are:

(2*11 + 1) = 23

(2*(11 + 1) + 1) = 25

(2*(11 + 2) + 1) = 27

(2*(11 + 3) + 1) = 29

(2*(11 + 4) + 1) = 31

Answer:

7sq rt = 2.6457513110645907 = sqrt y^3

Step-by-step explanation:

The solutions for the equation 23 - x² - 2x = 0 are:

x = 4

x = -6

Option A is the correct answer.

We have,

To solve the rational equation:

1/(x - 1) - 1/(x + 3) - 1/5 = 0

We need to find the common denominator and combine the fractions on the left-hand side.

The common denominator is (x - 1)(x + 3)(5).

Multiplying each term by the common denominator:

[(x + 3)(5) - (x - 1)(5) - (x - 1)(x + 3)] / [(x - 1)(x + 3)(5)] = 0

Simplifying:

[5(x + 3) - 5(x - 1) - (x - 1)(x + 3)] / [(x - 1)(x + 3)(5)] = 0

[5x + 15 - 5x + 5 - (x² + 3x  - x - 3)] / [(x - 1)(x + 3)(5)] = 0

[5x + 15 - 5x + 5 - x² - 3x + x + 3 ] / [(x - 1)(x + 3)(5)] = 0

Simplifying further:

[23 - x² - 2x ] / [(x - 1)(x + 3)(5)] = 0

Now, we set the numerator equal to zero since a fraction is zero if and only if its numerator is zero:

23 - x² - 2x = 0

To solve the quadratic equation 23 - x² - 2x = 0, we can rearrange it to the standard form:

x² + 2x - 23 = 0

Now, we can solve it using factoring, completing the square, or the quadratic formula. Let's solve it using the quadratic formula:

The quadratic formula states that for an equation in the form

ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation x² + 2x - 23 = 0, the coefficients are a = 1, b = 2, and

c = -23.

Substituting these values into the quadratic formula:

x = (-2 ± √(2² - 4(1)(-23))) / (2(1))

Simplifying:

x = (-2 ± √(4 + 92)) / 2

x = (-2 ± √96) / 2

x = (-2 ± 4√6) / 2

Simplifying further:

x = -1 ± 2√6

Therefore,

The solutions for the equation 23 - x² - 2x = 0 are:

x = -1 + 2√6 = 3.89 = 4

x = -1 - 2√6 = -5.89 = -6

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Answer:

14

Step-by-step explanation:

I'll show you how I did it.

3+4r+n3=?

3+(4*r)+(n*3)=?

3+8+3=?

11+3=14

Answer:

Because it is a mixed fraction and it should be renamed in order to solve your problem, for the other one CAN NOT be converted into a mixed fraction.

Answer:

[tex]7\frac{9}{14}[/tex]

Step-by-step explanation:

5  1/ 2 +2  1/ 7

= 11/ 2 +2  1/ 7

= 11/ 2 + 15/ 7

= 107/ 14

=7  9/ 14

Answer:

7 9/14

Step-by-step explanation:

Combine the whole numbers and fractions together:

(5 + 2) + ( 1/2 + 1/7)

The whole numbers part is:

5 + 2 = 7

For the fractions part:

The Least Common Multiple (LCM) of 2 and 7 is 14. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM:

1/2 + 1/7 = 1 × 7 + 1 × 2

                ---------   -------     =    7 /14 + 2/14 = 7 9/14

                2 × 7 +  7 × 2

Answer: Question 5 is 18

Question 6 is 11

Step-by-step explanation:

Answer:

I'm sorry I just need points

Step-by-step explanation:

Answer:

37/6 or 6 1/6

Step-by-step explanation:

make all the denominators the same and add the numerators

Answer:

25 feet

Step-by-step explanation:

using the sides 20 and 15, use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the 2 side lengths and the diagonal.

[tex]a^{2} +b^{2} =c^{2} \\20^{2} +15^{2} =c^{2} \\400+225=c^{2} \\625=c^{2} \\25=c[/tex]

Considering it's definition, an odd function is represented by the second function given.

An odd function is defined by the following rule:

f(x) = -f(x).

This means that for example:

The only graph for which this relation is valid in this problem is the second graph, from which all examples off the numeric values were taken, hence an odd function is represented by the second function given.

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