Question 43 of 50
The graph of an exponential function that is increasing is ƒ(x) = (1/5)x.

False

True

Answer: x=-2

Step-by-step explanation:

they’re corresponding angles meaning they’re congruent or equal to each other then solve like any other problem

Answer:

$33

Step-by-step explanation:

l=prt = 30 × 0.05 × 2=3

total save = 30+ 3= 33

[tex]\fbox{x=$\dfrac{3}{2}$}[/tex] or [tex]\fbox{x=1.5}[/tex]

Simplify Equation:

[tex]24-10x=9[/tex]

[tex]-10x+24=9[/tex]

Subtract 24 from both sides:

[tex]-10x+24-24=9-24[/tex]

[tex]-10x=-15[/tex]

Divide both sides by -10:

[tex]\dfrac{-10x}{-10} =\dfrac{-15}{-10}[/tex]

[tex]x=\dfrac{3}{2}[/tex] or [tex]x=1.5[/tex]

Answer:

1/3

Step-by-step explanation:

shaded is 10 and unshaded is 15

so the answer is 1/3 because

5 can be multiplied both sides

5 times 3 is 15

5 times 1 is 5

So both sides can be multiplied by 5

Answer: alt account

Step-by-step explanation:

Answer:

a=9+b−c

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 1/4-3/4=5/4-3/4=(5-3)/4=2/4=1/2

(-2/3)3=-8/27

Answer:

It's 32.

Step-by-step explanation:

Multiply 16 x 2 = 32.

I hope this helps.

Answer: x=3

Step-by-step explanation:

Assuming you want to solve the system,

You are already given y = 4, so plug 4 in for the other y in the other equation.

[tex]y=\frac{8}{3} x-4\\\\4=\frac{8}{3} x-4\\4+4=\frac{8}{3} x-4+4\\\frac{3}{8}\times 8=\frac{3}{8} \times\frac{8}{3}x\\\\x=3[/tex]

Compounded quarterly; annual interest rate is 7.875%

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

Explanation:

Let's say we are depositing P = 100 dollars, and we leave it in the account for a timespan of t = 1 year.

This will apply for options A through E.

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

If we go with option A, then we would have n = 1 and r = 0.08

Use the compound interest formula to get the following:

A = P*(1+r/n)^(n*t)

A = 100*(1+0.08/1)^(1*1)

A = 108

We'll have $108 dollars in the account at the end of 1 year if we go with option A. The amount of interest only is A-P = 108-100 = 8 dollars.

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

For option B, we have: n = 4 and r = 0.07875

A = P*(1+r/n)^(n*t)

A = 100*(1+0.07875/4)^(4*1)

A = 108.110625948487

A = 108.11

So far option B is slightly better since you've earned an extra $0.11, aka 11 cents.

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

For option C, we have: n = 4 and r = 0.07875

A = P*(1+r/n)^(n*t)

A = 100*(1+0.0775/12)^(12*1)

A = 108.031299777277

A = 108.03

This amount is less compared to the $108.11 with option B. Therefore, option B is still the best so far.

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

For option D, we have: n = 52 and r = 0.07625

A = P*(1+r/n)^(n*t)

A = 100*(1+0.07625/52)^(52*1)

A = 107.917207523206

A = 107.92

This is worse compared to option C.

Option B is still the best so far.

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

For option E, we have: n = 365 and r = 0.075

A = P*(1+r/n)^(n*t)

A = 100*(1+0.075/365)^(365*1)

A = 107.787584644

A = 107.79

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

Here's a table comparing the balance after 1 year for options A through E. Those balances all have a starting point of $100 as the deposit.

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Option} & \text{Balance after 1 year}\\\cline{1-2}A & \$108\\\cline{1-2}\boldsymbol{B} & \boldsymbol{\$108.11}\\\cline{1-2}C & \$108.03\\\cline{1-2}D & \$107.92\\\cline{1-2}E & \$107.79\\\cline{1-2}\end{array}[/tex]

Option B is the best choice earning the most ($108.11) if you deposit $100.

There's nothing special about the $100, so feel free to change it to something else to try other starting deposits. You'll find that option B will still provide the highest return.

Answer:

B

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Use the Compound Interest Formula with the given values for each option to calculate a final equation where A equals a multiple of P.  

The option with the greatest coefficient of P is the account which yields the highest interest after one year, and is therefore the best deal.

