Jerome deposits $3,700 in a certificate of deposit that pays 1.8% interest, compounded
annually. How much interest does Jerome earn in 1 year?

Answer:

He is going need to buy 2 packs of blue sticks and 3 packs of red packs

Step-by-step explanation:

Answer:

LCM = 24

Step-by-step explanation:

The multiples of 8 are: 8, 16, 24, 32, 40, … .

The multiples of 12 are: 12, 24, 36, 48, 60, … .

Answer:

false

Step-by-step explanation:

The probability that by the time the sum has been even three times, the sum has already been 7 twice is 1/36.

This is because the total number of possible combinations of two dice is 36, and only one combination, (3,4), has the sum of 7 and is also an even number.

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The solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

To simplify the equation 3(x-6) - 1/2(8x+10) = -25, we can start by applying the distributive property and then combining like terms.

First, let's distribute the 3 and the -1/2 to the terms inside the parentheses:

3(x-6) - 1/2(8x+10) = 3x - 18 - (4x + 5)

Now, let's simplify further by combining like terms:

3x - 18 - 4x - 5 = -x - 23

So, the simplified equation is -x - 23 = -25.

To solve for x, we can isolate the variable by adding 23 to both sides of the equation:

-x - 23 + 23 = -25 + 23

This simplifies to:

-x = -2

Finally, we can solve for x by multiplying both sides of the equation by -1:

(-1)(-x) = (-1)(-2)

This gives us:

x = 2

Therefore, the solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

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The value of  ∠EBD is 66°

Vertical angles are a pair of opposite angles formed by intersecting lines. Vertical angles are equal. Therefore,

∠EBA≅∠CBF

Therefore,

∠EBA = 40 - x

∠EBA  + ∠EBD = 90°(complementary angles)

Therefore,

40 - x + 6x - 30 = 90

5x = 90 + 30 - 40

5x = 80

x = 80 / 5

x = 16

Therefore,

∠EBD = 6(16) - 30 =  66°

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The given statement "the probability of an earth-impacting asteroid causing a person's death" is empirical probability, which is based on observations and data.

Empirical probability, also known as experimental probability, is based on observations or data. It involves collecting data through repeated trials of an experiment and calculating the probability of an event based on the frequency of its occurrence.

Subjective probability, also known as personal probability, is based on personal judgment or belief. It reflects an individual's degree of belief in the likelihood of an event occurring, based on their own knowledge and experience.

Now, let's classify the statement in the prompt. The statement is "the probability of an earth-impacting asteroid causing a person's death is." We can see that the statement does not specify which type of probability is being used.

In conclusion, probability is a crucial concept in mathematics and science, and there are different types of probability, including classical, empirical, and subjective probability.

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The need to survey 26,304 freshmen to cut the margin of error in half.

a) To cut the stated margin of error in half, the sample size must be quadrupled.

The formula for the margin of error in a proportion is:

Margin of error = z* (sqrt(p*q/n))

where z is the z-score corresponding to the desired level of confidence, p is the proportion of interest (74% in this case), q = 1-p, and n is the sample size.

If we want to cut the margin of error in half, we need to solve the equation above for n, keeping all other variables constant.

Assuming a 95% confidence level and the proportions observed in the original study, we have:

Margin of error = 1.96 * sqrt(0.74 * 0.26/n)

If we want to cut the margin of error in half, we need to solve for n in the following equation:

1.96 * sqrt(0.74 * 0.26/n) = 1.96 * sqrt(0.74 * 0.26/4n)

Simplifying this equation, we get:

n = 16*1644=26,304

Therefore, we would need to survey 26,304 freshmen to cut the margin of error in half.

b) Yes, there are some concerns about this sample. Quadrupling the sample size will increase the precision of the estimate, but it may also increase the cost and the potential for nonresponse bias or other sources of error. Moreover, the original study was already stratified by type of college, which suggests that ACT, Inc. may be interested in analyzing the data at this level of disaggregation. In that case, a sample of 26,304 students may not be feasible or necessary. Finally, it's important to consider the representativeness of the sample and potential sources of bias, such as the sampling method, the response rate, or the exclusion of certain types of colleges or students.

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There are 6,561 integers between 1 and 10,000 inclusive that are divisible by at least one of 3, 5, 7, or 11.

We can solve this problem using the inclusion-exclusion principle.

First, we find the number of integers between 1 and 10,000 inclusive that are divisible by each of the four prime numbers 3, 5, 7, and 11.

-The number of integers divisible by 3 is 3333 (since 3, 6, 9, ..., 9999 are divisible by 3).

-The number of integers divisible by 5 is 2000 (since 5, 10, 15, ..., 10000 are divisible by 5).

-The number of integers divisible by 7 is 1428 (since 7, 14, 21, ..., 9999 are divisible by 7).

-The number of integers divisible by 11 is 909 (since 11, 22, 33, ..., 9999 are divisible by 11).

Next, we need to subtract the number of integers that are divisible by each pair of the four prime numbers, because we have counted them twice.

-The number of integers divisible by both 3 and 5 is 666 (since 15, 30, 45, ..., 10005 are divisible by both 3 and 5).

-The number of integers divisible by both 3 and 7 is 476 (since 21, 42, 63, ..., 10017 are divisible by both 3 and 7).

-The number of integers divisible by both 3 and 11 is 303 (since 33, 66, 99, ..., 9999 are divisible by both 3 and 11).

-The number of integers divisible by both 5 and 7 is 285 (since 35, 70, 105, ..., 10010 are divisible by both 5 and 7).

-The number of integers divisible by both 5 and 11 is 181 (since 55, 110, 165, ..., 9995 are divisible by both 5 and 11).

-The number of integers divisible by both 7 and 11 is 136 (since 77, 154, 231, ..., 9944 are divisible by both 7 and 11).

Finally, we need to add back the number of integers that are divisible by all four prime numbers, because we have subtracted them three times and added them back once.

The number of integers divisible by 3, 5, 7, and 11 is 45 (since 3 x 5 x 7 x 11 = 1155, and the multiples of 1155 between 1 and 10000 are divisible by all four prime numbers).

Using the inclusion-exclusion principle, the number of integers between 1 and 10,000 inclusive that are divisible by at least one of 3, 5, 7, or 11 is:

3333 + 2000 + 1428 + 909 - 666 - 476 - 303 - 285 - 181 - 136 + 45 = 6561

Therefore, there are 6,561 integers between 1 and 10,000 inclusive that are divisible by at least one of 3, 5, 7, or 11.

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The Original price of the item  was $400.

Percentage can be defined as a number that denotes hundredth part of any quantity.

For Example , 50%of 30 =\(\frac{50}{100} *30=\frac{1500}{100} =15\).

In the given question

Amount paid by Joyce = $120

Let the original price =x

Percent of original price = 30%

According to the given Question

30% of x =120

\(\frac{30}{100} *x=120\\ \\ x=\frac{120*100}{30}\\ \\ \\ x=400\)

Therefore , the Original price of the item  was $400.

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Answer:

2x^3

Step-by-step explanation:

18 divided by 9 is 2

6 divided 2by 2 is 3

Answer:

\( {2 {? \times \frac{?}{?} }^{2} }^{2} \)

The value of the test statistic used to test the claim is -2.00.

And, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

Now, If a two-sided test of hypothesis is conducted at a 0.05 level of significance and the test statistic resulting from the analysis was 1.23, the potential type of statistical error is Type II error.

A Type II error occurs when we fail to reject a false null hypothesis, meaning that we conclude there is no significant difference or effect when there actually is one.

To answer the second question, we can perform a one-sample t-test to test the claim that the mean GPA for Psychology students at a certain college is less than 3.2.

The hypotheses are:

H₀: μ = 3.2

Ha: μ < 3.2

where μ is the population mean GPA.

We can use the t-statistic formula to calculate the test statistic:

t = (x - μ) / (s / √n)

where, x is the sample mean GPA, s is the sample standard deviation, n is the sample size, and μ is the hypothesized population mean.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

Therefore, the value of the test statistic used to test the claim is -2.00.

Since this is a one-tailed test with a significance level of 0.05, we compare the t-statistic to the critical t-value from a t-table with 48 degrees of freedom.

At a significance level of 0.05 and 48 degrees of freedom, the critical t-value is -1.677.

Since the calculated t-statistic (-2.00) is less than the critical t-value (-1.677), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean GPA for Psychology students at the college is less than 3.2.

To calculate the p-value of the test, we can perform a one-sample t-test using the formula:

t = (x - μ) / (s / √n)

where x is the sample mean GPA, μ is the hypothesized population mean GPA, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

The degrees of freedom for this test is 49 - 1 = 48.

Using a t-distribution table or calculator, we can find the probability of getting a t-value as extreme as -2.00 or more extreme under the null hypothesis.

Since this is a two-sided test, we need to find the area in both tails beyond |t| = 2.00. The p-value is the sum of these two areas.

Looking up the t-distribution table with 48 degrees of freedom, we find that the area beyond -2.00 is 0.0257, and the area beyond 2.00 is also 0.0257. So the p-value is:

p-value = 0.0257 + 0.0257

p-value = 0.0514

Rounding to three decimal places, the p-value of the test is 0.051.

Therefore, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

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Answer:

the greatest number I guess is 2

Step-by-step explanation:

18÷2= 9male to the 2group

24÷2=12female to the 2group

Answer:

1/8

Step-by-step explanation:

So if the entire recipe makes 7 loaves and calls for 7/8 of a cup, you would need to split the 7/8 cups flour into 7. 7/8 ÷ 7=1/8.

Option A: 1/8 of a cup

Answer:

X-Y=-3

Step-by-step explanation:

The height of the oak tree in front of Igor's castle is approximately 57.27 ft. To find the height of the oak tree, we can use the principle of similar triangles.

The height of the tree can be determined by comparing the ratio of the height of Igor to the distance between Igor and the mirror with the ratio of the height of the tree to the distance between the mirror and the tree.

Let's represent the height of the oak tree as 'h'. According to the problem, Igor's eye height is 4.5 ft, and he is 5.5 ft away from the center of the mirror. The mirror is placed 70 ft from the tree.

Using the similar triangles concept, we can set up the following proportion:

(height of Igor) / (distance between Igor and mirror) = (height of tree) / (distance between mirror and tree)

Plugging in the given values, we have:

4.5 ft / 5.5 ft = h / 70 ft

Solving this proportion, we find:

(4.5 ft * 70 ft) / 5.5 ft = h.

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The given number is

The scientific notation of the number is,

Ms. Wilson is paid $1728.97 every 2 weeks.

To find her annual salary, first, you have to calculate her monthly salary.

Each month has two payments, so you have to multiply her bi-weekly salary by 2:

Her monthly income is $3451.82

To determine her annual income you have to multiply her monthly income by 12

Her annual salary is $41493.84

Answer:

not D

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer: the answer is B. Cookies and cream/ mint chocolate chip

Step-by-step explanation:

The ice cream shop should choose option (D) Mint chocolate chip when it sells its products at the local grocery shop.

The “pie chart” is also known as a “circle chart”, dividing the circular statistical graphic into sectors or sections to illustrate the numerical problems. Each sector denotes a proportionate part of the whole.

Given a Pie chart reflecting the favorite choices of the consumers, when asked during a survey covering around 25 people.

Now, in order to produce the highest profit and the highest consumer numbers when selling its products, the ice cream shop should have to consider the results of the survey while setting up its business. The product which was the favorite of the majority of the people in the survey, will tend to take the first spot while deciding what to sell.

As the pie chart clearly shows that the Mint Chocolate Chip is the favorite of the majority of the people participating in the survey, the ice cream shop should sell its mint chocolate chip in the local grocery shops.

Hence, the ice cream shop should choose option (D) Mint chocolate chip when it sells its products at the local grocery shop.

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Point G is a circumcenter, then the x = 37.5 where G is (2x + 15)°.

Point G is a circumcenter.

The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcenter. It is denoted by P(X, Y).

We can see image,

Then,

(2x + 15)° = 90°

2x + 15 = 90

2x = 90 - 15

We can sum or difference of products,

2x = 75

x = 75/2

We can divide the products,

x = 37.5

Therefore,

Point G is a circumcenter, then the x = 37.5 where G is (2x + 15)°.

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a) The average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. b) The estimated coefficients of REDS and TRAINS in the regression model are 1.3353 (REDS). c) The absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis.

a) To find the average estimated time in minutes for Bill to drive to work when he leaves on time at 6:30 and there are no red lights and no trains at the crossroad to wait, we substitute the values into the regression model:

TIME = -19.9166 + 0.3692(DEPART) + 1.3353(REDS) + 2.7548(TRAINS)

Given:

DEPART = 0 (as he leaves on time at 6:30)

REDS = 0 (no red lights)

TRAINS = 0 (no trains to wait for)

Substituting these values:

TIME = -19.9166 + 0.3692(0) + 1.3353(0) + 2.7548(0)

    = -19.9166

Therefore, the average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. However, it's important to note that negative values in this context may not make practical sense, so we should interpret this as Bill arriving approximately 19.92 minutes early to work.

b) The estimated coefficients of REDS and TRAINS in the regression model are:

1.3353 (REDS)

2.7548 (TRAINS)

Interpreting the coefficients:

- The coefficient of REDS (1.3353) suggests that for each additional red light, the estimated time to drive to work increases by approximately 1.3353 minutes, holding all other factors constant.

- The coefficient of TRAINS (2.7548) suggests that for each additional train Bill has to wait for at the crossing, the estimated time to drive to work increases by approximately 2.7548 minutes, holding all other factors constant.

c) To test the hypothesis that each train delays Bill by 3 minutes, we can conduct a hypothesis test.

Null hypothesis (H0): The coefficient of TRAINS is equal to 3 minutes.

Alternative hypothesis (Ha): The coefficient of TRAINS is not equal to 3 minutes.

We can use the t-test to test this hypothesis. The t-value is calculated as:

t-value = (coefficient of TRAINS - hypothesized value) / standard error of coefficient of TRAINS

Given:

Coefficient of TRAINS = 2.7548

Hypothesized value = 3

Standard error of coefficient of TRAINS = 0.1390

t-value = (2.7548 - 3) / 0.1390

       = -0.2465 / 0.1390

       ≈ -1.7733

Using a significance level of 5% (or alpha = 0.05) and looking up the critical value for a two-tailed test, the critical t-value for 230 degrees of freedom is approximately ±1.9719.

Since the absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that each train delays Bill by 3 minutes.

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The correct statements about given synthetic division are C, D, and F

"It is a polynomial with degree 2."

"It is defined as a way of dividing one polynomial by another polynomial of first degree."

For given question,

We have been given a quadratic polynomial \(F(x)=4x^{2} -17x-15\)

We can factorize above quadratic polynomial as,

\(F(x)\\=4x^{2} -17x-15\\=4x^{2} -20x+3x-15\\=4x(x-5)+3(x-5)\\=(x-5)(4x+3)\)

This means the factors of \(4x^{2} -17x-15\) are (x - 5) (4x + 3)

And the roots of the polynomial would be,

\(\Rightarrow F(x)=0\\\Rightarrow 4x^{2} -17x-15=0\\\Rightarrow (x-5)(4x+3)=0\\\Rightarrow x-5=0~~,~~4x+3=0\\\Rightarrow x=5~~,~~x=-\frac{3}{4}\)

This means, the roots of \(4x^{2} -17x-15\) are 5 and \(\frac{-3}{4}\)

Therefore, the correct statements about given synthetic division are C, D, and F

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Answer:

x = 19 and if that is wrong then it might be 5x = 85 but i am 98% sure it is x=19

Answer:

x = 19

Step-by-step explanation:

5 x 19 = 95

95 - 5 = 90

The given statement can be formulated as follows: A batch of 150 iPads is inspected by choosing a sample of four iPads. Eight of the 150 iPads do not conform to specifications.

How many samples of four contain exactly one non-conforming iPad?

Let's solve the given problem step by step.

Step 1: We have 8 non-conforming iPads and 142 conforming iPads in the batch of 150 iPads. We need to find the number of ways to choose 4 iPads that include exactly one non-conforming iPad.

Step 2: We choose one non-conforming iPad in 8 ways and choose 3 conforming iPads in 142C3 ways, where nCk is the number of ways to choose k objects from n distinct objects without regard to order.

Thus the total number of ways to choose 4 iPads with exactly one non-conforming iPad is given by:

=8 × 142C3

\(8 \times \frac{142 \times 141 \times 140}{3 \times 2 \times 1}\)

= 2,107,280

Therefore, there are 2,107,280 samples of four that contain exactly one non-conforming iPad.

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The distance between  the following case in the Angels house are,

Bottom of the ladder to the house = 2.5ft.

Top of the ladder placed against the wall to the ground = 9.683ft.

Wall of the house is perpendicular to the ground.

Ladder placed against the wall forms a right angle triangle.

In the figure of Sarah house,

Height of the wall from where ladder is placed = 11.62ft

length of the ladder = 12 ft

Distance between foot of the ladder to the house = 3ft

Now, length of the ladder placed by Angel = 10ft

Angle formed against the wall is equal .

Let the angle be α.

let the distance between Angle's ladder and house be 'x' ft.

sinα = x / 10  ___(1)

In case of Sarah's house

sinα = 3ft / 12 ft __(2)

From (1) and (2) we have,

x/ 10 = 3 / 12

⇒ x = ( 1/4) × 10

⇒ x = 2.5 ft

let the distance from the top of the ladder to the ground be y.

In Angels house

cosα = y / 10____(3)

In Sarah's house

cosα = 11.62 /12 ____(4)

From (3) and (4) we have,

y/10 = 11.62/12

⇒ y = ( 11.62 / 12) × 10

⇒ y = 9.683 ft

Therefore, in Angels house the distance between ,

Foot of the ladder to the bottom of the house = 2.5ft.

Top of the ladder to the ground = 9.683ft.

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Step-by-step explanation:

9x+6x=135

15x=135

x=9

9x=81

6x=54

Answer:

q 3 = 3/12.2/9 q4 = 15/40.14/39

Based on the given information, we know that the arrival rate is 9 customers per hour and the service rate is 14 customers per hour. Since the arrival and service distributions are not known, we cannot use the m/m/1 formulas to calculate the average waiting time and total time spent in the system.

However, we can still use the Little's Law formula to relate the average number of customers in the system to the average waiting time. Little's Law states that the average number of customers in the system (N) is equal to the product of the arrival rate (λ) and the average time spent in the system (T), or N = λT.

Since we want to find the total time spent in the system, we can rearrange the formula to solve for T. Thus, T = N / λ.

We know from the given information that the average waiting time in the line is 18 minutes. Therefore, the average time spent in the system for a customer is T = 18 minutes + (1/14 hour), which is equal to 1.9 hours.

To calculate the total time spent in the system, we need to add the waiting time to the service time. Since the service rate is 14 customers per hour, the service time per customer is 1/14 hour or approximately 4.3 minutes. Thus, the total time spent in the system is approximately 22.3 minutes or 0.37 hours.

In summary, the average time spent in the system for a customer is 1.9 hours, and the total time spent in the system is approximately 22.3 minutes or 0.37 hours.

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Answer:

She earns $0.65 per paper

Step-by-step explanation:

1. She earns $3.90 per 6 papers

2. take $3.90 and divide by 6.

3. you will get the cost per paper.

4. to check the work if you'd like then take 7.80 and divide it by 12 and again you will get $0.65 per paper.

(you don't need to find a special calculator you can use one on your phone since each dollar has 100 cents so you just need to go out to the hundredths place in a decimal or the second decimal place)