Which equation is the result of subtracting the second equation from the first?
4x-6y=13
-5x+2y=5

Answer:

A) Null Hypothesis; H0: μ = $41,500

Alternative hypothesis; H1: μ > $41,500

B) Reject H0 is t > 2.821433

C) t = 1.79

D) there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average

Step-by-step explanation:

A) The hypotheses is given as;

Null Hypothesis; H0: μ = $41,500

Alternative hypothesis; H1: μ > $41,500

B) From online t-score calculator attached using significance level of 0.01 and DF = n - 1 = 10 - 1 = 9, we have;

t = 2.821433

Normally, when the absolute value of the t-value is greater than the critical value, we reject the null hypothesis. However, when the absolute value of the t-value is less than the critical value, we fail to reject the null hypothesis.

Thus, if t > 2.821433, we will reject the null hypothesis H0.

C) Formula for the test statistic is;

t = (x' - μ)/(s/√n)

We have, μ = 41500, x' = 47500, s = 10600, n = 10

t = (47500 - 41500)/(10600/√10)

t = 1.79

D) So, 1.79 is less than the t-critical value of 2.821433. Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average

Answer:

25 CAN be written as a fraction.

=> 250/10 = 25

Square root of 14 is 3.74165738677

It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION,  but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION

=> 374/100

-1.25 CAN be written as a fraction.

=> -5/4 = -1.25

Square root of 16 CAN also be written as a fraction.

=> sqr root of 16 = 4.

4 can be written as a fraction.

=> 4 = 8/2

Pi = 3.14.........

It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION

=> 314/100

.6 CAN be written as a fraction.

=> 6/10 = .6

Answer: n is a positive odd number.

Step-by-step explanation:

Ok, we know that the function is something like:

f(x)=a(x+k)^1/n + c

In the graph we can see two thigns:

All the values of the graph are positive values (even for the negative values of x), but in the left side we can see that the function decreases and is different than the right side.

So this is not an even function, then n must be an odd number (n odd allows us to have negative values for y = f(x) that happen when x + k is negative).

Also, we can see that the function increases, if n was a negative number, like: n = -N

we would have:

[tex]f(x) = \frac{a}{(x+k)^{1/N}} + c[/tex]

So in this case x is in the denominator, so as x increases, we would see that the value of y decreases, but that does not happen, so we can conclude that the value of n must be positive.

Then n is a positive odd number.

Answer:

D) Positive Even Integer

Step-by-step explanation:

just did it

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▹ Answer

80

▹ Step-by-Step Explanation

(2²)³ + (2³)² ÷ 4

Rewrite:

2⁶ + 2⁶ ÷ 2²

Divide:

2⁶ + 2⁴

Factor:

(2² + 1) * 2⁴

Evaluate:

(4 + 1) * 2⁴

Calculate:

5 * 16

= 80

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Option A.

Step-by-step explanation:

The given equation of ellipse is

[tex]4x^2+9y^2=36[/tex]

Divide both sides by 36.

[tex]\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=1[/tex]

[tex]\dfrac{x^2}{9}+\dfrac{y^2}{4}=1[/tex]

[tex]\dfrac{x^2}{3^2}+\dfrac{y^2}{2^2}=1[/tex]    ...(1)

The standard form of an ellipse is

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]    ...(2)

where, (h,k) is center, (h±a,k) are vertices and (h±c,k) are foci.

On comparing (1) and (2), we get

[tex]h=0,k=0,a=3,b=2[/tex]

Now,

Center [tex]=(h,k)=(0,0)[/tex]

Vertices [tex]=(h\pm a,k)=(0\pm 3,0)=(3,0),(-3,0)[/tex]  

We know that

[tex]c=\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=\sqrt{5}[/tex]

Foci [tex]=(h\pm c,k)=(0\pm \sqrt{5},0)=(\sqrt{5},0),(-\sqrt{5},0)[/tex]

Therefore, the correct option is A.

Answer:

y= -0.8x + 4

Midpoint is 0,4

Answer: the number = 6

Step-by-step explanation:

Let x be the number.

