Solve 2 log x = log 64.
x= 1.8
x=8
x= 32
x=128

The equation of the cross-section of the reflector which is in the form of a parabola is y² = -10x

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Given that, The cross-section of the reflector in a flashlight is a parabola, the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.

We know that, the equation of the parabola turned to the left i.e. to the negative side of the coordinate system is:

y² = -2px  

where p is the parameter of the parabola

The relationship between the parameter and the focus is.

p = 2 f  

p = 2×2.5 = 5 cm  

Since, the equation of the parabola is:

y² = -2p

Therefore, put p = 5

y² = - 2×5x = -10x

y² = -10x

Hence, the equation is y² = -10x

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a. The y-intercept of the graph is 35,000, which represents the original purchase price of the car. Therefore, the car was purchased for $35,000.

b. We can see from the graph that the car's value becomes 0 after 9 years. Therefore, the car totally depreciates after 9 years.

c. The equation of a straight line can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope of the graph is the rate of depreciation, which is -4000. The y-intercept is the original price of the car, 35000.

So the equation of the straight line depreciation graph is: y = -4000x + 35000

This equation represents the value of the car, where y is the value of the car (in dollars) x is the number of years since the car was purchased and -4000 is the rate of depreciation and 35000 is the original price of the car.

Answer:

Ruth is 36 years old

Step-by-step explanation:

let Colin's age be x , then

Dave's age is x + 4

Ruth's age is 3(x + 4) = 3x + 12

sum their ages and equate to 56

x + x + 4 + 3x + 12 = 56

5x + 16 = 56 ( subtract 16 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

Then

Ruth's age = 3x + 12 = 3(8) + 12 = 24 + 12 = 36

The age of Ruth is 36 years while Dave is 12 years old and Colin is 8 years old.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Using variables to represent the ages of Colin and Dave:

C = Colin's age

D = Dave's age

From the given statement,

D = C + 4 (Dave is 4 years older than Colin)

We know that Ruth's age is three times Dave's age:

R = 3D (Ruth is three times as old as Dave)

Now, the sum of their ages is 56:

C + D + R = 56

Substituting the expressions for D and R in terms of C, we get:

C + (C + 4) + 3(C + 4) = 56

Simplifying and solving for C:

5C + 16 = 56

5C = 40

C = 8

So Colin is 8 years old. Using the expression for Dave's age in terms of C, we get:

D = C + 4 = 8 + 4 = 12

So, Dave is 12 years old.

Ruth's age in terms of D:

R = 3D = 3(12) = 36

Therefore, Ruth is 36 years old.

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To the nearest whole percent, the percentage Yvette paid over the price of the sandwiches is 27%.

The percentage represents a proportion of a whole value.

The percentage is determined as the quotient of the difference (increase or decrease) and the initial value, multiplied by 100.

The purchase price of restaurant sandwiches = $22

Sales tax = 8.5%

= $1.87 ($22 x 8.5%)

Additional tip for delivery = 18%

= $3.96 ($22 x 18%)

Total bill = $27.83 ($22 + $1.87 + $3.96)

Difference between the total bill and the purchase price = $5.83 ($27.83 - $22)

Percent difference = 26.5% ($5.83/$22 x 100)

= 27%

Thus, Yvette paid 27% above the price of the sandwiches in form of sales tax and tips.

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DE and FG have the same slope, so both the sides are parallel. The opposite side of the quadrilateral are equal. Because, the opposite side of the quadrilateral are equal and parallel, DEFG is a parallelogram.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

DE and FG have the same slope, so both the sides are parallel.

Since, DE = FG, the opposite side of the quadrilateral are equal.

Because, the opposite side of the quadrilateral are equal and parallel, DEFG is a parallelogram.

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The person is 16. 55ft from the boat

From the information given, we have that;

To determine the distance between the boat and the person, let's use the trigonometric identity, sine

sine θ = opposite side/hypotenuse side

Given that;

Substitute the value

sin 65 = 15/d

cross multiply

d = 15/sin 65

Find the value

d = 15/0.9063

divide the values

d = 16. 56 ft

Hence, the value is 16.56ft

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If 500m is split in the ratio of 1:4, then the first part would equal 125m and the second part would equal 375m.

The ratio is a comparison of two or more related values or amounts. It is expressed as a fraction or a decimal number, and is used to compare the relative size of two or more values. Ratios can be used to compare numbers, objects, people, or other elements in order to study their relative size or relationships.

If 500m is split in the ratio of 1:4, then the first part would equal 125m and the second part would equal 375m. This is because the ratio of 1:4 can be simplified to 1/5 and 1/5 of 500m is 125m. Therefore, the first part is 125m and the second part is 375m.

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The equation x / y = 4 is an example of direct variation formula. (Correct choice: A)

Herein we find four types of equations, of which we must determine what choice represents a direct variation formula, whose definition is shown below:

y ∝ x

y = k · x

Where k is the constant of proportionality.

This form is equivalent to the following expressions:

y / x = k, x / y = 1 / k

Then, by direct inspection, we see that equation x / y = 4 represents a direct variation formula.

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The table that shows a proportional relationship between x and y is:

C. x 1 5 8 10 y 15 75 120 150

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of that constant.

If every pair of data values is related in the same way, by multiplying by a factor, then the relationship is proportional. A proportional relationship can be identified by looking at data, an equation, or a graph.

In this case, the constant based on the information will be:

= 15 / 1

= 15

Also when x is 5, y will be:

= 5 × 15.

= 75..

The correct option is C.

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Therefore ,  solving the provided question, we can say that the, probability P( 24 period hour) = 5/24

The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number from 0 and 1, in which about 0 represents how likely the event should be to occur and 1 represents certainty. A probability is a quantitative illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrence in a whole set all equally likely options that lead to a specific occurrence.

Here,

=> E1 = stops at 5 clock

=>  E2 = start at 24 hours

=> P( 24 period hour) = 5/24

=> the, probability P( 24 period hour) = 5/24

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Answer: A: x=6

Step-by-step explanation: If we plug in 6 for X in the equation we get

33 - 6. 33 - 6 does equal 27.

Now to make sure X = 4 is not an answer, we plug that in too. 33 - 4.

33 - 4 = 29, so this is not the answer.

Answer:

A: x = 6 is a solution, but x = 4 is not.

Step-by-step explanation:

33-x=27

-33    -33

-x=-6

-x/   -x/

x=6

Answer:

Step-by-step explanation:

77/100 or 0.77

The value of y in the equation that we have here is given as , y = x + (10 + y)i

To solve for y, we can start by isolating y on one side of the equation. We can do this by adding yi to both sides:

x+10i+yi = y-yi+yi

This simplifies to:

x+10i+yi = y

We can then rearrange the equation to get:

y = x+10i+yi

So, y = x + (10 + y)i

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A situation which could be represented by the equation 18x = 19 + 12x include the following: J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?

In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.

Assuming the variable x represents the number of hours spent tutoring, an algebraic expression which relates the number of hours which these two tutors must spent during tutorial to earn the same amount of money is given by:

18x = 19 + 12x

18x - 12x = 19

6x = 19

x = 19/6 hours.

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Complete Question:

Which situation can be represented by this equation?

18x = 19 + 12x

F Krystal reads 12 pages per hour. Jondo reads 18 pages per hour.

How many hours, x, would it take for Krystal and Jondo to read

the same number of pages?

G Krystal paid a deposit of $19 plus $18 per hour to rent a dining

room at a restaurant. Jondo paid $12 per hour to rent a dining

room at a restaurant. How many hours, x, would it take for

Krystal and Jondo to pay the same amount of money?

H Krystal installs 12 tiles per hour. Jondo installs 19 tiles per hour

and started with 18 tiles already installed. How many hours, x,

would it take for Krystal and Jondo to install the same number

of tiles?

J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?

Answer: The domain of a function is the set of all input values (x-values) for which the function produces a valid output value (y-value).

For the function y = 3^√x, the input value x can't be negative because the value under the square root should be non-negative and 3^√x is defined for all x in the domain of real numbers. This means that the domain of the function y = 3^√x is (-∞,∞).

Step-by-step explanation:

The domain of the function is  [0, ∞).

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function y = 3^√x has a base of 3, which means that the output of the function is always a positive number.

For the function to be defined, the input x must also be a positive number or zero, as the square root of a negative number is not a real number.

Therefore,

The domain of the function is all non-negative real numbers, or [0, ∞).

In interval notation, the domain can be written as [0, ∞).

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The product of 6√8 and 3√24 in simplest radical form is 144√3

We can solve this problem by using the distributive property and simplifying the radicals.

6√8 * 3√24 = (6 * 3) * √(8 * 24)

Evaluate the products

6√8 * 3√24 = 18 * √(8 * 24)

Evaluate the products of radicals

6√8 * 3√24 = 18 * √(192)

Simplify the radical

6√8 * 3√24 = 18 * 4 * √12

So, we have

6√8 * 3√24 = 72√12

Now to simplify the radical, we can divide the radicand by the greatest perfect square that is a factor of it.

So, we have

72√12 =  72 * 2 * √3

= 144√3

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The answer to the work shown is x = 8.

The law of indices are laws that has to be applied to expressions involving powers or fractions. These laws have individual application.

Considering the given question, we have;

16^(3x - 6) = 64^(x + 4)

It can be deduced that, the factors of;

16 = 4 x 4

   = 4^2

and

64 = 4 x 4 x 4

    = 4^3

So that;

4^2(3x - 6) = 4^3(x + 4)

Divide through by 4 to have;

2(3x - 6) = 3(x + 4)

6x - 12 = 3x + 12

collect like terms,

6x - 3x = 12 + 12

6x = 24

x = 24/6

  = 8

The answer to the work shown in the question is: x = 8

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Answer:

Step-by-step explanation:

Answer: C. Inside the school cafeteria.

Step-by-step explanation:

Answer:

don’t care 9

Step-by-step explanation:lol

The pints of punch that Jason served were 52 pints.

The number of pints that make up a gallon is 8 pints. So, in 8 gallons, we can expect that there will be 64 pints. Now, we are told that Jason served 1 pint container and now he has 12 points remaining, what we are to do is to subtract the remaining pints from the original pints that he had.

Since the original was 64 pints, removing 12 pints will amount to 52 pints. This means that 52 pints of punch were served in the 1-pint containers.

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Answer: Paula spent $2 for each song.

Step-by-step explanation: For this question, we have to find the unit rate that Paula paid per song. As we're already given the amount of songs downloaded and the total cost, all that we really have to do is divide!

Because we want to know the amount of money spent on one song, we divide the amount of money spent by the amount of songs purchased. This gives us 32/16 = 2.

Paula spent $2 (don't forget the units!) for each song. This is out unit rate. Hope this helps!

This calculation yields a volume of a cube equal to 1728 cube inches. In order to calculate the volume, the length must be multiplied by itself three times.

Volume =[tex]a^{3}[/tex], where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.

A.) 12 × 3 cubic inches

B.) Volume of a cube equals length × breadth × height, which is                    12× 12 × 12 = 123 = 144 × 12 = 1728 cube inches. V=[tex]a^{3}[/tex]=123=1728 [tex]cm^{3}[/tex]is the result, giving the cube's volume.

1,728 times twelve cubed. The term "x cubed," or cubing a number, is identical to: x cubed equals x 3. A real number with a cube equal to 12 is the cube root of 12. It is about equal to 2.289 to take the cube root of 12. Volume per volume, or % v/v, is the way volume concentrations in solutions are stated. This is employed when a solution contains liquid versions of both compounds.

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The value of the expression x² - 9x - 7 when x = 6 is -25.

Quadratic equations are second degree polynomial equations which are of the form ax² + bx + c = 0, where a, b and c are real numbers and x is the variable with the highest degree of 2.

Given the quadratic expression,

x² - 9x - 7

We have to find the value of the expression when x = 6.

Substitute x = 6, we get,

6² - (9 × 6) - 7 = 36 - 54 - 7

                       = -25

Hence the value of the given expression when the value of x = 6 is -25.

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For a combined energy of 15 students in a week, a truck will drive for 914.24 meters subjective to the number of students.

To find the meters a truck will drive when the energy of a class is combined in one week;

1 day per person = 32 kilometers

One week = 7 days

Assuming a math class with 15 students for 7 days = (15 students x 7 days)

= 1/(15 x 7) x 32

= 1/35 x 32 = 0.02857 x 32 = 0.91424 kilometers

Changing 0.91424 kilometers to meter = 0.91424 x 1000 = 914.24 meters. It will take 15 students 914.24 meters truck drive in one week.

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Answer:

Step-by-step explanation:

26.25 divided by three = 8.75

The equation in slope intercept form is y=-9x-8

Slope is defined the rate of change of y with respect to x.  the slope is also denoted by increase in y over increase in x.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The equation of the slope intercept form is in the form y= mx +c

The given equation  y= -9x +9

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The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

You can find the standard mean error and then use that to find the confidence interval limits.

The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by

Lower limit = 0.0104

Upper limit = 0.0496

The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

To find the confidence interval for proportions

Let the sample size be n

Let the interested quantities in the sample be present x times

Let the confidence level be of p%.

Then the level of significance is given by

The standard mean error is calculated by:

Then the confidence interval limits can be found by

Using the above formula for finding the confidence interval

We have n = 500, x = 15 and

Finding the standard mean error:

From the z tables, we get z = 2.5758

Thus, the confidence interval is obtained by

Lower limit = 0.0104

Upper limit = 0.0496

Thus,

The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by

Lower limit = 0.0104

Upper limit = 0.0496

Therefore, The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

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The value of the variable, x is 7

Algebraic expressions are defined as expressions that are composed of terms, coefficients, variables, constants and factors.

These mathematical operations are also made up of arithmetic operations. These operations includes;

From the information given, we have;

-5(2x+14)=-2(x+63)

expand the bracket

-10x -70 = -2x - 126

Now, collect like terms

-10x + 2x = -126 + 70

Add or subtract the terms

-8x = -56

Make 'x'' the subject

x = 7

Hence, the value is 7

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Using dimensional analysis we have converted 44 yards/sec = 90 miles/hour.

Dimensional analysis is the study of how dimensions and units of measurement affect the relationship between physical quantities.

Dimensional analysis is crucial because it maintains the consistency of the units, which facilitates accurate mathematical computation.

As we use conversion factors to obtain the same units, dimensional analysis is also known as the Factor Label Method or Unit Factor Method.

We know that 1 yards/sec = 2.04545 miles/hour

Here given that 44yds/s = ? miles/hour

Lets solve

1 yards/sec = 2.04545 miles/hour

44 yards/sec = 44 × 2.04545 miles/hour

44 yards/sec = 89.9998 miles/hour

44 yards/sec = 90 miles/hour

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