Write and solve a system of equations representing the following number puzzle. The sum of two numbers is 11. Four times the first number is 2 more than two times the second number. When you've found the two numbers, enter the value of the larger number as your answer

Answer:

4 to power of 3 in expanded form is 4 x 4 x 4.

HOPE THIS HELPS :)

The part of marketing copy that asks the audience to do something with the information you've just provided is known as call to action. Option B

Marketing copy can be defined as a content that is written to boost sales or to promote a product or service and also to persuade the readers to take a certain actions.

It is an important tool that is used to educate customers, and it provides the resources and contact details information to help various businesses increase the awareness of their products and services.

Call-to-action can be defined as the part of an advertisement or content that encourages the audience to do something.

In marketing, it help in converting a reader or visitor to a lead for the business sales team.

It also drives other marketing actions depending on the content's goal.

Hence, the marketing copy is call-to-action

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Answer:

Step-by-step explanation: B

the approximate amount in the account after eight years, with monthly compounding at a 6% interest rate, is $18,377.79.

To calculate the amount in the savings account if the interest is compounded monthly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal (initial investment)

r is the annual interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the number of years

In this case:

P = $12,500

r = 6% = 0.06 (decimal form)

n = 12 (monthly compounding)

t = 8 years

Plugging in these values into the formula:

A = 12500(1 + 0.06/12)^(12*8)

Simplifying the expression:

A = 12500(1 + 0.005)^(96)

A = 12500(1.005)^(96)

Using a calculator, we can evaluate this expression to find the final amount in the savings account. The result may vary slightly depending on rounding, but the approximate value will be:

A ≈ $18,377.79

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Answer:

Producer's surplus = (1/2) x (2) x (10) = 10

Step-by-step explanation:

To find the producer's surplus, we need to first determine the equilibrium quantity and price at which the supply and demand functions intersect.

Setting the supply function S(x) equal to the demand function D(x) and solving for x, we get:

4x + 2 = 14 - x^2

Rearranging and simplifying, we get a quadratic equation in standard form:

x^2 + 4x - 12 = 0

Using the quadratic formula, we get:

x = (-4 ± √(4^2 - 4(1)(-12))) / (2(1))

x = (-4 ± √64) / 2

x = -2 ± 4

x = -6 or x = 2

Since we're interested in a positive quantity, we'll take x = 2 as the equilibrium quantity.

To find the equilibrium price, we substitute x = 2 into either the supply or demand function:

D(2) = 14 - 2^2 = 10

So the equilibrium price is P = 10.

The producer's surplus is the area above the supply curve and below the equilibrium price. Since the supply function is linear, we can find the producer's surplus by calculating the area of a triangle with base x = 2 and height S(2) = 10:

Producer's surplus = (1/2) x (2) x (10) = 10

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Answer:

120

Step-by-step explanation:

Pretend to rubber-band TEA together so it counts as one letter. The problem then becomes: How many ways can you rearrange 5 letters (M, I, L, K, TEA)? To solve that, it's 5! or 120 ways. I hope this is correct and it helps! :)

Answer:

5

Step-by-step explanation:

Answer:

B. 6

Step-by-step explanation:

50 times 3/5 = 150/5 = 30

30 times 4/5 = 120/5 = 24

24 times 1/4 = 24/4 = 6

Answer:

992

Step-by-step explanation:

1. 800/1 x 6/100 = 48 x 4 = 192 +800 = 992

2. 6 x 4 =24

800/1 x 24/100 = 192 + 800 = 992

The correct option is (a).

The numbers are statistics.

Explanation: Statistics are measures or characteristics calculated from a sample, while parameters are measures or characteristics calculated from the entire population. In this case, the survey collected data from a random sample of 100 students, so the mean number of semester units (10.2) and the standard deviation (3) are statistics because they are calculated from the sample of students and not from the entire population of students.

(b) The mean number of semester units is represented by the symbol (x-bar), and the standard deviation is represented by the symbol s.

Therefore, the correct answer is A. The numbers are statistics because they are for a sample of students, not all students.

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At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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The learning rate in gradient descent determines the step size and should be not too small or too large, as it can cause the algorithm to converge slowly or overshoot the minimum; adjusting the value of the learning rate can fix the problem, but the optimal value depends on the problem and data set.

According to the given information:

When running gradient descent,

The learning rate α determines the step size taken in each iteration toward the optimal solution.

If α is too small, the algorithm will take small steps and will converge slowly, or may even get stuck in a local minimum.

If α is too large, the algorithm may overshoot the minimum and diverge, or bounce back and forth without converging.

In the scenario described, the learning rate α of 0.5 appears too large, causing J(θ) to increase over time.

