People were given three choices of soft drinks and asked to choose one favorite. The following table shows the results.

Start 4 By 4 Table 1st Row 1st Column 2nd Column diet cola 3rd Column root beer 4st Column lemon drop 2nd Row 1st Column under 18 years of age 2nd Column 40 3rd Column 25 4st Column 20 3rd Row 1st Column font size increased by 1 Subscript Baseline font size increased by 1 font size decreased by 1 between 18 and 40 2nd Column 35 3rd Column 20 4st Column 30 4st Row 1st Column over 40 years of age 2nd Column 20 3rd Column 30 4st Column 35 EndTable

diet cola
root beer
lemon drop
under 18 years of age
40
25
20
between 18 and 40
35
20
30
over 40 years of age
20
30
35

Answer:

C

Step-by-step explanation:

B and D are equal. You could call their sum = 2x

a = 25 degrees (Vertically Opposite Angles)

C = 95 degrees. (Vertically Opposite Angles)

The total is 360 degrees. So let's add everything up and see what we get.

a+b+c + 25 + d + 95 = 360 degrees.      Substitute for the known letters.

25 + x + 95 + 25 + x + 95 = 360             Combine like terms on the left

50 + 2x + 95 + 95  = 360                        Combine numbers on the left

240 + 2x = 360                                        Subtract 240 on both sides

240 - 240 + 2x = 360 - 240                    Combine

2x = 120                                                    Divide by 2

x = 60

b = 60

a = 25

a + b =60 + 25 = 85

The midpoint of the line segment with endpoints (-2, 5) and (4, -9) is found using the midpoint formula and is (1, -2).

To find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9), you use the midpoint formula, which is derived from finding the average of the x-coordinates and the y-coordinates of the endpoints respectively.

The midpoint formula is:

( (x1 + x2) / 2, (y1 + y2) / 2 )

Plugging in our given endpoints (-2, 5) and (4, -9) into the formula, it becomes:

( (-2 + 4) / 2, (5 + (-9)) / 2 )

This simplifies to:

( 2 / 2, -4 / 2 )

And finally:

( 1, -2 )

Therefore, the midpoint of the line segment is at coordinates (1, -2).

1172. 08 in²

Hi there !

A(prism) = 2(lw + lh + wh) - Ab(cylinder)

= 2(16*11 + 16*11 + 11*11) - πr²

= 2(176 + 176 + 121) - 3.14*16

= 2*473 - 50.4

= 946 - 50.24

= 895.76 in²

A(cylinder) = πr² + 2πr*h

= 3.14*16 + 2*3.14*4*9

= 50.24 + 226.08

= 276.32 in²

A(total) = 895.76in² + 276.32in² = 1172.08 in²

Good luck !

Answer:

1. C. Jana

2. I. Matthew and Jake

The y-intercept of a line that has a slope of –3 and passes through point (–5, 4) is -11.

The slope-intercept of a line is

[tex](y-y_{1})=m(x-x_{1})[/tex]

Here, [tex](x_{1},y_{1})[/tex] is the point through which the line passes and 'm' is the slope of the line.

Given, the line has a slope of –3 and passes through point (–5, 4).

Therefore, [tex](y-4)=-3[x-(-5)][/tex]

⇒ [tex](y-4)= -3(x+5)[/tex]

⇒ [tex](y-4)= -3x-15[/tex]

⇒ [tex]3x+y = -11[/tex]

⇒ [tex]y = -3x-11[/tex]

Comparing it with the standard form of equation, we get:

the y-intercept of the required line is -11.

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It would take Petra 104 minutes to jog 13 miles

because 40/5 is 8 minutes per mile

you'd multiply 13 miles by 8 minutes

Answer:

y+5=-1/2(x+3)

Step-by-step explanation:

as perpendicular,

compare that given eqn with y-y1=m(x-x1),

m1=2

then,

perpendicular case,

m1×m2=-1

m2=-1/2

now,

as the eqn passes through point (-3,-5),

we know,

y-y1=m(x-x1)

then putting value,

y+5=-1/2(x+3)

Answer:

y + 5 = - [tex]\frac{1}{2}[/tex](x + 3)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line.

y - 4 = 2(x - 6) is in this form with slope m = 2

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

Hence the equation passing through (- 3, - 5) is

y - (- 5) = - [tex]\frac{1}2}[/tex] (x - (- 3)), that is

y + 5 = - [tex]\frac{1}{2}[/tex](x + 3) ← equation of perpendicular line

Answer:

144°

Step-by-step explanation:

step 1

Find the measure of the central angle of the regular pentagon

Divide 360 degrees by 5 (the number of sides)

[tex]360\°/5=72\°[/tex]

Let

c----> the center of the pentagon

we know that

m∠ECA=72°

m∠ACB=72°

therefore

m∠ECB=m∠ECA+m∠ACB

substitute the values

m∠ECB=72°+72°=144°

The measure of angle ECB is equal to the degrees that the pentagon rotate

Answer:

Third length =

12-7 = 5

12+7 = 19

Third length can be only in this range

5Means the third length must be greater than 5 and less than 19.

Step-by-step explanation:

Answer:

C) a+3

Step-by-step explanation:

We are given the following data:

Tom's Age:  10  11  12  a

Kim's Age:   13  14  15  

We have to evaluate Kim's age when Tom's age is a.

We have to build a relationship between Tim's age and Kim's age. If we look at their ages carefully we can see a pattern and their relation can be described as:

[tex]\text{Kim's age = Tim's age + 3}[/tex]

Thus, when Tim's age is a, we can compute Kim's age as:

[tex]\text{Kim's age = a + 3}[/tex]

Answer:

answer is A

Step-by-step explanation:

The formula for circumference of a circle using diameter is pi times "d". "d" means diameter. 3.14 x 16= 50.24

C = pi•d

C = 3.14(16)

C = 50.24 inches

ANSWER

GCF=4

EXPLANATION

The given monomials are:

[tex]8m = {2}^{3} m[/tex]

[tex]36 {m}^{3} = {2}^{2} \times {3}^{2} {m}^{3} [/tex]

[tex]12 = {2}^{2} \times 3[/tex]

The greatest common factor is the product of all the least powers of the common factors.

We can see that:

[tex] {2}^{2} [/tex]

is the common to all the factors.

Therefore the greatest common factor is

[tex] {2}^{2} = 4[/tex]

Answer: [tex]GCF=4[/tex]

Step-by-step explanation:

To find the Greatest Common Factor (GCF) of 8m, 36m³, and 12, you need to descompose them into their prime factors. Then:

[tex]8m=2*2*2*m=2^3*m\\\\36m^3=2*2*3*3*m^3=2^2*3^2*m^3\\\\12=2*2*3=2^2*3[/tex]

You can observe that the common factor with the lowest exponent is the following:

[tex]2^2[/tex]

Therefore,  the Greatest Common Factor (GCF) of 8m, 36m³, and 12 is:

[tex]GCF=2^2\\GCF=4[/tex]

Answer:

Line segment TU is parallel to line segment RS because 32/36 = 40/45.

Step-by-step explanation:

The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The converse theorem states that if TU || RS, then the ratio of the corresponding sides will be constant.

32 / 36 = 40 / 45 = 8 / 9 = constant

The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.

Then the correct option is A.

The graph is given below.

More about the triangle link is given below.

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Answer:

1. trapezoid

A quadrilateral with at least one pair of parallel sides.  

2. bases of a trapezoid

The parallel sides

3. legs of a trapezoid  

The nonparallel sides.  

4. median of a trapezoid  

The segment connecting the midpoints of the legs.  

5. isosceles trapezoid

A trapezoid with legs of the same length.

Answer:

A trapezoid is defined as a quadrilateral with at least one pair of parallel sides, when the trapezoid as equal legs, it's called an isosceles trapezoid.

The bases of a trapezoid are the pair of parallel sides, both of them are called base, the longer one is the major base, and the shorter one is the minor base.

The legs of a trapezoid are the nonparallel sides, because if they were parallel, that wouldn't be a trapezoid, it would be another quadrilateral.

The median of a trapezoid is a segment that connects the midpoints of the legs. Remember that medians are always line that intercept midpoints.

As we said before, an isosceles trapezoid are those which have legs with equal legs. The name isosceles refers to equality.

Therefore, the right matches are

1. Trapezoid: A quadrilateral with at least one pair of parallel sides.  

2. Bases of a trapezoid: The parallel sides.

3. Legs of a trapezoid: The nonparallel sides.  

4. Median of a trapezoid: The segment connecting the midpoints of the legs.  

5. Isosceles trapezoid: A trapezoid with legs of the same length.

Answer:

the second one

Step-by-step explanation:

Answer:

the second one

Step-by-step explanation:

the one that says +14

Answer:1/2

Step-by-step explanation:

the slope of a line in an equation comes before x

since we know parallel lines have the same slope it is 1/2

Answer:

(3a2 + 3a2) + [–5ab + (–8ab)] + [b2 + (–2b2)]

Step-by-step explanation:

Answer: c. (3a^2+3a^2)+[-5ab+(-8ab)]+[b^2+(-2b^2)]

for the second part: =a. 6a^2-13ab-b^2

Step-by-step explanation:

i did it

Answer:

[tex](x-5)^{2} +(y+4)^{2} =10^{2}[/tex]

Step-by-step explanation:

To calculate the formula of a circle that is not in the center fo the graph, you need two things, the point where the cirlce is centered and any point in the circumference, and with this you can calculate the radius, to calculate the first part you just need the next formula:

[tex](x-x^{c})+(y-y^{c})=r^{2}[/tex]

Where [tex]x^{c}y^{c}[/tex] are the x and y where the center of the circle is, so you just evaluate with the values you are given:

[tex](x-x^{c})+(y-y^{c})=r^{2}[/tex]

[tex](x-(5))+(y-(-4))=r^{2}[/tex]

[tex](x-5)+(y+4)=r^{2}[/tex]

Now that you have the first part, we can calculate the radius, remember taht the radius of any given circumference in the graph is the hypotenuse of the X´s and Y´s that are part of those two points given, so we just calculate it like any hypotenuse:

[tex]c=\sqrt{x^{2}+ y^{2} }[/tex]

To calculate this we would rest to the point in the circumference, the center of the circumference, like this:

[tex]c=\sqrt{(x^{2}-x^{1})^{2}+ (y^{2}-y^{1})^{2} }[/tex]

[tex]c=\sqrt{(-3-5)^{2}+ (2-(-4))^{2} }[/tex]

[tex]c=\sqrt{(-8)^{2}+ (6)^{2} }[/tex]

[tex]c=\sqrt{64+ 36 }[/tex]

[tex]c=\sqrt{100 }[/tex]

[tex]c=10[/tex]

So your radius would be 10, now we just put that into our previous formula:

[tex](x-5)+(y+4)=r^{2}[/tex]

[tex](x-5)+(y+4)=10^{2}[/tex]

So the formula for the circle that is centered at (5,-4) and passes through the point (-3,2) would be:

[tex](x-5)+(y+4)=10^{2}[/tex]

there were D. 1163 books left on the shelves or in circulation.

///////////////////////////////////////////////////////////////////////////

let us count the number of books that are NOT on the shelves now.

1st step: 32 + 24 = 56

2nd step: the total number of books minus the amount of books that are damaged or out:  1,219 - 56 = 1163

Answer:

C. 1,163

Step-by-step explanation:

Total books = books on shelves + books lost + books out for repair

What do we know

1219 =  books on shelves + 32 + 24

1219 = books on selves + 56

Subtract 56 from each side

1219-56 = books on shelves - 56

1163 = books on shelves

Answer:

C

Step-by-step explanation:

To evaluate (f ￮ g)(x)

Substitute x = g(x) into f(x)

f(x² + 14) = x² + 14 - 14 = x² → C

The value of (fog)(x) = x^2. So, option C is correct.

The functions f(x) and g(x) are composite functions then,

(fog)(x) = f(g(x)).

Given that,

f(x) = x - 14

g(x) = [tex]x^2+14[/tex]

Then,

(fog)(x) = f(g(x))

           = ([tex]x^2+14[/tex]) - 14

           = x² + 14 - 14

           = x²

Therefore, the value of (fog)(x) = x².

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Answer:

There are [tex]4.93\times 10^{22}[/tex] copper atoms in 5.2 gram of metallic copper.

Step-by-step explanation:

Start by finding the number of moles of copper atoms in that 5.2 gram of metallic copper. Look up the relative atomic mass of copper on a modern periodic table.

In other words, the mass of one mole of copper atoms is 63.546 gram.

[tex]M(\mathrm{Cu}) = \rm 63.546\; g\cdot mol^{-1}[/tex].

How many moles of copper atoms in that 5.2 gram sample?

[tex]\displaystyle n = \frac{m}{M} =\rm \frac{5.2\; g}{63.546\; g\cdot mol^{-1}} = 0.0818305\; mol[/tex].

Now, how many atoms is [tex]\rm 0.0818305\; mol[/tex]?

The Avogadro's Number gives the number of particles in one mole:

[tex]N_A \approx \rm 6.022\times 10^{23}\;mol^{-1}[/tex]. (Encyclopedia Britannica)

There are [tex]6.022\times 10^{23}[/tex] particles (a very large number) in one mole. [tex]\rm 0.0818305\; mol[/tex] of copper atoms will thus contain

[tex]N = n\cdot N_A \approx \rm 0.0818305\; mol\times 6.023\times 10^{23}\;mol^{-1} \approx 4.93\times 10^{22}[/tex]

copper atoms.

any point that is on the circle will  have a distance of "radius" units, namely 13 units, since the radius is just that.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{origin}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{12})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-5-0)^2+(12-0)^2}\implies d=\sqrt{(-5)^2+12^2} \\\\\\ d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13[/tex]

Final answer:

The point (-5, 12) lies on the circle with a radius of 13 and a center at the origin because it satisfies the equation [tex]x^2 +[/tex] [tex]y^2 = 13^2.[/tex]

Explanation:

The student is asking which point lies on the circle with a center at the origin and a radius of 13. To determine if a point lies on a circle defined by the equation [tex]x^2 + y^2 = r^2,[/tex] where r is the radius, we plug the point's coordinates into the equation and see if they satisfy it.

Let's examine each point:

[tex](-5, 12): (-5)^2 + (12)^2 = 25 + 144 = 169[/tex]

[tex](13, 13): (13)^2 + (13)^2 = 169 + 169 does not equal 169[/tex]

[tex](6, -7): (6)^2 + (-7)^2 = 36 + 49 = 85 does not equal 169[/tex]

Therefore, the point (-5, 12) lies on the circle because it satisfies the equation [tex](-5)^2 + (12)^2 = 13^2.[/tex]

Answer:

A. 12x + 7y = 20

Step-by-step explanation:

Obviously, 12x + 7y cannot both be equivalent to unique [different] quantities.

Option A (12x + 7y = 20) would make the system of linear equations with 12x + 7y = 25 have no solution because the lines would be parallel and never intersect.

Second equation would make a system of linear equations with 12x + 7y = 25 have no solution. A system of linear equations will have no solution if the two lines represented by the equations are parallel, which means they have the same slope but different y-intercepts. Since the first equation is 12x + 7y = 25, we need a second equation with the same coefficients for x and y but a different constant term in order to represent parallel lines.

Option A (12x + 7y = 20) meets the criteria for causing the system to have no solution because it has the same coefficients for x and y as the first equation but a different constant term. This indicates that the lines are parallel and will never intersect, hence no solution exists for this pair of equations.

Answer:

5(5 + 2)

Step-by-step explanation:

The distributive property states that If 2 numbers have a common factor you can divide the common factor out. Similarily, if they share a common factor, you can distribute the common factor into each number in the parenthesis.

Find the factors of 25 & 10:

25: 1, 5, 25

10: 1, 2, 5, 10

Note that the largest common factor is 5. Divide 5 from both number:

(25 + 10)/5 = 5(5 + 2)

5(5 + 2) is your answer.

~

Answer:

5/6 is larger

Step-by-step explanation:

5/6 * (6/6) = 30/36

30/36 > 29/36

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Answer:

iii) P=65h

iv) P=70h

Step-by-step explanation:

Payment of First day = $300

Number of hours = 5

Payment per hour = $60

Payment of First day = $240

Number of hours = 4

Payment per hour = $60

Payment of First day = $360

Number of hours = 6

Payment per hour = $60

Hence the rate of Payment for an hour is $60

Hence the rates

P=65h

and

P=70h

are more than the rate of payment made to labor.

Answer: B. It can be concluded that the strength training program does not reduce the number of muscular injuries that occur during an athletic event.

Step-by-step explanation: In the question it states the average number of muscular injuries for athletes enrolled in the strength training program is equal to the average number of muscular injuries for athletes not enrolled in the strength training program.

From the coach's report, it can be concluded that the strength training program does not reduce the number of muscular injuries that occur during athletic events. This conclusion is drawn from the experiment's finding that both participants in the training program and those who did not participated had the same average number of injuries.

The student's question concerns the effectiveness of a strength training program in reducing the number of muscular injuries during athletic events. The coach conducted an experiment with 30 athletes, where half participated in a strength training program and the other half did not. After both groups were monitored for five athletic events, it was found that the average number of muscular injuries was the same for both groups. Hence, from the given information, the correct conclusion would be:

It's important to note that this conclusion does not necessarily imply that strength training is ineffective in all contexts, just that in this specific experiment, it did not lead to a reduction in injuries. Further, the conclusion does not indicate that the strength training program increases injuries, which eliminates option C. Meanwhile, option D is also incorrect because the data indicates no reduction in injuries.

Answer:

LCM = 30

Step-by-step explanation:

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Answer:

$675

$850

$1200

Step-by-step explanation:

Use formula for simple interest:

A = P (1+rt)

where

A = accrued amount (principal + interest) = what we want to find

P = Principal (initial) amount = Given as $500

r = rate of interest = Given as 7% = 0.07

t = time

For 5 years, t = 5

A = 500 [ 1 + 0.07(5) ] = $675

For 10 years, t = 10

A = 500 [ 1 + 0.07(10) ] = $850

For 20 years, t = 20

A = 500 [ 1 + 0.07(20) ] = $1200

Answer:

d

Step-by-step explanation: