If you spent 24 weeks working on a project for your job and was rewarded with 3 days of vacation, write the ratio of time on vacation to time working as a fraction in lowest terms.

Answer:

200 miles were driven

Step-by-step explanation:

We know that [tex]C (m) = 0.50m + 30[/tex] represents the cost of renting a car

Where m represents the number of miles driven

If we know that the cost was $ 130 then we can equal C(m) to 130 and solve for m.

[tex]C(m) =0.50m + 30=130[/tex]

[tex]0.50m + 30=130[/tex]

[tex]0.50m=130-30[/tex]

[tex]0.50m=100[/tex]

[tex]m=\frac{100}{0.50}[/tex]

[tex]m=200\ miles[/tex]

Answer:

1961

Step-by-step explanation:

replace x with 8

25(8)^2-28(8)+585

25(64)-28(8)+585

1600-224+585

1961

f(8) = 1961.

The quadratic function given is: f(x) = 25x2 - 28x + 585

To predict f(x) when x = 8:

Substitute x = 8 into the function:

f(8) = 25(8)2 - 28(8) + 585

f(8) = 25(64) - 224 + 585

f(8) = 1600 - 224 + 585

f(8) = 1961

Therefore, f(8) equals 1961.

The answer is -65

X+(-13)=-5

x=13*-5

13 * -5= -65

x=65

An equation is formed when two equal expressions. The solution of the equation x+(-13) = -5 is 8.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the equation x+(-13) = -5 is,

x + (-13) = -5

x - 13 = -5

x = -5 + 13

x = 8

Hence, The solution of the equation x+(-13) = -5 is 8.

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Answer:

6

Step-by-step explanation:

You are given the radius, 3

The diameter is twice the radius, so 6.

Answer:

[tex]7+\sqrt{x+3}[/tex]

Step-by-step explanation:

The conjugate of a radical expression is obtained by changing the sign of the middle term.

The conjugate of [tex]a+\sqrt{b}[/tex] is simply [tex]a-\sqrt{b}[/tex]

Therefore, to obtain the conjugate of the given expression we simply shall be  changing the negative sign to positive;

The conjugate of [tex]7-\sqrt{x+3}[/tex] is simply;

[tex]7+\sqrt{x+3}[/tex]

Answer:

The set of equations has an infinite number of solutions

Step-by-step explanation:

The system of linear equations represented by the following equations:

Line A: 4x + 4y = 16 and Line B: x + y = 4 are dependent.

This is because both equations represent the same line;

if we divide both sides of the equation of line A by 4, we would obtain

x + y = 4, which is basically the equation of line B

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

Answer:

Step-by-step explanation:

The largest number is 5. Therefore x ≥ 6.

Convert numbers from x system to decimal system:

[tex]42_x=4x+2\\\\53_x=5x+3\\\\125_x=1x^2+2x+5[/tex]

Solve the equation for x:

[tex]42_x+53_x=125_x\Rightarrow4x+2+5x+3=x^2+2x+5\qquad\text{combine like terms}\\\\(4x+5x)+(2+3)=x^2+2x+5\\\\9x+5=x^2+2x+5\qquad\text{subtract 5 from both sides}\\\\9x=x^2+2x\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\0=x^2-7x\\\\x^2-7x=0\qquad\text{distributive}\\\\x(x-7)=0\iff x=0\ \vee\ x-7=0\\\\x=0<7\qquad\bold{it's\ not\ a\ solution}\\\\x-7=0\qquad\text{add 7 to both sides}\\\\x=7\qquad\bold{it's\ a\ solution}[/tex]

Answer:

108,000 females

Step-by-step explanation:

12% of 900,000 is 108,000.

Therefore, there are 108,000 female officers in the U.S.

Answer: 108,000

Step-by-step explanation:

In 2014, 900,000 sworn law enforcement officers who were serving in the United States and 12% of those officers were female. To find the number of females that were law enforcement officers, we multiply the percentage of females by the total number of law enforcement officers. This will be:

= 12% of 900000

= 12/100 × 900000

= 0.12 × 900000

= 108,000

There were 108,000 females as law enforcement officers serving in the United States.

Answer:

Commutative Property because it only switched the numbers around.

The property represented by the equation 3x(4x5)=(3x4)x5 is the Associative Property of Multiplication, which indicates that numbers' grouping does not influence the outcome of multiplication.

The property represented by the equation 3x(4x5)=(3x4)x5 is called the Associative Property of Multiplication. This property states that the way in which numbers are grouped when being multiplied does not change the product. In your equation, whether you multiply 4 and 5 first (in the expression 3x(4x5)) or 3 and 4 first (in the expression (3x4)x5), the result is the same.

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Answer:

negative infinity

Step-by-step explanation:

f(x) = 3 x^7

As x approaches - infinity we do not care about the 3 since it is positive

f(-inf) = (- inf)^7

We can take the negative out since it is to a negative power

f(-inf) = - (inf)^7

inf raised to a power is still infinity

F(-inf) = - inf

It will approach negative infinity

Answer:

x = 5 + √3,  5 - √3

which is 6.73 , 3.27 to the nearest hundredth.

Step-by-step explanation:

(x - 5)^2 = 3

Take the square root of both sides:

x - 5 = +/- √3

x = 5 + √3, 5 - √3

Answer:

x = 5 + √3 or x = 5 - √3

Step-by-step explanation:

Equation: (x - 5)² = 3

Square root: x - 5 = ±√3 <-- the square root of a number can be positive or negative.

Subtract: x = 5 + √3 or x = 5 - √3

Answer:

-14336

Step-by-step explanation:

We are given the first term (a) = 14, the common ratio (r) = -2 and the number of term (n) = 11 that we are to find for a geometric sequence.

We know that the formula of nth term for a geometric sequence is given by:

[tex]n^{th}term = ar^{n-1}[/tex]

Substituting the given values in the above formula to find the 11th term:

11th term = [tex] 14 \times 2^{11-1}[/tex] = -14336

Answer:

Half a block ( 0.5 or 1/2 )

Step-by-step explanation:

8 1/2  blocks can also be written as 8.5 blocks.

If Kira walks 8.5 blocks in 17 minutes [and continues to walk at this steady pace], divide 8.5 by 17.

8.5/17 = 0.5

So, Kira walked 0.5 or 1/2 blocks in a minute.

I hope this helps! :)

Kira walks at a rate of 0.5 blocks per minute when she walks 8 and a half blocks in 17 minutes.

Kira walks 8 and a half blocks in 17 minutes. To find out how many blocks she will walk each minute, we need to calculate the rate by dividing the total number of blocks by the total number of minutes:

Rate = Total Blocks Walked / Total Minutes

Rate = 8.5 blocks / 17 minutes

Rate = 0.5 blocks per minute.

Therefore, at a steady pace, Kira will walk half a block every minute.

-75 = -8b - 7b

To solve for "b"  you must isolate it, meaning that "b" must be the only thing on the right side of the equation.

First you must combine like terms. Like terms are numbers that have matching variables OR are numbers with out variables. In this case the like terms are -8b and -7b, since they both have the variables "b" attached.

-8b + (-7b) = -15b

so...

-75 = -15b

Next, to completely isolate b, divide -15 to both sides. Since -15 is being multiplied by b, division (the opposite of multiplication) will cancel -15 out (in this case it will make -15 one) from the right side and bring it over to the left side.

-75/-15 = -15b/-15

5 = 1b

b = 5

Check:

-75 = -8(5) - 7(5)

-75 = -40 - 35

-75 = -75

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

8b is the answer to this question.

Step-by-step explanation:

Answer:

480 mm³

Step-by-step explanation:

The volume (V) of a pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × height, hence

V = [tex]\frac{1}{3}[/tex] × 96 × 15 = 32 × 15 = 480

Answer:

15

Step-by-step explanation:

First add 20 to both sides to get x/3 = 5

Then multiply both sides by 3 to get 15.

You can check it by substituting it into the equation

15/3 - 20 = -15

5 - 20 = -15

-15 = -15

Step-by-step explanation:

x/3 - 20 = -15

x/3 = -15 + 20

x/3 = 5

x = 15

Answer:

2×2×2×7=56

Step-by-step explanation:

Find the multiples that goes into 56

Each number that goes into 56 put then from least to greatest and you got your prime numbers

Answer: a lower annual interest fee is better than a low annual fee if you expect to pay your balance in full during most months

Final answer:

A lower annual interest fee is generally better than a low annual fee when it leads to significant savings over time, especially with large amounts or long-term financial products. Interest rates dictate the overall cost of borrowing more than annual fees, particularly for longer terms or larger sums. However, for small, short-term borrowing, a low annual fee might be more beneficial.

Explanation:

When comparing a lower annual interest rate versus a low annual fee, it is essential to consider the specific financial situation and the amount of money involved. As a general rule, a lower interest rate is beneficial when it leads to significant savings on the overall interest paid throughout the loan or credit product term. This is often the case for larger amounts or longer terms where the interest accumulates considerably over time.

For example, financial investors who choose a Certificate of Deposit (CD) earn a higher interest rate compared to savings accounts, as they agree to leave the money deposited for a fixed period, forgoing liquidity. However, if interest rates rise after a loan is made, the existing loan with the lower interest rates becomes less attractive. On the other hand, if the economy experiences a fall in interest rates, the value of the loan with the previously fixed lower rate increases.

Therefore, while a low annual fee can seem attractive, it's the annual interest that ultimately has a more significant impact on the cost of borrowing, especially over longer periods or with larger sums of money. Conversely, for small short-term loans or when the outstanding balance is frequently paid off, a low annual fee might be more advantageous than a lower interest rate, as the interest charges could be minimal.

Answer:

Only option C: The shortest side can equal 7 cm.

Step-by-step explanation:

Let the length of the shortest side be x cm, then the length of the longest side is 4x cm. Let the length of the middle side be y cm. Note that

[tex]x<y<4x[/tex]

The perimeter is

[tex]x+y+4x=60\\ \\5x+y=60[/tex]

A. The value x cannot be 40 cm, because then y is negative

B. If the longest side is 30 cm long, then

[tex]4x=30\\ \\x=7.5\\ \\y=60-5\cdot 7.5=22.5[/tex]

But

[tex]x+y=7.5+22.5=30\ cm[/tex]

This means that such triangle does not exist

C. If x=7 cm, then 4x=28 cm,

[tex]y=60-5\cdot 7=25\ cm[/tex]

Since,

[tex]7+25=32>28\\ \\7+28=35>25\\ \\25+28=53>7,[/tex]

such triangle exists and this option is possible

D. If x=25 cm, then y is negative

E. If x=5 cm, then 4x=20 cm and

[tex]y=60-5\cdot 5=35\ cm[/tex]

But this triangle does not exist, because [tex]5+20<35[/tex]

The longest side of this scalene triangle with a perimeter of 60 cm can equal 30 cm or the shortest side can equal 7 cm.

We can use the variables x, y and z to represent the shortest (x), medium (y) and longest (z) sides.  The perimeter of a triangle is found by adding together all of the sides; this gives us the equation

x + y + z = 60

We know that the longest side, z, is equal to 4 times the length of the shortest side, x.  This means that z = 4x; we can now write our equation as

x + y + 4x = 60

Combining like terms, we have

5x + y = 60

1.  Checking all of the possible options, we first determine if x can equal 40:

This would give us a negative side length, which is impossible.

2.  Let the longest side be 30 cm.  This means that the shortest side is 1/4 of that; 30÷4 = 7.5.  Using 7.5 for x,

This is within the range of acceptable side lengths, since it is between the smallest (7.5) and the largest (30).

3.  Let the shortest side be 7 cm.  This means x = 7:

This is between the longest side, 7 cm, and the longest side, 4(7) = 28 cm.  This is acceptable.

4.  Let the value of x be 25:

This will give us a negative value for the medium side, which is impossible.

5.  Let the shortest side be 5 cm.  This means x = 5:

This means the medium value, 35, would be greater than the longest side, 20; this is incorrect.

This means the correct options are that the longest side can be 30 cm and the shortest side can be 7 cm.

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Keywords:  perimeter of scalene triangle, finding side lengths of scalene triangles, finding perimeter

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Answer Attached In Image Below.

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Answer:

5/8

Step-by-step explanation:

0.625 as a fraction is equal to 5/8

When you place 625 over 1000 you get 5/8 when simplified:

625/1000 = 5/8

Answer:

A, C and D are continuous

Step-by-step explanation:

A is a set of any number x which 30 < x <=45

B is a set that contains only 3 and 7

C is a set of any number x which 60 <= x < 100

D is a set of any number x which -infinity < x < + infinity

E is a set that contains only even whole numbers

A continuous data set is a quantitative data set representing a scale of measurement that can consist of numbers other than whole number, like decimals and fractions.

Answer:

x is in the element of all real numbers.

Step-by-step explanation:

Simplify the equation.

[tex]y=x+6-7[/tex]

[tex]y=x-1[/tex]

This means that the equation [tex]y=x[/tex] has just been moved down one.

Since the equation can be any number on the x axis, the domain is all real numbers.

Answer: X is all numbers I think.

Step-by-step explanation:

Answer: Option C

h = 6 or h= -7

Step-by-step explanation:

We have the expression

[tex]h^2-42 = -h[/tex]

To solve add h on both sides of the equality

[tex]h^2+h-42 = -h+h[/tex]

[tex]h^2+h-42 = 0[/tex]

For an equation of the form [tex]ah^2 +bh +c[/tex]  the quadratic formula is

[tex]h=\frac{-b \± \sqrt{b^2 -4ac}}{2a}[/tex]

In this case

[tex]a = 1\\b= 1\\c =-42[/tex]

[tex]h=\frac{-1 \± \sqrt{1^2 -4(1)(-42)}}{2(1)}[/tex]

[tex]h_1=6[/tex]

[tex]h_2=-7[/tex]

The answer is the option C

1 hour = 60 minutes

1 minute = 60 seconds

therefore 2.07 hours = (2.07*60*60) seconds

=7452 seconds

Answer:

7452

Step-by-step explanation:

There are 3600 seconds per hour

60*60= 3600

To find how many seconds are in 2.07 hours you need to multiply 3600 by 2.07

2.07* 3600 = 7452 seconds

Hope This helps

It is 24 yards long.

Let the width = x

Given that the rectangular field is 3 times as long as it is wide.

So, the length = 3x.

So area = Length * width = [tex](3x)*(x) = 3x^2[/tex].

Given:  it has an area of 192 square yards.

So,

[tex]3x^2=192\\x^2=64\\x=\sqrt{64}\\x=8[/tex]

So length = 3x = 3(8) = 24.

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Answer:

The domain is all real numbers. The range is {y|y ≤ 16}

Step-by-step explanation:

we have

[tex]f(x)=-x^{2}-2x+15[/tex]

This is a the equation of a vertical parabola open downward

The vertex is a maximum

The vertex is the point (-1,16)

see the attached figure

therefore

The domain of the function is all real numbers ----> interval (-∞,∞)

Te range of the function is

[tex]y\leq 16[/tex]

All real numbers less than or equal to 16 ----> interval  (-∞,16]

Answer:b

Step-by-step explanation:

To solve the equation 10 ln(100x) - 3 = 117, first isolate the ln(100x) by adding 3 to both sides and then divide by 10. Exponentiate both sides with base e to remove the ln, and finally divide by 100 to solve for x.

We are given the equation 10 ln(100x) – 3 = 117. To solve for x, follow these steps:

10 ln(100x) = 120

ln(100x) = 12

100x = e^12

x = (e^12) / 100

Now, by using a calculator we can find the value of e^12 and then divide it by 100 to find the value of x.

Final answer is:  x = 1627.54

Answer:

At 10 hours there will be 10 milligrams

Step-by-step explanation:

On a graph your slope would be y= -1x+20 because there where 20 mill at 0 hours and 12 mill at 8 hours. 20-8=12 meaning 1 mill would be deluded every hour. Hope this helps.

Final answer:

Using the exponential decay formula, we can find the half-life of the medication from the initial and given 8-hour amounts and then use it to calculate the amount of medication remaining after 10 hours.

Explanation:

To determine the remaining medication after a given number of hours, we will apply the exponential decay formula which accounts for substances with a half-life. Thus, given that there are initially 20 milligrams of the medication and that it decreases to 12 milligrams after 8 hours, we need to calculate the half-life and then use it to predict the amount remaining after 10 hours.

First, finding the half-life 't1/2' can be done using the formula A = A0×2−t/t1/2, where A is the remaining amount (12 mg), A0 is the initial amount (20 mg), and t is the time elapsed (8 hours). Solving for the half-life gives us t1/2 as the unknown in this equation.

12 mg = 20 mg ×2−(8 hours)/t1/2
Reducing this equation, we find that:
t1/2 = 8 hours / (log2(20 mg/12 mg))

After finding 't1/2', we can then determine the amount remaining after 10 hours. The calculation would be as follows:
A = 20 mg ×2−(10 hours)/t1/2

This will give us the final amount of medication left in the system at the 10-hour mark, rounded to the nearest hundredth.

Note that [tex]\sqrt[2]{x}=x^{\frac{1}{2}}[/tex]

[tex]\sqrt[2]{16x^{36}}=\sqrt[2]{4^2x^{18\cdot2}}[/tex]

[tex]4^{2\cdot\frac{1}{2}}x^{18\cdot2\cdot\frac{1}{2}}=4^{\frac{2}{2}}x^{\frac{18\cdot2}{2}}[/tex]

[tex]\boxed{4x^{18}}[/tex]

Hope this helps.

r3t40