Explain whether the Federal Reserve reducing interest rates helps to expand economic growth. (1 point) Responses
1. Reducing interest rates does not help the economy expand because prices of goods and services decrease from reduced demand.
2. Reducing interest rates does not help the economy expand because businesses save instead of spend with low-interest rates, slowing economic growth.
3. Reducing interest rates helps the economy expand because it lowers the cost of borrowing for business to expand, leading to more jobs and economic growth.
4. Reducing interest rates helps the economy expand because businesses earn a greater return on their savings, leading to additional spending and economic growth.

Answer:

See below

Step-by-step explanation:

-1.887 x10^2   would be one answer

- 18.87 x 10^1    could be another

Answer:

Step-by-step explanation: Wowee! That's pretty hard.

Scientific Notation:

-1.887 × 102

E-Notation:

-1.887e2

Engineering Notation:

-188.7 × 100

Real Number:

-188.7

Hope this helps!

The distance between the given parallel lines is 4 units

In the given statement is :

The equations of the pair of each parallel lines is:

y=-0.75 x-1

3 x+4 y=20

To find the distance between each pair of parallel lines.

Two lines a₁x +b₁y + c₁=0   and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.

As we know that distance between the parallel lines (d) is given as:-

d = [tex]\frac{c_{2}-c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]

Parallel lines equation as:

y=-0.75 x-1...(1)

3 x+4 y=20....(2)

Divide by -3 in equation (2)

Now, The equations is

-0.75x -y -1 =0

-0.75x -y +4 =0

Here,

a = -0.75 , b = -1, c1 = -1 , c2 = 4

Therefore, putting the values

[tex]d =\frac{4-(-1)}{\sqrt{(-0.75^{2} )+(-1)^{2} } } \\\\d=\frac{5}{\sqrt{0.5625+1} }\\ \\d = \frac{5}{\sqrt{1.5625} }[/tex]

d = 4 units

Hence, The distance between the given parallel lines is 4 units

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The value of k is 5/9(F-32) + 273.15.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other.

Given:

F=9/5(k-273.15)+32

On solving for k

F-32 = 9/5 (k-273.15)

(F-32)*5/9 = (k-273.15)

5/9(F-32) + 273.15 = k

k=5/9F - 290.927

Hence, the value of k is 5/9F - 290.927.

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Answer:

1 hour has 3600 seconds

to get how many dollars Jack earns we have to do this

3600 sec x $0.02 = $72

40 weeks x $72 = $2880

Answer:

$149,760

Step-by-step explanation:

As:

⇒ 1 hour = 60 × 60 seconds = 3600 seconds

As:

⇒ 52 × 40 = 2080 hours per year

Therefore, the number of seconds Jack works per year is:

⇒ 2080 × 3600 = 7,488,000 seconds

If Jack earns $0.02 per second, then the number of dollars per year he earns is:

⇒ $0.02 × 7,488,000 = $149,760

Answer:

The first one would be -11x + 3

The second on would be 29x + 3

Step-by-step explanation:

For the first equation you add -2 to 5 so you have 9x+3-20x. Then you add the 9x to -20x which will leave you with -11x+3.

For the second equation you add the -2 to 5 and have 9x+3+20x. You add 9x to 20x which will leave you with. 29x+3

Answer:

1.55N

Step-by-step explanation:

F=ma

m=310g=0.31kg

a=5m/s^-2.

F=0.31×5

F=1.55N

The equation for the slant asymptote of g(x) = [tex]\frac{3x^2+5x+6}{x+3}[/tex] is 3x-4

The function, g(x) = [tex]\frac{3x^2+5x+6}{x+3}[/tex]

We need to find its slant asymptote. The slant asymptote is determined by checking [tex]\lim_{x \to \infty}( g(x)-(ax+b)) = 0[/tex] .

So we first divide the polynomial [tex]3x^2+5x+6[/tex] by x+3 to find such an (ax+b).

        3x - 4  

x+3 | [tex]3x^2+5x+6[/tex]

    -   [tex]3x^2+9x[/tex]

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

       -4x + 6

       -4x - 12   -

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

               18  

Therefore, [tex]\frac{3x^2+5x+6}{x+3}[/tex] = 3x - 4 + [tex]\frac{18}{x+3}[/tex]

⇒  [tex]\frac{3x^2+5x+6}{x+3}[/tex] - 3x - 4 =  [tex]\frac{18}{x+3}[/tex]

⇒ [tex]\lim_{x \to \infty}(\frac{3x^2+5x+6}{x+3}-(3x-4)) = 0[/tex]  , since [tex]\frac{18}{x+3}[/tex] [tex]\rightarrow \infty[/tex] as [tex]x \rightarrow \infty[/tex].

So the equation for the slant asymptote of g(x) = [tex]\frac{3x^2+5x+6}{x+3}[/tex] is 3x-4

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By elimination, the solution of the system of equations, x - y + z = -1, x + y + 3z = -3 and 2x - y + 2z = 0, is  (4 , 2 , -3).

Given:

x - y + z = -1     (equation 1)

x + y + 3z = -3     (equation 2)

2x - y + 2z = 0     (equation 3)

Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.

Subtracting equations 1 and 3 will eliminate the variable y.

2x - y + 2z = 0     (equation 3)

 x - y + z = -1   (equation 1)

x        + z = 1     (equation 4)

Adding equations 2 and 3 will eliminate the variable y.

x + y + 3z = -3     (equation 2)

2x - y + 2z = 0     (equation 3)

3x      + 5z = -3     (equation 5)

Multiply equation 4 by -5 and add with equation 5.

x + z = 1     (equation 4)

⇒ -5x - 5z = -5

+    3x + 5z = -3     (equation 5)

-2x             = -8

x = 4

Substitute the value of x to either equation 4 or 5 and solve for z.

x + z = 1     (equation 4)

4 + z = 1

z = 1 - 4

z = -3

Finally, substitute the value of x and z to any of the first three equations, and solve for y.

x - y + z = -1     (equation 1)

4 - y + (-3) = -1

-y = -1 - 4 + 3

-y = -2

y = 2

Checking if the values x = 4, y = 2, and z = -3 satisfies all the three equation.

x - y + z = -1     (equation 1)

4 - 2 + (-3) = -1

-1 = -1

x + y + 3z = -3     (equation 2)

4 + 2 + 3(-3) = -3

-3 = -3

2x - y + 2z = 0     (equation 3)

2(4) - 2 + 2(-3) = 0

0 = 0

Hence, the solution of the system of equations is (4 , 2 , -3).

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Answer:

Adding +6 in turn

Step-by-step explanation:

-13 + 6 = (-7)

(-7) + 6 = (-1)

(-1) + 6 = 5

5 + 6 = 11

11 + 6 = 17

17 + 6 = 23

23 + 6 = 29

29 + 6 = 35

...........And so on

Answer:

Step-by-step explanation:

In all three pictures, the data are correctly matching except this one..

~~

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

They are congruent triangles.

What do you mean by congruent?

In the triangle JKL, the sides can be calculated as following:

J(2;5); K(1;1)

            => JK = [tex]\sqrt{( ( 1 - 2 )^{2} + ( 1 - 5 )^{2} } = \sqrt{( -1 )^{2} + ( -4)^{2} } \\= \sqrt{ 1 + 16 } = \sqrt{17}[/tex]

J(2;5); L(5;2)

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

                 = [tex]\sqrt{ 9 + 9 } = \sqrt{18} = 3\sqrt{2}[/tex]

K(1;1); L(5;2)

            =>  KL = [tex]\sqrt{ ( 5 - 1 )^{2} + ( 2 - 1 )^{2} } = \sqrt{4^{2} + 1^{2} } = \sqrt{ 1 + 16} = \sqrt{17}[/tex]

In the triangle QNP, the sides can be calculate as following:

Q(-4;4); N(-3;0)

            => QN  = [tex]\sqrt{[ -3 - ( -4)^{2} ] + ( 0-4)^{2} } = \sqrt{1^{2} + 16 } = \sqrt{17}[/tex]

Q (-4;4); P(-7;1)

  => QP =  [tex]\sqrt{ [ -7 - ( -4 )^{2} + ( 1 - 4 )^{2} } = \sqrt{( -3)^{2} + ( -3)^{2} } = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}[/tex]

N(-3;0); P(-7;1)

      =>  NP = [tex]\sqrt{[-7 -( -3)]^{2} + ( 1 - 0 )^{2} } = \sqrt{ - 4^{2} + 1 } = \sqrt{ 16 + 1} = \sqrt{ 17}[/tex]

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

=> They are congruent triangles

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Yes; The jenni write the converse statement properly. it is an equilateral triangle.

A statement is a declarative sentence that is either true or false but not both. It is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

We have been Given that each angle of a triangle measures 60°, then the sum of the measures of all the angles is 180°.

And the converse is that the sum of all the angles inside of a triangle is 180°, then each angle measures 60°.

However,  we know that the sum of all angles of an equilateral triangle is 180. each having 60 degrees.

The jenni write the converse statement properly.

Therefore, the correct statement is Yes; an equilateral triangle.

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Answer:

d. Yes; a scalene triangle

Step-by-step explanation:

The correct option is E. √26.

The distance between the points A and B is √26.

Algebraic representation that gives the distances between two points based on of those coordinates (see coordinate system). The distance formulas for points throughout rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.

Now, as per the given question;

The coordinates of the points A and B are  (-2,4) and (3,3).

The formula of distance formula is written as for the points A and B ia-

AB² = (x₂ - x₁)² + (y₂ - y₁)²

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

The coordinates of A and B are-

(x₁,y₁) = (-2,4)  and (x₂,y₂) = (3,3).

Substituting the values in the formula;

AB = √[(3 + 2)² + (3 - 4)²]

AB = √[(5)² + (-1)²]

AB = √[25 + 1]

AB  = √26

Therefore, the distance between the coordinates A and B is found to be √26.

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If a red string of holiday lights blinks every 3 seconds. a blue string of holiday lights blinks every 4 seconds, then the number of times the red and blue string of holiday lights will blink in one minute is equal to 20 and 15 respectively.

The number of times each string of holiday lights will blink can be determined by using division.

As we have to calculate the number of times they blink in one minute, we can convert one minute into seconds.

One minute = 60 seconds

Now, the number of times each string of light blinks can be calculated by dividing the total seconds by the seconds after which the light blinks

For the red string of holiday lights :

The number of times the light will blink in one minute = 60 ÷ 3 = 20

For the blue string of holiday lights :

The number of times the light will blink in one minute = 60 ÷ 4 = 15

Hence the red string of holiday lights will blink 20 times and the blue string of holiday lights will blink 15 times in one minute.

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The first, second, third, fourth, and fifth term of the sequence are -1, 0, 3, 8, and 15.

According to the given question.

We have a formula or rule for finding the terms of a sequence i.e.

an =n² -2 n.

Therefore,

The first term of the sequence an =n² -2 n is given by

a(1) = 1^2 - 2(1) = 1 - 2 = -1

The second term of the sequence an =n² -2  is given by

a(2)  = 2^2 - 2(2) = 4 - 4 = 0

The third term of the sequence an =n² -2 is given by

a(3) = 3^3 - 2(3) = 9 - 6 = 3

The fourth term of the sequence  an =n² -2 is given by

a(4) = 4^2 - 2(4) = 16 - 8 = 8

The fifth term of the sequence an =n² -2 is given by

a(5) = 5^2 - 2(5) = 25 - 10 = 15

Hence, the first, second, third, fourth, and fifth term of the sequence are -1, 0, 3, 8, and 15.

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Answer: Since the radius of the circle is perpendicular to AB, AB is tangent to the circle.

Step-by-step explanation:

Answer:

perpendicular and tangent

Step-by-step explanation:

The surface area of the concerned cylinder is 263.76 sq. ft..

As per the question statement, we are provided with a reference picture of a cylinder, attached hereby, having a height of 11 feet and a base radius of 3 feet and also, the formula to calculate the surface area, along with the value of Pi to be considered for calculations and instructions about not rounding off our final answer.

We are required to calculate the surface area of the above mentioned cylinder.

The formula to calculate the surface area of the cylinder is provided in the reference picture itself which goes as [SA = (2πr² + 2πrh)], where, "r" is the base radius of the cylinder, and "h" is the height of the cylinder.

Here, (r = 3) and (h = 11), and using these values in the above mentioned formula to calculate the surface area of the cylinder, we get,

Surface Area of our concerned cylinder

[tex]= [(2*3.14*3^{2})+(2*3.14*3*11)]\\= [(2*3.14*9)+(66*3.14)]\\=(56.52+207.24)\\=263.76[/tex]

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An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.

If the expression be (-3)(-9) then the value of (-3)(-9) is 27.

Let (-3)(-9) be the given expression

We know the rule , (-) × (-) = (+)

(-3) × (-9) = +27

Therefore, the value of (-3)(-9) is 27.

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Answer:

See proof below

Step-by-step explanation:

[tex]4cos^2(x) +4sin(x) = 5\\\\\sf Divide\; both \; sides\; by\; 4\\== > cos^2(x) + sin(x) = \dfrac{5}{4} .................(1)\\\\cos^2(x) + sin^2(x) = 1\\\\cos^2(x) = 1- sin^2(x) \\\\\textsf {Substituting into equation (1) }\\1-sin^2(x) + sin(x) = \dfrac{5}{4}\\\\\\sf Subtract\; 1\; from\; both \; sides\\\mathsf{-\sin^2(x) + \sin(x) = \dfrac{5}{4} - 1}\\\\ \dfrac{5}{4} - 1 = \dfrac{5}{4} - \dfrac{4}{4} = \dfrac{1}{4}\\[/tex]

[tex]\sf {-\sin^2(x) + \sin(x) = \dfrac{1}{4}\\[/tex]

[tex]\sf Subtract\; \dfrac{1}{4}\;from\;both\;sides\\[/tex]
[tex]{-\sin^2(x) + \sin(x) - \dfrac{1}{4} = 0\\\\[/tex]

Multiply throughout by -1
[tex]\sf \sin^2(x) - \sin(x) + \dfrac{1}{4} = 0\\\\[/tex]

Let u = sin(x). Substituting we get
[tex]\sf u^2 - u + \dfrac{1}{4} = 0[/tex]

This is a quadratic equation which can be solved using sum of squars

Note that

[tex]\sf (u - \dfrac{1}{2})^2 = u^2 -2\cdot \dfrac{1}{4}u + (\dfrac{1}{2})^2 \\= \sf u^2 - u + \dfrac{1}{4} = 0[/tex]

So
[tex]\sf (u - \dfrac{1}{2})^2 = 0\\Solution\; is \;u = \dfrac{1}{2}\\\\Substituting\sin(x) \;for\;u \;gives\\sin(x) = \dfrac{1}{2}[/tex]

PROVED

There was a question like this before. And the Answer to that question was: 95% or 95/100

The equation that we need to solve and the solution is:

A = 11.7mi/3 = 3.9 mi

We conclude that he needs to ride an average of 3.9 miles per day.

Here we know that Carter wants to ride his bicycle 28.7 miles this week, and he has already ridden 17 miles, so the distance left is:

D = 28.7 mi - 17mi = 11.7mi

Now, if he has 3 days to complete that distance, then the average distance that he needs to travel each day is given by the quotient:

A = 11.7mi/3 = 3.9 mi

So that is the equation that we need to solve and the solution, we conclude that he needs to ride an average of 3.9 miles per day.

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The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

R = x^2/y

Where

y = 3.8 x 10^5

x = 5.9 x 10^4

Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y

So, we have

R = (5.9 x 10^4)^2/3.8 x 10^5

Evaluate the exponent in the above equation

So, we have

R = 34.81 x 10^8/3.8 x 10^5

Evaluate the quotient in the above equation

So, we have

R = 9.16052631579 x 10^3

Approximate the above expression

So, we have

R = 9.2 x 10^3

Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

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Answer:

B. 4/5

Glad to help :)

Answer:

see explanation

Step-by-step explanation:

(8x - 75) and (5x) are vertically opposite angles and are congruent , then

8x - 75 = 5x ( subtract 5x from both sides )

3x - 75 = 0 ( add 75 to both sides )

3x = 75 ( divide both sides by 3 )

x = 25

Then

5x = 5(25) = 125°

8x - 75 = 8(25) - 75 = 200 - 75 = 125°

Answer: (5x)°=(8x-75)°=125°

Step-by-step explanation:

Property of vertical angles: vertical angles are equal

Hence,

[tex](8x-75)^0=(5x)^0\\(8x)^0-75^0=(5x)^0\\(8x)^0-75^0-(5x)^0=(5x)^0-(5x)^0\\(3x)^0-75^0=0\\(3x)^0-75^0+75^0=0+75^0\\(3x)^0=75^0\\[/tex]

Divide both parts of the equation by 3 :

[tex]x^0=25^0\\(5x)^0=(5*25)^0\\(5x)^0=125^0[/tex]

[tex]format \: \: y = mx + c[/tex]

[tex]m = \frac{5 - 0}{10 - 0} = \frac{5}{10} = \frac{1}{2} [/tex]

[tex]c = 0 \: since \: the \: line \: passes \: through \: the \: origin \\ [/tex]

[tex](d) \: \: \: y = \frac{x}{2} [/tex]

The amount that she would earn in one year at her part time job is 1440

Note that a function is an expression, rule or law that shows the relationship between a dependent and an independent variable.

Given the expression as;

12(100+20)

To determine the amount, we need to use the BODMAS rule by solving the bracket, we have

Amount = 12(100+20)

Amount = 12(120)

Expand the bracket

Amount = 1440

Thus, the amount that she would earn in one year at her part time job is 1440

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Number of songs that will be downloaded in 2020 = 2600 million

Given that in 2004, 200 million songs were downloaded and in 2006, 500 million songs were downloaded from the internet.

When we graph this trend, these data corresponds to the points (4,200) and (6, 500).

Also it will be a straight line. So its slope can be found.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150

This means that there is an increase of 150 million songs downloads pe year.

Also 2020-2006 = 14 years

So the number of songs downloaded in 2020 = Number of songs downloaded in 2006 + 14 x 150 = 500 + 14 x 150

                                                     = 500 +2100

                                                     = 2600 million

So 2600 million songs will be downloaded legally from the internet by 2020.

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Answer:

x = 0

Step-by-step explanation:

You are solving for x

[tex]\frac{x}{5}[/tex] + 2 = 2  Subtract 2 from both sides of the equation

[tex]\frac{x}{5}[/tex] = 0  Multiply both sides by

[tex]\frac{x}{5}[/tex]  [tex](\frac{5}{1})[/tex] =  0 [tex]\frac{5}{1}[/tex]

x = 0

One side of the garage length​ is 16.69ft

the length of one side of the garage​ now has 18 ft

increase in the one​ side's length is 70 %

According to the given data,

Floor of square garage given in the question is 216 ft

then, we get length of one side of the garage is √216

                                                                                   = 16.69 ft

after built an addition to it  garage has ​ 50% more floor space

216 × (1 + 0.5) = 324

√324 = 18 ft

The garage's one side is 18 feet long.

The length of one​ side = [tex]\frac{18}{16.69}[/tex]

                                        = 1.07

The percentage increase in one side's length is 1.07-1 = 0.07 = 70 percent.

Area of square : The area is the space covered by square object. It is the approximately occupied by any shape. While estimating the area of a square, we consider only the length of the square because all the sides of a square are equal.

Similarly, we get the area of the other shapes such as rectangle, triangle or any polygon shape, based on its sides. Area of the surface is compute based on the radius or the distance of its outer line from the axis for curved surface objects.

Area of a Square Formula

area of square formula used for calculating the area occupied, let us we find area. You are required to calculate the area of a side 5 cm. Using this dimension,  a square  having 1 cm × 1 cm squares. The square covers 36 complete squares.

Thus, the area of the square is 36 square cm, which can be written as 6cm × 6 cm, that is, side ×  side.

We know the area of a square is:

Area of a Square = Side ×  Side

and the perimeter of any square = 4 ×  side units

Here given, Some conversions of units:

1 m = 100 cm

1 sq. m = 10,000 sq. cm

1 km = 1000 m

1 sq. km = 1,000,000 sq. m

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