Please show your work, tysm :D

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Answer:

A)  $40 total interest

B) $440

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &75000\\ P=\textit{initial amount}\dotfill &400000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &39\\ \end{cases} \\\\\\ 75000=400000(1 - \frac{r}{100})^{39}\implies \cfrac{75000}{400000}=\left( \cfrac{100-r}{100} \right)^{39}[/tex]

[tex]\cfrac{3}{16}=\left( \cfrac{100-r}{100} \right)^{39}\implies \sqrt[39]{\cfrac{3}{16}}=\cfrac{100-r}{100}\implies 100\sqrt[39]{\cfrac{3}{16}}=100-r \\\\\\ r=100-100\sqrt[39]{\cfrac{3}{16}}\implies r\approx 4.2[/tex]

When the variances are known and the sample size is high, a z-test is used to assess if two population means vary. The mean of the two players is not the same.

When the variances are known and the sample size is high, a z-test is used to assess if two population means vary.

In order to execute an appropriate z-test, the test statistic is expected to have a normal distribution, and nuisance factors such as standard deviation should be known.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ H_a: \mu_1 & \ne & \mu_2 \end{array}[/tex]

This corresponds to a two-tailed test, and a z-test for two means, with known population standard deviations, will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is [tex]z_c = 1.96[/tex]

The rejection region for this two-tailed test is R={z:∣z∣>1.96}

(3) Test Statistics

The z-statistic is computed as follows:

[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]

[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]

(4.) The decision about the null hypothesis

Since it is observed that |z| = 2.475 > z_c = 1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0133p=0.0133, and since p = 0.0133 < 0.05p=0.0133<0.05, it is concluded that the null hypothesis is rejected.

(5.) As it is concluded that the null hypothesis H₀ is rejected. Therefore, there is enough evidence to claim that the population mean μ1  is different than μ2.

Hence, the mean of the two players is not the same.

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Answer:

1,000

Step-by-step explanation:

just took the quiz

Add the amount it was reduced to the new price:

3.49 + 31.38 = 34.87

Original price = $34.87

Answer:

When finding the unknown original price, add the sale reduction to the new sale price to get the old sale price.

[tex]3.49 + 31.38 = 34.87[/tex]

Therefore, the original sales price was 34.87

Answer:

-1/12

Step-by-step explanation:

1/4 - 1/3 =   3/12 - 4/12   = - 1/12

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The measure of the ∠B=29.5°.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Given that sides a=10, b=5 and the measure of the ∠A=100°. Therefore, the using the sine law,

[tex]\rm \dfrac{Sin\ A}{a} = \dfrac{Sin\ B}{b}[/tex]

[tex]\rm \dfrac{Sin\ 100^o}{10} = \dfrac{Sin\ B}{5}\\\\\rm \dfrac{(Sin\ 100^o) \times 5}{10} = Sin\ B\\\\Sin\ B = 0.04924\\\\\angle B = 29.498^o \approx 29.5^o[/tex]

Hence, the measure of the ∠B=29.5°.

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Using the binomial distribution, it is found that there is a 0.8295 = 82.95% probability that at least 5 received a busy signal.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that at least 5 received a busy signal is given by:

[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]

In which:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{1300,0}.(0.0054)^{0}.(0.9946)^{1300} = 0.0009[/tex]

[tex]P(X = 1) = C_{1300,1}.(0.0054)^{1}.(0.9946)^{1299} = 0.0062[/tex]

[tex]P(X = 2) = C_{1300,2}.(0.0054)^{2}.(0.9946)^{1298} = 0.0218[/tex]

[tex]P(X = 3) = C_{1300,3}.(0.0054)^{3}.(0.9946)^{1297} = 0.0513[/tex]

[tex]P(X = 4) = C_{1300,4}.(0.0054)^{4}.(0.9946)^{1296} = 0.0903[/tex]

Then:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0009 + 0.0062 + 0.0218 + 0.0513 + 0.0903 = 0.1705.

[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.1705 = 0.8295[/tex]

0.8295 = 82.95% probability that at least 5 received a busy signal.

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Answer:

6 1/2

Step-by-step explanation:

Use the area formula: A=LengthxWidth

Plug in what we know: 24 3/8= 3 3/4x Width

We need to isolate the width; get it by itself.

Do this by (24 3/8)/(3 3/4). The best way is to enter this into a calculator.

Your answer is 6 1/2

Answer:

hope this is what you ask for and i hope it helps

Step-by-step explanation:

Answer:

It took 12.5 hours to catch up with the men

Question:

the hooded men rushed out of town at 100 miles per hour one hour later the masked men left town in pursuit at 125 mph how many hours did it take the masked men to catch up to the hooded men

Answer:

12.5

Step-by-step explanation:

This doesn't say it in the question but the hooded man drove 125 miles,
his speed was 100 mph.

The masked man drove also drove 125 miles but he drove at 125 mph.

Ok sorry lets make this simpler.

divide 1250 by 100 and your answer is:

12.5

So, it took the masked man 12.5 hours to catch up with the hooded man.

Answer:

30

Step-by-step explanation:

10 x 3 = 30

Answer:

30 centimeters squared

Step-by-step explanation:

The area of a parallelogram can be found by using the formula base x height. The base of this parallelogram is 10, and the height is 3. Therefore the area is 30 square centimeters.

Answer:

If each tile has a number from 0 thru 9 then the possible outcomes for each tile are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Answer:

The Height is 15in

Step-by-step explanation:

V=L.W.H

300=10x2xH

300=20xH

300/20=H

H=15in

[tex]\frac{2}{13}[/tex]

Probability is finding the chance that some specific outcome will occur. In this case, we are looking for the probability of one of two outcomes.

Equally Likely Outcomes

When drawing a card from a well-shuffled deck, all outcomes (cards) are equally likely to be drawn. Each card was a 1/52 probability of occurring.

Probability of Two Outcomes

In a deck of cards, there are 4 cards of each number. This means that the probability of drawing a 2 is 4/52, the same for a queen.

So, to find the probability of one of the two desired outcomes is equal to adding the probabilities together.

This fraction can then be simplified further:

Answer:

[tex]\displaystyle \lim_{x \to -\infty} (-7x^5 + x^3) = \infty[/tex]

General Formulas and Concepts:
Calculus

Limits

Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \lim_{x \to -\infty} (-7x^5 + x^3)[/tex]

Step 2: Evaluate

Recall that x⁵ is a "faster" function than x³. Also recall that we have 2 negatives, which would turn positive. Therefore, we can ignore the 2nd part of the limit and focus on the first:
[tex]\displaystyle \begin{aligned}\lim_{x \to -\infty} (-7x^5 + x^3) & = -7(- \infty)^5 + (- \infty)^3 \\& = -7(- \infty)^5 \\& = -7(- \infty) \\& = 7(\infty) \\& = \boxed{\infty} \\\end{aligned}[/tex]

∴ we have found the limit to equal infinity.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Answer:

the 1.5 goes between -1 and 0 and -3/2 too and -4/3 between the-2 and the 3/2 between the 0 and 1

Step-by-step explanation:

Step-by-step explanation:

5x + 80 = 180

x = 20

2x = 40

3x=60

7x=140

Answer:

5xsquared+x+5

Step-by-step explanation:

first combine x squared with 4x squared and you will get 5xsquared.

next combine 6x and -5x and you will get 1x or just simply x. Finally combine 3 and 2 (3+2) = 5.

Answer:

576cm³

Step-by-step explanation:

8×6=48

48×12=576

The appropriate null and alternate hypotheses are (d) H0: p = 0.10 and H1: p ≠ 0.10

From the question, we understand that:

The proportion of reports that have their cars stolen is given as 10%

Null hypothesis is represented with the equality sign.

So, the null hypothesis is H0: p = 0.10

The alternate hypothesis is represented with the unequal sign.

So, the alternate hypothesis is H1: p ≠0.10

Hence, the appropriate hypotheses are (d) H0: p = 0.10 and H1: p ≠ 0.10

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Answer:

center: (2,-12)

radius: 9

Step-by-step explanation:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

[tex]h=2\\k=-12\\r=9[/tex]

get r by getting square root of 81

center = (h,k)

Answer:

center: (2,-12)

radius: 9

Step-by-step explanation:

(x-h)^2+(y-k)^2=r^2

h=2

k=-12

r=9

Answer:

40m^2 :)

Step-by-step explanation:

Area of a triange = (h·b)/2

Now lets solve :)

4 + 6 = 10

(8·10)/2

80/2

40

Have an amazing day!!

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Answer:

7

Step-by-step explanation:

3/10+4/10 =7/10

Answer:

7/10, or 70%

Step-by-step explanation:

You just add the fractions together and get 7/10. You could also find a common denominator and the add them together. You would do, 9/30+ 12/30= 21/30, or 7/10.

The values that are required to complete the table above indicating the distance traveled by the tortoise in the time elapsed are calculated below.

Mathematically, the distance traveled by the tortoise would be calculated by using this formula:

Distance = speed (rate) × time

When time = 1 min, we have:

D₁ = 20 × 1

D₁ = 20 meters.

When time = 2 min, we have:

D₂ = 20 × 2

D₂ = 40 meters.

When time = 3 min, we have:

D₃ = 20 × 3

D₃ = 60 meters.

When time = 4 min, we have:

D₄ = 20 × 4

D₄ = 80 meters.

When time = 5 min, we have:

D₅ = 20 × 5

D₅ = 100 meters.

When time = 6 min, we have:

D₆ = 20 × 6

D₆ = 120 meters.

When time = 7 min, we have:

D₇ = 20 × 7

D₇ = 140 meters.

When time = 10 min, we have:

D₁₀ = 20 × 10

D₁₀ = 200 meters.

When time = 15 min, we have:

D₁₅ = 20 × 15

D₁₅ = 300 meters.

When time = 20 min, we have:

D₂₀ = 20 × 20

D₂₀ = 400 meters.

When time = 25 min, we have:

D₂₅ = 20 × 25

D₂₅ = 500 meters.

When time = 30 min, we have:

D₃₀ = 20 × 30

D₃₀ = 600 meters.

When time = 35 min, we have:

D₃₅ = 20 × 35

D₃₅ = 700 meters.

When time = 40 min, we have:

D₄₀ = 20 × 40

D₄₀ = 800 meters.

When time = 50 min, we have:

D₅₀ = 20 × 50

D₅₀ = 1,000 meters.

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