Set equation according to the information given

2 + 8x = 2 × 25

Simplify by multiplication

2 + 8x = 50

Subtract 2 on both sides

2 + 8x - 2 = 50 - 2

8x = 48

Divide 8 on both sides

8x / 8 = 48 / 8

[tex]\boxed {x=6}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:

The interval for 95% will be given as,

Pr(X) = μ ± 2σ

Pr(X) = 200 ± 2(40)

Pr(X) = 200 ± 80

Pr(X) = (200 - 80, 200 + 80)

Pr(X) = (120, 280)

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

More about the normal distribution link is given below.

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Answer:

2

Step-by-step explanation:

2,8 to 4,12 has a rise of 4 and a run of 2.

4/2 = 2

The slope is 2.

Remember rise/run!

Answer:

2

Step-by-step explanation:

We take take two points and use the slope formula

m = (y2-y1)/(x2-x1)

m = (12-8)/(4-2)

   = 4/2

   = 2

Answer:

vertical asymptotes

x=6, x=-6

horizontal asymptotes

y=0

zeros (0,0)

Step-by-step explanation:

f(x) = 6x / ( x^2 - 36)

First factor

f(x) = 6x / ( x-6)(x+6)

Since nothing cancels

The vertical asymptotes are when the denominator goes to zero

x-6 = 0   x+6=0

x=6          x= -6

Since the numerator has a smaller power than the denominator (1 < 2), there is an asymptote at y = 0

To find the zeros, we find where the numerator = 0

6x=0

x=0

[tex]\\ \rm\Rrightarrow y=\dfrac{6x}{x^2-36}[/tex]

The h orizontal asymptote

As x has less degree than x²

Vertical asymptote

Answer:

7. 20 + 5 + 3/10 + 6/100

8. 7 + 4/10 + 2/100 + 5/1000

Step-by-step explanation:

We are writing two numbers in expanded form, to help, we can use the guide above both numbers. Expanded form is all about breaking apart a number by place value and putting them in an additional sequence.

Let's look at 7, 25.36.

There are the tens, ones, tenths, and hundredths place being used, therefore :

20 + 5 + 3/10 + 6/100

We can do the same for 8, 7.425.

There are ones, tenths, hundredths, and thousandths being used, therefore :

7 + 4/10 + 2/100 + 5/1000

Answer:

RS 17.10

Step-by-step explanation:

If they earn 0.95 a day, you can multiply that income by the number of days, which is 18.

RS 17.10

Answer:

.33

Step-by-step explanation:

Hey there!

1 / 3

= .333333333

.33 rounded to the nearest hundredth

Hope this helps :)

Answer:

990/23

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

23 × 43 = 989

Step 2

Add the answer from Step 1 to the numerator

989 + 1 = 990

Step 3

Write answer from Step 2 over the denominator

990/23

Answer: No, the orders are not independent.

Step-by-step explanation:

If event 1 has some possible outcomes, suppose that we choose a given outcome 1 with a probability P1, and event 2, also with different possible outcomes, we can select an outcome 2, that has a probability P2, and the two events are independent (meaning that the outcome in event 1 does not affect the outcome in event 2, and vice versa)

Then the probability of outcome 1 and outcome 2 happening at the same time is equal to the product of their individual probabilities.

P = P1*P2.

In this case, event 1 is the selection of the pizza, and outcome 1 is the selection of the square pizza, with a probability of 55%.

Event 2 is the selection of the drink, outcome 2 is the order of a soft drink, with a probability of 72%.

If those two events were independent, then the probability that a customer orders a square pizza and a soft drink would be:

P = 0.55*0.72 = 0.396 (or 39.6%)

But we know that the actual probability is 48%.

So this is larger, which means that the outcomes are not independent.

Answer:

$3385 per week

Step-by-step explanation:

so, he gets $370 plus 4.5% of what he is selling.

$67000 = 100% of selling

1% = 100%/100 = 67000/100 = $670

4.5% = 1% × 4.5 = 670 × 4.5 = $3015

so, he gets $370 + $3015 = $3385 per week

Answer:

YES

Step-by-step explanation:

1 million minutes = 1.9 years

An average man can live upto 78 years.

So, an average man can easily live upto 1,000,000.

Answer:

There will be (365 x 24 x 60) minutes each year.

and that is 525600.

and 525600 x 78 is 40,996,800.

so, It is definitely more than 1 million minutes.

Hop it helps!

Bye!

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

A (- 1, - 17 ) → A' (- 1, 17 )

B (0, - 12 ) → B' (0, 12 )

C (- 5, - 11 ) → C' (- 5, 11 )

D (- 6, - 16 ) → D' (- 6, 16 )

Answer:

B

Step-by-step explanation:

P(AUB)=P(A)+P(B)-P(A∩B)

191/400=7/20+P(B)-49/400

P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4

The value of P(B) is 1/4.

The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:

Probability(Event) = Favorable Outcomes/Total Outcomes = p/q

Given data as :

P(A) = 7/20,

P(A∪B) = 191/400,

P(A∩B) = 49/400 ,

P(AUB) = P(A) + P(B) - P(A∩B)

Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,

191/400 = 7/20 + P(B) - 49/400

Rearrange the terms in the equation,

P(B) = 191/400 + 49/400 - 7/20

P(B) = 240/400 - 7/20

P(B) = 12/20 - 7/20

P(B) = 5/20

P(B) = 1/4

Hence, the value of P(B) is 1/4.

Learn more about probability here :

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Answer:

Ordinary Least Square (OLS) for the multiple regression model involves selecting parameters of a straight line function that will minimize the sum of the squares of the variance in the given dataset and those forecasted by the straight-line function.

Cheers

Answer:

16x⁴+16x³-12x²-32x-16

Step-by-step explanation:

(8x²-4x-8)(2x²+3x+2)

= 16x⁴+24x³+16x²-8x³-12x²-8x-16x²-24x-16

= 16x⁴+16x³-12x²-32x-16

Answer:

Area of ΔEDF = 2.7 in²

Step-by-step explanation:

It's given in the question,

ΔBAC ~ ΔEDF

In these similar triangles,

Scale factor of the sides = [tex]\frac{\text{Measure of one side of triangle BAC}}{\text{Measure of one side of triangle EDF}}[/tex]

                                        [tex]=\frac{\text{BC}}{\text{EF}}[/tex]

                                        [tex]=\frac{3}{2}[/tex]

Area scale factor = (Scale factor of the sides)²

[tex]\frac{\text{Area of triangle BAC}}{\text{Area of triangle EDF}}=(\frac{3}{2})^2[/tex]

[tex]\frac{6}{\text{Area of triangle EDF}}=(\frac{9}{4})[/tex]

Area of ΔEDF = [tex]\frac{6\times 4}{9}[/tex]

                       = 2.67

                       ≈ 2.7 in²

Therefore, area of the ΔEDF is 2.7 in²                            

A certain​ animal's body temperature has a mean of 94.72° F and a standard deviation of 0.57°F. Convert the given temperatures to z scores.

a. 93.52 °F  b. 95.22 °F      c. 94.72 °F

Answer:

a. z = - 2.1053

b. z = 0.87719

c. z = 0

Step-by-step explanation:

Given that :

The population mean μ = 94.72

The standard deviation σ = 0.57

the formula for calculating the standard normal z score, which can be represented as:

[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]

For  a.

The sample mean [tex]\bar x[/tex] = 93.52

The z score can be computed as follows:

[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]

[tex]z= \dfrac{93.52 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{-1.2}{0.57}[/tex]

z = - 2.1053

For  b.

The sample mean [tex]\bar x[/tex]  =  95.22    

[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]

[tex]z= \dfrac{95.22 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{0.5}{0.57}[/tex]

z = 0.87719

For  c.

The sample mean [tex]\bar x[/tex]  = 94.72

[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]

[tex]z= \dfrac{94.72 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{0}{0.57}[/tex]

z = 0

Answer:

Final population after 10 years

= 288911718

Step-by-step explanation:

Present population p = 258,316,051

Rate of growth R%= 1.12%

Number of years t= 10 years

Number of times calculated n = 10

Final population A

= P(1+r/n)^(nt)

A= 258,316,051(1+0.0112/10)^(10*10)

A= 258,316,051(1+0.00112)^(100)

A= 258,316,051(1.00112)^100

A= 258,316,051(1.118442762)

A= 288911717.6

Approximately A= 288911718

Final population after 10 years

= 288911718

Answer:

67.49

Step-by-step explanation:

Let the number of HCF be x.

Let the cost be y.

You are given 2 points of a line: (15, 32.84) and (43, 79.04).

Now we find the equation of the line that passes through those points.

y - y1 = m(x - x1)

y - 32.84 = [(79.04 - 32.84)/(43 - 15)](x - 15)

y - 32.84 = (46.2/28)(x - 15)

y - 32.84 = 1.65(x - 15)

y = 1.65x - 24.75 + 32.84

y = 1.65x + 8.09

Now we let x = 36 and solve for y.

y = 1.65(36) + 8.09

y = 67.49

Answer:

-20x / (x-12) = y

Step-by-step explanation:

3/x  - 5/y  = 1/4

Multiply each side by 4xy to clear the fractions

4xy ( 3/x  - 5/y  = 1/4)

Distribute

12y - 20x = xy

Subtract 12y from each side

-20x = xy -12y

Factor out y

-20x = y(x-12)

Divide each side by (x-12)

-20x / (x-12) = y

Answer:

9 is a positive number and -10 is negative. Positive numbers are bigger than negative numbers so yes 9 is bigger than -10

Step-by-step explanation:

Answer:

Yes it is

Step-by-step explanation:

here is how the numbers appear numerically

-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Hey there! I'm happy to help!

We want to find the equation of a line in y-intercept form, which is y=mx+b, where x and y are a point on the line, m is the slope, and b is the y-intercept.

We already know that our slope is -3.

y=-3x+b

We want to solve for b now. We can plug in our point (-9,-9) to solve for it.

-9=-3(-9)+b

-9=27+b

b=-36

So, our equation is y=-3x-36.

I hope that this helps! Have a wonderful day! :D

Answer:

Step-by-step explanation:

Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).

x = rcosθ and y = rsinθ.

Substituting the value of x and y in their polar form into the given expression we have;

x²+y²−4x=0

( rcosθ)²+( rsinθ)²-4( rcosθ) = 0

Expand the expressions in parenthesis

r²cos²θ+r²sin²θ-4rcosθ = 0

r²(cos²θ+sin²θ)-4rcosθ = 0

From trigonometry identity, cos²θ+sin²θ =1

The resulting equation becomes;

r²(1)-4rcosθ = 0

r²-4rcosθ = 0

Add 4rcosθ to both sides of the equation

r²-4rcosθ+4rcosθ = 0+4rcosθ

r² = 4rcosθ

Dividing both sides by r

r²/r = 4rcosθ/r

r = 4cosθ

Hence the correct equation in polar coordinates is r = 4cosθ

Dan is Correct by concluding  that adults spend a mean of 3 hours each day doing leisure and sports activities. because [tex]3.08[/tex] hours or [tex]3.09[/tex] hours which are the mean time of sample A and B  is approximately equal to 3 hours

From the question we are told that:

Total Sample size [tex]n=500[/tex]

Dan's mean  [tex]\=x_D= 3hr[/tex]

Bret's mean   [tex]\=x_D= 4hr[/tex]

Generally, the  Total hours spent doing leisure and sports activities  is mathematically given by

For Sample A

[tex]T_a=(1*70)+(2*90)+(3*135)+(4*140)+(5*65)\\\\[/tex]

[tex]T_a=1540 hours[/tex]

For Sample B

[tex]T_b=(1*80)+(2*80)+(3*130)+(4*135)+(5*75)[/tex]

[tex]T_b=1545[/tex]

Therefore

Mean Time spent doing leisure and sports activities by an American Adult

For Sample A

[tex]T_A=\frac{T_a}{n}[/tex]

[tex]T_A=\frac{1540}{500}[/tex]

[tex]T_A=3.08[/tex] hours

[tex]T_A \approx 3[/tex] hours

For Sample B

[tex]T_A'=\frac{T_b}{n}[/tex]

[tex]T_A'=\frac{1545}{500}[/tex]

[tex]T_A'=3.09[/tex] hours

[tex]T_A' \approx 3[/tex] hours

In conclusion

Dan is Correct because [tex]3.08[/tex] or [tex]3.09[/tex] which are the mean time of sample A and B is approximately equal to [tex]3[/tex]

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