If a person invested half of her money at 9% and half at 7% and received $160 interest, find the total amount of money invested.

First, we find the point estimate, given by the sample mean. Then, with this, and the standard deviation of the population given, we can find the margin of error, and then, we can find the confidence interval and the minimum sample size necessary.

Doing this, we get that:

a) The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.

b) The 95% margin of error is $1.64.

c) The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.

d) The sample size needed is 135.

Question a:

The point estimate for the population mean is the sample mean, which is of $18.21.

The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.

Question b:

We have to find our  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 Z-table as such z has a p-value of .

That is z with a p-value of , so Z = 1.96.

Now, find the margin of error M as such

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

In which  is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{5.92}{\sqrt{50}} = 1.64[/tex]

The 95% margin of error is $1.64.

(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.

The lower end of the interval is the sample mean subtracted by M. So it is 18.21 - 1.64 = 16.57

The upper end of the interval is the sample mean added to M. So it is 18.21 + 1.64 = 19.85

The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.

(d) What sample size is needed if the error must not exceed $1.00?

This is n for which M = 1. So

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

[tex]1 = 1.96\frac{5.92}{\sqrt{n}}[/tex]

[tex]\sqrt{n} = 1.96*5.92[/tex]

[tex](\sqrt{n})^2 = (1.96*5.92)^2[/tex]

[tex]n = 134.6[/tex]

Rounding up:

The sample size needed is 135.

For a question in which you find a confidence interval using the z-distribution, you can check https://brainly.com/question/24175328

To find the minimum sample size for a confidence interval, you can check https://brainly.com/question/22667000

Answer:

47.1

Step-by-step explanation:

We know side LM corresponds with side OP with a factor of some number. The value of side LM is 8, and the value of side OP is 29. If we divide the two numbers, we will find the scale factor of which triangle NOP is larger than KLM. 29/8 simplifies to 3.625. Now, to find the value of side PN, we must find the side it corresponds to on triangle KLM. Because K corresponds with N, and M corresponds with P, we know the side that PN corresponds with on triangle KLM is side KM. Side KM has a value of 13, so side PN must be 3.625 times larger than 13.

13 times 3.625 = 47.125. The question says to round to the nearest tenth, so the answer would be 47.1

Answer: B. f(x - 3) = 6x - 16

Concept:

When encountering a question that gives you a function and the evaluation value, then basically plug the given value into the function.

Solve:

Given function and value

f(x) = 6x + 2

f(x - 3)

Substitute the value into the given expression

f(x - 3) = 6 (x - 3) + 2

f(x - 3) = 6x - 18 + 2

f(x - 3) = 6x - 16

Hope this helps!! :)

Please let me know if you have any questions

Answer:

2 sqrt(2) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 45 = x/4

4 sin 45 = x

4 ( sqrt(2)/2) =x

2 sqrt(2) = x

Answer: D

Use sine to find the x-value:

[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]  

Answer:

51°

Step-by-step explanation:

Reference angle (θ) = ?

Opposite side length = 31

Hypotenuse length = 40

Apply SOH, which is;

Sin θ = Opp/Hyp

Plug in the values

Sin θ = 31/40

θ = sin^{-1}(31/40)

θ = 51° (neatest whole degree)

Answer:

Move triangle ABC over 2 and up 1

Step-by-step explanation:

A transformation in geometry is to essentially move a shape. To move ABC onto A1B1C1 you would move triangle ABC over 2 and up 1.

Answer:

FnH = {Meagan}

Step-by-step explanation:

Given the following sets and events:

S = {Albert, Betty, Abel, Jack, Patty, Meagan}

F = {Betty, Patty, Meagan},

H = {Abel, Meagan}

P = {Betty, Abel}.

In order to get FnH

The intersection of F and H is the element that is common to both sets. Hence for the set given, we can see that Meagan is common to both sets, therefore:

FnH = {Meagan}

Answer:

The slope is 2

Step-by-step explanation:

The Slope formula is y2-y1/x2-y1.

1. Plug the numbers into the slope equation which is 1-(-5)/4-1=2

Answer:  [tex]-\infty < y < \infty[/tex] which is choice A

This is the set of all real numbers.

===========================================================

Explanation:

If you were to graph this function, then it spans infinitely upward and infinitely downward as well. That means that we can land on any y value we want, and that's why the range is the set of all real numbers.

Another approach we could take is to swap x and y to get [tex]x = \sqrt[3]{y+8}[/tex] which solves to [tex]y = x^3-8[/tex] . This is the inverse of the original function your teacher gave you. Recall that the domain and range swap roles when going from the original function to the inverse. What this means is that because the domain of

Domain of inverse = set of all reals

Range of original = set of all reals

Answer:

99, 113

Step-by-step explanation:

X-the first bus

X+14-the second bus

5x+5(x+14)=1060

10x+70=1060

10x=990

X=99-the first bus

99+14=113-the second bus

Answer:

A. It was decreasing by -138,629.44 barrels

B. 26 years of time

Step-by-step explanation:

Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.

A. At 1200000

Bt = 1200000

-1/6ln2 x 1200000

Solve this using a calculator

= -138,629.4361

So the amount of oil is decreasing by -138,629.44 barrels

Answer:

11, 18, 25, 32, .....

Option D

Step-by-step explanation:

The formula for the nth term of an AP is a+(n-1)d

a+(n-1)d=a+(n-1-1)d+7

a+nd-d=a+nd-2d+7

d=7

As the common difference is 7.

The only option given which is in an AP is the 4th option

Answer:

16

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

==========================================================

Explanation:

I'm assuming you meant to say

y = (3/2)*tan( (1/3)x )

If so, then that equation is in the form

y = A*tan(Bx)

The B coefficient is B = 1/3 and it directly ties together to the period T.

T = pi/B

T = pi/(1/3)

T = pi*(3/1)

T = 3pi .... answer is choice C

Side note: This formula only works for tangent and cotangent functions.

Answer:

17d/20

Step-by-step explanation:

100-25=85

85/100×d

=17/20×d

=17d/20

6 19/24

Step-by-step explanation:

I can't really explain things properly, but I hope it helps

Answer:

The solutions of this system of equation is (-5,3) and (-1,-5).

Answer: (-3,-1) and (-5,3)

Step-by-step explanation:

Answer:

the last one

Step-by-step explanation:

this is because it is an equalactral triangle meaning that the line at the side is the only one which its degrees is 90 so if u add 45 and 45 its 90(hope this helps)

Answer:

Two sides have the same length, which iS less than

the length of the third side.

Step-by-step explanation:

Hypotenuce is a sode opposite to right angle, which is always bigger then any side of right triangle. since both angles are the same, Adjacent and Opposite are similar size as well.

Answer:

y ≥  x^2 - 1

Step-by-step explanation:

First, we can see that the shaded region is above what seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)

Then:

y ≥ a*x^2 + b*x + c

where a*x^2 + b*x + c is the general quadratic equation.

Now let's find the equation for the parabola:

f(x) = a*x^2 + b*x + c

We also can see that the vertex of the parabola is at the point (0, -1)

This means that:

f(0) = -1 = a*0^2 + b*0 + c

     = -1 = c

then we have that c = -1

Then:

f(x) = a*x^2 + b*x - 1

Now we can look at the graph again, to see that the zeros of the parabola are at +1 and -1

Which means that:

f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1

f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1

Then we got two equations:

a + b - 1 = 0

a - b - 1 = 0

from this we can conclude that b must be zero.

Then:

b = 0

and these equations become:

a - 1 = 0

a - 1 = 0

solving for a, we get:

a = 1

Then the quadratic equation is:

f(x) = 1*x^2 + 0*x - 1

f(x) = x^2 - 1

And the inequality is:

y ≥  x^2 - 1

measure horizontally

measure vertically

measure depth..

Answer:

3 e^t/2 + 4 = 27

e^t/2 = 23 / 3

Taking natural log of both sides

t/2 = ln 23/3 = ln 7.667 = 2.037

t = 4.074

Check:

3 e^4.074/2 + 4 = 27

27 = 27

Answer:

4 + 42s

Step-by-step explanation:

When y = 6 and x = 4,

Answer:

Option (C)

Step-by-step explanation:

Surface area of a right prism = 2(Area of the triangular base) + Ph

Here, P = Perimeter of the base

h = Height of the prism

Area of the triangular base = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]

                                             = [tex]\frac{1}{2}(5)(12)[/tex]

                                             = 30 cm²

Height of the prism = 15 cm

Perimeter of the base = (5 + 12 + 13)

                                     = 30 cm

Surface area of the right prism = 2(30) + 30(15)

                                                   = 60 + 450

                                                   = 510 cm²

Therefore, Option (C) will be the correct option.

Step-by-step explanation:

One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.

To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140

Answer: B. X It passes the vertical line test :)

Step-by-step explanation:

Answer:

b) LeBron is relatively taller because he has a larger z-score.

Step-by-step explanation:

Z-score:

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.

LeBron James:

Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when [tex]X = 81, \mu = 69.5, \sigma = 2.7[/tex]

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

[tex]Z = \frac{81 - 69.5}{2.7}[/tex]

[tex]Z = 4.26[/tex]

Candace Parker:

Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when [tex]X = 76, \mu = 64.2, \sigma = 3.2[/tex]

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

[tex]Z = \frac{76 - 64.2}{3.2}[/tex]

[tex]Z = 3.69[/tex]

Who is relatively taller?

Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.

it isn't possible to just give extra points in a simple and reliableway. anyways, let's starts.

a. is simple, just put the terms in order

r² +6r -5

because:

[tex] {r}^{2} + {6r}^{1} + {5r}^{0} [/tex]

anything to the power of 0 equals 1,

because it's the same as r/r, and 5 * r/r = 5*1

b. same logic as above

a²b² -5ab +33

c.

-c³ +ab +d +9

d.

-9y^5 - 2x³y²z +4x² +10x +1

^5 = to the power of five, it's the fastest way to type it without the special math input tool.

hope it helps you

Answer:

I agree with the above one.

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

It is given that,

→ 10(2x-3) = 10

Then find required value of x,

→ 10(2x-3) = 10

→ 20x-30 = 10

→ 20x = 10+30

→ 20x = 40

→ x = 40/20

→ [x = 2]

Hence, the value of x is 2.

In this question, the relations between velocity, distance and time are explored to first express the dependence of s on v, given the data in the exercise, and then to find the value of v for which s = 363.

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

Relation between velocity, distance, and time:

We have that velocity is distance divided by time, that is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance, and t is the time.

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

A car traveled s kilometers in 6 hours with a speed of v kilometers per hour.

This means that [tex]d = s, t = 6[/tex]

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

Express the dependence of s on v.

Taking the above values of d and t, and the formula, we have that:

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{s}{6}[/tex]

[tex]s = 6v[/tex]

Thus, the dependence of s on v can be expressed as: [tex]s = 6v[/tex]

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

Using the formula, find: v for s=363

We have that:

[tex]s = 6v[/tex]

And thus

[tex]v = \frac{s}{6}[/tex]

Considering [tex]s = 363[/tex]:

[tex]v = \frac{363}{6} = 60.5[/tex]

Thus, for s = 363, v = 60.5.

For an example of a problem using this formula, you can check here: https://brainly.com/question/14307500

Answer:

v=s/6 is the formula

and if s=363, v=60.5

hope this helped!