What interest is needed to earn $137.50 on a deposit of $500 for five years if it earns simple interest?

Answer:

B

Step-by-step explanation:

The meaning in the situation is B; positive correlation; as time passes, the CPI increases.

The correlation coefficient is the degree of association between two quantities in terms of linear relation. The range of correlation coefficient is -1 to 1

If the correlation is -1, then that refers as the one quantity increases, the other quantity decreases , also the correlation is 0, then there is no linear relationship between two variables.

There are two types of Correlation;

Positive Correlation= With Increase in x value, y value also increases, we call it positive correlation.

Negative Correlation= With Increase in x value, if y value decreases, we call it negative correlation.

As we can see from the points plotted on the graph ,with increase in x value , y value decreases.

Hence, positive correlation; as time passes, the CPI increases.

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Answer:

X=29

Step-by-step explanation:

Sin62=x/33

X=29.137≈29

Total number of possible outcomes:

Number of ways to choose 3 numbers from 56 (56 choose 3): 56! / (3! * (56 - 3)!) = 22,957

Number of ways to choose 1 number from 49: 49

Total number of possible outcomes = 22,957 * 49 = 1,128,593

Number of favorable outcomes:

Number of ways to choose 1 number from 49: 1

Number of favorable outcomes = 1

Probability of winning the minimum award:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 1,128,593 ≈ 0.000000888, or approximately 0.0000888%

Answer:

no it gate 19/15 or 1 4/15

Step-by-step explanation:

Answer:

Michelle weighs 120.15 lb. now.

You can calculate it by

145lb x (1-.17) = 145lb x .83 = 120.15lb

Answer:

56

Step-by-step explanation:

7 times 8=56

Answer:

A. 2.5 pounds

B. 12.5 pounds

Step-by-step explanation:

Answer:

a 2.5 b 12.5

Step-by-step explanation:

162 inches is 13.5 feet or 13 feet 6 inches, so it would not fit underneath the bridge

Answer:

The truck cannot pass safely under the bridge. The truck is 13 inches taller than the maximum height.

If you're looking for the cube roots of √(3 + i ), you first have to decide what you mean by the square root √(…), since 3 + i is complex and therefore √(3 + i ) is multi-valued. There are 2 choices, but I'll stick with 1 of them.

First write 3 + i in polar form:

3 + i = √(3² + 1²) exp(i arctan(1/3)) = √10 exp(i arctan(1/3))

Then the 2 possible square roots are

• √(3 + i ) = ∜10 exp(i arctan(1/3)/2)

• √(3 + i ) = ∜10 exp(i (arctan(1/3)/2 + π))

and I'll take the one with the smaller argument,

√(3 + i ) = ∜10 exp(i arctan(1/3)/2)

Then the 3 cube roots of √(3 + i ) are

• ∛(√(3 + i )) = ¹²√10 exp(i arctan(1/3)/6)

• ∛(√(3 + i )) = ¹²√10 exp(i (arctan(1/3)/6 + π/3))

• ∛(√(3 + i )) = ¹²√10 exp(i (arctan(1/3)/6 + 2π/3))

On the off-chance you meant to ask about the cube roots of 3 + i, and not √(3 + i ), then these would be

• ∛(3 + i ) = ⁶√10 exp(i arctan(1/3)/3)

• ∛(3 + i ) = ⁶√10 exp(i (arctan(1/3)/3 + 2π/3))

• ∛(3 + i ) = ⁶√10 exp(i (arctan(1/3)/6 + 4π/3))

Answer:

alright if you give me brianliest on this, when you answer one of my questions ill give you brainliest. brailiest for a brianliest?

Step-by-step explanation:

Answer

Catfishing, In LOl rate 0-10 Im bored

Step-by-step explanation:

Answer: (1.5,-0.5)

Step-by-step explanation:

Step-by-step explanation:

→ 4 + 5(3x - 2) - 3x

→ 4 + 15x - 10 - 3x

→ 12x - 6

therefore, option A is correct.

hope this answer helps you dear!

The required simplified solution of the given expression is 12x -6. Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= 4 + 5(3x -2) - 3x
Following the distributive property,
= 4 + 15x - 10 - 3x
Following the associative property,
= 4 - 10 + 15x - 3x
= -6 + 12x
= 12x - 6

Thus, the required simplified solution of the given expression is 12x -6. Option A is correct.

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Answer:

Step-by-step explanation:

\(6x + 7 = 3x - 6\)

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

\(6x - 3x = - 6 - 7\)

Collect like terms

\(3x = - 6 - 7\)

Calculate

\( 3x = - 13\)

Divide both sides of the equation by 3

\( \frac{3x}{3} = - \frac{13}{3} \)

Calculate

\(x = - \frac{13}{3} \)

Hope this helps...

Best regards!!

Answer:

x= -13/3

Step-by-step explanation:

To solve for x, we need to get x by itself.

6x+7= 3x-6

First, move all the terms with variables to the left side of the equation.

Subtract 3x from both sides of the equation.

6x-3x +7 = 3x-3x-6

(6x-3x)+7=-6

3x+7=6

Now, we must move all the constants (terms without variables) to the right side of the equation.

Subtract 7 from both sides of the equation.

3x+7-7=-6-7

3x= -6-7

3x= -13

Now all the variables are on side and the constants are on the other. x is not by itself yet, it is being multiplied by 3. The inverse of multiplication is division. Divide both sides by 3.

3x/3= -13/3

x= -13/3

This fraction cannot be simplified, therefore it is our final answer.

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics:

Try 1 Try 2 Gain

n x s x s x s

Coached 427 500 92 529 97 29 59

Uncoached 2733 506 101 527 101 21 52

Use Table C to estimate a 90% confidence interval for the mean gain of all students who are coached.

at 90% confidence.

Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ1 be the score gain for all coached students. Let μ2 be the score gain for uncoached students.

(a) Give the alternative hypothesis:

μ1 - μ2.

(b) Give the t test statistic:

(c) Give the appropriate critical value for \alpha =5%:

Solution:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean score gain for all coached students

x2 = sample mean score gain for all uncoached students

s1 = sample standard deviation score gain of coached students

s2 = sample standard deviation score gain of uncoached students

For a 90% confidence interval, the z score is 1.645

From the information given,

x1 = 29

s1 = 59

n1 = 427

x2 = 21

s2 = 52

n2 = 2733

x1 - x2 = 29 - 21 = 8

z√(s1²/n1 + s2²/n2) = 1.645√(59²/427 + 52²/2733) = 4.97

90% Confidence interval = 8 ± 4.97

a) The population standard deviations are not known. it is a two-tailed test. The random variable is μ1 - μ2 = difference in the score gain for coached and uncoached students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 > μ2 H1 : μ1 - μ2 > 0

This is a right tailed test.

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (29 - 21)/√(59²/427 + 52²/2733)

t = 2.65

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [59²/427 + 52²/2733]²/[(1/427 - 1)(59²/427)² + (1/2733 - 1)(52²/2733)²] = 9.14/0.1564

df = 58

c) from the t distribution table, the critical value is 1.67

In order to reject the null hypothesis, the test statistic must be smaller than - 1.67 or greater than 1.67

Since - 2.65 < - 1.67 and 2.65 < 1.67, we would reject the null hypothesis.

Therefore, at 5% significance level, we can conclude that the score gain for coached students is greater than the score gain for uncoached students.

Answer:

4x-4 < -76

Step-by-step explanation:

Four times a number (x), minus 4, is less than -76.

Answer:

x is less than —18

Step-by-step explanation:

Check out the attached photo

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:

11C4 = (11!)/(4!(11-4)!) = 330

where nCr is the number of combinations of n things taken r at a time.

Now let's find the number of favorable outcomes for each part of the problem.

Part 1: Exactly two white balls and two red balls

To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:

6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150

So the probability of selecting exactly two white balls and two red balls is:

P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)

Part 2: At least two white balls

To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.

The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.

To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:

6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100

So the total number of favorable outcomes for selecting at least two white balls is:

150 + 100 = 250

And the probability of selecting at least two white balls is:

P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)

The volume of the largest right circular cone that can be inscribed in a sphere of radius 18 cm is approximately 11622.85 cubic centimeters.

To find the largest right circular cone that can be inscribed in a sphere of radius 18 cm, we need to find the cone with the largest possible volume that can fit inside the sphere.

Let's assume that the apex of the cone is at the center of the sphere. Since the cone is a right circular cone, the base of the cone will lie on the surface of the sphere, forming a circle with radius equal to the radius of the sphere, which is 18 cm.

Let's call the height of the cone "h" and the radius of the base of the cone "r". Then we can use the Pythagorean theorem to relate the height, radius, and slant height (which is equal to the radius of the sphere):

r^2 + h^2 = (18 cm)^2

The volume of a cone can be expressed as V = (1/3)πr^2h. We want to maximize this expression subject to the constraint above. We can use the constraint to eliminate one of the variables in the volume expression, then differentiate with respect to the remaining variable and set the derivative equal to zero to find the maximum.

From the constraint, we can solve for h^2:

h^2 = (18 cm)^2 - r^2

Substituting into the volume expression, we get:

V = (1/3)πr^2(18 cm - sqrt(r^2 + h^2))

Simplifying this expression, we get:

V = (1/3)πr^2(18 cm - sqrt((18 cm)^2 - r^2))

Differentiating with respect to r, we get:

dV/dr = (1/3)π(36 cm)r - (1/3)πr^3/sqrt((18 cm)^2 - r^2)

Setting this equal to zero and solving for r, we get:

r = (18 cm)/sqrt(2)

Substituting this value of r back into the expression for h, we get:

h = (18 cm)/sqrt(2)

Finally, substituting these values of r and h into the expression for the volume, we get:

V = (1/3)π((18 cm)/sqrt(2))^2((18 cm) - sqrt(((18 cm)/sqrt(2))^2 + ((18 cm)/sqrt(2))^2))

Simplifying this expression, we get:

V ≈ 11622.85 cubic centimeters

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Answer:

Step-by-step explanation:

0.1 g = 100 mg

85 mg / 100 mg = x mL / 1.5 mL

x = 1.275 mL

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

The 99% confidence interval for the mean germination time is (12.3, 19.3).

Step-by-step explanation:

The question is incomplete:

Recorded here are the germination times (in days) for ten randomly  chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.

We start calculating the sample mean M and standard deviation s:

\(M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\\)

\(s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\\)

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=15.8.

The sample size is N=10.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

\(s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075\)

The degrees of freedom for this sample size are:

df=n-1=10-1=9

The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.

The margin of error (MOE) can be calculated as:

\(MOE=t\cdot s_M=3.25 \cdot 1.075=3.49\)

Then, the lower and upper bounds of the confidence interval are:

\(LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3\)

The 99% confidence interval for the mean germination time is (12.3, 19.3).

The value of m∠Q as shown in the right-angled triangle below is 62.59°.

The Formula used is:

m∠Q = cos⁻¹(s/r)........................ (1)

Where:

s = 29 m

r = 63 m

Now, Substitute these values into equation 1

m∠Q = cos⁻¹(29/63)

m∠Q = cos⁻¹(0.46)

m∠Q = 62.59°

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Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

\(a_{n+1} = a_{n} + d\)

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

\(a_{n} = a_{1} + (n-1)*d\)

The sum of the first n terms of an arithmetic sequence is given by:

\(S_{n} = \frac{n(a_{1} + a_{n})}{2}\)

In this question:

\(a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6\)

We want the sum of the first 37 terms, so we have to find \(a_{37}\)

\(a_{n} = a_{1} + (n-1)*d\)

\(a_{37} = a_{1} + (36)*d\)

\(a_{37} = -27 + 36*6\)

\(a_{37} = 189\)

Then

\(S_{37} = \frac{37(-27 + 189)}{2} = 2997\)

The sum of the first 37 terms of the arithmetic sequence is 2997.

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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To subtract 47.96 from 320.041, you can align the decimal points and then subtract each digit from right to left.

First, write the numbers with the decimal points aligned:

320.041

- 47.960

Next, subtract the digits in the ones place, which is 1 minus 0, resulting in 1. Then, subtract the digits in the tenths place, which is 4 minus 6. Since 4 is less than 6, you need to borrow 1 from the digit to the left, making the 2 into a 1 and adding 10 to the 4, giving you 14. So, 14 minus 6 equals 8.

Continue subtracting each digit in the same way:

   320.041

-   47.960

= 272.081

Therefore, 320.041 minus 47.96 is equal to 272.081.

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Answer:

x = 4/5

Step-by-step explanation: