The union of sets P = {1, 2, 3, 4, 5, 6} Q = {4, 5, 6, 7, 8, 9} is given by which of the following?



{1, 2, 3, 4, 5, 6, 7, 8, 9}

{1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9}

ø

{4, 5, 6}

Answer:

k = 3

Step-by-step explanation:

the equation relating x and y is

y = kx ← k is the constant of proportionality

to find use the given conditions

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{36}{12}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Answer:

1.4

Step-by-step explanation:

im 100% right here is the proof

Answer: The price of each shirt she bought was $22.95.

Step-by-step explanation:

Hi, to answer this, first, we have to add to the discounted price (52.22) the amount of the credit (39.58), to obtain the original total cost (without discount).

So:

52.22+39.58 = $91.8

Since she bought 4 shirts, we have to divide the total cost by 4:

91.8 /4 = $22.95

The price of each shirt she bought was $22.95.

Answer:

B

Step-by-step explanation:

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

A) 9, 12, 21

9 + 12 = 21  YES :)

B) 9, 11, 12

9 + 11 = 20 > 12  NOT :(

C) 12, 14, 16

12 + 14 = 26 > 16  NOT :(

D) 16, 18, 25

16 + 18 = 34 > 25  NOT :(

Answer:

The rate of change is 7/3

Step-by-step explanation:

To find the average rate of change, we subtract  the value of the function at the 2 points, over the difference of the 2 points.

f(3) -f(0)

-----------

3-0

f(3) = 2^(3)+1 = 8+1 =9

f(0) = 1 +1 = 1

9 -2

-----------

3-0

7/3

The rate of change is 7/3

Each line is one unit.

When X = 0, the blue line is at Y = 2

When x = 3, the blue line is at Y = 9

The average rate of change would be the change in y over the change in x.

The change in y = 9 - 2 = 7

The change in x = 3-0 = 3

The average rate of change would be 7/3

Answer:

The correct answer is option C

Step-by-step explanation:

Area is usually the planar lamina of a two dimensional figure and usually expressed in units square meter, square feet, square inches etc.

While Volume is the total space occupied by an object in a 3-D setting and is usually expressed in cubic meter, cubic feet, cubic inches etc.

A 2-D dimension can not represent a 3-D structure and thus units of area inappropriate to measure volume

There are 8 possibilities: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Of these 4 have at least two heads. Assuming a fair coin, the probability of tossing at least two heads is 4/8 or 1/2. The Answer would probably be 3/8 though.

C) 3/8

The probability of heads is 1/2, so the probability of not-heads is 1/2.

Then the probability of 2 heads and a tails is (1/2)²·(1/2) = 1/8.

There are 3 choose 2 = (3·2)/(2·1) = 3 ways that the pair of heads may appear among the three tosses. Thus the probability of 2 heads in 3 tosses is ...

... 3·(1/8) = 3/8

_____

Or you can simply count the favorable outcomes among the possible outcomes:

TTT TTH THT THH HTT HTH HHT HHH . . . . 3 of 8 are favorable.

Answer:

1. 50%

2. 30.372

3. 569.99

5. 29.99

7. 479.99

8. 65%

9. 306.33

10. 20%

11. 31,491

Answer:

7<x<17

Step-by-step explanation:

a+b>x

5+12>x

17>x

5+x>12

x>7

12+x>5

x>-7 (ignore then since it is negative and you would use the one that makes the range smaller which is the one above)

To calculate the shaded area, determine the area of the entire shape and the area of the shaded region. Subtract the area of the shaded region from the area of the entire shape to find the shaded area.

To calculate the shaded area, we first need to determine the area of the entire shape. Let's say the shape is a rectangle with a length of 10 units and a width of 6 units. The area of the rectangle is given by multiplying the length by the width, so in this case, the area is 10 units x 6 units = 60 square units.

Next, we need to determine the area of the shaded region. Let's say the shaded region is a right triangle with a base of 4 units and a height of 3 units. The area of a triangle is given by multiplying the base by the height and dividing by 2. So, the area of the shaded triangle is (4 units x 3 units) / 2 = 6 square units.

Finally, we can calculate the shaded area by subtracting the area of the shaded triangle from the area of the entire shape. The shaded area is 60 square units - 6 square units = 54 square units.

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Given:

A motorist traveled 250 miles on 11 gallons of gas.

To Find:

In the same vehicle, the distance that can be traveled in 16 gallons.

Answer:

Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.

Step-by-step explanation:

We first find the number of miles that can be traveled on 1 mile of gas.

We do this by using the unitary method.

Given that in 11 gallons, 250 miles can be traveled in a certain vehicle.

So in 1 gallon, 250 ÷ 11 miles can be traveled. This is roughly equal to 22.72.

