15. A savings account earns interest. The account initially had $1,500 deposited in it. The worth of the account

after t-years can be calculated using the formula:

A(t)=1500e^0.3r

So, on solving the question we can say that the **linear equation **A(t)=1500e^0.3r = A(t) = 1232

A linear equation is one that has the form y=mx+b in **algebra**. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two **variables**" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

A(t)=1500e^0.3r

the linear equation

A(t) = 1232

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Which factor of 24 can help you solve 24 divided by 4?

**Answer:**

im an expert

**Step-by-step explanation:**

ABCD is a rectangle. If AC is 20 inches, what is DE?

B

Al

E

C

D

The **measurement **of DE is 10 inches.

If we know that E is the **point **where the diagonals of the **rectangle **intersect, then we know that DE is equal to half the length of the diagonal BD.

Using the **Pythagorean** **theorem**, we can relate the length of the diagonal** **BD to the sides of the rectangle.

Let's assume that the length of the **rectangle **is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:

BD = √(L^2 + W^2)

Since we know that the **diagonals **of a rectangle are **equal**, we have:

AC = BD

BD = 20

Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.

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A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 13.2 inches and standard deviation of 2.3 inches. If a sample of 37 items are chosen at random, what is the probability the sample's mean length is greater than 12.1 inches? Round answer to four decimal places.

The **probability** that the sample's** mean** length is greater than 6.3 inches is0.8446.

Here, we have,

Given** mean** of 6.5 inches, **standard deviation** of 0.5 inches and sample size of 46.

We have to calculate the** probability** that the sample's **mean** length is greater than 6.3 inches is 0.8446.

**Probability** is the likeliness of happening an event.

It lies between 0 and 1.

**Probability **is the number of items divided by the total number of items.

We have to use z statistic in this question because the sample size is greater than 30.

μ=6.5

σ=0.5

n=46

z=X-μ/σ

where μ is **mean** and

σ is** standard deviation**.

First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required** probability**.

z=6.3-6.5/0.5

=-0.2/0.5

=-0.4

p value from z table is 0.3446

**Probability** that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.

Hence the **probability** that the mean length is greater than 6.3 inches is 0.8446.

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A golf ball rolls at a speed of 8 m/s for 12 seconds. Mandy hits the golf ball and it rolls

for 16 seconds at a speed of 12 m/s. What is the total distance travelled by the golf ball?

Using the given information, the **total distance travelled **by the golf ball is 288 m

From the question, we are to calculate the **total distance travelled **by the golf ball

The distance travelled by the golf ball can be calculated by using the formula,

Distance = Speed × Time

From the given information,

The golf ball rolls at a speed of 8 m/s for 12 seconds

Thus,

The distance travelled at this time is

Distance = 8 m/s × 12 s

Distance = 96 m

Also,

Mandy hits the golf ball and it rolls for 16 seconds at a speed of 12 m/s

The distance travelled at this time is

Distance = 12 m/s × 16 s

Distance = 192 m

The total distance travelled by the golf ball is 96 m + 192 m

=

Hence, the **total distance travelled** by the golf ball is 288 m

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The figure below shows the distance between two cities on a map. The scale of the map is 1 }8 inch to 12 miles.

The** actual distance **between the two cities is 432 miles.

The figure shows a map of two cities, with a distance between them measured at 4.5 inches.

The **scale **of the **map **is given as 1/8 inch to 12 miles.

This means that 1/8 inch on the map represents a distance of 12 miles in real life.

To determine the actual distance between the **two cities**, we can use the scale provided.

1/8 inch on the map represents 12 miles in real life.

A proportion to find the actual distance between the cities:

1/8 inch on map = 12 miles in real life

4.5 inches on map = x miles in real life

To solve for x, we can cross-multiply and simplify:

1/8 × x = 12 × 4.5

x = 12 × 4.5 × 8

x = 432 miles

Maps with scales can be useful for determining distances, sizes, and proportions of objects in real life.

It allows us to visually represent complex spatial relationships and make measurements without physically being present at the location.

Remember to use the correct scale and make sure to convert units properly in order to accurately determine **real-life** measurements.

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1459 divided by 6 with remainder as fraction

**Answer:**

6 1/243

**Step-by-step explanation:**

6 goes into 1459, 243 times

243*6=1458

1459-1458=1

So there is a remainder of 1

So the answer would be 6 1/243

1459 divided by 6 equals 243.166666667

This as a fraction is also 1459/6.

This with a remainder is 1459 R1

Hope this helps :D

This as a fraction is also 1459/6.

This with a remainder is 1459 R1

Hope this helps :D

help me please!! I’m not quite sure how to solve this so explanations for this will be appreciated

The solution is:

the** area **of this figure is 21.9 ft².

Here, we have,

To find the** area** of this figure, we must find the area of the 6 x 6 square and subtract the area of a semi-circle with a diameter of 6.

**Area **square:

6 x 6

36

**Area **semi-circe:

A = 1/2(πr²)

A = 1/2(6/2)²π

A = 1/2(9π)

A = 14.1

**Area **shape:

36 - 14.1

21.9

The units are ft², so the answer is 21.9 ft².

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Gavin is working two summer jobs making $14 per hour tutoring and $13 per hour landscaping. Last week Gavin worked a total of 10 hours and earned a total of $137. Determine the number of hours Gavin worked tutoring last week and the number of hours he worked landscaping last week.

**Answer:**

3 landscaping, 3 tutoring

**Step-by-step explanation:**

This is a system of equations.

Let T = number hours tutoring and L = number hours landscaping.

T + L = 10

137 = 14T + 13L

Now solve the system of equations.

We can rearrange the first equation so that T = 10-L. Substitute that in the 2nd equation.

137=14(10-L) + 13L

137 = 140-14L + 13L

-3=-L

3=L

He worked 3 Landscaping Hours. Substitute back into the original equation to solve for T (tutoring hours).

T+L = 10

T+3 = 10

T = 7.

We worked 7 tutoring hours.

Now double check with the earnings equation.

137 = 14T + 13L

137 = 14*7+ 13*3

137 = 98 + 39

137=137

URGENT HELP PLEASE!!!

In a class of students, the following data table summarizes how many students have a

a

cat or a dog. What is the probability that a student chosen randomly from the class

has a cat and a dog?

**Answer: 5/13**

**Step-by-step explanation:**

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

P(A|B) = P(A and B) / P(B)

where P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

Let's first calculate the total number of people in the class:

Total number of people = 5 + 6 + 2 + 11 = 24

Now, let's calculate the probability of having a cat and a dog:

P(cat and dog) = 5 / 24

Next, let's calculate the probability of having a cat:

P(cat) = (5 + 6 + 2) / 24 = 13 / 24

Finally, let's calculate the probability of having no dog:

P(no dog) = (6 + 11) / 24 = 17 / 24

Using the formula for conditional probability, we can calculate the probability of having both a cat and a dog given that a person has a cat:

P(cat and dog | cat) = P(cat and dog) / P(cat) = (5 / 24) / (13 / 24) = 5 / 13

Therefore, the probability that a student chosen randomly from the class has a cat and a dog is 5/13.

6% pay increases 62,900 thanks i look forward to the additional _ per month

**Answer:**

**Step-by-step explanation:**

$314.50

To calculate the additional pay per month, we need to multiply the current salary by the percentage increase and divide by 12 (months).

The pay increase is 6% of $62,900, which is:

0.06 x $62,900 = $3,774

Therefore, the additional pay per month is:

$3,774 / 12 = $314.50

So, Ciara can look forward to an additional $314.50 per month.

The pay increase is 6% of $62,900, which is:

0.06 x $62,900 = $3,774

Therefore, the additional pay per month is:

$3,774 / 12 = $314.50

So, Ciara can look forward to an additional $314.50 per month.

An object in the shape of a rectangular prism has a length of 9 inches, a width of 5 inches, and a height of 4 inches. The object's density is 11.1 grams per cubic centimeter. Find the mass of the object to the nearest gram.

**Answer:**

---------------------------

**Mass is the product of the volume and density** and the **volume **of the rectangular prism **is the product of its three dimensions**.

Find the **volume **first:

**Convert **volume to cm³, taking 2.54 cm per in:

Find the **mass**:

Out of 1000 students who appeared in an examination,60% passed the examination.60% of the failing students failed in mathematics and 50% of the failing students failed in English.If the students failed in English and Mathematics only, find the number of students who failed in both subjects.

The value of **number **of **students **who failed in both mathematics and English is 40.

Since, Given that;

60% of the 1000 **students **passed the examination,

Hence, we can calculate the number of students who **passed** the exam as follows:

60/100 x 1000 = 600

So, 600 students passed the **examination**.

Now, let's find the number of students who failed the examination.

Since 60% of the students passed, the remaining 40% must have failed. Therefore, the number of students who failed the examination is:

40/100 x 1000 = 400

Of the 400 failing students, we know that 60% failed in mathematics.

So, the number of **students **who failed in mathematics is:

60/100 x 400 = 240

Similarly, we know that 50% of the failing students failed in English.

So, the number of students who failed in **English **is:

50/100 x 400 = 200

Now, we need to find the number of students who failed in both subjects.

We can use the formula:

Total = A + B - Both

Where A is the number of **students **who failed in mathematics, B is the number of students who failed in English, and Both is the number of students who failed in both subjects.

Substituting the values we have, we get:

400 = 240 + 200 - Both

Solving for Both, we get:

Both = 240 + 200 - 400

Both = 40

Therefore, the** number of students **who failed in both mathematics and English is 40.

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Round 73,609 to the nearest thousand

**Answer:**

74,000

**Step-by-step explanation:**

use intelligence

A bag contains 40 marbles. 12 of the marbles are red. What is the percent of red marbles in the bag?

**Answer:**

the percentage of red marbles in the bag is 30%.

**Step-by-step explanation:**

To find the percentage of red marbles in the bag, we need to divide the number of red marbles by the total number of marbles and then multiply by 100:

Percentage of red marbles = (Number of red marbles / Total number of marbles) x 100

Number of red marbles = 12

Total number of marbles = 40

Percentage of red marbles = (12/40) x 100

= 0.3 x 100

= 30%

Therefore, the percentage of red marbles in the bag is 30%.

There are 5,144 blocks to be placed

evenly into 8 storage containers. How

many blocks are in each storage

container?

Divide the total number of blocks by the total number of storage containers.

5144/8 = 643 blocks in each storage container.

Troys toy box is 4 ft x 3ft x 5 ft. What is the Volume of his toy box?

**Answer:**

60 ft^2

**Step-by-step explanation:**

To get the total volume we will need to multiply all the lengths. This means we will have to do 4 x 3x 5.

4 x 3 x 5 = 15x 4 = 60

**Answer:**

60 ft³

**Step-by-step explanation:**

V = 4 ft × 3 ft × 5 ft

V = 12 ft² × 5 ft

V = 60 ft³

#CMIIWHow does Mathematics differ from language to language across the world

The answer is explained below.

In order to be considered a **language**, a system of **communication** must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a **language**. Linguists who don't consider math a language cite its use as a written rather than spoken form of **communication**.

Mathematics is pure language - the language of **science**. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken **language**, there exist words, like "happiness", that defy definition.

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513.4497 rounded to the hundredths place

**Answer:**

513.45

**Step-by-step explanation:**

use intelligence

The answer is 513.45

X/5-y = m-1 resolver para y

Okay, let's solve this step-by-step:

X/5-y = m-1

Add y to both sides:

X/5 = m

Multiply both sides by 5:

X = 5m

So in this equation, X = 5m.

To find y, we subtract m-1 from both sides of the original equation:

X/5 = 5m

X/5 - (m-1) = 5m - (m-1)

X/5 - m + 1 = 4m

(X - 5m) / 5 = m - 1

X - 5m = 5(m - 1)

X = 20m - 5

So if we let m = any value, we can calculate y. For example:

If m = 3, then:

X = 20*3 - 5

= 55 - 5 = 50

50/X = 5(m - 1) = 5*2 = 10

y = 10

Does this make sense? Let me know if you have any other questions!

Carlos is a door to door vacuum salesman. His weekly salary, S, is $400 plus $35 for each vacuum he sells.

This can be written as S = 400+35v , where v is the number of vacuums sold.

If Carlos earns $1590 for a week's work, how many vacuums did he sell?

**Answer:**

34

**Step-by-step explanation:**

1. Plug in the week's salary into the formula

S=400+35v

1590=400+35v

2. Solve for v.

1590=400+35v

Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.

1190=35v

Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.

34=v

The graph represents a relation where x represents the independent variable and y represents the dependent variable.

A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.

What is the domain of the relation?

{−4, −3, −2, 0, 1, 3, 4, 5}

{−4, −2, 0, 3, 5}

{−3, −2, 0, 1, 4}

{0, 3, 4, 5}

The **domain **of the relation of the **graph **representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

The domain of a relation is the **set **of all possible input values (**independent variable**) for which the relation is defined.

Looking at the given points, the **x-coordinates** are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the **relation **is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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Tommy and Ruth are cycling to meet each other. Tommy cycles twice as fast as Ruth and they both set off at the same time. At which coordinate will they meet?

Tommy and Ruth will meet at a **coordinate** that is **0.5x** **km** away from Ruth's **starting point**.

In this problem, Tommy and Ruth are cycling towards each other. We are given that Tommy cycles twice as fast as Ruth and they both start cycling at the same time. Our goal is to determine at which coordinate they will meet.

To solve this problem, we need to use the concept of distance, speed, and time. Let's assume that Ruth cycles at a **speed** of "x" km/hr. Since Tommy cycles twice as fast as Ruth, his speed will be "2x" km/hr.

Let's say that Tommy and Ruth meet at a **distance** of "d" km from Ruth's starting point. Now, let's calculate the time taken by both Tommy and Ruth to reach this point.

Time taken by Ruth = Distance/Speed = d/x

Time taken by Tommy = Distance/Speed = d/2x

Since they both start cycling at the same time, we can set these two equations **equal** to each other:

d/x = d/2x

We can then **simplify** this equation by multiplying both sides by 2x:

2d/x = d

Now we can solve for "d" by **multiplying** both sides by "x":

2d = dx

d = 0.5x

This means that Tommy and Ruth will meet at a **coordinate** that is **0.5x** km away from Ruth's starting point. To determine the exact coordinates, we need to know where Ruth started cycling from and in which direction they are cycling. If we assume that Ruth started cycling from the origin (0,0) and they are cycling towards each other on a straight path, then they will meet at the coordinate (0.5x, 0).

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A study of religious practices among college students interviewed a sample of 125

students; 105

of the students said that they prayed at least once in a while. What is the sample proportion who said they pray?

0.84

1.19

105

84

The **sample proportion** who said they** pray** is approximately 0.84, or 84%.

The sample proportion of **college students **who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).

Sample proportion = Number of students who said they pray / Total number of students in the sample

Sample proportion = 105 / 125

Sample proportion = 0.84

Therefore, the **sample proportion** who said they pray is approximately 0.84, or 84%.

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The dosage the pharmacy carries in stock (on hand), is different than the prescribers order. Use ratio and proportion to calculate the total quantity of tablets to dispense for each of the prescriptions below: Order: Zocor 40 mg po qd for 60 days On hand: 20 mg tabs How many 20 mg tabs should be given? Give:

Using **ratios** and **proportions**, the number of 20 mg tabs that should be given in place of 40 mg po qd for 60 days is 120 tabs.

Using **ratios** and **proportions**, the number of tabs of 20 mg that should be given in place of 40 mg qd for 60 days is determined as follows:

Order: Zocor 40 mg po qd for 60 days

= 60 tabs since it is once per day (qd)

Total mg = 2,400 mg (40 mg x 60 tabs)

On hand: 20 mg tabs

**Proportionately**, 20 mg = 120 tabs (2 x 60) since 40 mg is for 60 tabs

Total mg = 2,400 mg (20 mg x 120 tabs)

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please help fast i don’t feel like typing

**Answer:**

he should have subtracted 17 from both sides of the equation

**Step-by-step explanation:**

x+ 17 = 22

subtract 17 from both sides

X + 17 = 22

-17 -17

x = 5

The Nut Shack sells cashews for $6.80 per pound and Brazil nuts for $4.70 per pound. How much of

each type should be used to make a 37 pound mixture that sells for $5.78 per pound?

Round answers to the nearest pound.

pounds of cashews

pounds of Brazil nuts

> Next Question

**Answer:**

**Step-by-step explanation:**

$6.80 x 19 pounds = $129.2

$4.70 x 18 pounds = $84.6

+___________________

37 pounds = $213.8

$213.8 divided by 37 pounds = 5.77837......

= $5.78 per pound

Scores on a final exam in a large class were normally distributed with a mean of 75 and a standard deviation of 8. What percent of the students scored above an 83?

Using** z - score**, the **percentage** of students above 83 is 15.9%

To find the number of students that scored above 83 can be calculated using z - score formula.

This is given as

z = x - μ / σ

μ = meanσ =Substituting the values into the formula;

z = 83 - 75 / 8

z = 1

The z-score is 1

Let's find the **percentage** of **z -score** under the score

p(x > 83) = 1 - P(x < 83) = 0.15866

p = 15.9%

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A natural food company produces and sells organic almond milk for $9.00 per gallon. This company

estimates its fixed costs to be 1121 dollars per month and the variable cost to produce each gallon of

almond milk is $7.50.

What is the margin of profit if 1494 gallons of almond milk are produced and sold each month?

A Select an answer of $

Okay, here are the steps to solve this problem:

Fixed costs per month: $1121

Variable cost per gallon: $7.50

Selling price per gallon: $9.00

Monthly sales (gallons): 1494

Cost of goods sold = Variable cost per gallon * Monthly sales

= $7.50 * 1494 gallons

= $11,105

Gross margin = Revenue - Cost of goods sold

= $9 * 1494 gallons

= $13,446

- $11,105 (Cost of goods sold)

= $2,341

Margin of profit = Gross margin - Fixed costs

= $2,341 - $1121

= $1,220

So the margin of profit if 1494 gallons are produced and sold each month is $1,220.

The answer is:

B $1,220

A student has scores of 63, 65, and 73 on his first three tests. He needs an average of at least 70 to earn a grade of C in the class.

What is the minimum score that the student needs on the fourth test to ensure a C?

Answer: 79

Step-by-step explanation:

63+65+73+×/4=79

multiply by 4 on both sides

201+x=280

subtract 201 from both sides

x= 79

Find surface area without mistaking the lateral height.

The total "**surface-area**" of **cone **having "slant-height" as 10, and base-radius as 6, is 301.44 square units.

The **total **surface area of a cone can be calculated by adding the area of the base to the lateral surface area.

Let us first calculate the **lateral **surface area of the cone:

Lateral surface area = πrl; where r is radius , and 'l" = **slant-height**,

The **radius **of base = 6 units and slant height is = 10 units.

So, we have:

Lateral surface area = π × 6 × 10

Lateral surface area = 60π square units

Next, Area of the base = πr²;

Area of the base = π × 6²,

Area of the **base **= 36π square units,

Total surface area = Lateral surface area + Area of the base

Total surface area = 60π + 36π

Total surface area = 96×3.14 = 301.44 square units.

Therefore, the total surface **area **of cone is 301.44 square units.

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What level of structure in proteins is held together by intermolecular R group interactions? Also provide the importance of this structural level in protein function and highlight the type of bonds found in this structure. Explain your detailed answer in a five-sentence paragraph (do not make Table):
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