Jocelyn’s plane travelled 500 mph for 7.3 hours. How far did her plane travel?

Answer:

The null hypothesis is [tex]H_0: \mu = 6658[/tex]

Tha alternate hypothesis is [tex]H_a: \mu > 6658[/tex]

The decision rule is that if [tex]t < 1.976[/tex], the null hypothesis is not rejected, that is, there is no evidence to conclude that these households paid more interest than the survey result, and that if [tex]t > 1.976[/tex], the null hypothesis is reject and there is evidence to conclude that these households paid more interest than the survey result.

The test statistic is [tex]t = 1.94[/tex]

As the test statistic of [tex]t = 1.94[/tex] is higher than the critical value of t, it is reasonable to conclude that these households paid more interest than the survey result

Step-by-step explanation:

A recent survey by nerdwallet indicated Americans paid a mean of $6,658 interest on credit card debt in 2017. Test if it is reasonable to conclude that these households paid more interest than the survey result.

At the null hypothesis, we test if they paid the same, that is:

[tex]H_0: \mu = 6658[/tex]

At the alternate hypothesis, we test if they paid more, that is:

[tex]H_a: \mu > 6658[/tex]

Test statistic:

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

State the decision rule for 0.05 significance level.

Right-tailed test(test if the mean is higher than the value) with 12 - 1 = 11 degrees of freedom, has a critical value of t = 1.976.

So

The decision rule is that if [tex]t < 1.976[/tex], the null hypothesis is not rejected, that is, there is no reasonable evidence to conclude that these households paid more interest than the survey result, and that if [tex]t > 1.976[/tex], the null hypothesis is reject and there is reasonable evidence to conclude that these households paid more interest than the survey result.

6658 is tested at the null hypothesis:

This means that [tex]\mu = 6658[/tex]

Sample mean and standard deviation:

With the given data-set:

Mean of [tex]X = 7163.6[/tex]

Standard deviation of [tex]s = 902.25[/tex]

Sample of 12:

This means that [tex]n = 12[/tex]

Compute the value of the test statistic.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{7163.6 - 6658}{\frac{902.25}{\sqrt{12}}}[/tex]

[tex]t = 1.94[/tex]

As the test statistic of [tex]t = 1.94[/tex] is higher than the critical value of t, it is reasonable to conclude that these households paid more interest than the survey result

Answer:

Answer is 5 3/4

Step-by-step explanation:

Thanks Hope this helps

Answer:

4. x = 6

5. x = 31

6. x = 34

Step-by-step explanation:

4. vertical angles

- 36/6 = 6

5. supplementary angles

180 - 56 = 124

124/4 = 31

6. complementary angle

90 - 22 = 68

68/2 = 34

Answer:

4. x = 6°

5. x = 31°

6. x = 34°

Step-by-step explanation:

4. Vertical Angles theorem states that the two opposite angles formed by 2 intersecting lines are congruent.

6x = 36°

x = 36 / 6

x = 6°

5.

180° - 56° = 4x

124° = 4x

x = 31°

6.

90° - 22° = 2x

68° = 2x

x = 34°

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

Function 1: exponential

Function 2: exponential

Function 3: quadratic

Step-by-step explanation:

I used a graphing calculator.

Hope this helps:)

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The rate of investment on $1000 is 7.5$ and on $12,000 is 8%.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let the rate of interest be represented by r. Given that the annual interest on a $12,000 investment exceeds the interest earned on a $1000 investment by 885. The $12,000 is invested at a 0.5% higher rate of interest than the $1000. Therefore, the equation for the interest can be written as,

$12,000(r + 0.005) - $1,000(r) = $885

12000r + 60 - 1000r = 885

11000r = 825

r = 0.075

r = 7.5%

Hence, the rate of investment on $1000 is 7.5$ and on $12,000 is 8%.

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Answer:

1: 62

2: 118

3: 62

4: 118

Step-by-step explanation:

1 and 3 are opposite angles so they have the same measure. 2 and 1 are adjacent angles on a linear plane. since a line is 180 degrees and we know that one of the angles on this plane is 62, that means that angle 2 must be 180 - 62 which 118 degrees

The equivalent value of the function is f ( a ) = ( 1/6 ) , when a > 3

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 1 / ( x + 2 )

Now , the value of x > 3

So , the value of f ( x ) = f ( a )

And , when x > 3

f ( 4 ) = 1 / ( 4 + 2 )

f ( 4 ) = 1 / 6

Hence , the function is f ( 4 ) = 1 / 6

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Answer:

x=2   y=-3

Step-by-step explanation:

We first need to isolate x to get x+2y=-4:x=-4-2y

-4-2y-2y=8

simplify:

-4-4y=8.

We can also do the same for y which is -4-4y=8:y=-3

for the x, we can now substitute it to give us:

x=-4-2(-3)

-4-2(-3)=2

x=2

So, our answers are x=2 and y=-3

Answer:

Step-by-step explanation:

x+2y=-4

x-2y=8                       Add

2x = 4                        Divide by 2

2x/2 = 4/2

x = 2

x + 2y = - 4                Substitute 2 for x

2 + 2y = - 4               Subtract 2 from both sides

2y = - 4 - 2

2y = - 6                     Divide by 2

2y/2 = - 6/2

y = - 3

Answer:

no

Step-by-step explanation:

6x² + 4x - 10 in factored form is:

2(3x+5)(x-1)

Answer:

Assuming that you actually mean that if [tex](x+2)[/tex] is a factor of [tex]x^{3}+6x^{2}+3x-10[/tex], the answer is yes.

Step-by-step explanation:

We need to do long division of the polynomial to figure out if this is true. I would show it here, but it is extremely difficult to do so. (Maybe someone could help me.) When I factor it, it does not leave a remainder, so this is true.

[tex]x^{3}+6x^{2}+3x-10= (x+2)(x^2+4x-5)[/tex]

Another way one could figure this out is by graphing the equation [tex]x^{3}+6x^{2}+3x-10[/tex] on your graphing calculator or on just a graphing website, lake Desmos. The screenshot below shows the graph.

The polynomial will have a factor of [tex](x-c)[/tex] if the point [tex](0,c)[/tex] exists on the graph. The graph has the following three zeroes.

[tex](0,-2)[/tex], [tex](0, -5)[/tex], and [tex](0,1)[/tex]

As such, it has the three factors [tex](x-(-2))[/tex], [tex](x-(-5))[/tex], and [tex](x-1)[/tex].

Since [tex](x-(-2)=(x+2)[/tex], it is a factor of the polynomial.

Answer:

Test statistic = - 0.851063

- 2.520463

Step-by-step explanation:

H0 : μ ≥ 15

H1 : μ < 15

Sample mean, xbar = 14.5

Sample standard deviation, s = 4.7

Sample size = 64

Teat statistic :

(xbar - μ) ÷ (s/√(n))

(14.5 - 15) ÷ (4.7/√(64))

= - 0.851063

The critical value at α = 0.05

Using the T - distribution :

Degree of freedom, df = 64 - 1 = 63

Tcritical(0.05, 63) = 1.6694

Test statistic - critical value

-0.851063 - 1.6694

= - 2.520463

Answer:

x = 3

Step-by-step explanation:

2x + 12 = 18

The variable is "x" and to find the value of x we must get rid of everything on the left side of the equation.

We can easily do this by using inverse operations

To get rid of the 12, we subtract 12, because in the expression its adding and the inverse of addition is subtraction.

But remember whatever we do to one side we have to do to the other, so we subtract 12 from each side

12 - 12 cancels out

18 - 12 = 6

we now have 2x = 6

now we want to get rid of the 2

2x is the same as 2 times x which is multiplication

The inverse of multiplication is division, so to get rid of the 2 we divide each side by 2

2x / 2 = x

6 / 2 = 3

we're left with x = 3

Answer:

[tex]x = 8.64^o[/tex]

Step-by-step explanation:

Given

The attached rectangle

Required

Find x

To do this, we make use of:

[tex]11x - 5 = 90[/tex] ---- angle at diagonal

Collect like terms

[tex]11x = 5 + 90[/tex]

[tex]11x = 95[/tex]

Solve for x

[tex]x = \frac{95}{11}[/tex]

[tex]x = 8.64^o[/tex] --- approximated

Answer: A B and C

Step-by-step explanation:

D has an area of 15 and A B and C have an area of 12.

Answer:

B. 8cm*12cm

Step-by-step explanation:

Area is the product of the two sides:

6*16 = 96

8*12 = 96

10*10 = 100

Perimeter is the sum of all four sides:

6+16+6+16 = 44

8+12+8+12 = 40

The answer is B. 8cm*12cm

Answer:

I will have to work 11 hours to take my parents to a $ 120 cost dinner, and I will have $ 1 left in return.

If I wanted to tip 15%, I would have to work 13 hours and have $ 5 left over.

In turn, to determine the money generated from an indeterminate number of hours worked, the applicable formula would be 11X = Y, where Y is the money generated and X is the number of hours worked.

Step-by-step explanation:

Since I have just gotten my first job, and I have decided I want to take my parents out for dinner to celebrate and I have anticipated it will cost approximately $ 120 for the three of us to go out for dinner, and at my job, I make an hourly wage of $ 11, to determine how many hours would I need to work to pay for the dinner, and what if I wanted to add a 15% tip, and determine if my strategy could also allow me to find out how much money and or made for any number of hours, the following calculations must be performed:

120/11 = X

10.9 = X

11 x 11 = 121

Therefore, I will have to work 11 hours to take my parents to a $ 120 cost dinner, and I will have $ 1 left in return.

(120 x 1.15) / 11 = X

138/11 = X

12.54 = X

11 x 13 = 143

Therefore, if I wanted to tip 15%, I would have to work 13 hours and have $ 5 left over.

In turn, to determine the money generated from an indeterminate number of hours worked, the applicable formula would be 11X = Y, where Y is the money generated and X is the number of hours worked.

Answer:

[tex]t_{0.35,14}= 0.3933306[/tex]

Step-by-step explanation:

From the question we are told that:

Degree of freedom [tex]df=14[/tex]

Significance Level [tex]\alpha=0.35[/tex]

Generally the expression for critical value t is mathematically given by

  [tex]t_{\alpha,df}[/tex]

  [tex]t_{0.35,14}[/tex]

Therefore From Students T Value Table

 [tex]t_{0.35,14}= 0.3933306[/tex]

 [tex]T-Value (right-tailed): 0.3933306[/tex]

Answer:

The 95% confidence interval for the mean zinc concentration in the river is between 1.75 and 3.45 grams per milliliter.

The 99% confidence interval for the mean zinc concentration in the river is between 1.48 and 3.72 grams per milliliter.

Step-by-step explanation:

95% confidence interval:

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 = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.96\frac{2.6}{\sqrt{36}}[/tex]

[tex]M = 0.85[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 2.6 - 0.85 = 1.75 grams per milliliter.

The upper end of the interval is the sample mean added to M. So it is 2.6 + 0.85 = 3.45 grams per milliliter.

The 95% confidence interval for the mean zinc concentration in the river is between 1.75 and 3.45 grams per milliliter.

99% confidence level:

By the same logic as for the 95% confidence interval, we have that [tex]Z = 2.575[/tex]. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 2.575\frac{2.6}{\sqrt{36}}[/tex]

[tex]M = 1.12[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 2.6 - 1.12 = 1.48 grams per milliliter.

The upper end of the interval is the sample mean added to M. So it is 2.6 + 1.12 = 3.72 grams per milliliter.

The 99% confidence interval for the mean zinc concentration in the river is between 1.48 and 3.72 grams per milliliter.

Answer:

no

Step-by-step explanation:

Answer:

it's not

Step-by-step explanation:

Answer:

[tex]\angle 2 = 48[/tex]

Step-by-step explanation:

Given

[tex]\angle 1 = 48[/tex]

Required

Find [tex]\angle 2[/tex]

[tex]\angle 1[/tex] and [tex]\angle 2[/tex] are vertically opposite angles.