This suggests that the algorithm is not converging and is overshooting the minimum.

To fix this,
The value of α can be adjusted by reducing it to a smaller value,

Such as 0.1 or 0.01.

This should allow the algorithm to take smaller steps towards the minimum and eventually converge to a lower value of J(θ).

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Answer:

y=720

Step-by-step explanation:

Multiply both sides of the equation by −15.

−675+1y=45

Add 675 to both sides.

1y=45+675

1y=720

--   -----

1      1

y=720

Answer: The total number of sweets in the 10th bag is 53 and this can be determined by using the formula of the mean.

Given :

The total number of bags is 10.

The mean number of sweets in the bags is 42.

The table shows how many sweets there are in 9 of the bags.

The following steps can be used in order to determine the total number of sweets in the 10th bag:

Step 1 - The formula of the mean can be used in order to determine the total number of sweets in the 10th bag.

Step 2 - The formula of mean is given below:

Step 3 - Now, substitute the values of the known terms from the given table in the above expression.

Step 4 - Simplify the above expression.

So, the total number of sweets in the 10th bag is 53.

Step-by-step explanation:

The required answer is the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.

Explanation:-

a. Economic order quantity (EOQ) is defined as the optimal quantity of inventory to be ordered each time to reduce the total annual inventory costs.

It is calculated as follows: EOQ = sqrt(2DS/H)

Where, D = Annual demand = 100 x 52 = 5200S = Order cost = $57 per order H = Annual holding cost = 0.30 x 10.75 = $3.23 per bag per year .Therefore, EOQ = sqrt(2 x 5200 x 57 / 3.23) = 234 bags. The average time between orders (TBO) can be calculated using the formula: TBO = EOQ / D = 234 / 100 = 2.34 weeks ≈ 2 weeks (rounded to nearest whole number).

Hence, the EOQ is 234 bags and the average time between orders is 2 weeks (approx).b. R is the reorder point, which is the inventory level at which an order should be placed to avoid a stockout.

It can be calculated using the formula:R = dL + zσL

Where,d = Demand per day = 100 / 5 = 20L = Lead time = 1 week (5 working days) = 5 day

z = z-value for 92% cycle-service level = 1.75 (from standard normal table)σL = Standard deviation of lead time demand = σ / sqrt(L) = 16 / sqrt(5) = 7.14 (approx)

Therefore,R = 20 x 5 + 1.75 x 7.14 = 119.2 ≈ 120 bags

Hence, the reorder point R should be 120 bags.c. An inventory withdraw of 10 bags was just made. Is it time to reorder?The current inventory level is 310 bags, which is greater than the reorder point of 120 bags. Since there are no open orders or backorders, it is not time to reorder.d. The store currently uses a lot size of 500 bags (i.e., Q = 500).What is the annual holding cost of this policy.

Annual ordering cost. Without calculating the EOQ, how can you conclude the lot size is too large?Annual ordering cost = (D / Q) x S = (5200 / 500) x 57 = $592.80 per year.

Annual holding cost = Q / 2 x H = 500 / 2 x 0.30 x 10.75 = $806.25 per year. Total annual inventory cost = Annual ordering cost + Annual holding cost= $592.80 + $806.25 = $1,399.05Without calculating the EOQ, we can conclude that the lot size is too large if the annual holding cost exceeds the annual ordering cost.

In this case, the annual holding cost of $806.25 is greater than the annual ordering cost of $592.80, indicating that the lot size of 500 bags is too large.e.

The annual cost saved by shifting from the 500-bag lot size to the EOQ can be calculated as follows:Total cost at Q = 500 bags = $1,399.05Total cost at Q = EOQ = Annual ordering cost + Annual holding cost= (D / EOQ) x S + EOQ / 2 x H= (5200 / 234) x 57 + 234 / 2 x 0.30 x 10.75= $245.45 + $93.68= $339.13

Annual cost saved = Total cost at Q = 500 bags - Total cost at Q = EOQ= $1,399.05 - $339.13= $1,059.92

Hence, the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.

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a. The number of teenagers that like hard rock is of: 272.

b. The number of teenagers surveyed is of: 200.

c. A percentage greater than 100% is when the percentage of an amount is calculated relative to an smaller amount.

The measures are obtained applying the given proportions and percentages in the context of the problem.

For item a, the amount is of 32% of 850, hence:

0.32 x 850 = 272 teenagers like hard rock.

For item b, we have that 75% = 0.75 of the amount x is of 150, hence the total amount of teenagers surveyed is obtained as follows:

0.75x = 150

x = 150/0.75

x = 200 teenagers were surveyed.

A percentage is calculated as the division of an amount a by an amount b. Hence, if the amount a is greater than the amount b, the percentage will be greater than 100%.

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Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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Answer:

Juanita and Esperanza run 400 meters and 8400 meters respectively and Evelyn make 4.125 laps.

Step-by-step explanation:

The complete question is: A telesecundaria school has a race track that measures one kilometer .

Three students ran the following distances Juanita: 1 laps, Esperanza  21 laps and Evelyn: 1650 m. How many meters did Juanita and Esperanza run?  And how many laps did Evelyn make?

As we know that 1 meter = 0.0025 laps

So, the number of laps Evelyn make = 1650 \(\times\) 0.0025

                                                             = 4.125 laps

Also, 1 lap = \(\frac{1}{0.0025}\) meters

        1 lap = 400 meters

So, the meters that Juanita run = 1 \(\times\) 400 = 400 meters

Similarly, the meters that Esperanza run = 21 \(\times\) 400

                                                                   = 8400 meters

Hence, Juanita and Esperanza run 400 meters and 8400 meters respectively and Evelyn make 4.125 laps.

Answer:

3  3.14  \(\pi\)  3.142  22/7

Recall that the volume of a cube equals (side)^3. We can create an equation to model this.

1728 in^3 = (side)^3

We can get the cube root of both sides.

12 in = side

Each side is 12 inches long.

Answer:

f[g(1)]=6.

Explanation:

Given f(n) and g(n) defined below:

First, we evaluate g(1):

Therefore:

Therefore, f[g(1)]=6.

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them. So the monthly charge for Danielle's cable bill is $5.

Danielle pays a monthly charge of $69 for her cable bill.

She also pays a fee every time she watches a movie on demand.

Last month Danielle watched 7 movies on demand, and her total monthly bill was $104.

We have to find the monthly charge for Danielle's cable bill to choose.

Remove the monthly fee of 69 dollars for cable service from the total of 104 dollars, then check the statement to see that there is still a mystifying 35 dollars on it.

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them, giving you the result of $5 per on-demand movie.

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The target population is the population of interest that researchers aim to generalize their findings to.

The correct answer is c. sample.

In a research study, the population of interest is often too large or too difficult to access entirely. Therefore, researchers select a representative subset of the population to study, which is called a sample. In this case, patients with inflammatory bowel disease are the population of interest, and those who participate in the study are the sample.

The accessible population refers to the portion of the population that is accessible to the researcher. For example, if a researcher is studying the prevalence of a disease in a certain region, the accessible population would be the individuals living in that region.

An element refers to a single member of the population or sample.

The target population is the population of interest that researchers aim to generalize their findings to.

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Answer:

x = 6

Step-by-step explanation:

Given

\(\frac{4}{3}\) = \(\frac{8}{x}\) ( cross- multiply )

4x = 24 ( divide both sides by 4 )

x = 6

Answer:

Therefore, based on the given scatter plot, the set of numbers that matches the points is C. 8,9,8,10,8,11.

Step-by-step explanation:

The scatter plot shown represents a set of nine points on a coordinate plane. Each point consists of an x-coordinate and a y-coordinate. To determine which set of numbers corresponds to the scatter plot, we need to analyze the pattern in the given points.

Looking at the scatter plot, we observe that the x-coordinates range from 0 to 10 with an increment of 1, while the y-coordinates seem to vary.

Now let's examine the given answer choices:

A. .4,4,5,5,6,6

B. .4,10,4,11,4,12

C. 8,9,8,10,8,11

D. 10,10,10,11,10,12

Set C (8,9,8,10,8,11) among these answer choices matches the pattern observed in the scatter plot. The x-coordinates in the scatter plot range from 0 to 10, and the y-coordinates correspond to the numbers provided in set C.

Therefore, based on the given scatter plot, the set of numbers that matches the points is C.

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The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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Answer:

The solution of the equation    y = 36

Step-by-step explanation:

Explanation:-

Given equation -3x-y =-51

Given that x =15 in equation -3x-y=-51

                 ⇒        - 3(15) - y = -51

                ⇒         - 15 - y =-51

                 ⇒         -15+ 51 = y

               ⇒            y = 36

Answer:

Step-by-step explanation:

Given,

Number of words Lucy can type in 5 minutes

= 300 words

So,

Number of words Lucy can type in 1 minute

\( = \frac{300}{5} \: words\)

= 60 words

Therefore,

Number of words Lucy can type in 27 minutes

= (60 × 27) words

= 1,620 words

Hence, Lucy can type 1620 words in 27 minutes.

Answer:

x=60 degrees

Step-by-step explanation:

The sum of angles in a triangle is 180 so if all angles in the triangle are equal, you just do 180 divided by 3 to get 60.