What is the slope of the line passing through the points (−1, −7) and (−9, −2) ?

Step-by-step explanation:

The given sequence:

[tex]\dfrac{1}{2}+1+\dfrac{3}{2}+2+ ...[/tex]

Here, first term (a) = [tex]\dfrac{1}{2}[/tex], common difference(d) =[tex]1-\dfrac{1}{2}=\dfrac{1}{2}[/tex] and

the number of terms (n) = 25

The given sequence are in AP.

To find, the value of [tex]S_{25}[/tex] = ?

We know that,

The sum of nth terms of an AP

[tex]S_{n}=\dfrac{n}{2}[2a+(n-1)d][/tex]

The sum of 25th terms of an AP

[tex]S_{25}=\dfrac{25}{2}[2(\dfrac{1}{2})+(25-1)(\dfrac{1}{2})][/tex]

⇒ [tex]S_{25}=\dfrac{25}{2}[1+(24)(\dfrac{1}{2})][/tex]

⇒ [tex]S_{25}=\dfrac{25}{2}[1+12][/tex]

⇒ [tex]S_{25}=\dfrac{25}{2}[13][/tex]

⇒ [tex]S_{25}=\dfrac{325}{2}[/tex]

∴ [tex]S_{25}=\dfrac{325}{2}[/tex]

Answer:

2.21936352 feet

Step-by-step explanation:

420334*5280 (thats feet in a mile) divided by 1000000000

Yo sup??

Average shoulder width=total lenght / number of people

since we want it in inches therefore

Final answer=Average shoulder width*63360

=420334*63360/1,000,000,000

=26.62 inches

Hope this helps

The value of the expression is [tex]0.25[/tex]

Explanation:

The expression is [tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}$[/tex]

Since, the base of the expression is the same. Then, by "product rule", when multiplying two powers that have the same base, you can add the exponents.

Thus, we have,

[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{4-2}$[/tex]

Adding the exponents, we have,

[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{2}$[/tex]

Applying exponent rule, [tex]$\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}$[/tex], we have,

[tex]$\left(\frac{1}{2}\right)^{2}=\frac{1^{2}}{2^{2}}$[/tex]

Simplifying, we get,

[tex]\frac{1}{4}[/tex]

Dividing, we have,

[tex]0.25[/tex]

Thus, the value of the expression is [tex]0.25[/tex]

Answer:

8 ounces of each must be mixed to make 16 ounces of a 10%solution.

Step-by-step explanation:

The careful analysis and detailed calculation is as shown in the attached file.

Answer:

COPD

Step-by-step explanation:

COPD is a lung disease caused by tobacco use and other factors

Answer:

The width of path is 1.5 m                                        

Step-by-step explanation:

We are given the following in the question:

Field:

Length = 45 m

Width = 35 m

Area of filed =

[tex]\text{Area} = \text{Length}\times \text{Width} = 45\times 36 = 1620[/tex]

The area of rectangular field the is 1620 square meter.

Area of path = 234 m

Let x be the width of path.

Area of field without path = 1620 - 234 = 1386 square meter.

Now, dimensions of field without path is:

Length = [tex]45 -x - x = 45 -2x[/tex]

Width = [tex]36 -x - x = 36 - 2x[/tex]

[tex]\text{Area} = \text{Length}\times \text{Width}[/tex]

Thus, we can write:

[tex](45-2x)(36-2x) = 1386[/tex]

[tex]1620 - 90x - 72x + 4x^2 = 1386\\4x^2 - 162x + 234 = 0\\2x^2 - 81x + 117 = 0\\(2x - 3)(x - 39) = 0\\x = 1.5, x = 39[/tex]

We cannot take the width as 39 m, thus, the width of path is 1.5 m.

Answer:

Step-by-step explanation:

Part 1:

An equation of sine wave can be written as y = 5 Sin(2x + 3).

The amplitude of the above equation is 5.

The period of the function is [tex]\frac{2\pi }{2} = \pi[/tex].

The frequency of the function is [tex]\frac{1}{\pi }[/tex].

Part 2:

[tex]y = 2 Sin(3x + 5) + 9.......(1)\\y = 5 Sin(4x + 8) + 12.....(2)\\y = 3 Sin(x + 6) + 2......(3)[/tex]

The above given equations numbered 1, 2 and 3 represents three different sound waves.

For (1), the frequency is [tex]\frac{1}{\frac{2\pi }{3} } = \frac{3}{2\pi }[/tex].

For (2), the frequency is [tex]\frac{4}{2\pi } = \frac{2}{\pi }[/tex].

For (3), the frequency is [tex]\frac{1}{2\pi }[/tex].

Frequency of sounds refers the speed of vibration.

The taken three siounds has different frequencies.

Answer: The  length of the shorter side of a golden rectangle is about 24.7 inches.

Step-by-step explanation:

Given : A golden rectangle has side lengths in the ratio of about 1 to 1.62.

Since 1.62 > 1 , so

[tex]\dfrac{\text{Length of shorter side}}{\text{Length of longer side}}=\dfrac{1}{1.62}[/tex]

If the length of the longer side is 40 inches , then we have

[tex]\dfrac{\text{Length of shorter side}}{\text{40 inches}}=\dfrac{1}{1.62}\\\\ \Rightarrow\ \text{Length of shorter side}=\dfrac{1}{1.62}\times \text{40 inches}\\\\ \Rightarrow\ \text{Length of shorter side}=24.6913580247\approx24.7\text{ inches}[/tex]

Hence, the  length of the shorter side of a golden rectangle is about 24.7 inches.

To find the length of the shorter side of a golden rectangle with a longer side of 40 inches, divide 40 by the golden ratio (1.62), yielding approximately 24.7 inches as the length of the shorter side, rounded to the nearest tenth.

To calculate the length of the shorter side of a golden rectangle with a longer side length of 40 inches, we use the ratio of the sides of a golden rectangle. Given that this ratio is about 1 to 1.62, we divide the length of the longer side by the golden ratio (approximately 1.62) to find the length of the shorter side.

Using this method:

Let's do the calculation:

Length of shorter side ≈ 24.7 inches (rounded to the nearest tenth)

Answer:

the least is 40

Step-by-step explanation:

if u multiply each money amount times the amount they bought you get the awnser

The true statement is: d. The conclusion is incorrect because the range is limited to the set of positive real numbers.

The function is given as:

[tex]\mathbf{f(x) =2x}[/tex]

The above function implies that:

The above highlights mean that: Geraldine's claims are incorrect.

Because y increases or decreases by 2, when x increases or decreases by 1

In other words, the value of y does not get doubled or halved.

Hence, both statements are incorrect

Read more about range at:

https://brainly.com/question/21853810

Answer: $116.99

Step-by-step explanation:

By using compound interest formula which said:

A = P ( 1 + r/n )^(n×t)

P=Principal= 1000

r=rate=4/100

n=1

t= 4

Apply the above formula

A = P ( 1 + r/n )^(n×t)

A = 1000(1 + 0.04/1)^(1 × 4)

A= 100(1.04)^4

A= 100 × 1.17

A = 116.99

Answer:

P = 2(5W + W)

Step-by-step explanation:

P = 2(L +W)

L = 5W

P = 2(5W + W)

P = 10W + 2W

P = 12W

Answer: the wire should be cut into 12 cm and 28 cm

Step-by-step explanation:

All sides of a square is equal.

The perimeter of a square is the distance around the square.

Let L represent the length each side of one of the squares. Then the perimeter of this square is 4L.

The length of a side of one square is to be 4 longer than length of a side of the other. This means that the length of each side of the other square is L + 4

The perimeter of the other square would be 4(L + 4) = 4L + 16

Since the piece of wire is 40 cm long, then

4L + 4L + 16 = 40

8L = 40 - 16 = 24

L = 24/8 = 3

The perimeter of the first square is

4L = 4 × 3 = 12

The perimeter of the second square is

4L + 16 = 4 × 3 + 16= 28

Final answer:

To make two squares with one side being 4 cm longer than the other, a 40 cm wire should be cut into pieces of 12 cm and 28 cm.

Explanation:

The question concerns cutting a 40 cm long piece of wire into two pieces to form two squares, where the length of a side of one square is 4 cm longer than the length of a side of the other square. Let's denote the length of the side of the smaller square as x cm. Thus, the side of the larger square will be x + 4 cm. Since the perimeter of a square is four times its side length, the total length of wire used for the smaller square will be 4x cm, and for the larger square will be 4(x + 4) cm.

Combining the total length of both squares, we have:

4x + 4(x + 4) = 40

This simplifies to:

8x + 16 = 40

Subtracting 16 from both sides, we get:

8x = 24

Dividing both sides by 8, we find:

x = 3

Therefore, the side of the smaller square is 3 cm, and the side of the larger square is 7 cm. To find out how long each piece of wire must be cut, we calculate the perimeters:

Smaller square wire length: 4(3) = 12 cm

Larger square wire length: 4(7) = 28 cm

So the wire should be cut into one 12 cm piece and one 28 cm piece.

Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?  

$450.71

____________________________

*100% CORRECT ANSWERS

Question 1

A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the monthly payment?

$1082.84    

Question 2

A family is purchasing a house and needs to finance a 195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the total amount the family will pay back to the bank (to the nearest dollar)?

$389,822    

Question 3

Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?  

$450.71

Answer:

10 years

40 years

Step-by-step explanation:

let present ag e of son=x

5 years ago age of son=x-5

5 years ago age of man=7(x-5)=7x-35

present age of man=7x-35+5=7x-30

after 5 years

age of son=x+5

age of man=7x-30+5=7x-25

also 7x-25=3(x+5)

7x-25=3x+15

7x-3x=15+25

4x=40

x=10

age of son=10 years

age of man=7*10-30=70-30=40 years

Final answer:

By creating equations from the given information and solving them, it was found that the man is currently 40 years old, and his son is 10 years old.

Explanation:

Let's solve the problem using algebra. Suppose the current age of the man is M years and the current age of his son is S years.

According to the problem, 5 years ago, the age of the man was 7 times the age of his son. Therefore, M - 5 = 7(S - 5).

After 5 years, the age of the man will be 3 times the age of his son from now. Therefore, M + 5 = 3(S + 5).

Solving these equations:

M - 5 = 7S - 35

M + 5 = 3S + 15

Simplifying both:

M = 7S - 30

M = 3S + 10

Equating both equations we get:

7S - 30 = 3S + 10

4S = 40

S = 10

Substituting the value of S in the first equation:

M = 7*10 - 30 = 40

Therefore, the man is currently 40 years old, and his son is 10 years old.

Answer:

3 employees

Step-by-step explanation:

The complete question is

The manager of a fast food restaurant collected data to study the relationship between the number of employees working registers and the amount of time customers waited in line to order. He made a scatter plot of the data and created a trend line with the equation y = -70x + 300, where y is the total amount of time waited in seconds and x is the number of employees working registers. Maria went to the restaurant and waited 90 seconds to place her order. Use the trendline equation to predict how many employees were working. Round to the nearest whole number if necessary.

Let

x ---> is the number of employees working registers

y ---> is the total amount of time waited in seconds

we have

[tex]y=-70x+300[/tex]

This is the equation of a line in slope intercept form

where

The slope is equal to

[tex]m=-70\ \frac{seconds}{employee}[/tex] ---> is negative because is a decreasing function

The y-intercept is equal to

[tex]b=300\ sec[/tex]

For y=90 seconds

substitute in the linear equation and solve for x

[tex]90=-70x+300[/tex]

[tex]70x=300-90\\70x=210\\x=3\ employees[/tex]

To predict the number of employees based on a 90-second wait time, substitute 90 into the given trend line equation and solve for y. For example, using y = -0.1x + 10, we get approximately 1 employee. Ensure you use the specific trend line equation provided for accurate results.

To predict how many employees were working based on Maria's wait time of 90 seconds, we need the trend line equation that describes the relationship between waiting time and the number of employees.

Assuming we have a trend line equation of the form y = mx + b,

you can substitute 90 for x and solve for y.

For example, if the trend line equation is y = -0.1x + 10, substituting 90 for x:

y = -0.1(90) + 10

y = -9 + 10

y = 1

Therefore, according to this trend line, approximately 1 employee would be working. Always remember to check your specific trend line equation and solve accordingly.

The function f(x) has a removable discontinuity at x=0. To make f(x) continuous at x=0, we must redefine f(0) as -1/3.

To determine if f(x) has a removable discontinuity at x=0, we need to check if f(x) is either not defined or not continuous at x=0.

Looking at the definition of f(x), we see that f(0) is defined as 3. Therefore, f(x) is defined at x=0.

Next, let's examine the continuity of f(x) at x=0. We need to evaluate the limit of f(x) as x approaches 0.

Using the given definition of f(x), we have:

lim(x->0) (6/x) + (-5x + 18)/(x(x-3))

To evaluate this limit, we can simplify the expression by finding a common denominator. The common denominator is x(x-3):

lim(x->0) [6(x-3) + (-5x + 18)] / [x(x-3)]

Simplifying the numerator:

lim(x->0) (6x - 18 - 5x + 18) / [x(x-3)]

= lim(x->0) (x) / [x(x-3)]

Now, we can cancel out the x term:

lim(x->0) 1 / (x-3)

As x approaches 0, the denominator (x-3) approaches -3. Therefore, the limit is:

lim(x->0) 1 / (x-3) = 1 / (-3) = -1/3

Since the limit of f(x) as x approaches 0 exists and is equal to -1/3, we can redefine f(0) to be -1/3 to make f(x) continuous at x=0.

Thus, f(x) has a removable discontinuity at x=0, and we must redefine f(0)=-1/3 to make f(x) continuous at x=0.

Step-by-step explanation:

The given four sides of quadrilateral = (1,3), (5,3), (7,-1) and (1,-1)

To find, the area of the shape (quadrilateral) = ?

We know that,

The area of quadrilateral = [tex]\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]

= [tex]\dfrac{1}{2} [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)][/tex]

= [tex]\dfrac{1}{2} [1(4)+5( 0)+7( -4)+1}( 0)][/tex]

= [tex]\dfrac{1}{2} [4+0-28+0][/tex]

= [tex]\dfrac{1}{2} [32][/tex]

= 16 square units.

Thus, the area of the shape (quadrilateral) is 16 square units.

Answer:

1/10 of pizza

Step-by-step explanation:

Let x represent size of equal pieces.      

We have been given that a pizza is cut into five pieces. Four of the pieces are the same size, and the fifth size is 0.5 the size of each of the others.

This means that size of small piece would be half the size of other pieces, that is [tex]\frac{x}{2}[/tex].

Since the pizza is divided in 5 pieces, so we will divide [tex]\frac{x}{2}[/tex] by 5 as:

[tex]\frac{\frac{x}{2}}{5}=\frac{x}{2\cdot5}=\frac{x}{10}=\frac{1}{10}x[/tex]

Therefore, the smallest piece is 1/10 of the pizza.

Answer:

A. 15, 20, and 25

Step-by-step explanation:

Note that 3-4-5 is a pythagorean triple via following:

[tex]\sqrt{ (3^2 + 4^2 )} = 5^2[/tex]

Dividing 15, 20, and 25 by 5 nets you the pythagorean triple 3-4-5.

Answer:

  2 1/2

Step-by-step explanation:

Each term is 1/2 added to the previous term. The first term is -3/2, so the first 9 terms of the sequence are ...

  -3/2, -1, -1/2, 0, 1/2, 1, 1 1/2, 2, 2 1/2

a9 is 2 1/2.

I'm pretty sure the answer to

a1=−32

an=an−1+12

is 5/2

Answer:

43

Step-by-step explanation:

We have the following data:

Total number of hikers: 136

Minimum: 9 days

Q1 : 18 days

Median: 21 days

Q3: 28 days

Maximum: 56 days

Using the 1.5 Interquartile rule means:

Left boundary: Q1 - 1.5 × IQR

Right boundary: Q3 + 1.5 × IQR

We first calculate the IQR (Interquartile Range): Q3 - Q1

⇒ 28 - 18 = 10

Right boundary: 28 + 1.5 × 10

= 28 + 15

= 43

Hence the right boundary is 43.

Answer: she has 310 small marbles, 62 medium marbles and 188 large marbles.

Step-by-step explanation:

Let w represent the number of small marbles Amy has.

Let x represent the number of medium marbles Amy has.

Let y represent the number of large marbles Amy has.

a) She has five times as many small marbles as medium marbles. This means that

w = 5x

b) The number of large marbles is two more than three times the number of medium marbles. This means that

y = 3x + 2

c) If Amy has a total of 560 marbles, it means that

5x + x + 3x + 2 = 560

9x = 560 - 2

9x = 558

x = 558/9 = 62

w = 5x = 62 × 5

w = 310

y = 3x + 2 = 3 × 62 + 2

y = 188

Answer:

A. s = 5x

B. y = 3x + 2

C y=166

Step-by-step explanation:

Answer:

B, An  n-by-m array.

Step-by-step explanation:

when working with  2D arrays, rows come first and then columns. so all options here are correct except option B

Answer:

Step-by-step explanation:

Triangle DEF is a right angle triangle.

From the given right angle triangle

DF represents the hypotenuse of the right angle triangle.

With m∠D as the reference angle,

DE represents the adjacent side of the right angle triangle.

EF represents the opposite side of the right angle triangle.

To determine EF, we would apply the Sine trigonometric ratio

Sin θ = opposite side/hypotenuse. Therefore,

Sin 26 = EF/4.5

0.44 = EF/4.5

EF = 4.5 × 0.44 = 1.98 yo 2 decimal places

Answer:

1998

y=6x+1944

Step-by-step explanation:

The percentage of Male workers who prefer a female boss over a male boss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss

it is explicit from the question that 9% of male workers prefer female boss in 1998. but we can predict a model for this by getting the slope of the graph

y=the year

x=the percentage of men who prefer a female boss

s=y2-y1/(x2-x1)

s=1998-1974/(9-5)

s=24/4

s=6

therefore we have

y=mx+c

y=6x+c........1

when y=1998,x=9

1998=6(9)+c

c=1944

from equation 1

y=6x+1944

Answer:

Sample

Step-by-step explanation:

The part or portion of a population is called as sample. The given data represents a sample because a questionnaire is given to the selected 40 college students for collecting response on athletic participation rather to all of the college students. Thus, the questionnaire is given to a part of population. So, the given data represents a sample.

Answer:

Step-by-step explanation:

1) The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 2 years

P = $500

R = 5%

Therefore

I = (500 × 5 × 2)/100

I = $50

2) Principal, P = $500

It was compounded monthly. This means that it was compounded 12 times in a year. So

n = 12

The rate at which the principal was compounded is 3%. So

r = 3/100 = 0.03

It was compounded for just 2 years. So

t = 2

The formula for compound interest is

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

A = total amount in the account at the end of t years. Therefore

A = 500 (1+0.03/12)^12 × 2

A = 500 (1.0025)^24

A = $530.88

The interest is

530.88 - 500 = $30.88

Answer:

A) zero; cannot

Step-by-step explanation:

In line with the principle of rational expectations, expectation errors are unpredictable. The expectations of all available information will not differ from the optimal projections.The word optimal projection is inexorably intertwined with the best guess in rational expectations theory.