So:

[tex]\angle 2 = \angle 1[/tex]

Substitute [tex]\angle 1 = 48[/tex]

[tex]\angle 2 = 48[/tex]

Answer:

The probability that the outcome is less than 6 is 58.333%.

Step-by-step explanation:

Since a 6-sided die with sides numbered 1 through 6 is tossed, ya penny is then tossed, and if the penny comes up heads, the value of the die is multiplied by 2, but otherwise, the value of the die is left unchanged, to determine what is the probability that the outcome is less than 6 the following calculation must be performed:

(5/6 + 2/6) / 2 = X

(0.8333 + 0.0333) / 2 = X

1.1666666 / 2 = X

0.583333 = X

Therefore, the probability that the outcome is less than 6 is 58.333%.

Answer:

the answer is Hence, a leap year has 52 Sundays

Step-by-step explanation:

I hope this helps

Answer:

it is 10%

Step-by-step explanation:

60 - 50 = 10

Answer:

The equation of the parabola is [tex]y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4[/tex], whose real vertex is [tex](x,y) = (2, -5.333)[/tex], not [tex](x,y) = (2, -5)[/tex].

Step-by-step explanation:

A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:

[tex](x_{1}, y_{1}) = (-2, 0)[/tex], [tex](x_{2}, y_{2}) = (6, 0)[/tex], [tex](x_{3}, y_{3}) = (0, -4)[/tex]

From definition of second order polynomial and the three points described above, we have the following system of linear equations:

[tex]4\cdot a -2\cdot b + c = 0[/tex] (1)

[tex]36\cdot a + 6\cdot b + c = 0[/tex] (2)

[tex]c = -4[/tex] (3)

The solution of this system is: [tex]a = \frac{1}{3}[/tex], [tex]b = - \frac{4}{3}[/tex], [tex]c = -4[/tex]. Hence, the equation of the parabola is [tex]y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4[/tex]. Lastly, we must check if [tex](x,y) = (2, -5)[/tex] belongs to the function. If we know that [tex]x = 2[/tex], then the value of [tex]y[/tex] is:

[tex]y = \frac{1}{3}\cdot (2)^{2}-\frac{4}{3}\cdot (2) - 4[/tex]

[tex]y = -5.333[/tex]

[tex](x,y) = (2, -5)[/tex] does not belong to the function, the real point is [tex](x,y) = (2, -5.333)[/tex].

Answer:

2(x - 4)(x + 4) = 0

x = {-4, 4}

Step-by-step explanation:

2x² - 32 = 0

factor out 2

2(x² - 16) = 0

This is a difference of squares

Factor

2(x - 4)(x + 4) = 0

x = {-4, 4}

Answer:

Step-by-step explanation:

Hope it helps you!!

Answer:

OQ

Step-by-step explanation:

The lines would never hit each other going on to infinity making them parallel.

Answer:

Total cost of the loan $55,969.8.-

Step-by-step explanation:

Giving the following information:

An amount of $32,000 is borrowed for 10 years at 5.75% Interest, compounded annually.

To calculate the total cost of the loan, we need to use the Future Value (FV) formula:

FV= PV*(1 + i)^n

PV= loan

i= interest rate

n= number of periods

FV= 32,000*(1.0575^10)

FV= $55,969.8

Answer:

4/5

Step-by-step explanation:

Given :

And we need to find the value of sinZ .

We know that , sine is the ratio of perpendicular and Hypotenuse. So that ,

[tex]:\implies[/tex] sinZ = p/h

[tex]:\implies[/tex] sin Z = 32/40

[tex]:\implies[/tex] sin Z = 4/5

Hence the renquired answer is 4/5.

Answer:c

Step-by-step explanation:

I think

Answer:

11/320

Step-by-step explanation:

the probability of a senior being chose first is 22 (seniors) divided my total number of students (80) is .275 percent.

multiplied by the probability of a sophomore being chosen 10/80 which equals .125.

multiply those together and you get your probability. 0.034375 or 11/320