1.
A rectangular swimming pool is represented by x as the width and one less than twice the width as the length. If the area of the swimming pool is given by 28 sq. ft., which equation could be used to model the area of the swimming pool?

A) 28 = 2x - 1•x

B) 28x = 2x - 1

C) 28 = (2x - 1) + (x)

D) 28 = (2x - 1)(x)

Answer:35%

Step-by-step explanation:

Answer:

Step-by-step explanation:

An exponential function is of the form

[tex]y=ab^x[/tex]

where a is the initial value and b is the growth/decay rate.  Our initial value is 64.  That's easy to plug in.  It goes in for a.  So the first choice is out.  Considering b now...

If the rate is decreasing at .5% per week, this means it still retains a rate of

100% - .5% = 99.5%

which is .995 in decimal form.

b is a rate of decay when it is greater than 0 but less than 1; b is a growth rate when it is greater than 1.   .995 is less than 1 so it is a rate of decay.  The exponential function is, in terms of t,

[tex]f(t) = 64(.995)^t[/tex]

Answer:

f(t) = 64 ⋅ 0.995t

Step-by-step explanation:

Add me on S n a p c h a t :) yofav_tai

Answer:

A.) Multiply 46 by 5/9

Step-by-step explanation:

The formula to convert Fahrenheit degrees to Celsius degrees is as follows:

[tex]\\ C = \frac{5}{9}*(F-32) [/tex]

So, converting 78°F to °C, according this previous equation is:

[tex]\\ C = \frac{5}{9}*(78-32) [/tex] [Barbara subtracts 32 from 78]

[tex]\\ C = \frac{5}{9}*(46) [/tex]  [Barbara multiplies 46 by 5/9]

[tex]\\ C = \frac{5*46}{9} [/tex]

[tex]\\ C = \frac{230}{9} = 25.56 [/tex] or 25.56°C

Answer:

A) multiply 46 by 5/9

Step-by-step explanation:

Answer: it took T.J. 48 months to pay the car loan.

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P = principal or amount loaned

R = interest rate

T = time in years.

I = interest

From the information given,

P = $5800

R = 6.5%

Over the course of the loan, he paid a total of $1508 in interest. Therefore,

I = $1508 Therefore,

1508 = (5800×6.5×T)/100

1508 = 377T

T = 1508/377 = 4 years

Assuming there are 12 months in a year, the number of months in 4 years would be 4×12 = 48 months

Answer:

A. 18%

Step-by-step explanation:

For independent events:

P(A and B) = P(A) × P(B)

P = 0.30 × 0.60

P = 0.18

There is an 18% probability that it will rain on both days and the game will be canceled.

Final answer:

Using the Central Limit Theorem, the probability that the stock's price will exceed $105 on the 10th day is calculated to be approximately 13.14%, assuming that the daily change of the stock price is a random variable with a mean of 0 and a variance of 2 and starting from a stock price of $100.

Explanation:

The question is asking to calculate the probability that a company's stock price will exceed $105 on the 10th day, given that the stock price today is $100 and that the daily change of price is a random variable with a mean of 0 and a variance of 2. To answer this, we can use the Central Limit Theorem (CLT) since we have a sum of independent and identically distributed random variables. According to the CLT, the sum of these random variables (or the stock price on the 10th day) will approximate a normal distribution as the number of days increases. For the 10th day, the expected price is the initial price (which is $100) plus 10 times the expected daily change (10*0 = 0), so the expected price is still $100. The variance of the sum of the daily changes is 10 times the variance of a single day (10*2), which equals 20, and the standard deviation is the square root of the variance, which is approximately 4.47.

We are trying to find the probability that the stock price is greater than $105. To do this, we convert the stock price into a z-score using the formula:

z = (X - μ) / σ

where X is the stock price we are interested in ($105), μ is the mean of the stock price on the 10th day ($100), and σ is the standard deviation (approximately 4.47). So we have:

z = (105 - 100) / 4.47 = 1.12

Using standard normal distribution tables or a calculator, we find that the probability of a z-score being greater than 1.12 is approximately 0.1314 (or 13.14%). Therefore, the probability that the stock's price will exceed $105 on the 10th day is about 13.14%.

Answer:

Total Number of Coconuts which fell from tree are 14.

Step-by-step explanation:

Given:

Some coconuts fall out of a tree.

Mercy is greedy and takes half,

Joe grabs what he can, and gets five more than Frank.

Frank gets one coconut.

We need to find Total number of coconuts fell from tree.

Number of Coconuts franks has = 1

Now Given that Joe grabs what he can, and gets five more than Frank.

Number of Coconuts Joe has = Number of Coconuts franks has + 5 = 1 + 5 = 6

Also Given Mercy is greedy and takes half.

It means mercy took half of coconuts and rest half were took by Frank and Joe

Hence Number of Coconuts Mercy has = Number of Coconuts franks has +  Number of Coconuts Joe has = 6 + 1 = 7

Now Total Number of Coconuts is equal to sum of Number of Coconuts Mercy has and Number of Coconuts Joe has and Number of Coconuts frank has.

Total Number of Coconuts = 7 + 1 + 6 = 14

Hence Total Number of Coconuts which fell from tree are 14.

Answer:

Tom required 23 months to save at least $2175.

Step-by-step explanation:

Given:

Money already Saved = $450

Money Needs to be saved  = $2,175

Each month saving = $75

We need to find the Number of months required to save at least $2,175

Solution:

Let the number of months be 'x'.

Now We can say Total Money which is already save plus Each month saving multiplied by number of months should be equal to Money Needs to be saved.

Framing in equation form we get;

[tex]450+75x=2175[/tex]

Solving the equation we get;

We will Subtract  both side by 450 we get;

[tex]450+75x-450=2175-450\\\\75x=1725[/tex]

Now By dividing 75 on both side we get;

[tex]\frac{75x}{75}= \frac{1725}{75}\\\\x= 23\ months[/tex]

Hence Tom required 23 months to save at least $2175.

Multiplying is simply the same as repeated addition. For example:

[tex]5 \times 3 = 5 + 5 + 5[/tex]

Or:

[tex]4 \times 7= 4 + 4 + 4 + 4 + 4 + 4 + 4[/tex]

Answer:

Below.

Step-by-step explanation:

Adding the number the same number of times as the multiplier.

For example

2 * 3  = 2 + 2 + 2.

Answer:

[tex] MAD= \frac{1}{14} 27.286 = 1.949 \approx 2.0[/tex]

Step-by-step explanation:

Previous concepts

The mean absolute deviation or MAD "is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values)". And is given by this formula:

[tex] MAD= \frac{1}{n} \sum_{i=1}^n |x_i -\bar X|[/tex]

Solution to the problem

Assuming the info from the picture. So then the data is this one:

66,69,70,70,71,72,72,72,73,73,74,75,75,75

So the first step is find the mean for the dataset with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And if we replace the values we got:

[tex]\bar X = \frac{66+69+70+70+71+72+72+72+73+73+74+75+75+75

}{14}=71.929[/tex]

And now we need to subtract for each value the mean like this:

Data      [tex] X_i -\bar X[/tex]

66               5.929

69               2.929

70               1.929

70               1.929

71                0.929

72               0.0714

72               0.0714

72               0.0714

73               1.0714

73               1.0714

74               2.0714

75               3.0714

75               3.0714

75               3.0714

Now we need to add the deviations and divide by the the number of data values and we got:

[tex] MAD= \frac{1}{14} 27.286 = 1.949 \approx 2.0[/tex]

Answer:

0.0414

Step-by-step explanation:

Each error is uniform between -0.5 and 0.5, so the mean error is 0, and the variance is (b-a)²/12 = (0.5-(-0.5))²/12 = 1/12

If we sum 50 numbers, the errors will sum with each other, and the resultant mean and variance will be summed, because the errors are independent. The mean of the sum of 50 number is 0*50 = 0, and the variance in 50/12.  

The central limit theorem states that the sum of identically distributed random variables has distribution approximately normal. In this case, if we call X the sum of the 50 random numbers, then X has distribution approximately N(μ = 0,σ = √(50/12)). If we divide X with its standard deviation √(50/12), we obtain (approximately) a standard normal random variable. Lets call Y = X/√(50/12). Y distribution is approximately N(0,1). Y is called the standarization of X.

The values of the cummulative distribution of the standard Normal random variable, denoted by Ф, are tabulated; you can find those values in the attached file. We want the error to be greater than 3. We will calculate the complementary event: the probability for the error to be between -3 and 3, and substract from 1 that result

P(-3 ≤ X ≤ 3) = P( -3/√(50/12) ≤ X/√(50/12) ≤ 3/√(50/12)) = P(-3/√(50/12) ≤ Y ≤ 3/√(50/12)) = Ф(3/√(50/12)) - Ф(-3/√(50/12))

Since the density function of a normal random variable centered at 0 is symmetric, then  Ф(-3/√(50/12)) = 1- Ф(3/√(50/12)), as a result

P(-3 ≤ X ≤ 3) = Ф(3/√(50/12)) - Ф(-3/√(50/12))  = 2 Ф(3/√(50/12)) - 1 = 2 * Ф(2.04) - 1 = 2*0.9793 - 1 = 0.9586

hence, the probability for the error to be greater thar 3 is 1-0.9586  = 0.0414

Answer:

At 20 miles both companies cost will be same.

Step-by-step explanation:

Let Number of miles be 'x'.

Given:

Quick movers charges $50 a day and $0.50 per mile .

So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.

framing in equation form we get;

Quick movers charges = [tex]50+0.5x[/tex]

Also Given:

ABC movers charges $45 a day and $0.75 per mile .

So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.

framing in equation form we get;

ABC movers charges = [tex]45+0.75x[/tex]

We need to find the number of miles at which both companies cost are are same.

Solving to find the same we get;

[tex]50+0.5x=45+0.75x[/tex]

Combining like terms we get;

[tex]0.75x-0.5x=50-45\\\\0.25x=5[/tex]

By Division property of equality we will divide both side by 0.25 we get;

[tex]\frac{0.25x}{0.25} =\frac{5}{0.25} \\\\x= 20 \ miles[/tex]

Hence at 20 miles both companies cost will be same.

Final answer:

By setting up an equation to equate the charges of Quick Movers and ABC Movers, it is determined that at 20 miles, the costs for both companies will be the same.

Explanation:

To find at how many miles the cost for both Quick Movers and ABC Movers is the same, we set up an equation where the cost of each company is equal. Quick Movers charges $50 a day plus $0.50 per mile, and ABC Movers charges $45 a day plus $0.75 per mile. Let's use m to represent the miles.

The equation based on the costs given will be:

50 + 0.50m = 45 + 0.75m

To solve the equation, we first bring all the m terms to one side and the constants to the other:

0.50m - 0.75m = 45 - 50

This simplifies to:

-0.25m = -5

Dividing both sides by -0.25, we find:

m = 20

Therefore, the cost for both companies is the same at 20 miles.

Answer: basically just set them equal and solve

Step-by-step explanation: vertical angles are xongruent

Lizzie's answer is not right as two sides are not equal.

Step-by-step explanation:

Given equation is;

2+3x+3=3(x+3)+2x

Lizzy got;

x=2

We will put this value of x in Equation to determine if the sides are equal or not.

[tex]2+3(2)+3=3(2+3)+2(2)\\2+6+3=3(5)+4\\11=15+4\\11\neq 15[/tex]

Lizzie's answer is not right as two sides are not equal.

Keywords: linear equation, addition

Learn more about addition at:

#LearnwithBrainly

Answer:

  (x +5)²/4 +(y +8)²/36 = 1

Step-by-step explanation:

The equation of an ellipse with center (h, k) and semi-axes "a" and "b" (where "a" is in the x-direction and "b" is in the y-direction) can be written as ...

((x -h)/a)² +((y -k)/b)² = 1

Here, the center is at (h, k) = (-5, -8), and the semi-minor axis is a=2, while the semi-major axis is b=6.

The equation can be written as ...

  ((x +5)/2)² +((y +8)/6)² = 1

More conventionally, it is written ...

  (x +5)²/4 +(y +8)²/36 = 1

Answer:

The answer to your question is  [tex]\frac{(x + 5)^{2} }{4} + \frac{(y + 8)^{2} }{36} = 1[/tex]

Step-by-step explanation:

From the graph we know that the center = (-5, -8) and a= 6 and b = 2.

See the picture below

Here, we have a vertical ellipse so the equation is

                [tex]\frac{(x - h)^{2} }{b^{2} } + \frac{(y - k)^{2} }{a^{2} } = 1[/tex]

Substitution

                [tex]\frac{(x + 5)^{2} }{2^{2} } + \frac{(y + 8)^{2} }{6^{2} } = 1[/tex]

                [tex]\frac{(x + 5)^{2} }{4} + \frac{(y + 8)^{2} }{36} = 1[/tex]

Answer:

Check it down.

Step-by-step explanation:

Injective functions or One to one functions are functions in each one element of A set is is mapped to another element of B set

1) Let's start by listing supposition and their respective Reasons

Suppose:

[tex]g\circ f[/tex] is injective then [tex]f:A\rightarrow B[/tex] is also injective.

Reason: Given

2) Since we are dealing with injective (one to one) functions,  we can rightly proceed:

[tex]f(x)=f(y) \:such \:as\: x,y \in A[/tex]

[tex]g(f(x))=g(f(y))[/tex]

Given the fact that [tex]g\circ f[/tex]

[tex]x=y[/tex]

Then we can say that since [tex]g\circ f[/tex]  f: A is an injective too ("one to one" ) function.

Answer:the ratio of Julia’s frogs to Rimma’s frogs is 1.8 : 1

Step-by-step explanation:

Let x represent the total number of frogs that Rimma had.

Julia’s frogs are 2/5 of the amount of Rimma’s frogs. This means that the number of frogs that Julia had is

2/5 × x = 2x/5

If Rimma gives 1/2 of her frogs to Julia, the number of frogs that Julia gets from Rimma would be

1/2 × x = x/2 frogs. Total number of frogs that Julia would have becomes

2x/5 + x/2 = (4x + 5x)/10 = 9x/0

The number of frogs that Rimma has left would be 1/2 × x = x/2

The ratio of Julia’s frogs to Rimma’s frogs would be

(9x/10) / (x/2) = (9/5)/1

= 1.8 : 1

Answer:

The New world colonization enabled by the vessel affect the European economy as it increased the amount of gold and silver brought into Europe, this lead to the development of the banking sector and also helped to promote the transition of Europe into a capitalist economy.

it brought a great deal of gold and silver into Europe, stimulating the banking industry and promoting Europe’s transition of capitalism

Answer:

B

Step-by-step explanation:

210=1200*.035*5

Answer:

Total Amount made by Mailing in a week is $3395.

Step-by-step explanation:

Given:

Fixed Salary = $385

Percentage of Commission on Sale = 70%

Total Sale = 4300

we need to find Total amount made by Mailing in a week.

We will first find the amount made on commission.

Amount made on commission  = [tex]\frac{70}{100} \times 4300 = \$3010[/tex]

Now Total Amount made by Mailing in a week is equal to sum of Fixed Salary and  Amount made on commission.

Framing in equation form we get;

Total Amount made by Mailing = $385 + $3010 = $3395.

Hence Total Amount made by Mailing in a week is $3395.

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y on the vertical axis) / (change in the value of x on the horizontal axis)

The equation of the given line is

9x+7y=4

7y = 4 - 9x = -9x + 4

y = -9x/7 + 4/7

Comparing with the slope intercept form, slope = -9/7

If the line passing through the given point is perpendicular to the given line, it means that its slope is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line passing through (7,-4) is 7/9

To determine the intercept, we would substitute m = 7/9, x = 7 and y = - 4 into y = mx + c. It becomes

- 4 = 7/9×7 + c = 49/9 + c

c = - 4 - 49/9

c = - 85/9

The equation becomes

y = 7x/9 - 85/9

Answer:

Angle

Step-by-step explanation:

In the image I added you can observe that the common endpoint is called a vertex, and the "turn" or aperture formed between the two straight lines (or arms) that converge in the vertex, is the angle and it can be measured on degrees.

I hope you find this information usefun and interesting! Good luck!

Final answer:

The amount of turn between two straight lines that have a common end point is referred to as an angle. This concept is central to the study of geometry and aids in measuring the difference in direction where two lines meet. Angles are typically measured in degrees as a part of spherical trigonometry and other geometric calculations.

Explanation:

The amount of turn between two straight lines that have a common end point is called an angle. An angle measures the difference in direction between two lines that extend from the same point. The concept of angle is found in the principles of geometry, where it is foundational to understanding shapes and their properties.

In more mathematical terms, the angle between two intersecting lines can also be seen as the distance between their poles when conceptualized on a sphere, a concept from advanced geometry and spherical trigonometry. The measurement of this angle is generally given in degrees, where a full circle is 360 degrees, and this system of measurement allows us to apply the angle measure to various geometric constructions and theorems, such as determining the sum of the angles of a triangle.

Answer:

f(x) = x*3/4 + 42.5

Step-by-step explanation:

The original difference between the pair is 70 - 30 = 40

The new difference between the pair is 95 - 65 = 30

Since the differences are not the same, Mrs Bailey must first perform a (slope) multiplication by a factor of 30/40 or 3/4

Then 30 * 3/4 = 22.5

Then she can shift the scores up by 65 - 22.5 = 42.5 in order to get the range from 65 to 95

Therefore, f(x) = x*3/4 + 42.5. We can test that

f(30) = 30*3/4 + 42.5 = 65

f(70) = 70*3/4 + 42.5 = 95

Answer:

857164 magnetic block.

Step-by-step explanation:

Given: Each cube constructed with 1331 magnetic block.

          Mrs. cady has 256 student in her school and 388 student in another school make an identical cube.

First lets find out total number of students in both schools.

Total student= [tex]256+388= 644\ students[/tex]

∴ Total number of students is 644, who make identical cube.

Now, finding number of magnetic blocks do student use in all.

We will use unitary method.

Each cube require 1331 magnetic blocks.

As there are total 644 students making each cube

∴ 644 cubes require = [tex]644\ cubes\times 1331\ magnetic\ block= 857164[/tex]

∴ 857164 magnetic blocks, student use in all.

Answer:

120 seconds

Step-by-step explanation:

if the elevator is moving at a constant rate, then it takes 10 seconds to move up one floor, to travel from the 4th to the 16th floor, it will take 120 seconds total to travel 10 floors

Answer: A No, the student should have added 3 + 4 to get the total number of sections, and used the fraction Three-sevenths instead of Three-fourths.

Step-by-step explanation:

Answer:the two equations that model the situation are

x + y = 48

3x + 2y = 15

Step-by-step explanation:

Let x represent the total number of hours that Derek worked.

Let y represent the total number of hours that Donnie worked.

Derek and Donnie mow 15 lawns over two 2 days. There are 24 hours in a day. Therefore, the number of hours in 2 days would be 2 × 24 = 48 hours. Therefore

x + y = 48 - - - - - - - - - -1

If Derek mows 3 lawns per hour and Donnie mows 2 lawns per hour, it means that

3x + 2y = 15 - - - - - - - - - 2

Answer:

(2, 2)

Step-by-step explanation:

According to the distance formula, the distance between two points is:

d² = (x₂ − x₁)² + (y₂ − y₁)²

If one point is (x, y) and the other point is (1, 4), then:

d² = (x − 1)² + (y − 4)²

We know y² = 2x, so x = ½ y².  Substituting:

d² = (½ y² − 1)² + (y − 4)²

The minimum distance is when dd/dy equals 0.  We can either simplify first by distributing, or we can immediately take the derivative using chain rule.

If we distribute and then take the derivative:

d² = ¼ y⁴ − y² + 1 + y² − 8y + 16

d² = ¼ y⁴ − 8y + 17

2d dd/dy = y³ − 8

If we use chain rule instead without distributing:

2d dd/dy = 2(½ y² − 1) (y) + 2(y − 4)

2d dd/dy = y³ − 2y + 2y − 8

2d dd/dy = y³ − 8

Setting dd/dy equal to 0:

0 = y³ − 8

y = 2

x = ½ y²

x = 2

(2, 2) is the point on the parabola closest to (1, 4).

Graph: desmos.com/calculator/m4apqwsduk

Answer:

A) the average value of Halloween spending of $52 in 2007 is claimed population mean and the value of Halloween spending $58 per household found out through survey done in 2008 is the sample mean

B) the average GPA 3.37 in 2001 is the claimed population mean and the average GPA through survey of 203 students is sample mean.

Step-by-step explanation:

'Claimed population mean' means the average value not taken through a survey of a sample size therefore in both options the average value is Claimed population mean

'Sample mean' is taken from a group of population therefore the value in both options taken through a survey of a sample population is Sample mean

A sample is a portion of a whole group. We use sample to predict data about the whole group(called population).

A) The sample mean is: average Halloween spending was $58 per household (survey in year 2008)

The population mean is: American households spent an average of about $52 in 2007

B) The sample mean is: average GPA of 3.59 (survey in 2012)

The population mean is: average GPA of students in 2001 at a private university was 3.37

Sample is a portion researchers or any interested person or community takes out from a big group(called population) so as to predict properties of that big group.

We work on sample because big groups are sometimes too big that we can't cover it all in normal time. There are some other reasons too because of which we work on samples instead of population.

Sample mean is the mean obtained in the sample taken.

Population mean is hypothesized mean of population(since we don't know real mean of population, that's why hypothesized).

Thus, for given condition, we have:

A) The sample mean is: average Halloween spending was $58 per household (survey in year 2008)

The population mean is: American households spent an average of about $52 in 2007

B) The sample mean is: average GPA of 3.59 (survey in 2012)

The population mean is: average GPA of students in 2001 at a private university was 3.37

Learn more about sample mean and population mean here:

https://brainly.com/question/20747890

Step-by-step explanation:

In the morning cat and dog walked 2 miles.

Total distance traveled in the morning = 2 x 2 = 4 miles

In the afternoon the dog walked 3 miles

Total distance traveled in the afternoon = 3 miles

We need to find how many miles did the cat and dog walk.

Total distance traveled by cat and dog = Total distance traveled in the morning + Total distance traveled in the afternoon

Total distance traveled by cat and dog = 4 + 3

Total distance traveled by cat and dog = 7 miles