Question 4 (2 points)
Determine if the following statements are always, sometimes, or never true.

Answer:

Rayshawn originally had $30.

Step-by-step explanation:

i) Rayshawn has a certain amount of money. Let us say this amount is $x.

ii) Rayshawn spends $20 which means that he is left with $(x - 20)

iii) it is also given that amount of money left after spending $20 is [tex]\dfrac{1}{3}[/tex] of the original amount, $x, the amount remaining is [tex]\dfrac{\$x}{3}[/tex].

iv) from the information given in ii) and iii) we get

     $(x - 20) = [tex]\dfrac{\$x}{3}[/tex],  Therefore we get 3x - 60 = x , therefore 2x = 60,

  Therefore x = $30. Rayshawn originally had $30.

Therefore, Rayshawn had $60 initially.

If Rayshawn spends $20 and ends up with 1/3 of the original amount, we can deduce that $20 represents 2/3 of the original amount.

since 1 - 1/3 = 2/3. Thus, each part (1/3) of the original amount corresponds to $20. Consequently, to find the original amount, we multiply $20 by 3, yielding $60. Therefore, Rayshawn originally had $60. This conclusion emerges from understanding that after spending $20, Rayshawn retains 1/3 of his original funds, implying that the $20 spent was equal to 2/3 of his initial sum. Thus, the inverse operation, multiplying by 3, unveils the original amount. Therefore, Rayshawn had $60 initially.

Answer: (x−3)(x+7)

=(x+−3)(x+7)

=(x)(x)+(x)(7)+(−3)(x)+(−3)(7)

=x^2+7x−3x−21

=x^2+4x−21

The product of (x-3) and (x+7) is x² + 4x - 21

The product of (x - 3) and (x + 7) can be found as follows:

(x - 3)(x + 7)

open the bracket by multiplying

Therefore,

x(x) +x(7) - 3(x) - 3(7)

x² + 7x - 3x - 21

combine like terms

x² + 4x - 21

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Answer:

B is the answer. ........

Answer:

B

Step-by-step explanation:

it intercepts the y line at -1 and the rise over run is 3

Expression that gives the ticket cost in dollars for a group of g girls and b boys is (8g + 8b) dollars

Solution:

Given that tickets to play cost $ 8 each

To find: Expression that gives the ticket cost in dollars for a group of g girls and b boys

From given,

cost of 1 ticket = $ 8

Number of girls = g

Number of boys = b

Thus the expression can be framed for total cost as:

Total cost = (number of girls + number of boys)(cost of 1 ticket)

[tex]Total\ Cost = (g + b) \times 8\\\\Total\ Cost = 8g + 8b[/tex]

Thus the expression that gives total cost is (8g + 8b) dollars

Answer:

12

Step-by-step explanation:

Answer: 4,690.33

Step-by-step explanation:

The formula for calculating amount is given by :

A = P [tex](1+r)^{n}[/tex]

Where :

A = amount = ?

P = Principal = 3500

r = rate = 0.05

n = number of years  = 6

substituting the given values into the formula , we have

A = 3500[tex](1+0.05)^{6}[/tex]

A = 3500 [tex](1.05)^{6}[/tex]

A = 3500 (1.340095640625)

A = 4690.3347421875

A = 4,690.33

Final answer:

To calculate Colin's investment with compound interest after 6 years, we use the formula for compound interest and determine that he will have £4690.33 to the nearest penny.

Explanation:

To calculate how much Colin will have after 6 years with compound interest, we use the formula for compound interest:

A = P(1 + r/n)nt

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

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

t is the time the money is invested for, in years.

In Colin's case, we have:

P = £3500

r = 5% or 0.05

n is not mentioned, so we assume it is compounded once per year, thus n = 1

t = 6 years

Plugging these values into the formula:

A = £3500(1 + 0.05/1)1×6 = £3500(1 + 0.05)6

A = £3500 × (1.05)6 = £3500 × 1.340095

A = £4690.3325

To the nearest penny, Colin will have
£4690.33 after 6 years.

Answer:

20 + 10w = total cash saved

=======================================

C(n, r) = (n!)/(r!*(n-r)!) is the combination formula

C(7, 5) = (7!)/(5!*(7-5)!)

C(7, 5) = (7!)/(5!*2!)

C(7, 5) = (7*6*5!)/(5!*2!)

C(7, 5) = (7*6)/(2!) ..... note the "5!" terms divided and canceled

C(7, 5) = (7*6)/(2*1)

C(7, 5) = 42/2

C(7, 5) = 21

Answer:

(4+1+2)3= 21

Step-by-step explanation:

you add the cost of snacks then multiply by 3 because there are 3 people to get total cost.

Answer:

4+4+4+1+1+1+2+2+2=25

Answer:

Step-by-step explanation:

Since the candy bar is just one

Giving 1/4 of it to her younger sister make her left with 3/4 of the candy bar i.e 1 - 1/4 = 3/4

Then giving 1/3 of the left over to her elder sister it becomes 3/4 * 1/3 =1/4

Then the remaining candy bar will be 3/4 - 1/4 = 1/2

Then she will be left with 1/2 i.e half of the candy bar.

Answer:

See below for the graph:

Step-by-step explanation:

Answer: x≈3

Step-by-step explanation:

0.48 = log x , this could also be written as :

[tex]log_{10}[/tex] x = 0.48 , that is

x = [tex]10^{0.48}[/tex]

x = 3.01995172

x≈ 3

The solution to the equation 0.48 = log x is approximately 3.02 after converting it from logarithmic form into exponential form and calculating 10 to the power of 0.48.

To solve the logarithmic equation 0.48 = log x we have to rewrite this equation in exponential form. A logarithm log_b(x) = y in exponential form is represented as b^y = x. Considering that in your question it's not specified, this likely means a base of 10 is being used. Hence, the equation 0.48 = log x can be converted into exponential form: 10^0.48 = x.

Performing the calculation with a calculator (or by hand if you know how), we find x ≈ 3.02. Therefore, the solution for x in the given equation is approximately 3.02.

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Answer:

x=11

Step-by-step explanation:

since ad bisects bac, bad=dac

32=3x-1

+1    +1

3x=33

/3    /3

x=11

The given polygons are similar

Step-by-step explanation:

By observing the given diagrams, we can see that the respective angles are congruent.

Two shapes are said to be similar if they have same shapes or one shape is created by uniformly increasing or decreasing the side of other.

For this purpose we find the scale factor of greater to smaller image, if the scale factor is same for each side then the two shapes are similar

So,

The scale factor is:

[tex]\frac{EF}{AB} = \frac{3}{1} = 3\\\\\frac{FG}{BC} = \frac{9}{3} = 3\\\\\frac{GH}{CD} = \frac{15}{5} = 3\\\\\frac{EH}{AD} = \frac{21}{7} = 3[/tex]

We can see that the scale factor is same for all sides.

Hence,

The given polygons are similar

Keywords: Polygons, similarity

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Answer:

[tex]AE=20\ units[/tex]

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles AEB and DEC are similar by AA Similarity Theorem

so

[tex]\frac{AB}{DC}=\frac{AE}{DE}[/tex]

substitute the given values and solve for x

[tex]\frac{10}{4}=\frac{2x+10}{x+3}[/tex]

Multiply in cross

[tex]10x+30=8x+40\\10x-8x=40-30\\2x=10\\x=5[/tex]

Find the length side AE

[tex]AE=2x+10[/tex]

substitute the value of x

[tex]AE=2(5)+10=20\ units[/tex]

The perimeter of original garden is 42 feet

The perimeter of enlarged garden is 82 feet

Solution:

The perimeter of rectangle is given as:

Perimeter = 2(length + width)

Given that,

The garden is rectangular with width 6 feet and length 15 feet

Length = 15 feet

Width = 6 feet

Therefore, perimeter is given as:

Perimeter = 2(15 + 6)

Perimeter = 2(21)

Perimeter = 42

Thus perimeter of original garden is 42 feet

The new garden will be similar to the original one, but will have a length of 35 feet.

Length = 35 feet

Width = 6 feet

Therefore, perimeter is given as:

Perimeter = 2(35 + 6)

Perimeter = 2(41) = 82

Thus perimeter of enlarged garden is 82 feet

Answer:

Step-by-step explanation:

Answer:

She will need 191.55 pounds of flour.

Step-by-step explanation:

Given:

Audrey needs 2.4 pounds if flour for birthday cakes and 3.75 pounds of flour for wedding cakes.

If she plans on baking 72 birthday cakes and 5 wedding cakes.

Now, to find pounds of flour will she need.

So, the pounds of flour for 72 birthday cakes:

[tex]2.4\times 72[/tex]

[tex]=172.8\ pounds.[/tex]

And, the pounds of flour for 5 wedding cakes:

[tex]5\times 3.75[/tex]

[tex]=18.75\ pounds.[/tex]

Now, to get the pounds of flour she need we add the pounds of flour to make 72 birthday cakes and 5 wedding cakes:

[tex]172.8+18.75[/tex]

[tex]=191.55\ pounds.[/tex]

Therefore, she will need 191.55 pounds of flour.

Given the function [tex]f(x)[/tex]

[tex]f(x)+k[/tex] — will shift the graph vertically by k

[tex]f(x-k)[/tex] — will shift the graph horizontally by k

[tex]kf(x)[/tex] — will stretch the graph vertically by k

[tex]f(kx)[/tex] — will stretch the graph horizontally by k

Answer:

c

Step-by-step explanation:

going negative stops at 4

1. The possible solution for x + y is 8 ⇒ d

2. The possible solution for m - n is 16 ⇒ a

Step-by-step explanation:

Lets explain some notes about the even numbers

1.

∵ x and y are both even whole numbers

∴ Their sum is even whole number

∵ 5 and 9 are odd numbers ⇒ impossible

∵ 4.6 is not a whole number ⇒ impossible

∵ 8 is an even whole number ⇒ possible

∴ x + y could be 8

The possible solution for x + y is 8

2.

∵ n and m are both even whole numbers

∵ m > n

∴ m - n must be positive even whole number

∵ 1/2 is not a whole number ⇒ impossible

∵ 0 is not a positive number ⇒ impossible

   (zero is not positive nor negative)

∵ -2 is not a positive number ⇒ impossible

∵ 16 is a positive even whole number ⇒ possible

∴ m - n could be 16

The possible solution for m - n is 16

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Answer:

what is the question

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Okun's law says that a country's gross domestic product (GDP) must grow at about a 4% rate for one year to achieve a 1% reduction in the rate of unemployment.

Option D is correct.

Since, According to Okun's law a country's gross domestic product (GDP) must grow at about a 4% rate for one year to achieve a 1% reduction in the rate of unemployment.

So, if the unemployment rate goes from 6% to 2%, that is reduce by 4%

Therefore, GDP is increase by 4(4 %) = 16 %

Thus, most appropriate answer is option D, that is GDP will increase by 11% .

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An exterior angle is equal to the sum of the two opposite inside angles.

T + 31 = t + t-29

Simplify:

T + 31 = 2t -29

Add 29 to both sides:

T + 60 = 2t

Subtract 1t from both sides:

T = 60

Answer:

x = -43/6

Step-by-step explanation:

To solve this equation, you solve for 'x' by isolating it. This means to move every other number to the other side of 'x'. You can move numbers when they 'cancel' out by doing the opposite (Adding and subtracting are opposites. Dividing and multiplying are opposites).

[tex]\frac{3x-2}{6}-\frac{4x+1}{4} = 3[/tex]

[tex]\frac{3x-2}{6}*\frac{2}{2}-\frac{4x+1}{4}*\frac{3}{3} = 3[/tex]     Multiply each fraction by a fraction that equals '1'. (2/2 = 1 and 3/3 = 1). This will give them a common denominator.

[tex]\frac{(3x-2)*2}{6*2}-\frac{(4x+1)*3}{4*3} = 3[/tex]     Multiply

[tex]\frac{(6x-4)}{12}-\frac{(12x+3)}{12} = 3[/tex]

[tex]\frac{(6x-4)-(12x+3)}{12}= 3[/tex]     Combine the fractions with the same denominator

[tex]\frac{(6x-4)-12x-3}{12}= 3[/tex]     Subtract binomials. -(12x+3) is -12x-3

[tex]\frac{6x-4-12x-3}{12}= 3[/tex]     Remove unnecessary brackets

[tex]\frac{-6x-7}{12}= 3[/tex]     Combined like terms.

[tex]\frac{-(6x+7)}{12}= 3[/tex]     Factor out the negative in the top.

[tex]-(6x+7)= 3*12[/tex]     Multiplied both sides by 12

[tex]-(6x+7)= 36[/tex]     Simplified right side

[tex]6x+7= -36[/tex]     Divided both sides by -1

[tex]6x= -36-7[/tex]     Subtract 7 from both sides

[tex]6x= -43[/tex]     Simplified right side

[tex]x= \frac{-43}{6}[/tex]     Divided both sides by 6. Answer in fraction form.

x = 7.166..67     Answer in decimal form

Therefore x is -43/6 or about 7.17.

Answer:

x = 130°

Step-by-step explanation:

Segment AC tangent to circle O then ∠A = 90°

Segment BC tangent to circle O then ∠B = 90°

finally ,

x = 360 -(90+90+50) = 360-230 = 130

Answer:

x = 130°

Step-by-step explanation:

Answer:

2/4, 3/6, 4/8, 5/10, 6/12

Step-by-step explanation:

Equivalent fractions are fractions that have the same value or represent the same part of an object. If a pie is cut into two pieces, each piece is also one-half of the pie. If a pie is cut into 4 pieces, then two pieces represent the same amount of pie that 1/2 did. We say that 1/2 is equivalent to 2/4.

Fractions are determined to be equivalent by multiplying the numerator and denominator of one fraction by the same number. This number should be such that the numerators will be equal after the multiplication. For example if we compare 1/2 and 2/4, we would multiply 1/2 by 2/2 which would result in 2/4 so they are equivalent.

To compare 1/2 and 3/7 we would multiply 1/2 by 3/3 to produce 3/6. Since 3/6 is not the same as 3/7, the fractions are not equivalent.

Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12 ...

Fractions equivalent to 1/3 are 2/6, 3/9, 4/12, 5/15, ...

Fractions equivalent to 1/4 are 2/8, 3/12, 4/16, 5/20, ...

Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25, ...

Fractions equivalent to 2/5 are 4/10, 6/15, 8/20, 10/25, ...

Answer:2/4 3/6 4/8 5/10 6/12

Answer:

b

Step-by-step explanation: