A survey asked a group of students to choose their favorite type of refreshment from the choices of ice cream, soda, and popsicles. The results of the survey are shown in the graph.
Based on the graph, how many more students in a class of 210 students would be expected to choose ice cream than popsicles?
A) 80
B) 120
C) 160
D) 180

Answer:

Multiply 60 by .40

60 * .40 = 24

Answer is B

Step-by-step explanation:

Answer: p(x) = 8.7x - 1940

              p(500) = $2410

              p(1000) = $6760

              p(5000) = $41,560

Step-by-step explanation:

p(x) = r(x) - c(x)

      = 9.5x - (0.8x + 1940)

      = 9.5x - 0.8x - 1940

      = 8.7x - 1940

**********************************************************************

p(500) = 8.7(500) - 1940

           = 4350 - 1940

           = 2410

p(1000) = 8.7(1000) - 1940

             = 8700 - 1940

             = 6760

p(5000) = 8.7(5000) - 1940

              = 43,500 - 1940

              = 41,560

***************************************************************************

p(500) =    r(500)    -    c(500)

           = 9.5(500)  -  [0.8(500) + 1940]

           =    4750     - (400 + 1940)

           =     4750    -      2340

           =              2410

p(1000) =   r(1000)    -    c(1000)

            = 9.5(1000)  -  [0.8(1000) + 1940]

            =     9500     - (800 + 1940)

            =     9500     -      2740

            =              6760

p(5000) =    r(5000)    -    c(5000)

           = 9.5(5000)  -  [0.8(5000) + 1940]

           =    47500     - (4000 + 1940)

           =    47500     -      5940

           =              41,560

The standard form:

[tex]Ax+By=C[/tex]

[tex]4x-y-7=0\qquad\text{add 7 to both sides}\\\\\boxed{4x-y=7}[/tex]

[tex]3x+9=\dfrac{7}{2}y\qquad\text{multiply both sides by 2}\\\\6x+18=7y\qquad\text{subtract 18 and 7y from both sides}\\\\\boxed{6x-7y=-18}[/tex]

[tex]y=-4x+12\qquad\text{add 4x to both sides}\\\\\boxed{4x+y=12}[/tex]

[tex]y=-\dfrac{3}{4}x+\dfrac{5}{4}\qquad\text{multiply both sides by 4}\\\\4y=-3x+5\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=5}[/tex]

Step-by-step explanation:

This ≤ inequality sign means:

-5 ≤ 4

And then:

-3x ≤ 2

OR:

-5 ≤ 4 -3x ≤ 2

Hi!!! Sorry, I didn't know if they were suppose to be together or separate, so I just did it both ways!!! :) Really sorry if I am wrong...

Answer:

A.  (3,0)

Step-by-step explanation:

When the equations are graphed, the solution is where the two graphs cross.  For the red line and the blue line, the cross at (3,0)

We can check this by substituting x=3 into both equations and seeing if we get y=0

y = -x+3

y = -3+3

y =0

y = x-3

y = 3-3

y=0

In both cases, we got y=0.  

Therefore (3,0) is a solution to both equations and since it solves both equations, it solves the system.

Answer:

its 4 2/25 :P

Step-by-step explanation:

hi!!!

Answer:

$51.20

Step-by-step explanation:

A 20% discount makes it 80% of the original price.

80% is 0.8 of something so multiply $64 by 0.8 to get your answer of $51.20

Answer:

Step-by-step explanation:

I hope it will help you

Attachment

Answer:

A is the correct equation

Step-by-step explanation:

Hi there! :)

Answer:

The answer is D. 83°

Step-by-step explanation:

You should know that the interior angles of a triangle always add up to 180°.

So, what you will need to do, is add all 3 angles together and create an equation (equal to 180). Then you need to solve this equation by isolating "x":

(8x + 12) + (55 - 3x) + (10x + 23) = 180

Get rid of all the parentheses

8x + 12 + 55 - 3x + 10x + 23 = 180

Add all similar terms together

8x - 3x + 10x = 15x

12 + 55 + 23 = 90

15x + 90 = 180

Subtract "90" from each side of the equation → 180 - 90 = 90

15x = 90

Divide each side of the equation by "15" → 90 ÷ 15 = 6

x = 6

Since you now know that the value of "x" is 6, you can now find the measure of the angle at George's position by replacing the "x" by 6:

10x + 23 = Measure of the angle at George's position

10(6) + 23

Multiply 10 by 6 → 10 × 6 = 60

60 + 23

Add 60 and 23 together → 60 + 23 = 83

83 = Measure of the angle at George's position

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:

I believe the answer is 20.

Step-by-step explanation:

A secant is a line that intersects a circle at two points.

Therefore your answer is

[tex]\boxed{D.\ \overline{AD}}[/tex]

OB - radius

DE - tangent

FC - chord

AB - some segment

Answer: The right answer is this:

Katelyn did make an error. She also needs to multiply 4 by −2.

4−8−3=7

Step-by-step explanation:

Answer:

Katelyn did make an error. She also needs to multiply 4 by −2.

4x−8−3=7x

Step-by-step explanation:

Answer:

{0, -1, 11, 13 }

Step-by-step explanation:

the range of the function are the corresponding values of y from the set of points, in ascending order, that is

{0, -1, 11, 13 }

Answer:

Step-by-step explanation:

The range is the set of y values of the function.

{0, -1, 11, 13]

Answer:

GRAPH D

Step-by-step explanation:

BECASUE IT IS THE WRIGHT ANSWER

Answer:

1.524

Step-by-step explanation:

Answer:

1.52 meters

Step-by-step explanation:

Answer:

The inverse is sqrt(x+9)

Step-by-step explanation:

f(x)=x^2-9

To find the inverse of the function, we interchange x and y and solve for y

y = x^2 -9

x = y^2 -9

Add 9 to each side

x+9 = y^2 -9+9

x+9 = y^2

Take the square root of each side

sqrt(x+9) = sqrt(y^2)

sqrt(x+9) = y

f^-1 (x) = sqrt(x+9)

Answer: 137 + 4(n-1)

Step-by-step explanation:

137 + 4(n-1)

Okay, let's test this starting with week 1:

137 + 4(1-1)

137 + 4*0

137, which is correct because she starts with 137.

Week 2:

137 + 4 (2-1)

137 + 4 * 1

137 + 4

141

Alright, let's see if it is correct if we do week 5:

137 + 4 (5-1)

137 + 4(4)

137 + 16

153

To know that 153 is right we could do 137 + 4 + 4 + 4 + 4, which equals 153.

Answer:

18 number of glasses of lemonade can she pour

Step-by-step explanation:

Unit rate defined as rates are expressed as a quantity of 1, such as 3 feet per second or 8 miles per hour, they are called unit rates.

As per the statement: Rita has 3/4 gallon of lemonade she pours 1/24 gallon of lemonade into each glass.

Number of lemonade Rita has  = 3/4 gallon

[tex]\text{Unit rate per glass} = \frac{1}{24} \text{gallons}[/tex]

By definition of unit rate;

[tex]\text{Number of glasses} = \frac{\text{Number of lemonade}}{\text{Unit rate per glass}}[/tex]

Substitute the given values we get;

[tex]\text{Number of glasses} = \frac{\frac{3}{4}}{\frac{1}{24}}[/tex]

[tex]\text{Number of glasses} = \frac{3}{4} \times 24 = 3 \times 6 = 18[/tex]

Therefore, number of glasses of lemonade can she pour is, 18

Answer:

The standard deviation of the numbers is 16.154.

Step-by-step explanation:

The given observations are

77,45,72,56,98,60,70,89,50,80,95,70,34,77,65,70,70,82,86,86

Average or mean of the data is

[tex]\bar{X}=\frac{\text{Sum of observations}}{\text{Total number of observations}}[/tex]

[tex]\bar{X}=\frac{1432}{20}=71.6[/tex]

The Standard deviation of the data is

[tex]\sigma=\sqrt{\frac{\sum (X-\bar{X})^2}{n}}[/tex]

[tex]\sigma=\sqrt{\frac{5218.8}{20}}[/tex]

[tex]\sigma=\sqrt{260.94}[/tex]

[tex]\sigma=\sqrt{16.154}[/tex]

Therefore standard deviation of the numbers is 16.154.

Answer: 32 Rose Arrangements & 8 Tulip Arrangements

Step-by-step explanation: The number of arrangements for each flower is unknown (n) but the total is known, 40 arrangements. There are 4 times as many rose arrangements than tulip meaning 4n rose + n tulip = 40, 4n + n = 40, 5n = 40, 40 ÷ 5 = n, n = 8. Roses = 4n = 4x8= 32. Tulips = n = 8.

Answer:

a = (-7)/32  or a= 0.21875

Step-by-step explanation:

Solve for a:

-4 a - 4 = (4 a)/7 - 3

Put each term in (4 a)/7 - 3 over the common denominator 7: (4 a)/7 - 3 = (4 a)/7 - 21/7:

-4 a - 4 = (4 a)/7 - 21/7

(4 a)/7 - 21/7 = (4 a - 21)/7:

-4 a - 4 = (4 a - 21)/7

Multiply both sides by 7:

7 (-4 a - 4) = (7 (4 a - 21))/7

(7 (4 a - 21))/7 = 7/7×(4 a - 21) = 4 a - 21:

7 (-4 a - 4) = 4 a - 21

Expand out terms of the left hand side:

-28 a - 28 = 4 a - 21

Subtract 4 a from both sides:

(-28 a - 4 a) - 28 = (4 a - 4 a) - 21

-28 a - 4 a = -32 a:

-32 a - 28 = (4 a - 4 a) - 21

4 a - 4 a = 0:

-32 a - 28 = -21

Add 28 to both sides:

(28 - 28) - 32 a = 28 - 21

28 - 28 = 0:

-32 a = 28 - 21

28 - 21 = 7:

-32 a = 7

Divide both sides of -32 a = 7 by -32:

(-32 a)/(-32) = 7/(-32)

(-32)/(-32) = 1:

a = 7/(-32)

Multiply numerator and denominator of 7/(-32) by -1:

Answer:  a = (-7)/32

The solution to the equation is [tex]\(a = -\frac{25}{32}\)[/tex].

To solve the equation [tex]\(\frac{-4}{1}a - 4 = \frac{4}{7}a - 3\) for \(a\)[/tex], follow these steps:

1. Simplify the equation by multiplying both sides by their respective denominators to eliminate the fractions:

[tex]\[ 7(-4a - 4) = 1(4a - 3) \][/tex]

2. Distribute the numbers outside the parentheses:

[tex]\[ -28a - 28 = 4a - 3 \][/tex]

3. Move all terms containing a to one side of the equation and constants to the other side:

[tex]\[ -28a - 4a = -3 + 28 \][/tex]

4. Combine like terms:

[tex]\[ -32a = 25 \][/tex]

5. Solve for a by dividing both sides by -32:

[tex]\[ a = \frac{25}{-32} \][/tex]

Therefore, the solution to the equation is [tex]\(a = -\frac{25}{32}\)[/tex].

Answer:

Alright well solve for d by cross multiplying

Exact form: d = 115/8

Decimal form: d = 14.375 Hope this helps have a nice day : )

Step-by-step explanation:

Answer:

x = ± [tex]\sqrt{2}[/tex]

Step-by-step explanation:

given the 3 terms of a geometric sequence

[tex]\sqrt{x-1}[/tex], 1, [tex]\sqrt{x+1}[/tex], then the common ratio r

r = [tex]\frac{\sqrt{(x+1)} }{1}[/tex] = [tex]\frac{1}{\sqrt{(x-1)} }[/tex] ( cross- multiply )

[tex]\sqrt{(x+1)(x-1)}[/tex] = 1 ( square both sides )

(x + 1 )(x - 1 ) = 1 ← expand factors on left side )

x² - 1 = 1 ( add 1 to both sides )

x² = 2 ( take the square root of both sides )

x = ± [tex]\sqrt{2}[/tex]

The value of x is ±[tex]\sqrt{2}[/tex].

Given:

Geometric Sequence with first three terms.

[tex]\sqrt{x-1},1, \sqrt{x+1[/tex]

We have to find the value of x.

Now, if the given sequence is geometric then we can find the common ratio of the sequence.

The common ratio is given by:

r = [tex]\frac{1}{\sqrt{x-1} }[/tex] and r = [tex]\frac{\sqrt{x+1} }{1}[/tex]

Now, we can equate the both the values of r to solve for the value of x.

[tex]\frac{\sqrt{x+1} }{1} = \frac{1}{\sqrt{x-1} }[/tex]

Now, multiplying the numerator on both sides by [tex]\sqrt{x-1}[/tex], we get:

[tex]\sqrt{x+1} \sqrt{x-1} =1[/tex]

[tex]\sqrt{(x-1)(x+1)}=1[/tex]

[tex]\sqrt{x^2-1} =1[/tex]

Now, squaring on both sides of the equation, we get:

⇒ x² - 1 = 1

⇒ x² = 2

Now, taking square root on both the sides, we get:

⇒ x = ±[tex]\sqrt{2}[/tex]

Therefore, for a given geometric sequence the value of x will be ±[tex]\sqrt{2}[/tex].

Learn more about the Geometric Sequence here: https://brainly.com/question/14565307

#SPJ2

[tex]\dfrac{3\ boys}{5\ girls}\to\dfrac{3}{5}\\\\\dfrac{8}{10}=\dfrac{8:2}{10:2}=\dfrac{4}{5}\\\\\dfrac{15}{25}=\dfrac{15:5}{20:5}=\dfrac{3}{5}\\\\\dfrac{9}{15}=\dfrac{9:3}{15:3}=\dfrac{3}{5}\\\\\dfrac{30}{50}=\dfrac{30:10}{50:10}=\dfrac{3}{5}\\\\Answer:\\\\\boxed{\dfrac{3\ boys}{5\ girls}=\dfrac{15\ boys}{25\ girls}=\dfrac{9\ boys}{15\ girls}=\dfrac{30\ boys}{50\ girls}}[/tex]

Answer:

Answer is to increase trials

Step-by-step explanation:

Theoretical Probability is what it is expected to happen whereas Experimental Probability is what actually happens.

What Jamie should take into serious consideration is that Experimental probability gets gradually closer to theoretical probability as the number of trials increases.

In other words, Jamie needs to increase the number of trials in order to match experimental and theoretical probabilities every time more and more.

Answer: letter A

to increase the number of trials

Step-by-step explanation:

Equation for a

a= b/c - 1

Equation for b

b= ca - a

Equation for c

c=  b/a + 1