Next we will calculate how much distance he can go in 16 gallons. We multiply the distance traveled in 1 gallon by 16.

That is, in  16 gallons, the number of miles that can be traveled is 22.72 x 16 = 363.52.

Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.

Answer:363.6miles

Step-by-step explanation:

Answer:

(x, y ) = (3 , - 4 )

Step-by-step explanation:

given the 2 equations

2x - 3y = 18 → (1)

4x + y = 8 → (2)

multiply (2) by 3

12x + 3y = 24 → (3)

add (1) and (3) term by term to eliminate the term in y

(2x + 12x) + (- 3y + 3y) = (18 + 24)

14x = 42 ( divide both sides by 14 )

x = 3

substitute x = 3 in (1) or (2) to evaluate for y-coordinate

(2) → 12 + y = 8 ⇒ y = 8 - 12 = - 4

solution is (3, - 4 )

Answer:

The answer is 19.0000. 38 divided by two = t. (19)

Step-by-step explanation:

The approximate solution of an equation is simply an estimate of the solution.

The approximate solution of 2t = 38 is (d) 19.0000

The equation is given as:

[tex]\mathbf{2t =38}[/tex]

Start by dividing both sides of the equations by 2

[tex]\mathbf{\frac{2t}{2} =\frac{38}2}[/tex]

Divide 2t by 2, to give 2

So, we have

[tex]\mathbf{t =\frac{38}2}[/tex]

Divide 38 by 2 to give 19

[tex]\mathbf{t =19}[/tex]

From the list of given options, 19.0000 approximates to 19.

So, the solution of the equation can be rewritten as:

[tex]\mathbf{t =19.0000}[/tex]

Hence, the approximate solution is (d) 19.0000

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Hello from MrBillDoesMath!

Answer:

See Discussion section below

Discussion:

We know that

m<1  = m<2          ("measure" of angle 1 = measure of angle 2)

                     and

m<3 = m< 4

Adding these two equations gives

m<1 + m<3 = m<2 + m<4

From the diagram,  m<1 + m<3 =  m<CWE and m<2+m<4= m<FZH. Substituting these in the above equation gives:

m<CWE = m<FZH

Regards,  

MrB

Given equal angles in two figures, we prove that the angles formed by CWD and FZG, as well as DWE and GZH, are equal, thus showing m∠CWE = m∠FZH.

To prove that m∠CWE = m∠FZH, we can use the information given and apply the transitive property of equality. We have the following information:

Given:

1. m∠1 = m∠2 (angles 1 and 2 are congruent)

2. m∠3 = m∠4 (angles 3 and 4 are congruent)

We want to prove:

m∠CWE = m∠FZH

Now, let's construct a table to demonstrate the proof step by step:

| Statement         | Reason                               | Lines Used       |

|-------------------|--------------------------------------|------------------|

| 1. m∠1 = m∠2     | Given                                | Given            |

| 2. m∠3 = m∠4     | Given                                | Given            |

| 3. m∠CWD = m∠FZG | Corresponding angles are congruent   | Definition of ∠   |

| 4. m∠DWE = m∠GZH | Corresponding angles are congruent   | Definition of ∠   |

| 5. m∠CWD + m∠DWE = m∠FZG + m∠GZH | Adding equal quantities to equal quantities | Addition Property of Equality |

| 6. m∠CWE = m∠FZH | Angles CWD and DWE form ∠CWE, and angles FZG and GZH form ∠FZH | Definition of ∠ |

In lines 3 and 4, we use the definition of corresponding angles to show that angles CWD and FZG are congruent and angles DWE and GZH are congruent.

In line 5, we use the addition property of equality to add the two equal quantities, m∠CWD and m∠DWE on the left side, and m∠FZG and m∠GZH on the right side.

In line 6, we use the definition of angles to establish that m∠CWE is equal to m∠FZH.

In conclusion, we have successfully proven that m∠CWE = m∠FZH using the given information and the properties of angles.

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The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have

[tex]x_1=0,\ y_1=2.50\\\\x_2=1,\ y_2=5.00[/tex]

Substitute:

[tex]m=\dfrac{5-2.5}{1-0}=\dfrac{2.5}{1}=2.5[/tex]

y-intercept is for x = 0. Therefore y-intercept = 2.50.

The linear relationship: y = mx + b

m - slope

b - y-intercept

Substitute:

y = 2.5x + 2.5

Answer:

slope is 2.5

y intercept is 2.5

equation is y = 2.5x + 2.5

Step-by-step explanation:

We can find the slope by using the formula

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

   = (27.5-2.5)/(10-0)

    = (25/10)

    = 2.5

The y intercept is the y value when x = 0

The y intercept is 2.5

The equation for the line can be written using the formula

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

y = 2.5x + 2.5

[tex]\sqrt{\dfrac{64}{100}}=\dfrac{8}{25}[/tex]

Answer:

Number of countries in Florida=5×a-8

Number of countries in Georgia=2×f+25

Step-by-step explanation:

Given that the number of countries in Florida is denoted by f, number of countries in Arizona is given by a and the number of countries in Georgia is given by g.

as Florida has 8 less than five times the number of countries in Arizona

So f=5×a-8

Georgia has 25 more than twice the number of countries in Florida

So g=2×f+25

Now it is given that Arizona has 15 countries i.e. a=15

So f=5×15-8

f=67

g=2×67+25

g=159

Hence, number of countries in Florida is:67

number of countries in Georgia is:159

Florida has 67 counties and Georgia has 159 counties, based on the expressions given and the number of counties stated for Arizona.

The number of counties in Florida is represented by the expression 5a - 8, where 'a' is the number of counties in Arizona. Given that Arizona has 15 counties, we substitute 'a' with '15' in the expression to get 5*15 - 8 = 67. Hence, Florida has 67 counties.

The number of counties in Georgia is represented by the expression 2f + 25, where 'f' is the number of counties in Florida. Given that Florida has 67 counties, we substitute 'f' with '67' in the expression to get 2*67 + 25 = 159. Hence, Georgia has 159 counties.

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Answer:

Choice A) x and f(x) approach negative infinity

Choice D) x and f(x) approach positive infinity

Step-by-step explanation:

A cubic curve starts low and ends high if the leading coefficient is positive, which in this case it is. This means that the left side of the graph falls while the right side rises. Your teacher might say something like "fall to the left, rise to the right" to describe what the end behavior is doing.

More formally "fall to the left" means that as x approaches negative infinity, y = f(x) is approaching negative infinity as well. Similarly, "rise to the right" indicates that as x approaches infinity, y = f(x) heads off to infinity as well. Both x and y = f(x) move in the same direction along their respective number lines; eg, if one goes in the negative direction, then so does the other.

The graph below confirms the answer visually.

The set of angle measures could be the measures of the interior angles of a triangle are,

⇒ 55°, 90°, and 35°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

To find the set of angle measures could be the measures of the interior angles of a triangle.

Now, We know that;

Sum of all interior angles of a triangle is 180 degree.

A) 60°, 45°, and 70°

⇒ 60 + 45 + 70

⇒ 175 ≠ 180

Hence, It is not possible.

B) 30°, 85°, and 25°

⇒ 30 + 85 + 25

⇒ 140 ≠ 180

Hence, It is not possible.

C) 55°, 90°, and 35°

⇒ 55 + 90 + 35

⇒ 180

Hence, It is possible.

Thus, The set of angle measures could be the measures of the interior angles of a triangle are,

⇒ 55°, 90°, and 35°

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Answer:

Width of the rectangular side of that prism is, 9cm

Step-by-step explanation:

The formula for Perimeter of pentagonal prism is given by:

[tex]P = 5b[/tex]

where

P represents the perimeter of the pentagonal prism and

b is the base length of the pentagonal prism.

Given: Perimeter of pentagonal prism(P) is 45 cm.

Then;

45 = 5b

Divide both sides  by 5 we get;

[tex]b = \frac{45}{5} = 9 cm[/tex]

Therefore, the width of the rectangular side of that prism is, 9cm

Answer:

Width of the rectangular side of that prism is, 9cm

Step-by-step explanation:

sinB= 3/5 is correct

tanA= 4/3 is correct

and sinA= 4/5 is correct

hope this helps ^

Answer:

Each Child get = 0.928 pounds of candy

Step-by-step explanation:

Total no of girls are 3

total no of boys are 4

Total no boys and girls are = 3 + 4

                                             = 7

Now it is given that Mr Reese booth have some pound of candies and he wants to distribute it equally among each children

total candy Mr Reese have is [tex]6\frac{1}{2}[/tex]

Now converting it to proper fraction

[tex]6\frac{1}{2}[/tex] =[tex]\frac{6*2+1}{2}[/tex]

                                 =  [tex]\frac{13}{2}[/tex]

Now the amount of candy have =[tex]\frac{13}{2}[/tex]

Now we have to divide it into 7 kids

so

each kid get = total candy / total children

                     =[tex]\frac{13}{2}[/tex]÷7

Changing the divide sign to multiplication  

                      [tex]=\frac{13}{2}*\frac{1}{7}[/tex]

Which becomes

                      [tex]=\frac{13}{14}[/tex]

solving it gives

Each Child get = 0.928 pounds of candy

To find the better buy, we can find how much they cost for an ounce and find it by comparison.

First option:

20/4.4

=$4.545454...

Second option:

16/3.68

=$4.3478...

As $4.3478..< $4.5454.., the second option is cheaper and therefore is the better buy.

Hope it helps!

The 20 ounces for $4.40 is the better deal at $0.22 per ounce, compared to the 16 ounces for $3.68 at $0.23 per ounce.

To determine which cereal is the better buy, we need to calculate the cost per ounce for each option. For the first option of 20 ounces at $4.40, the cost per ounce is:

[tex]\frac{0.44}{20} = 0.22 ~per ounce[/tex]

For the second option of 16 ounces at $3.68, the cost per ounce is:

[tex]\frac{3.68}{16} = 0.23[/tex]

Comparing these two costs per ounce, the 20 ounces for $4.40 is the better buy because it has a lower cost per ounce.

Answer: B

Step-by-step explanation:

 2x - 3y =  -7   →   2(2x - 3y = -7)   →   4x - 6y = -14

-4x + 6y = -10  →   1(-4x + 6y = -10) → -4x + 6y = -10

                                                                    0  = -24

                                                                     FALSE

Since this makes a false statement, there are no solutions

Answer:

3/4

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−5, −4), B(−7, 3) and C(3, −2) to the image triangle A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25) and C' (2.25, −1.5).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A(−5, −4) ---> A' (−3.75, −3) = [tex]\frac{-3.75}{-5} , \frac{-3}{-4}=(\frac{3}{4} , \frac{3}{4})[/tex]

B(−7, 3) ---> B' (−5.25, 2.25) = [tex]\frac{-5.25}{-7} , \frac{2.25}{3}=(\frac{3}{4} , \frac{3}{4})[/tex]

C(3, −2) ---> C' (2.25, −1.5) = [tex]\frac{2.25}{3} , \frac{-1.5}{-2}=(\frac{3}{4} , \frac{3}{4})[/tex]

Therefore, the scale factor of the dilation is 3/4.

Answer: D. an angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive x-axis.

D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive [tex]x-[/tex]axis.

A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.

An angle can be defined as the figure formed by two rays meeting at a common end point.

D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive [tex]x-[/tex]axis.

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Answer:

A [tex]\alpha ,\beta[/tex]

Step-by-step explanation:

Step 1

The first step is to notice that the graphs of II and iv have the same y intercept. This means that we are looking for functions that match the condition that when t=0, the two functions have the same value.  The functions [tex]10(1.02)^t,10(1.05)^t[/tex] meet that condition. Additionally the functions  [tex]30(0.95)^t,30(1.05)^t[/tex] meet this condition.

Step 2

The other condition that must be met by the 2 functions is that they should both increase with the increase in increasing values of t.  the function  [tex]30(0.95)^t[/tex] does not meet this condition. This means that only the functions [tex]\alpha ,\beta[/tex] are the only functions that meet this condition.

Answer:

a. α and β

Step-by-step explanation:

One way to solve this exercise is by analyzing the y - intercept of the functions.

By looking at the graph, we can see that II and IV have the same y - intercept.

All the formulas below depend of the variable ''[tex]t[/tex]'' so if we want to find the y - intercept we only need to replace by ''[tex]t=0[/tex]'' in the formulas.

We can also see that the y - intercept of II and IV will be the lower that the another y - intercept of the functions.  

If we replace by [tex]t=0[/tex] :

(α)(t) = [tex]10.(1.02)^{t}[/tex] ⇒ [tex]10.(1.02)^{0}=10[/tex]

(β)(t) = [tex]10.(1.05)^{t}[/tex] ⇒ [tex]10.(1.05)^{0}=10[/tex]

(χ)(t) = [tex]20.(1.02)^{t}[/tex] ⇒ [tex]20.(1.02)^{0}=20[/tex]

(δ)(t) = [tex]30.(0.85)^{t}[/tex] ⇒ [tex]30.(0.85)^{0}=30[/tex]

(ε)(t) = [tex]30.(0.95)^{t}[/tex] ⇒ [tex]30.(0.95)^{0}=30[/tex]

(Φ)(t) = [tex]30.(1.05)^{t}[/tex] ⇒ [tex]30.(1.05)^{0}=30[/tex]

We find that the lowest y - intercept (also equal) are the y - intercept of α and β. Therefore, the correct option is a. α and β

Answer:

The expression is not equivalent to other three is 9(n-9) .

Option (B) is correct .

Step-by-step explanation:

Take first expression

= -9 -7n + 16n

= 9n-9

Take second expression

= 9(n-9)

= 9 × n - 9 × 9

= 9n - 81

Take third expression

= n-9+8n

= 9n-9

Take fourth expression

= 9n-9

Therefore expression is not equivalent to other three is 9(n-9) .

Option (B) is correct .

Answer:

B

Step-by-step explanation: