Use properties of logarithms to rewrite the given expression as the logarithm of a single quantity, then enter that single quantity in the answer box to complete the expression. Assume each of the given variable expressions is defined for appropriate values of the variable(s) contained in it.
1/4log(x)+1/2log(y)
answer: log(____)

Answer:

52

Step-by-step explanation:

3^3+3(3)^2-7(3)+19

27+27-21+19

54-2

52

Hope this helps

Answer: the commutative property

Step-by-step explanation: I took the test

Answer:

communicative property

Step-by-step explanation i just had it on my high school test also please thank me i just want to see if i get a notification

Answer:

              [tex]\boxed{\,\bold{y=-6\left(x-\frac14\right)^2+\,\frac{19}8}\,}[/tex]

Step-by-step explanation:

[tex]y= -6x^2 +3x+2\\\\y=-6\big(x^2-\frac16\cdot3x-\frac16\cdot2\big)\\\\y=-6\big(x^2-\frac12x-\frac13\big)\\\\ y=-6\big(\underline{x^2-2\cdot x\cdot\frac14+(\frac14)^2}-(\frac14)^2-\frac13\big)\\\\ y=-6\big((x-\frac14)^2-\frac1{16}-\frac13\big)\\\\ y=-6(x-\frac14)^2+\frac38+2\\\\ \underline{y=-6(x-\frac14)^2+\frac{19}8}[/tex]

Answer:

l

Step-by-step explanation:

9 houses receive both the news report and the city times.

Let's break down the problem to find the number of houses that receive both newspapers.

Veronica delivers 27 copies of the news report and 22 copies of the city times to a total of 38 houses on Oakland Street. Since each house can receive at most 1 copy of each newspaper, the maximum number of houses that can receive either newspaper is the sum of the copies delivered for each newspaper, which is 27 + 22 = 49.

However, we know that there are only 40 houses on Oakland Street. This means that at least 9 houses will not receive any newspaper.

To determine the number of houses that receive both newspapers, we need to subtract the number of houses that don't receive any newspaper from the total number of houses that can receive either newspaper.

Therefore, the number of houses that receive both newspapers is 49 - 40 = 9.

As a result, 9 households receive both the city times and the news report.

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Answer:

The distance is 7.81 when rounded to the nearest hundredth

Answer:

The amount will be y = 970

Step-by-step explanation:

Equation 1:

y =  60 + 65x

Equation 2:

y = 200 + 55x

Solve for x and y

60 + 65x = 200 + 55x

10x = 140

x = 14

y = 200 + 55 (14)

y = 970

HOPE THIS HELPS :)

Answer:

1) 14 months

2) $970

Step-by-step explanation:

We know that the Community Gym charges a $60 membership fee and a $65 monthly fee.

So, we can write the following equation:

[tex]y=60+65m[/tex]

Where y is the total cost, 60 is the one-time membership fee, and 65m is the cost for m months.

Workout Gym charges a $200 membership fee and a $55 monthly fee. So, we can write the following equation:

[tex]y=200+55m[/tex]

Where y is the total cost, 200 is the one-time membership fee, and 55m is the cost for m months.

Question 1)

We want to know after how many months will the total amount of money paid to both gyms be the same. So, let's set the equations equal to each other:

[tex]60+65m=200+55m[/tex]

To find the number of months, let's solve for m.

Subtract 55m from both sides:

[tex]60+10m=200[/tex]

Subtract 60 from both sides:

[tex]10m=140[/tex]

Divide both sides by 10:

[tex]m=14[/tex]

So, after 14 months, the cost of going to Community Gym or Workout Gym will be the same.

Question 2)

To find the amount, simply substitute 14 back into either equation. Let's do it for both.

We have:

[tex]y=60+65m[/tex]

Substitute 14 for m:

[tex]y=60+65(14)[/tex]

Multiply and add:

[tex]y=60+910=\$970[/tex]

We have:

[tex]y=200+55m[/tex]

Substitute 14 for m:

[tex]y=200+55(14)[/tex]

Multiply and add:

[tex]y=200+770=\$970[/tex]

So, after 14 months, both gym will cost $970.

And we're done!

Answer:

I think the answer is d

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

The profitability index for the investment is approximately 0.0211, given a 9 percent required return.

To calculate the profitability index, we need to divide the present value of the cash flows by the initial investment. The formula for the profitability index is as follows:

Profitability Index = Present Value of Cash Flows / Initial Investment

First, we need to calculate the present value of the cash flows. The present value is determined by discounting each cash flow to its present value using the required rate of return. Given a 9 percent required return, we can use the following formula to calculate the present value of each cash flow:

Present Value = Cash Flow / (1 + Required Rate of Return)ⁿ

Where n represents the year.

Let's calculate the present value of the cash flows:

Year 0:

Present Value of Cash Flow 0 = -109,000 / (1 + 0.09)⁰ = -109,000

Year 1:

Present Value of Cash Flow 1 = 47,300 / (1 + 0.09)¹ = 43,394.50

Year 2:

Present Value of Cash Flow 2 = 59,800 / (1 + 0.09)² = 50,961.99

Year 3:

Present Value of Cash Flow 3 = 15,900 / (1 + 0.09)³ = 12,338.83

Next, we sum up the present values of the cash flows:

Total Present Value = Present Value of Cash Flow 0 + Present Value of Cash Flow 1 + Present Value of Cash Flow 2 + Present Value of Cash Flow 3

Total Present Value = -109,000 + 43,394.50 + 50,961.99 + 12,338.83

Total Present Value = -2,304.68

Finally, we can calculate the profitability index:

Profitability Index = Total Present Value / Initial Investment

Profitability Index = -2,304.68 / -109,000

Profitability Index ≈ 0.0211

Therefore, the profitability index for the given cash flows and a 9 percent required return is approximately 0.0211.

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Answer:

84.134%

Step-by-step explanation:

We solve this question using the z score formula.

The formula for calculating a z-score is z = (x-μ)/σ

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

We are were asked in the question that:

Suppose that adult women in China have heights that are normally distributed with a

mean = 155 centimeters

standard deviation = 8 centimeters. Of the Chinese women, what percent are shorter than 163cm?

Using the z score formula

z = (x-μ)/σ

z = (163 - 155)/8

z = 8/8

z = 1

Determining the Probability value from Z-Table:

P(x ≤ 163) = P(x < 163)

= 0.84134

Converting to percentage

= 0.84134 × 100%

= 84.134%

The percent of Chinese women that are shorter than 163cm is 84.134%

Answer: 443

Step-by-step explanation:

The correct values are:

Angle x = 90°

Angle y = 90°

Considering the given information that points A, B, C, D, E, and F divide the circle into 6 equal parts, we can analyze the angles as follows:

Each section of the circle corresponds to an angle of 360° / 6 = 60°.

Now, let's examine angle x and angle y:

Angle x is formed by connecting points A, B, and F. Since A and B divide the circle into two equal parts, the angle AOB is 180° / 2 = 90°. As F divides the remaining portion of the circle, the angle x can be determined as follows:

x = 360° - (180° + 90°) = 90°.

Angle y is formed by connecting points C, D, and E. Similarly, since C and D divide the circle into two equal parts, the angle COD is 180° / 2 = 90°. Thus, the angle y can be calculated as follows:

y = 360° - (180° + 90°) = 90°.

Therefore, the correct values are:

Angle x = 90°

Angle y = 90°

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Answer:

32m

Step-by-step explanation:

Volume of cube = x³ [where x is the length of one side of the cube]

and given that volume is 32768m³

thus,

[tex]x^{3} = 32768\\ x = \sqrt[3]{32768} \\x = 32m[/tex]

Answer:

6.2 feet

Step-by-step explanation:

Triangle formed (in red) by the pet ramp is showing a right triangle.

By applying Pythagoras theorem in the given right triangle,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

Length of leg 1 = 6 ft

Length of leg 2 = 1.5 ft

By substituting the values in the formula,

(Hypotenuse)² = 6² + (1.5)²

                        = 36 + 2.25

                        = 38.25

Hypotenuse = [tex]\sqrt{38.25}[/tex]

                     = 6.18

                     ≈ 6.2 ft

Therefore, length of the pet ramp is 6.2 ft.

Josie purchased a total of 91 tickets for an Amtrak train. Children's tickets cost $21 each, and adult tickets cost $35 each. Josie paid a total of $2,723 for the tickets. We need to determine how many children's tickets and how many adult tickets Josie bought.

Let's assume Josie bought x children's tickets and y adult tickets. According to the given information, the total number of tickets is 91, so we have the equation:

x + y = 91 (Equation 1)

The cost of each child's ticket is $21, and the cost of each adult ticket is $35. The total amount Josie paid, $2,723, can be expressed as:

21x + 35y = 2723 (Equation 2)

To find the values of x and y, we can solve this system of equations (Equations 1 and 2). There are various methods to solve a system of equations, such as substitution or elimination. Let's use the substitution method in this case.

From Equation 1, we can rewrite it as x = 91 - y. Substitute this value of x into Equation 2:

21(91 - y) + 35y = 2723

Expanding and simplifying:

1911 - 21y + 35y = 2723

14y = 812

y = 58

Now substitute the value of y back into Equation 1 to find x:

x + 58 = 91

x = 33

Therefore, Josie bought 33 children's tickets and 58 adult tickets.

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Answer:

2^3.3^2

Step-by-step explanation:

[tex] {2}^{3 ?} = 8 \\ {?3}^{2?} = 9 \\ 8 \times 9 = 72[/tex]

Answer:

2.2.2.3.3.

72 / 2 = 36

36/2 = 18

18/2 = 9

9/ 3= 3.

So the answer to your question is 2.2.2.3.3.

Hope this helps!

Have a great day and stay safe! :))))))

Answer:

10 1/2 (ten and a half) teaspoons

Step-by-step explanation:

If 1 3/4 teaspoons of sugar can make 1 cup of hot cocoa

then how many teaspoons of sugar can make 6 cups?

that is,

1 3/4 tsps = 1 cup of hot cocoa

?               = 6 cups of hot cocoa

when you cross multiply

6 * 1 3/4

1 3/4 in whole number is 7/4

6 * 7/4 = 21/2

21/2 expressed in fraction is 10 1/2

therefore 10 1/2 teaspoons of sugar will make 6 cups of hot cocoa.

The sum of all probabilities of dying from all causes is equal to one. Hence, the probability of dying from some other cause is 1 - 0.45 - 0.22 = 0.33.Probabilities are numerical estimates of the chance of a given outcome occurring.

\Probability theory is the study of the ways in which probabilities can be calculated or estimated, as well as the mathematical laws that govern them. It's critical in virtually every area of human endeavour that includes elements of uncertainty or chance, from the weather to finance to the results of an election.

Therefore, from the above given data, it is quite clear that the probability of dying from some other cause is 0.33.

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Answer:

52?

Step-by-step explanation:

The (f∘g)(x) = -5x + 1.

The solutions are:

Part A: (f+g)(x) = -4x + 1

Part B: (f-g)(x) = 6x + 7

Part C: (f∘g)(x) = -5x + 1

To determine the values of (f+g)(x), (f-g)(x), and (f∘g)(x) for the given        linear functions f(x) = x + 4 and g(x) = -5x - 3, we'll perform the necessary operations.

Part A: (f+g)(x)

To find (f+g)(x), we add the two functions together:

(f+g)(x) = f(x) + g(x)

= (x + 4) + (-5x - 3)

= x - 5x + 4 - 3

= -4x + 1

Therefore, (f+g)(x) = -4x + 1.

Part B: (f-g)(x)

To find (f-g)(x), we subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

= (x + 4) - (-5x - 3)

= x + 5x + 4 + 3

= 6x + 7

Therefore, (f-g)(x) = 6x + 7.

Part C: (f∘g)(x)

To find (f∘g)(x), we substitute g(x) into f(x):

(f∘g)(x) = f(g(x))

= f(-5x - 3)

= -5x - 3 + 4

= -5x + 1.

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Answer:

I think so it's right ....

Answer:

square root of 80

Step-by-step explanation:

in order to get rid of the ^2 you must square root[tex]\sqrt{x}[/tex] both sides of the equation thus = [tex]\sqrt[n]{80}[/tex] then you can use a calculator or something to simplfiy it further which would get you to 8.94 something.

Hence, Y  =   -2x,  For  x  <   -5,   The Function  Y  =  | x  -  5 |  +  | x  +  5 |

Therefore,  For:   x  <  -5,  The Function:  Y  =  | x  -  5 |   +   | x  +  5 |

Simplifies to:   Y   =   -2x

To solve the problem, We need to consider the definition of the ABSOLUTE VALUE FUNCTION and the given condition:   x   <  -5

We will break the absolute value expressions into their respective cases and simplify the equation.

        Since:   x   <   -5,   We now have:

        x   -  5  <  0   and   x   +  5  <  0

        | x  -  5 |   =   -(x  -  5)   and  | x  +  5 |  =   -(x  +  5)

        Y  =   -(x  -  5)  +  ( -(x  +  5))

       Y   =   -x  +  5  -  x  -  5

        Y  =   -2x

        For  x  <   -5,   The Function  Y  =  | x  -  5 |  +  | x  +  5 |

        Simplifies to:    Y  =  -2x

Hence, Y  =   -2x,  For  x  <   -5,   The Function  Y  =  | x  -  5 |  +  | x  +  5 |

I hope this helps you!

Answer:

- 9/7

Step-by-step explanation:

7x + 13 = 4

- 13 = -13

7x= -9

x = -9/7

Answer: 4 2/7 or if they want improper 30/7

Step-by-step explanation:

-2(x + 13) + 9x = 4

Distribute the -2 to the parentheses

-2x - 26 + 9x = 4

Combine like terms

7x - 26 = 4

Add 26 to both sides to get x by itself

7x = 30

Divide by 7 to get x by itself.

x = 30/7

Mixed = 4 2/7 normal = 30/7

Answer:

Step-by-step explanation:

The true statements about the input and output values given in the question are :

The pair of point corresponds to an x and y value respectively, this means that for any point there is one input and one output.

Therefore, since there is a one to one relationship for each point, then there is only one input for every output and vice versa.

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Answer: r=1

Step-by-step explanation: r" is the correlation coefficient. It is always between -1 and 1, with -1 meaning the points are on a perfect straight line with negative slope, and r = 1 meaning the points are on a perfect straight line with positive slope.

60  visible sunspots were expected in the year 2020.

The number of visible sunspots varies sinusoidally, repeating over an 11 year period. The maximum number of sunspots is 110, and the minimum number is 10 per year.

Therefore, the amplitude of the function is (110 - 10) / 2 = 50. The average of the maximum and minimum numbers is (110 + 10) / 2 = 60. The sine function can be written as:f

(t) = A sin(ωt) + C

where A = amplitude, ω = angular frequency, C = vertical shift.

To find A, ω and C, we can use the information given as follows:

f(t) = 50 sin(2π/11(t - 2003)) + 60

Similarly, the cosine function can be written as:

f(t) = A cos(ωt) +

where A = amplitude, ω = angular frequency, C = vertical shift.

To find A, ω and C, we can use the information given as follows:

f(t) = 50 cos(2π/11(t - 2003)) + 60

To find the number of visible sunspots in 2020, we need to substitute t = 2020 in either of the functions. Let's use the sine function.

f(2020) = 50 sin(2π/11(2020 - 2003)) + 60

            = 50 sin(2π/11 × 17) + 60

            ≈ 60.7

Therefore, about 60 visible sunspots were expected in the year 2020.

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