Given:

Substitute the given values into the formula:

[tex]\implies \sf A=P\left(1+\dfrac{0.08}{1}\right)^1[/tex]

[tex]\implies \sf A=1.08P[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies \sf A=P\left(1+\dfrac{0.07875}{4}\right)^{4 \cdot 1}[/tex]

[tex]\implies \sf A=P\left(1.0196875)^4[/tex]

[tex]\implies \sf A=1.081106259P[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies \sf A=P\left(1+\dfrac{0.0775}{12}\right)^{12\cdot 1}[/tex]

[tex]\implies \sf A=P\left(1.006458333\right)^{12}[/tex]

[tex]\implies \sf A=1.080312998P[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies \sf A=P\left(1+\dfrac{0.0765}{52}\right)^{52\cdot 1}[/tex]

[tex]\implies \sf A=P\left(1.001471154\right)^{52}[/tex]

[tex]\implies \sf A=1.079441506P[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies \sf A=P\left(1+\dfrac{0.075}{365}\right)^{365\cdot 1}[/tex]

[tex]\implies \sf A=P\left(1.000205479\right)^{365}[/tex]

[tex]\implies \sf A=1.077875846P[/tex]

[tex]\begin{array}{|c|l|}\cline{1-2} \sf Answer\;Option & \sf Coefficient\;of\;P\\\cline{1-2} A & 1.08\\\cline{1-2} B & 1.081106259\\\cline{1-2} C & 1.080312998\\\cline{1-2} D & 1.079441506\\\cline{1-2} E & 1.077875846\\\cline{1-2} \end{array}[/tex]

Therefore, the option with the greatest coefficient of P and therefore the best deal is option B.

The value of the logarithm of 0.81 for logarithm properties is equal to - 0.1.

Herein we must use logarithm properties to simplify a given logarithm and solve the resulting expression. The properties to be used in this question are described below:

㏒ (a / b) = ㏒ a - ㏒ b

㏒ aᵇ = b · ㏒ a

First, write the logarithmic equation:

㏒ 0.81

㏒ 81 / 100

Second, use the logarithmic property for a division:

㏒ 81 - ㏒ 100

Third, use the logarithmic property for a power:

㏒ 3⁴ - ㏒ 10²

4 · ㏒ 3 - 2 · ㏒ 10

4 · ㏒ 3 - 2

4 · 0.477 - 2

- 0.092

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The total amount, if $10,000 is invested at an APR of 4% for 10 years is $14000.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

$10,000 is invested at an APR of 4% for 10 years.

Calculate the total amount at the end as shown below:

[tex]A = p + p\times r\times t / 100[/tex]

A = 10000 + 10000 × 4 × 10 / 100

A = 10000 + 4000

A = 14000

Similarly, solve all the questions using this formula.

Therefore, the total amount, if $10,000 is invested at an APR of 4% for 10 years is $14000.

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The complete question is:

$10,000 is invested at an APR of 4% for 10 years. Find the total amount after 10 years.

Answer: x= (2)/5 & x= (-2)/5

Step-by-step explanation:

Factor Form:

1. Use the sum product patturn

25x^2-4=0 → 25x^2+10-10-4=0

2. Common factors from each pair

25x^2+10-10-4=0 → 5x(5x+2)-2(5x+2)=0

3. Rewrite the factored form

5x(5x+2)-2(5x+2)=0 → (5x+2)(5x-2)=0

4. Create separate equations

(5x+2)(5x-2)=0 → 5x+2=0  5x-2=0

5. Solve

5x+2=0  5x-2=0 → x=(2)/5   x=(-2)/5

Answer: 72 for HJ.

Step-by-step explanation:

Answer:

z = 3.125 * x

Step-by-step explanation:

since y is 80 percent of z, we can represent it in the form of a ratio as 80:100.

Simplify it down: 80:100 = 8:10 = 4:5

therefore x:y = 2:5
and y:z = 4:5

"y" is common in both of these ratios. Therefore we now have to make the value of Y same in both of the ratios. Therefore we find the least common multiple of both the y values which is 5 and 4. It is 20.

Now we make the value of y in both the ratios 20. So we need to multiply 5 in 2:5 by 4. Since we multiplied one of the values by 4 we have to multiply the other one as well (2*4). Now our new ratio for x:y is 8:20. Do the same for the other ratio. the other ratio is 4:5. the y value here is 4. 4 needs to be multiplied by 5 to become 20. Therefore multiply 4 by 5 and multiply 5 by 4. our new ratio for y:z is 20:25

As  you can see both the y values are similar now.

x:y = 8:20

y:x = 20:25

therefore we can now write x:y:z as 8:20:25

that also means that x:z is now 8:25.

Now we know that when x is 8 z is 25. in this case. 8 and 25 are directly proportional.

therefore we can write an equation as
25 = k*8
k = 25/8

k = 3.125

therefore z = 3.125 * x

Answer:

Camilla will win.

Step-by-step explanation:

Camilla's rate = 12

Gabriella's rate = 10

The number is -136.

Two or more expressions with an equal sign are defined as an equation.

Let the number be x.

Given that, two more than the number, x, is 15 less than the product of 7/8 and the number, therefore:

x + 2 = (7/8)x - 15

x - (7/8)x = -15 -2

x/8 = -17

x = -136

Hence, the number is -136.

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Answer: 1.3 centimeters

Step-by-step explanation:

.013 x 100 = 1.3

Answer:

3cm,4cm,5cm

Step-by-step explanation:

5 is the longest side ( the hypotenuse)

and by Pythagoras theorem x=√(3²+4²)

= √(9+16)

=√(25)

= 5

so 3cm,4cm,5cm is a right angle triangle.

x=√(27²+36²)

=√(729+ 1296)

=√2025

=45

so 27cm,36cm,45cm is a right angle triangle

The distance between Texas and Rhode Island will be;

⇒ 2.59 × 10⁵ square miles

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

Texas 2.6* 10 to the 5th power square miles and Rhode Island 1.21 * 10 to the 3rd power square miles.

Now,

Since, Texas 2.6* 10 to the 5th power square miles and Rhode Island 1.21 * 10 to the 3rd power square miles.

Hence, The distance between Texas and Rhode Island will be find as;

⇒ 2.6 × 10⁵ - 1.21 × 10³

⇒ 260 × 10³ - 1.21 × 10³

⇒ (260 - 1.21) × 10³

⇒ 258.79 × 10³

⇒ 2.59 × 10⁵ square miles

Thus, The distance between Texas and Rhode Island will be;

⇒ 2.59 × 10⁵ square miles

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Answer:

range is { - 21, 4 , 14 }

Step-by-step explanation:

the domain gives the value of x , the input

the range is the corresponding values of y, the output

substitute values of x from the domain into the function

x = - 2 : y = - 5(- 2) + 4 = 10 + 4 = 14

x = 0 : y = - 5(0) + 4 = 0 + 4 = 4

x = 5 : y = - 5(5) + 4 = - 25 + 4 = - 21

then range is { - 21, 4 , 14 }

The point total possible for the given course is equal to 500.

What is a Percent?

In the question, it is given that you were 6 points shy of a B and the current total points you have is 394.

So, the total number of points you require for a B is calculated as,

[tex]394+6=400[/tex]

So, the value of x is 400.

It is given that you need 80% of the course total for a B.

[tex]\implies p=\frac{80}{100}\\ \implies p=0.8[/tex]

Here, we have to find the base number (b).

We have, x = 80% of b

[tex]\implies x=0.8 \times b\\\implies 400= 0.8 \times b\\\implies x=\frac{400}{0.8}[/tex]

Simplifying, we get

[tex]x=500[/tex]

Therefore, 500 points were possible in the course.

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The weight of the bicycle is 19.375 pounds.

In physics and engineering, the weight of an object refers to the gravitational force that pulls on it. Weight is frequently described as a scalar quantity that measures the gravitational force's strength.

The weight of the frame of the bicycle= 16 pounds

1 pound= 16 ounces

Therefore, 16 pounds= 16 x 16 = 256 ounces

The weight of one tire= 9 ounces

Therefore, the weight of two tires= 9 x 2 = 18 ounces

The weight of the seat= 12 ounces

The weight of handlebars= 24 ounces

Therefore, the total weight of the bicycle = 256 + 18 + 12 + 24                                                                              

                                                                     = 310 ounces

Therefore, the bicycle weighs 310 ounces

That is 310/ 16 = 19.375 pounds

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The correlation of the data shown on the graph is 0

In this question, the graph represents the given parameter

From the graph, we have the following observations

When the change (increase) in the x values causes a random change (increment) in the y values, then the correlation is 0

From the list of options, we have

-1, -0.5 and 1 are not zero i.e. 0

This means that the correlation is (a) 0

Hence, the correlation of the data is 1

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The fractions 25/150, 28/154, or 27/62 aren't equivalent.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In order to know if they're equivalent fractions, we can convert them to percentage. This will be:

25/150 × 100 = 16.7%

28/154 × 100 = 18.2%

27/62 × 100 = 43.5%

In this case they're not equivalent.

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Answer:1/8

Step-by-step explanation:

The reciprocal of a number is what you multiply by a number to give 1. Therefore

8x = 1

x = 1/8

Answer:6/39=2/13

Step-by-step explanation:the spell check need 2/13 like 1.5sec to check one words