5) Find the union and the intersection of the given intervals.
A1(0,3] ; A2 [2,6)

6) Find the union and the intersection of the given intervals.
A1= (-∞, 6) A2 =(6,∞)

Answer:

374 miles

Step-by-step explanation:

To see how many miles each gallon gets, divide 102/3 which is 34 meaning there are 34 miles per gallon so if you multiply 34 x 11 gallons it equals 374 miles.

Hope this helps!

To solve this problem, we will use the concept of a unit rate, which in this scenario is the car's miles per gallon (mpg). A unit rate compares a quantity to one unit of another quantity. Here's how to do it step by step:
1. **Find the unit rate (mpg).**
  The car travels 102 miles on 3 gallons of gas. To find out how many miles it travels per gallon, we'd divide the total number of miles by the number of gallons of gas used:
  \[ \text{mpg} = \frac{\text{miles traveled}}{\text{gallons used}} \]
  \[ \text{mpg} = \frac{102 \text{ miles}}{3 \text{ gallons}} \]
  \[ \text{mpg} = 34 \text{ miles per gallon} \]
  So the car travels 34 miles per gallon of gas.
2. **Calculate the distance the car can travel on 11 gallons of gas.**
  Now that we know the car travels 34 miles on one gallon of gas, we can find out how far it travels on 11 gallons by multiplying the mpg by the number of gallons:
  \[ \text{distance} = \text{mpg} \times \text{gallons available} \]
  \[ \text{distance} = 34 \text{ miles/gallon} \times 11 \text{ gallons} \]
  \[ \text{distance} = 374 \text{ miles} \]
So, the car can travel 374 miles on 11 gallons of gas.

V = Bh

144 = (8 x 4)h

144 = 32h

4.5 = h

Final answer:

To calculate the height of the rectangular prism, we use the formula for volume and the given values to solve for height, resulting in a height of 4.5 inches.

Explanation:

To find the height of a rectangular prism with a given volume where the length is two times the width and the width is known, we use the formula for the volume of a rectangular prism: volume = length × width × height.

Given that the volume is 144 cubic inches, the width is 4 inches, and the length is two times the width, which is 2 × 4 inches = 8 inches, we can substitute these values into the formula:

144 in³ = 8 in × 4 in × height

Next, we need to isolate 'height' by dividing both sides of the equation by the length times the width of the prism:

144 in³ / (8 in × 4 in) = height

144 in³ / 32 in² = height

4.5 in = height

Therefore, the height of the rectangular prism is 4.5 inches.

Your constant is 3 because it’s alone

Answer:3

Step-by-step explanation:

Answer:

Step-by-step explanation:

45 Mins

Answer: Option a:

[tex](f * g) (x) = 2x[/tex]

Step-by-step explanation:

The expression [tex](f * g) (x)[/tex] refers to the multiplication of two functions f and g.

In this case we know that the functions are:

[tex]f (x) = x\\\\g (x) = 2[/tex]

Then you must multiply the two functions we get.

[tex](f * g) (x) = f (x) * g (x)\\\\(f * g) (x) = 2 * x\\\\(f * g) (x) = 2x[/tex]

The correct answer is option a.

For this case we must find the quotient of [tex]x ^ 2 + 11x + 24[/tex] between [tex]x + 4[/tex]

As you can see in the figure, we must build a quotient in such a way that when multiplied by the divisor, we eliminate the terms of the dividend until we reach the remainder.

Answer:

Quotient: x + 7

Remainder: -4

See attached image

Answer:

The error was on the diameter. The tire diameter was supposed to be;

4.6+15+4.6=24.2

The student only includes one sidewall width

Step-by-step explanation:

The question is on circumerence of a tire

Here we apply the formulae for circumference of a circle

C=2 [tex]\pi[/tex]×r or [tex]\pi[/tex] × d where r is the radius of the tire and d is the diameter

Finding d= diameter of rim + sidewall to the right +sidewall to the left

d= 15+4.6+4.6=24.2 inches

r=d/2= 12.1

C=2 ×[tex]\pi[/tex]×r

C=2×3.14×12.1 =75.99 Inches

Answer:

25 gallons

Step-by-step explanation:

Given:

total no. of gallons= 50

Percentage of sulfuric acid= 50%

Number of gallons of sulfuric acid= total no. of gallons x Percentage of sulfuric acid

Putting values in above equation:

Number of gallons of sulfuric acid= 50 x 50/100

                                                        = 50 x 1/2

                                                        = 25 !

To find the number of gallons of sulfuric acid in a 50-gallon solution with a 50% concentration, multiply the volume of the solution by the concentration.

To find the number of gallons of sulfuric acid in a 50-gallon solution with a 50% concentration, you can use a simple calculation. The percent concentration represents the fraction of sulfuric acid in the solution, so you can calculate the amount of sulfuric acid by multiplying the volume of the solution by the concentration:

Volume of sulfuric acid = Volume of solution * Percent concentration

Volume of sulfuric acid = 50 gallons * 0.50 = 25 gallons

Therefore, there are 25 gallons of sulfuric acid in the 50-gallon solution.

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Answer:

[tex]P(green)+P(yellow)=\frac{3}{8}+\frac{1}{8}[/tex]

[tex]P(green)+P(yellow)=\frac{1}{4}+\frac{1}{4}[/tex]

[tex]P(green)+P(yellow)=\frac{3}{7}+\frac{1}{14}[/tex]

Step-by-step explanation:

The given probabilities are:

[tex]P(red)=\frac{2}{7}[/tex]

[tex]P(blue)=\frac{3}{14}[/tex]

Their sum is [tex]P(red)+P(blue)=\frac{2}{7}+\frac{3}{14}[/tex]

The probabilities that will complete the model should add up to [tex]\frac{1}{2}[/tex] so that the sum of all probabilities is 1.

[tex]P(green)+P(yellow)=\frac{2}{7}+\frac{2}{7}\ne\frac{1}{2}[/tex]

[tex]P(green)+P(yellow)=\frac{3}{8}+\frac{1}{8}=\frac{1}{2}[/tex]

[tex]P(green)+P(yellow)=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}[/tex]

[tex]P(green)+P(yellow)=\frac{5}{21}+\frac{11}{21}\ne\frac{1}{2}[/tex]

[tex]P(green)+P(yellow)=\frac{3}{7}+\frac{1}{14}=\frac{1}{2}[/tex]

Answer:

According to the information you provided, a probability model includes P(red) = 2/7 and P(blue) = 3/14. The probabilities that could complete the model are P(green) = 5/21 and P(yellow) = 11/21. This is because the sum of all probabilities in a probability model must equal 1. In this case, 2/7 + 3/14 + 5/21 + 11/21 = 1.

Answer:

the required quotient is 173.92

Step-by-step explanation:

If a÷b=c,

then,

a is the dividend

b is divisor

and c is quotient.

By the question,

a=2.26108

b=0.013

c=?

now,

a÷b=c

or, 2.26108÷0.013=c

or, 173.92=c

Answer:

[tex]1.738\cdot 10^{10}[/tex]

Step-by-step explanation:

We are asked to find the the quotient of the division problem, where [tex]2.26\cdot 10^8[/tex] is dividend and 0.013 is divisor.

Represent dividend and divisor as fraction:

[tex]\frac{2.26\cdot 10^8}{0.013}[/tex]

Convert 0.013 into scientific notation:

[tex]0.013=1.3\cdot 10^{-2}[/tex]

[tex]\frac{2.26\cdot 10^8}{1.3\cdot 10^{-2}}[/tex]

Using exponent property [tex]\frac{a^m}{a^n}=a^{m-n}[/tex], we will get:

[tex]\frac{2.26}{1.3}\cdot 10^{8-(-2)[/tex]

[tex]\frac{2.26}{1.3}\cdot 10^{8+2}[/tex]

[tex]1.738\cdot 10^{10}[/tex]

Therefore, our required quotient would be [tex]1.738\cdot 10^{10}[/tex].

Answer:

Yes, i believe that the generalization about the measure of a point angle of a star polygon is true.

First we find sum of interior angle of an n-sided star polygon.

number of triangle in a polygon = n - 2

sum of interior angle of a triangle = 180°

sum of interior angle of an n-sided star polygon = ( n - 2 ) × 180°

To find measure of a point angle, we use:

[tex]\frac{|n-2(d)|}{n}[/tex] × 180°                                                            

To find a point angle we eliminate density by multiplying d by 2  in the formula for finding number of triangle, divide the whole by total number of sides and then multiply by the sum of interior angle of triangle(180°).  

Since all the angle of a regular star polygon are equal, we can calculate each pointy interior angle of a regular star polygon using the formula given below:

[tex]\frac{|n-2(d)|}{n}[/tex] × 180°    

The answer is:

The average speed for the total trip is 753.19 mph.

To calculate the average speed for the total trip, we need to calculate the time of travel for both distances according to their speeds.

So, calculating we have:

- First distance and speed: 3334 miles at 760 mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{3334miles}{760mph=4.39hours}[/tex]

Therefore, we have that the first distance was covered in 4.39 hours.

- Second distance and speed: 2244.7 miles at 740mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{2244.7miles}{740mph=3.03hours}[/tex]

Therefore, we have that the second distance was covered in 3.03 hours.

Now, calculating the average speed, we have:

[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]

Substuting we have:

[tex]AverageSpeed=\frac{3344miles+2244.7miles}{4.39hours+3.03hours}[/tex]

[tex]AverageSpeed=\frac{5588.7miles}{7.42hours}=753.19mph[/tex]

Hence, we have that the average speed for the total trip is 753.19 mph.

Have a nice day!

Answer:

y = 1/2x represents a direct variation because it represents the direct variation formula: y = kx. In this case, the "k" is 1/2.

Answer:

1/2x

Step-by-step explanation:

For instance, if y shifts straightforwardly as x, and y = 6 when x = 2, the steady of variety is k = 3. Therefore, the condition depicting this immediate variety is y = 3x. ... As recently expressed, k is steady for each point; i.e., the proportion between the y-arrange of a point and the x-organize of a point is consistent.

Hello There!

First, let me just explain briefly what is an independent variable and a dependent variable.

An independent variable is the variable that changes during an experiment to see if it has an effect on another variable.

A dependent variable is what is being measured in the experiment. It’s also known as outcome or effect.

In this case, the dependent variable is the number of liters of water your drink because that’s what your measuring.

The independent variable is the number of times you drink all the water in your bottle because that changes during the experiment.

Answer:

2140

Step-by-step explanation:

Sofia paid a total of $7,440 over 24 months for a motorcycle with a sticker price of $5,300. The interest she paid can be found by subtracting the sticker price from the total amount paid, which comes to $2,140. Hence correct option C.

Sofia bought a motorcycle with a sticker price of $5300. If she paid $310 a month for 24 months, first we need to find out the total amount she paid over the 24 months. To do this, we multiply the monthly payment amount by the number of months:

$310 × 24 = $7,440

Now, to find the amount of interest paid, we subtract the original sticker price from the total amount paid:

$7,440 - $5,300 = $2,140

Therefore, Sofia paid $2,140 in interest.

Answer:

-20

Step-by-step explanation:

-Follow PEMDAS.

-2 negatives equal a positive.

-6 + 54/(-9) - 5 - 3

-6 + (-6) - 5 - 3

-12 - 5 - 3

-20

-20

Use PEMDAS

-6- -54/(-9) -5+-3

-6+54/(-9) -5+-3

-6+-6-5-3

-12-5-3

-17-3

-20

No, two ordered pairs in this list have a repeated of the domain element.

We know that the definition of functions tells us that a function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).

So here is important to know the term exactly one element, Why? because if you don't have this, you don't have a function. From the figure, two ordered pairs in this list have a repeated of the domain element. This can be proven by plotting these three points as indicated below. As you can see, the element 4 in the domain matches both 2 and -2 in the range. In conclusion, this relation is not a function.

Answer:

Step-by-step explanation:

We can first make y the subject of the formula by multiplying both sides of the equation by -1 ;

y = -x + 0

This is the equation of a line with a slope of -1, the coefficient of x, and passing through the origin.

In order to find three points that solve the equation, we can let x be;

0, 1, 2

then determine the corresponding values of y.

When x = 0, y = -(0) + 0 = 0

When x = 1, y = -(1) + 0 = -1

When x = 2, y = -2 + 0 = -2

Therefore, we have the following three sets of points that can be used to graph the linear equation;

(0,0)

(1,-1)

(2,-2)

Find the attached for the graph of the equation;

Answer: (-1,1) (0,0) (2,-2)

Step-by-step explanation:

Is 2/7 four time

so is 2•4/7=8/7 =1 1/7

the answer is 1 and 1/7

Answer:

The parallelogram.

Step-by-step explanation:

Line symmetry means that if you folded the shape in half, then both halves would be equal. There is no way to fold a parallelogram in half and have both halves be equal.

B. does not have the line symmetry

The line of symmetry is the line that cuts the shape exactly in half. it means that if you were to fold the shape along a line, both halves will match exactly. Equally, if you were to place the mirror along the line, the shape will remain unchanged. the square has four lines of symmetry.

A line of symmetry is a imaginary axis passing through the center of the object or divides into 2 equal halves. Since the diamond has all 4 sides equal, it has 2 lines of symmetry. the shape could have more than 1 line of symmetry.

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+5 is the additive inverse of (-5)

it is so as. -5 +5 =0

Hope it helps...

Regards,

Leukonov.

The additive inverse of a number is what you need to add to the given number to equal 0. This would be the opposite of the given number.

The opposite of -5 would be positive 5.

-5 + 5 = 0

The answer is 5

Flying a plane through your own imagination. This implies how dominoes make you think and create, using your mind to make comparisons. The other option is like banging my head against the wall. It’s pointless and painful.

Answer:

writing answers to math questions

Step-by-step explanation:

writing a sentance

writing an add

writing a book

Answer:

A. y = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

For horizontal asymptote, if the degree of numerator is equal to the degree of the denomenator, then we take the ratio of cofficient of highest degree variable

f(x) = [tex]\frac{6}{8}[/tex]

      = [tex]\frac{3}{4}[/tex]

The correct option is A.

The horizontal asymptote of the function f(x)=(6x^3 - 5x - 3)/(8x^3 - 2x + 5) is A. y=3/4. This answer is reached by comparing the degrees and coefficients of the numerator and denominator.

The question posed pertains to determining the horizontal asymptote of the function f(x)=(6x^3 - 5x - 3)/(8x^3 - 2x + 5). The horizontal asymptote of a rational function (a ratio of two polynomials) can be found by comparing the degrees of the numerator and denominator.

In this function, both the numerator and denominator are of the third degree, implying the coefficients of the leading term define the line of the horizontal asymptote. Hence, the horizontal asymptote of this function is y = 6/8 = 3/4 in shorthand.

So, the correct answer to your question, the horizontal asymptote of the given function, is A. y = 3/4.

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Answer:

AB, CA, BC is my answer

It goes AB,CA,BC hopefully this helped

Answer:

-x,y?

Step-by-step explanation:

if it's being reflected across the y-axis then that should go in to the negative side of the graph and the same if its being reflected across the x-axis, in which case it would be x,-y

Answer:

P'(-x,y)

Step-by-step explanation:

The question is asking you to reflect over the y-axis. You pick a random point in the first quadrant and reflect that point over the y-axis. The point will land in the second quadrant and the x-value will have been negated (changed sign).

Ex.

(5,4) would become (-5,4)

P(x,y) reflected over the y-axis P'(-x,y)

Answer:

$855355.656503296, but we round to $855355.66

Step-by-step explanation:

Set up an equation where f(x)=650000(1.04)^n. The 1.04 represents the growth because if it were just .04 we wouldn't be including the initial value and it would decay. The 650000 is the initial value, and we put 1.04 to the nth power because it represents the amount of years. To plug in seven years, simply do 650000(1.04)^7 in your calculator.

Answer:

c=$1.59-s

Step-by-step explanation:

Let

s ----> the sale price per pack

c ---> cost savings

we know that

The  equation that represent this situation is

c=$1.59-s

The volume of a cylinder is given by

[tex]V = A_bh[/tex]

Where [tex]A_b[/tex] is the base area and h is the height.

So, if we call [tex]V_1,\ V_2[/tex] the volumes with the original and the doubled area, we have

[tex]V_1 = A_bh,\quad V_2 = A_b(2h)[/tex]

Since the height was doubled. We deduce that

[tex]\dfrac{V_2}{V_1}=\dfrac{2A_bh}{A_bh}=2[/tex]

So, if the height is doubled, the volume will double as well.

Answer:

x = 56.7°

Step-by-step explanation:

Sin (x) = Oppo. / Hypo.

Sin (x) = 66/79

Sin (x) = 0.8354

     x = 56.7°

Answer:

x ≈ 56.7

Step-by-step explanation:

In the right triangle with hypotenuse 79 use the sine ratio to find x

sinx° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{66}{79}[/tex], hence

x = [tex]sin^{-1}[/tex] ([tex]\frac{66}{79}[/tex] ) ≈ 56.7

Answer:

40 + 20 + 10 + 5 is a geometric series

Step-by-step explanation:

* Lets revise the geometric series

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric Series:

∵ U1 = a  ,  U2  = ar  ,  U3  = ar2  ,  U4 = ar3  ,  U5 = ar4

∴ Un = ar^n-1, where a is the first term , r is the constant ratio

  between each two consecutive terms , and n is the position of

  the term in the series

* Now lets check the answers to find the correct one

# 40 + 50 + 60 + 70

∵ 50/40 = 5/4

∵ 60/50 = 6/5

∵ 5/4 ≠ 6/5

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 42 + 44 + 46

∵ 42/40 = 21/20

∵ 44/42 = 22/21

∵ 21/20 ≠ 22/21

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 80 + 40 + 120

∵ 80/40 = 2

∵ 40/80 = 1/2

∵ 2 ≠ 1/2

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 20 + 10 + 5

∵ 20/40 = 1/2

∵ 10/20 = 1/2

∵ 5/10 = 1/2

- There is a common ratio between each two consecutive terms

∴ 40 + 20 + 10 + 5 is a geometric series

Answer:

D 40 + 20 + 10 + 5