Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.

It's 1000 charges and not 1.000 charges

Answer:

A)Null Hypothesis;H0: μ = 1000

Alternative Hypothesis;Ha: μ ≠ 1000

B) t-statistic = 1.4286

C) p-value = 0.15628

D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges

Step-by-step explanation:

We are given;

x = 1002 charges

s = 14

μ = 1000 charges

n = 100

degree of freedom = n - 1 = 100 - 1 = 99

A) The hypotheses are;

Null Hypothesis;H0: μ = 1000

Alternative Hypothesis;Ha: μ ≠ 1000

B) t-statistic = (x - μ)/(s/√n)

(1002 - 1000)/(14/√100) = 1.4286

C) From the t-score calculator results attached, the p-value is approximately 0.15628

D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.

Answer:

Z > Zα

6.511 > 1.645

Step-by-step explanation:

                                 University A           University B

Sample Size                      50                        40

Average Purchase         $280                   $250

Standard Deviation         $20                     $23

We formulate

H0:   x1` > x2`  null hypothesis that the mean of the University A is greater than the mean of the University B

HA:  x1`≤ x2`   one tailed test

Test statistic

Z= x1`-x2`/ √s₁²/n₁ +s²₂/n₂

Z= 280-250/√400/50 + 529/40

Z= 30/√8 +13.225

Z= 30 /4.607

Z= 6.511

For one tailed test at α= 0.05 = 1.645

Z > Zα

6.511 > 1.645

Thus we reject null hypothesis.On the average, students at University A spend more on textbooks then the students at University B.

Answer:

a. 0.0368

b. 0.99992131

c. 0.2039

d. 0.0048

e. 0.6533

Step-by-step explanation:

Let the probability of obtaining a head be p = 65% = 13/20 = 0.65. The probability of not obtaining a head is q = 1 - p = 1 -13/20 = 7/20 = 0.35

Since this is a binomial probability, we use a binomial probability.

a. The probability of obtaining 11 heads is ¹²C₁₁p¹¹q¹ = 12 × (0.65)¹¹(0.35) = 0.0368

b. Probability of 2 or more heads P(x ≥ 2) is

P(x ≥ 2) = 1 - P(x ≤ 1)

Now P(x ≤ 1) = P(0) + P(1)

= ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹

= (0.65)⁰(0.35)¹² + 12(0.65)¹(0.35)¹¹

= 0.000003379 + 0.00007531

= 0.0007869

P(x ≥ 2) = 1 - P(x ≤ 1)

= 1 - 0.00007869

= 0.99992131

c. The probability of obtaining 7 heads is ¹²C₇p⁷q⁵ = 792(0.65)⁷(0.35)⁵ = 0.2039

d. The probability of obtaining 7 heads is ¹²C₉q⁹p³ = 220(0.65)³(0.35)⁹ = 0.0048

e. Probability of 8 heads or less P(x ≤ 8) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰ + ¹²C₃p³q⁹ + ¹²C₄p⁴q⁸ + ¹²C₅p⁵q⁷ + ¹²C₆p⁶q⁶ + ¹²C₇p⁷q⁵ + ¹²C₈p⁸q⁴

= = ¹²C₀(0.65)⁰(0.35)¹² + ¹²C₁(0.65)¹(0.35)¹¹ + ¹²C₂(0.65)²(0.35)¹⁰ + ¹²C₃(0.65)³(0.35)⁹ + ¹²C₄(0.65)⁴(0.35)⁸ + ¹²C₅(0.65)⁵(0.35)⁷ + ¹²C₆(0.65)⁶(0.35)⁶ + ¹²C₇(0.65)⁷(0.35)⁵ + ¹²C₈(0.65)⁸(0.35)⁴

= 0.000003379 + 0.00007531 + 0.0007692 + 0.004762 + 0.01990 + 0.05912 + 0.1281 + 0.2039 + 0.2367

= 0.6533

Answer:

86 degrees farenheit

Step-by-step explanation:

First, we plug 30 in for C.

Next, solve for F

Multiplying both sides by 9/5 gives us 54=F-32

Add 32 to both sides    86=F

Answer:    2⁹5³ = 64,000

Step-by-step explanation:

There are 9 questions with 2 options (true or false) = 2⁹

There are 3 multiple questions with 5 options = 5³

true/false questions AND multiple choice questions

                  2⁹               x                5³                            = 2⁹5³

Answer:

Step-by-step explanation:

The null hypothesis is described as the default hypothesis while the alternative hypothesis us always tested against this null ie the opposite of the null hypothesis.

In this case study, Let the proportion of houses that have home security be p

Thus, the null hypothesis is proportion of houses that have home security is 45% : p = 45%

The alternative hypothesis is proportion of houses that have home security is different than 45%: p =/ 45%

Answer:

The answer is below

Step-by-step explanation:

Given that:

mean (μ) = 138 lb, standard deviation (σ) = 34.9 lb

z score is used in statistic to determine by how many standard deviations the raw score is above or below the mean. It is given by:

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

a) For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.

For 150 lb:

[tex]z=\frac{x-\mu}{\sigma}=\frac{150-138}{34.9}=0.34[/tex]

For 201 lb:

[tex]z=\frac{x-\mu}{\sigma}=\frac{201-138}{34.9}=1.81[/tex]

From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(0.34 < z < 1.81) = P(z < 1.81) - P(z < 0.34) = 0.9649 - 0.6331 = 0.3318 = 33.18%

b) If 39 different pilots are randomly selected i.e. n = 39. For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.

For 150 lb:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{150-138}{34.9/\sqrt{39} }=2.15[/tex]

For 201 lb:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{201-138}{34.9/\sqrt{39} }=11.3[/tex]

From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(2.15 < z < 11.3) = P(z < 11.3) - P(z < 2.15) = 1 - 0.9842 = 0.0158 = 1.58%

c) The probability from part C is more important

Answer:

The answer is below

Step-by-step explanation:

a) y=3x-1

The standard equation of a line is given by:

y = mx + c

Where m is the slope of the line and c is the intercept on the y axis.

Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:

3 × d = -1

d = -1/3

To find the equation of the perpendicular line passing through (0,0), we use:

[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]

b) y=1/4 x+2

Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:

1/4 × f = -1

f = -4

To find the equation of the perpendicular line passing through (0,0), we use:

[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]

Each shell has radius [tex]x[/tex] and height [tex]x^3[/tex], so the volume of this solid is

[tex]\displaystyle2\pi\int_0^1x^4\,\mathrm dx=\boxed{\frac{2\pi}5}[/tex]

Answer:

y-intercept = (0,4)

Step-by-step explanation:

To find the y-intercept, the place at which the value of x is 0, simply plug zero into your function:

f(x) = 4 - 5x

f(0) = 4 - 5(0)

f(0) = 4

Hence, the y-intercept occurs at (0,4).

The  y-intercept of f(x) = 4 - 5x is 4.

Using the slope intercept formula the  y-intercept can be found below

where

m = slope

b = y-intercept

From the equation:

f(x) = 4 - 5x

According to the slope intercept format,

m = slope = -5

y- intercept = 4

Therefore, the  y-intercept of f(x) = 4 - 5x is 4.

read more: https://brainly.com/question/4023516?referrer=searchResults

Answer:

See picture attached

Step-by-step explanation:

Answer:

Perimeter= 40 units

Step-by-step explanation:

Ok

We are asked to look for the perimeter.

We have some clue given.

All at right angle and some sides are given it's full length.

We have the bae to be 11 unit

The height to be 7 unit.

What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.

Let's go for the other side of the height.

Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.

So we have 7+7+11

But it's not complete yet.

We are given a dimension 2.

And the 2 is in two places so it's total 2*2= 4

The two is for a small base .

The base is actually an extra to the 11 of the other base.

So summing up

We have 2*11 + 2*7 + 2*2

Perimeter= 22+14+4

Perimeter= 40 units

Answer:

Step-by-step explanation:

3x+4y = 17 _______ equation 1

-4x -7y= -18 _______ equation 2

muliply by 4 in equation 1

12x + 16y = 68 ______ equation 3

multiply by 3 in equation 2

-12x - 21y = -54 ________ equation 4

add equation 3 & 4

- 5y = 14

y = - 14/5

substitute y in equation 1

3x + 4 (-14/5) =17

3x = 17+ (56/5)

3x =( 85 + 56) / 5

3x = 141/5

x = 47/5

hence (a,b) = (47/5, -14/5)

Answer:  K = ¹/₃, V = 32in³

Step-by-step explanation:

Volume of s cylinder (V) = πr²h where πr² is the base area.

Now from the question,

V ∞ πr²h

V = kπr²h where k is the constant of proportionality which is also the variation constant.

40 = 6 x 20 x k

40 = 120k and

k   = ⁴⁰/₁₂₀

     = ¹/₃.

Now to find the volume when base area is 8in² and h is 12,

V = 8 x 12 x ¹/₃

V = 32in³

Answer: Continuous

If X is the random variable denoting the weights of employees,  X is a continuous random variable.

Step-by-step explanation:

Given: An entertainment company specifies that its employees must weigh between 40 kgs - 50 kgs.

here weights of the employees vary.

Also, weight is measured not counted , that means weight is a continuous variable.

If X is the random variable denoting the weights of employees,  X is a continuous random variable.

The weights of employees, X, is a: continuous random variable.

Therefore, the weights of employees, X, is a: continuous random variable.

Learn more about continuous random variable on:

https://brainly.com/question/15238425

Answer:

This is called an Inductive reasoning.

Step-by-step explanation:

It is a logical process in which a number of premises all believed true combine to come up with specific conclusions. This is a generalisation based on observations.

Hope it helps.

Answer:

Step-by-step explanation:

Confidence interval for the population mean is expressed by the formula;

CI = xbar ± Z(S/√n) where;

xbar is the sample mean = 12.5

Z is the z score at 99% confidence = 2.576

S is the standard deviation = √variance

S = √2.4 = 1.5492

n is the sample size = 25

Substituting the given values into the formula given above,

CI = 12.5 ± 2.576(1.5492/√25)

CI = 12.5 ± 2.576(0.30984)

CI = 12.5 ± 0.7981

CI = (12.5-0.7981, 12.5+0.7981)

CI = (11.2019, 12.7981)

Hence the 99% confidence interval for the population mean is 11.2≤[tex]\mu[/tex]12.8 (to 1 decimal place)

A 99% confidence interval for the population mean will be "11.2 [tex]\leq[/tex] 12.8".

According to the question,

Sample mean, [tex]\bar x[/tex] = 12.5

Z score at 99%, Z = 2.576

Standard deviation, S = √Variance

                                    = √2.4

                                    = 1.5492

Sample size, n = 25

We know the formula,

Confidence interval, CI = [tex]\bar x \ \pm[/tex] Z ([tex]\frac{S}{\sqrt{n} }[/tex])

By substituting the given values, we get

                                        = 12.5 [tex]\pm[/tex] 2.576 ([tex]\frac{1.5492}{\sqrt{25} }[/tex])

                                        = 12.5 [tex]\pm[/tex] 2.576 (0.30984)

                                        = 12.5 [tex]\pm[/tex] 0.7981

Now,

                                   Cl = (12.5 - 0.7981, 12.5 + 0.7981)

                                        = (11.2019, 12.7981) or,

                                        = (11.2, 12.8)

Thus the above answer is appropriate.        

Find out more information about mean here:

https://brainly.com/question/7597734

Answer: n = 2401

Step-by-step explanation:

Given;

Confidence level = 2% - 99%

n = ? ( which is the sample size is unknown ).

Solution:

Where;

n = [z/E]^2*pq

Since no known value for ( p ) estimate is given, the "least biased" estimate is p = 1/2

Substituting the given data into the formula.

n = [1.96/0.02]^2(1/2)(1/2)

n = 2401

The minimum number of truck drivers the statistician needs to sample for an accurate result is 2401

Answer:

Its D

Step-by-step explanation:

x=11 and x=18

Answer:

It is 6. The student who got a two did not use order of operations.

Step-by-step explanation:

PEMDAS

You must do division before subtraction. 4/2 = 2.

8 - 2 = 6

Answer:

Last option is correct.

Step-by-step explanation:

[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]

Multiply the terms with the same base by adding their exponents

[tex] - 2 {x}^{3 + 2} {y}^{4 + 3} [/tex]

Add the numbers

[tex] - 2 {x}^{5} {y}^{7} [/tex]

Hope this helps..

Best regards!

[tex] - 2 {x}^{5} {y}^{7} [/tex]

Solution:

[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]

[tex] = 2 {x}^{(3 + 2)} {y}^{(4 + 3)} [/tex]

[tex] = - 2 {x}^{5} {y}^{7} [/tex]

[tex]{\boxed{\blue{\textsf{Some Important Laws of Indices}}}}[/tex]

[tex]{a}^{n}.{a}^{m}={a}^{(n + m)} [/tex]

[tex]{a}^{-1}=\dfrac{1}{a}[/tex]

[tex]\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}[/tex]

[tex]{({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}[/tex]

[tex] {a}^{\frac{1}{x}}=\sqrt[x]{a}[/tex]

[tex]a^0 = 1[/tex]

[tex][\text{Where all variables are real and greater than 0}][/tex]

Answer:

8:3 is the ratio of kids to adults

32 kids, so there are 12 adults

Answer:

32 kids to 4 adults

Step-by-step explanation:

1st row- 8 kids to 3 adults

2nd row- 16 kids to 6 adults

3rd row- 24 kids to 9 adults

4th row- 32 kids to 12 adults

Answer:

Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%.

Step-by-step explanation:

In this case we need to test whether the popular charity has expenses that are higher than other similar charities.

The hypothesis for the test can be defined as follows:

H₀: The popular charity has expenses that are higher than other similar charities, i.e. μ > 0.31.

Hₐ: The popular charity has expenses that are less than other similar charities, i.e. μ < 0.31.

As the population standard deviation is not known we will use a t-test for single mean.

Compute the sample mean and standard deviation as follows:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{10}\cdot[0.26+0.12+...+0.26]=0.238\\\\s= \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 0.0674 }{ 10 - 1} } =0.08654\approx 0.087[/tex]

Compute the test statistic value as follows:

[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{0.238-0.31}{0.087/\sqrt{10}}=-2.62[/tex]

Thus, the test statistic value is -2.62.

Compute the p-value of the test as follows:

 [tex]p-value=P(t_{\alpha, (n-1)}<-2.62}[/tex]

                [tex]=P(t_{0.05,9}<-2.62)\\=0.014[/tex]

*Use a t-table.

Thus, the p-value of the test is 0.014.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.014 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Thus, concluding that there is sufficient evidence to conclude that the mean is less than 31%.

Answer:

90°

Step-by-step explanation:

Theres a right angke beside x

And Angles on a straight line = 180 so 180-90°= 90°

Answer:

90

Step-by-step explanation:

I looked it up on the internet

Answer:44

Step-by-step explanation:the two triangles are congruent , so we deduce from that the angle B=angle E =48

So, x+4=48 , x=44 degree

Answer:

2 /3 +5 = 3

5.666667≠3

False

Step-by-step explanation:

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              Hi my lil bunny!

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Lets do this step by step.

~~~~~~~~~~~~~~~~~~~~

Multiply both sides of the equation by [tex]\frac{3}{2}[/tex] .

[tex]\frac{3}{2} . \frac{2}{3} . x = \frac{3}{2} . 5[/tex]

Simplify both sides of the equation.

~~~~

Simplify [tex]\frac{3}{2} . \frac{2}{3} . x .[/tex]

[tex]x = \frac{3}{2} . 5[/tex]

Multiply [tex]\frac{3}{2} . 5[/tex]

[tex]x = \frac{15}{2}[/tex]

The result can be shown in multiple forms.

Exact Form: [tex]x = \frac{15}{2}[/tex]

Decimal Form: [tex]x = 7.5[/tex]

Mixed Number Form: [tex]x = 7\frac{1}{5}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

The  p-value is  [tex]p-value = 0.013167[/tex]

Step-by-step explanation:

From the question we are told that

     The  population mean is [tex]\mu[/tex] =  200 milligrams

     The sample size is [tex]n = 70[/tex]

     The sample  mean is  [tex]\= x = 205.7[/tex]

      The  sample standard deviation is  [tex]\sigma = 21 \ milligram[/tex]

Generally the Null hypothesis is  mathematically represented as

      [tex]H_o : \mu = 200[/tex]

The Alternative  hypothesis is  

     [tex]H_a : \mu < 200[/tex]

The test statistics is mathematically represented as

       [tex]t_s = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }[/tex]

substituting values  

     [tex]t_s = \frac{ 205.7 - 200 }{\frac{21}{\sqrt{70} } }[/tex]

     [tex]t_s = 2.270[/tex]

Now the p-value is mathematically represented as

      [tex]p-value = P(Z \le t_s )[/tex]

substituting values  

      [tex]p-value = P(Z \le 2.270 )[/tex]

Using the Excel function[=NORMDIST(2.270)] to calculate the p-value we obtain that

       [tex]p-value = 0.013167[/tex]

Answer:

A) 0.012

From CollegeBoard

Answer:

0.02906

Step-by-step explanation:

number of questions =30

getting exactly right : 12

30C12 the number of possibilities

probability to get it right (1/4)^12

probability of failure =1-1/4=(3/4)^18     ( 18 = 30 questions -12 right )

P(12)=30C12*(1/4)^12*(3/4)^18=0.02906

hope it helps

Answer:

9

Step-by-step explanation:

Answer:

24

Step-by-step explanation: