Which table represents a linear function?

Answer:

1.2Litres

Question:

Wes mixed different juices to make fruit punch. He filled one-half of the punch bowl with orange juice. Then he filled half of the remaining space with grape juice. Finally, he filled the rest of the punch bowl with 300 mL300\text{ mL}300 mL300, space, m, L of cherry juice. How many liters of fruit punch did Wes make?

Step-by-step explanation:

Let the total punch bowl be = P

Portion of Orange juice = ½ of total punch bowl

= ½ × P = P/2

Portion of grape = ½ of the remaining space

Remaining space = P - P/2 = P/2

Portion of grape = ½ × P/2 = P/4

The rest of the punch bowl is for cherry = 300mL

P/2 - P/4 = 300

(2P - P)/4 = 300

P/4 = 300

P = 300×4

P = 1200mL

1mL = 10^(-3)L

P = 1.2 ×10³ × 10^(-3)L

P = 1.2L

Wes made 1.2liters of fruit punch.

Answer:

4031.5

Step-by-step explanation:

Answer:

w=-16

Step-by-step explanation:

divide -192 by 12 to isolate w

Answer:

w=-16

Step-by-step explanation:

Answer:

(1, 10) and (40, 0)

Step-by-step explanation:

Given expression 50x+150

inequality is

50x + 150y > 1500

it means that if we plug value of x and y from given option in  50x+150 then it should be greater than 1500.

lets check for all the option

(1,10)

50*1 + 150*10 = 50+1500 = 1550

Since , 1550 is greater than 1500, (1,10) is the solution for the inequality given

(10, 1)

50*10 + 150*1 = 500+ 150 = 650

Since , 650 is less than 1500, (10,1) is not the solution for the inequality given

(0, 10)

50*0 + 150*10 = 0 + 1500 = 1500

Since , 1500 is equal to 1500 but not greater than 1500, (0,10) is not the solution for the inequality given

(40, 0)

50*40 + 150*0 = 2000 + 0 = 2000

Since , 200 is greater than 1500, (40,0) is the solution for the inequality given above.

Thus, from the given option there are two solution for 50x + 150y > 1500

(1, 10) and (40, 0)

(1, 10) (40, 0) as the person above/below stated.

Answer: x= -3 + 2[tex]\sqrt{2\\}[/tex] or -3 -2 [tex]\sqrt{2}[/tex]

Step-by-step explanation:

First you want to get the quadratic formula

in this case a=1 b=6 and c=1

plug it in and solve the equations

(sorry don't know how to put in equations here)

Answer:

Answer: x= -3 + 2\sqrt{2\\} or -3 -2 \sqrt{2}

Step-by-step explanation:

First you want to get the quadratic formula

in this case a=1 b=6 and c=1

plug it in and solve the equations

Answer:

256

Step-by-step explanation:

To calculate the mean, we simply divide the sum of the values by the count.

For the first set, the mean is as follows;

(9 + 5 + 2 + y + x)/5 = (x + y + 16)/5

For the second set;

(8 + x + 4 + 1 + 3)/5 = (16 + x)/5

Since both are divided by 5, we can eliminate it

Mean of first set is twice the second

This means that;

x + y + 16 = 2(16 + x)

x + y + 16 = 32 + 2x

y = 32-16+2x-x

y = 16 + x

Now we want to calculate

(y-x)^2

substitute the value of y here

(16+x-x)^2

= 16^2 = 256

Answer:

-9 ≤n ≤1

Step-by-step explanation:

-3 ≤ n+6 ≤ 7

Subtract 6 from all sides

-3  -6≤ n+6-6 ≤ 7-6

-9 ≤n ≤1

Answer:

QST = 2x= 2*20 = 40°

Step-by-step explanation:

RSQ+QST= RST

we know that RST is 124

So,

84+2x= 124

Bringing 84 to the other side it becomes negative

2x= 124-84

= 40

Therefore,

x= 40/2

= 20 °

Here's your answer :)

Answer:

a

Step-by-step explanation:

r = 2.5 cm

V=  3.14[tex](2.5 cm)^{2}[/tex](9 cm)/3 = [tex]59 cm^{3}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

D. Yes, because the amount of money on her gift card should decrease each week.

Step-by-step explanation:

The amount of money on the gift card decreases every Friday as it states in the problem.

Yes Kate's graph represent the situation, because the amount of money on her gift card should decrease each week. so option D is correct.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

We can see that the graph shows that the slope is decreasing, if you got $75 and spend $5.00 each Friday, wouldn't that be  decrease and Lastly, of course, they should not start at the origin as they started at $75.00.

The amount of money on the gift card decreases every Friday as it states in the given situation.

Learn more about finding the graphed function here:

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Hi! I'm here to help. So what you're gonna wanna do is do 6 divided by 2.

6 / 2 = 3

Have a good day/night!

Answer:

[tex]2/6=1/3[/tex]

Answer:

20%

Step-by-step explanation:

6/30 = blank/100

cross multiply

6 x 100

600/30 =20

Answer:

18.2%

Step-by-step explanation:

The total number of trees in the wood = 420 + 160 + 300

                                                                = 880 trees

∴ The percentage of the oak trees = [tex]\frac{160}{880} * \frac{100}{1}[/tex]

                                                            = [tex]\frac{2 * 100}{11}[/tex]%

                                                            = [tex]\frac{200}{11}[/tex]%

                                                            = 18.181818...%

In 1 decimal place = 18.2%

Hope this helps!!

( x - 12 ) ( x + 6 ) = 0

x - 12 = 0 and x + 6 = 0

x = 12 and x = -6

Answer:

[tex]x=12,\:x=-6[/tex] are your x intercepts

Step-by-step explanation:

[tex]\left(x-12\right)\left(x+6\right)=0\\\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\mathrm{Solve\:}\:x-12=0:\quad x=12\\x-12=0\\\mathrm{Add\:}12\mathrm{\:to\:both\:sides}\\x-12+12=0+12\\Simplify\\x=12\\\mathrm{Solve\:}\:x+6=0:\quad x=-6\\x+6=0\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\x+6-6=0-6\\Simplify\\x=-6\\The\:solutions\:to\:the\:quadratic\:equation\:are:\\x=12,\:x=-6[/tex]

Answer:

C. 68

Step-by-step explanation:

Explained in image attached

Answer:

Probability ≈ 0.0714

Step-by-step explanation:

Consider permutation and combination;

[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]

Answer:

1.17B

Step-by-step explanation:

Katie and her friends will pay 17% of the bill, B.

Therefore, we have to add 17% of B to B to find how much they will pay:

17/100 * B = 0.17B

Therefore, the total bill will be:

Bill + tip

= B + 0.17B = 1.17B

The expression that represents the total bill they will pay is 1.17B

Answer:

43.6%

Step-by-step explanation:

curved surface area (green) is found by circumference multiply by height

[tex]\pi[/tex] x d x h = [tex]\pi[/tex] x (15 x 2) x 12 = 360[tex]\pi[/tex]

total surface area is

blue circle + total curved surface area (blue + green)

= [tex]\pi[/tex][tex]r^{2}[/tex] + 15(2)(8)[tex]\pi[/tex] + 360[tex]\pi[/tex]

= [tex]15^{2}[/tex][tex]\pi[/tex] + 240[tex]\pi[/tex] + 360[tex]\pi[/tex]

= 825[tex]\pi[/tex]

percentage = 360[tex]\pi[/tex]/825[tex]\pi[/tex] x 100%= 22/55 x 100% = 43.63

Answer:the value is 20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Notice that the pair of angles are inside parallels, and at different sides of the transversal. So, those angles are alternate interior angles by definition, which means they are congruent.

Therefore, the right answer is B.

Answer: The answers are in the steps hope it helps.

Step-by-step explanation:

First solve or the equation and let it be in slope intercept form

y + 2 = 1/2( x + 2)   apply the distributive property first

y + 2= 1/2x + 1

    -2               -2

y= 1/2x -1      is not in slope intercept form so you could put  in any number for x and five y.

This are the points you could plot then draw a straight line between them.

x        y

0        -1

2         0

4          1

6          2

8           3

10          4

-2          -2

-4            -3

-6            -4

-8             -5

-10             -6

Answer:

The value of 9f(3) is 1683.

Step-by-step explanation:

This is a compound function, so let's call it [tex]g[/tex], where it is equal to:

[tex]g = 9*f(3)[/tex]

To solve it, we need to find [tex]f(3)[/tex] and apply it on the expression above, this is done below:

[tex]f(3) = 4*(3)^3 + 8*(3)^2 - 2*3 + 13\\f(3) = 4*27 + 8*9 - 6 + 13\\f(3) = 108 + 72 + 7\\f(3) = 187\\[/tex]

Applying it on [tex]g[/tex] we have:

[tex]g = 9*187 =1683[/tex]

Answer:

1,863

Step-by-step explanation:

First thing to do here is to substitute 3 for the value of x

f(3) =4)3)^3 + 8(3)^2 -2(3) + 13

= 4(27) + 8(9) -6 + 13

= 108 + 72 + 7 = 207

we now multiply this result by 9

= 9 * 207 = 1,863

Answer:

Since [tex]|Z| = 2.52 > 2[/tex], the difference is significant.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If |Z| > 2, the measure X is significent.

In this question:

[tex]|X - \mu = 1.74|, \sigma = 0.69[/tex]

So

[tex]Z = \frac{1.74}{0.69} = 2.52[/tex]

Since [tex]|Z| = 2.52 > 2[/tex], the difference is significant.

Answer:

-288

Step-by-step explanation:

math

Answer:

x ≈ 17.67 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 16² + 7.5² = 256 + 56.25 = 312.25 ( take the square root of both sides )

x = [tex]\sqrt{312.25}[/tex] ≈ 17.67 ( to 2 dec. places )

The measure of hypotenuse length x would be 17.67 cm

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|² = |AB|² + |BC|²  

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Using the Pythagoras' identity in the right angled triangle.

hypotenuse²  = perpendicular²  + base²

x² = 16² + 7.5²

x²= 256 + 56.25

x²= 312.25

Now take the square root of both sides

x = √312.25

x =  ≈ 17.67 ( to 2 dec. places )

Therefore, the measure of hypotenuse length x would be 17.67 cm

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Answer:

85 square units

Step-by-step explanation:

The area of a kite is half of the product of the diagonals.

The left half of the horizontal diagonal is labeled 5, so the entire horizontal diagonal measures 10.

Now we need to find the length of the vertical diagonal.

The vertical diagonal is made up of two segments. Each segment is a leg in a right triangle. We can use the Pythagorean theorem twice to find the lengths of the two segments of the vertical diagonal.

Upper vertical segment:

a^2 + b^2 = c^2

5^2 + x^2 = [5sqrt(2)]^2

25 + x^2 = 50

x^2 = 25

x = 5

The upper segment of the vertical diagonal has length 5.

Lower vertical segment:

a^2 + b^2 = c^2

5^2 + x^2 = 13^2

25 + x^2 = 169

x^2 = 144

x = 12

The lower segment of the vertical diagonal has length 12.

The length of the vertical diagonal is the sum of the lengths of the two vertical segments:

5 + 12 = 17

The diagonals of the kite measure 1`0 and 17.

area = d1 * d2/2

area = 10 * 17/2 = 170/2 = 85

Answer:

Step-by-step explanation:

[tex]\sqrt{x} Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\\sqrt{(5-3)^{2}+(6-k)^{2}}=2\sqrt{2}\\\\\sqrt{(2)^{2}+[(6)^{2}-(2*6*k)+(k)^{2}]}=2\sqrt{2}\\\\\sqrt{4+[36-12k+k^{2}]}=2\sqrt{2}\\\\\sqrt{40-12k+k^{2}}=2\sqrt{2}\\[/tex]

Take square both side

[tex]40-12k+k^{2}=(2\sqrt{2})^{2}\\\\40-12k+k^{2}=4*2\\\\40-12k+k^{2}=8\\\\k^{2}-12k+40-8=0\\\\k^{2}-12k+32=0\\[/tex]

Factorize,

Sum = -12

Product = 32

Factors = -8 , -4

k² - 8k - 4k + (-8)*(-4) = 0

k(k - 8) - 4(k - 8) = 0

(k - 8)(k - 4) = 0

k = 8 or 4

The points are (3,k) and (5,6).

Given, distance = 2√2 units

Applying distance formula,

Distance = √(x2-x1)^2 + (y2-y1)^2

2√2 = √(x2-x1)^2 + (y2-y1)^2

Squaring both sides,

(2√2)^2 = [√(x2-x1)^2 + (y2-y1)^2]^2

8 = (x2-x1)^2 + (y2-y1)^2

8 = (5-3)^2 + (6-k)^2

8 = 2^2 + (6^2 - 2x6xk + k^2)

8 = 4 + 36 - 12k + k^2

8 = 40 - 12k + k^2

= k^2 - 12k + 32 = 0

On factorising,

=> k^2 - 4k - 8k + 32 = 0

=> k(k-4) -8(k-4) = 0

=> (k-4)(k-8) = 0

=> k-4 = 0 , k-8 = 0

=> k = 4 , k = 8

Answer:

[tex]=24a^2[/tex]

Step-by-step explanation:

[tex]4a\cdot \:6a=24a^2\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:6=24\\=24aa\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\aa=\:a^{1+1}\\=24a^{1+1}\\=24a^2[/tex]

Answer:

Simply multiply across.

since they both have the same base(a),add the powers ie.(1+1)=2.

Hence 4a×6a=24a²