suppose set a contains 26 elements and set b contains 56 elements. if the total number elements in either set a or set b is 78, how many elements do sets a and b have in common?

The values based on the functions given will be:

1. f(g(9)) = V33 + 3

2. g(f(6)) = 4V6 + 9

3. g(h(1)) = 21

4. h(g(0)) = -6

5. h(S(-2)) = -3

6. f(h(5)) = V18 + 3

7. &(g(1.5)) = 3

8. f(f(-2)) = 2

f(g(9)) = f(4(9) - 3) = f(33) = V33 + 3

g(f(6)) = g(V6 + 3) = 4(V6 + 3) - 3 = 4V6 + 9

g(h(1)) = g(3(1) + 3) = g(6) = 4(6) - 3

h(g(0)) = h(4(0) - 3) = h(-3) = 3(-3) + 3

h(S(-2)) = h(-2) = 3(-2) + 3

f(h(5)) = f(3(5) + 3) = f(18) = V18 + 3

&(g(1.5)) = &(4(1.5) - 3) = &(3) = 3

f(f(-2)) = f(V(-2) + 3) = V(V(-2) + 3) + 3 = V1 + 3 = 2

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Logarithmic functions and exponential functions are inverse functions of each other

The value of x in the equation  log₃ (x + 5 ) = 4  is 76

The format of the logarithmic function log₃ (x + 5 ) = 4  is

solving  the equation

3⁴ = x + 5

81 = x + 5

x = 76

the solution to the equation log3 (x + 5) = 4 is x = 76.

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Answer:

45 = 40 tens + 5

Step-by-step explanation:

Hope this helps

Brainliest pls ❤️

Answer:

4

Step-by-step explanation:

4x10=40 40+5=45

The person's survey that the most people drink at least 64 ounces of water is Douglass.

In the first case, Joes reported that 14 of the 36 people he surveyed drink at least 64oz. of water. This will be:

= 14/36

= 0.389

Nicole reported that 2/5 of the people she surveyed drink at least 64oz. of water. The decimal will be:

= 2/5

= 0.40

Douglas reposted that 0.55 of the people he surveyed drink at least 64oz of water.

From the information, Douglass has the highest decimal.

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Answer:

x = 57

Step-by-step explanation:

180 degrees in a triangle

67 + 56 = 57

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

Explanation:

The three angles of any triangle always add to 180

x+67+56 = 180

x+123 = 180

x+123-123 = 180-123 .... subtract 123 from both sides

x = 57

The missing angle is 57 degrees

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

Check:

x+67+56 = 57+67+56 = 180

Answer is confirmed.

Answer:

The coordinates of point p are:

x = -3.2

y = 9.6

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Then if we know that L1 passes through the points (6, 5) and (10, 3) the slope of this line will be:

a = (3 - 5)/(10 - 6) = -0.5

Then this line will be something like:

y = -0.5*x + b

To find the value of b we can just replace the values of one of the points in the above equation. For example if we use the point (6, 5), this means that:

x = 6

y = 5

Then we get:

5 = -0.5*6 + b

5 = -3 + b

5 + 3 = b

8 = b

Then the equation for line L1 is:

y = -0.5*x + 8

Now, for line L2 we know that it has a gradient -3 (for linear equations, the gradient is the same as the slope)

Then line L2 has a slope equal to -3

y = -3*x + b

And we know that this line passes through the origin, (0, 0)

Then if we replace the values of that point in our equation, we get:

0 = -3*0 + b

0 = b

Then line L2 is:

y = -3*x

Then our two lines are:

y = -0.5*x + 8

y = -3*x

Now we want to find the point where these lines intersect. The lines will intersect in one point that belongs to both lines, then we can use the relation:

-0.5*x + 8 = y = -3*x

-0.5*x + 8 = -3*x

now we can solve this for x.

-0.5*x + 8 = -3*x

8 = -3*x + 0.5*x

8 = -2.5*x

8/-2.5 = x = -3.2

Now we need to evaluate one of the lines on this value, i will use line L2

y = -3*(-3.2) = 9.6

Then we can conclude that the lines do intersect in the point:

x = -3.2

y = 9.6

this point is written as: (-3.2, 9.6)

(0.624, 3.91)

The interval is formatted as

(x, y)

Answer:

3,036

Step-by-step explanation:

x=12*253

Answer:

the tree will be 11.04 feet tall

Step-by-step explanation:

4 x 0.22 (22%) = 0.88

every year it grows 0.88 foot.

0.88 x 8 = 7.04

4 + 7.04 = 11.04 feet tall

sorry if this is wrong!

The height of the tree after 8 years will be 11.04 feet.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a  4-foot tree was planted in 1984. The tree grows continuously by 22% each year from this point forward.

The height after 8 years will be calculated as:-

4 x 0.22 (22%) = 0.88

Every year it grows 0.88 feet.

0.88 x 8 = 7.04

4 + 7.04 = 11.04 feet tall

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Answer:

2 cos (x + pi/2)

Step-by-step explanation:

Of the choices given, this looks like a cos curve that is shifted to the Left by pi / 2  and   multiplied to give an amplitude of 2

The present value of the loan is found to be  approximately $70.28.

To find the present value of a loan, we can use the formula:

Present Value = Future Value / (1 + (interest rate * time))

Given that the future value is $1,321.17, the interest rate is 7.75%, and the time is 230 days, we can plug in these values into the formula:

Present Value = 1321.17 / (1 + (0.0775 * 230))

Calculating the expression in the parentheses first:

Present Value = 1321.17 / (1 + 17.8075)

Simplifying further:

Present Value = 1321.17 / 18.8075

Evaluating the division:

Present Value ≈ $70.28

Therefore, the present value of the loan is approximately $70.28.

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The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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Answer:

y= -2x

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

   = ( -4- -2)/(2-1)

   = ( -4+2)/( 2-1)

   -2/1

  -2

Using y = mx+b where m is the slope and b is the y intercept

y = -2x+b

Substitute a point into the equation

-2 = -2(1)+b

-2 = -2+b

b=0

y= -2x

The most appropriate type of graph for graphing heart rate data over the time period of 120 seconds would be a line graph or a scatter plot.

A line graph is useful when we want to show the trend or changes in a variable over time. It would allow us to plot the heart rate on the y-axis and the time on the x-axis, connecting the data points with a line to represent the change in heart rate over the 120-second period.

A scatter plot can also be used to display heart rate data over time. In a scatter plot, each data point represents a heart rate measurement at a specific time point. By plotting the heart rate on the y-axis and the time on the x-axis, we can observe the distribution of the data points and any potential patterns or trends.

Ultimately, the choice between a line graph and a scatter plot depends on the specific nature of the data and the purpose of the graph. If the heart rate data is continuous and measured at regular intervals, a line graph would be a suitable choice. If the heart rate data is more discrete or irregularly measured, a scatter plot would be more appropriate.

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The percentage of the new quantity in letter b is 40% and the Percentage of the new quantity in letter c is 76%.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum.

Given data:

letter b: Original Quantity: 20 new quantity: 8

letter c: original quantity: 50 new quantity: 38

Calculate the percentage as shown below,

Percentage of new quantity in letter b = new quantity / Original Quantity × 100

Percentage of new quantity in letter b = 8 / 20 × 100 = 40%

Percentage of new quantity in letter c = new quantity / Original Quantity × 100

Percentage of new quantity in letter c = 38 / 50 × 100 = 76%

Therefore, the percentage of the new quantity in letter b is 40% and the Percentage of the new quantity in letter c is 76%.

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The given augmented matrix represents a system of linear equations. To find the general solution, we need to perform row operations to bring the augmented matrix into row-echelon form or reduced row-echelon form. Then we can solve for the variables.

Performing row operations, we can eliminate the variables one by one to obtain the row-echelon form:

\[ \left[\begin{array}{rrrrrr} 1 & -3 & 0 & -1 & 0 & -8 \\ 0 & 1 & 0 & 0 & -4 & 1 \\ 0 & 0 & 0 & 1 & 7 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right] \]

From the row-echelon form, we can see that there are infinitely many solutions since there is a row of zeros but the system is not inconsistent. We have three variables: x, y, and z. Let's denote z as a free variable and express the other variables in terms of z.

From the third row, we have:

\[ 0z + 0 = 1 \implies 0 = 1 \]

This equation is inconsistent, meaning there is no solution for x and y.

Therefore, the system of equations is inconsistent, and there is no general solution.

If there was a typo in the matrix or more information is provided, please provide the corrected or complete matrix so that we can help you find the general solution.

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Answer: Its 39x + 45

Step-by-step explanation:

yes

Assuming you're trying to find the value of r...

Answer:

r = 1

Step-by-step explanation:

Take your starting equation:

16 = 16r

Since r is multiplied by 16, divide both sides by 16 to isolate r.

16 / 16 = 1

16r / 16 = r

The result is 1 = r, which can be written as:

r = 1

Answer:

I hope this helps.

Step-by-step explanation:

Divide 8 by 10, whatever that gets you may be able to add up to 35.

Again, I hope this helps at least a little.

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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The x-coordinate on the x axis where the electric field produced by the particles is equal to zero is: x = 373 cm

b.

The electric field due to a point charge is given by:

E = k|q|/r^2

where k is a constant, q is the charge of the point charge, and r is the distance from the point charge.

In this case, there are two point charges, so the electric field is the sum of the electric fields due to each point charge:

E = k|q1|/r1^2 + k|q2|/r2^2

where q1 and q2 are the charges of the point charges, and r1 and r2 are the distances from the point charges.

We want the electric field to be zero, so we set the expression above to zero:

0 = k|q1|/r1^2 + k|q2|/r2^2

We can solve for the x-coordinate where the electric field is zero by rearranging the equation and substituting in the values for the charges and distances:

x = (k|q2|r1^2)/(k|q1|r2^2) = (3.24 × 10^-8 C * 0.230 m^2) / (1.77 × 10^-8 C * 0.790 m^2) = 373 cm

In conclusion, the x-coordinate on the x axis where the electric field produced by the particles is equal to zero is 373 cm.

The electric field is a vector field, which means that it has both a magnitude and a direction. The magnitude of the electric field is a measure of how strong the electric field is, and the direction of the electric field is the direction in which the force on a positive charge would point.

The electric field produced by a point charge is inversely proportional to the square of the distance from the point charge. This means that the electric field gets weaker as the distance from the point charge increases.

In this case, the electric field produced by the two point charges is zero at a point that is halfway between the two point charges. This is because the electric fields due to the two point charges cancel each other out at this point.

The x-coordinate of the point where the electric field is zero can be calculated by using the expressions for the electric fields due to the two point charges and setting the expression equal to zero. The x-coordinate of the point where the electric field is zero is 373 cm.

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There are multiple ways to decompose the fraction 6/10 into a sum. Two possible ways are 3/10 + 3/10 and 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10.

1. 3/10 + 3/10: One way to decompose 6/10 into a sum is by adding two equal fractions. By splitting 6/10 into two fractions of 3/10 each and adding them together, we get 3/10 + 3/10 = 6/10.

2. 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10: Another way to decompose 6/10 into a sum is by breaking it down into several fractions of the same value. In this case, we can represent 6/10 as the sum of six fractions, each equal to 1/10. Adding them together, we get 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 6/10.

These two examples illustrate different ways to decompose the fraction 6/10 into a sum using equal or repeated fractions.

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Answer:

AB=18

CD=16

BD=36

Step-by-step explanation:

To get AB

Subtract the total leanth of 54 with 36

AB=18

To get CD Subtract 36 from BC or 20

CD= 16

To get BD its 36 cuz that's what it shows

Answer:

AB=18

CD=18

BD=36

Step-by-step explanation:

To get AB you subtract 36 from 36

CD is the same lenght as AB

And BD is already measured

The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Answer:

The first choice

Step-by-step explanation:

You are setting up as you read it.  The left side has 5 x and 6 units, so you would set up 5 positive x times and 6 positive unit tiles.  On the the right you are setting up 4 positive x tiles and 3 negative unit tiles.  It is not asking you to solve with the algebra tiles, just to set it up.

Answer:

you combine the numbers that are the same and see the signs if it's positive with the negative, it's going to be negative

Answer: y = -2x

M is the midpoint of PQ

=> M(0;0)

the line PQ passes through P(2;1) and Q(-2;-1)

=> (PQ): 2x - 4y = 0

have:

(d): perpendicular (PQ)

     passes throgh M(0;0)

=> (d): 4x + 2y = 0 ⇔ y = -2x

Step-by-step explanation:

The equation of the perpendicular bisector of PQ is,

⇒ y = - 2x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point P has coordinates (2, 1) and the point Q has coordinates(-2, -1).

Hence, The slope of line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 1) / (- 2 - 2)

m = - 2 / - 4

m = 1/2

Thus, The slope of perpendicular line is,

⇒ m = - 2

The midpoint of coordinates (2, 1) and (- 2, - 1) is,

⇒ (- 1 + 1) / 2 , (- 2 + 2) / 2

⇒ (0, 0)

Hence, The equation of line is,

⇒ y = mx + b

⇒ 0 = - 2 × 0 + b

⇒ b = 0

Hence, The equation of the perpendicular bisector of PQ is,

⇒ y = - 2x

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