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Divide bags of sand by gallons of water:

14 /6 = 2.33

21/9 = 2.33

The ratio is the same, so this means for every gallon of water you need 2.33 bags of sand.

Convert the fractions into decimals and you will get 7/3 = 2.33

The answer for Part 1 is D) 7/3

For part 2, multiply the gallons of water by 2.33 to get the number of sand bags needed:

12 x 2.33 = 27.99, which rounds to 28.

The answer is C) 28 bags.

Answer:

A) [tex]\frac{3}{7}[/tex]

C) 28 bags

Step-by-step explanation:

Part 1 :

By the given table,

[tex]\frac{\text{Gallon of water}}{\text{bags of sand}}=\frac{6}{14}=\frac{9}{21}=\frac{15}{35}=\frac{3}{7}[/tex]

Hence, the proportion of gallons of water to bags of sand is same,

Which is [tex]\frac{3}{7}[/tex]

OPTION A) is correct.

Part 2 : Let x bags of sand should be mixed with 12 gallon of water,

Then the ratio of gallon of water and number of bags of sand = [tex]\frac{12}{x}[/tex]

By part 1,

[tex]\frac{12}{x}=\frac{3}{7}[/tex]

[tex]84 = 3x[/tex] ( by cross multiplication )

[tex]\implies x = \frac{84}{3}=28[/tex]

Hence, 28 bags of sand should be mixed.

OPTION C) is correct.

Answer:

D, (-6,-2)

Step-by-step explanation:

the first quadrant of a coordinate plane has the x coordinate being a negative number, and the y coordinate being a positive number

the second quadrant of a coordinate plane has the x and y coordinates being a positive number

the third quadrant of a coordinate plane has the x and y coordinates being a negative number

the fourth quadrant of a coordinate plane has the x coordinate being a positive number, and the y coordinate being a negative number

i have attached a graph showing the quadrants for a visual point of view

The coordinate pair that identifies a point in the third quadrant of the coordinate plane, where both x and y coordinates are negative, is (-6,-2)

The question is asking about identifying which pair of coordinates falls into the third quadrant of the coordinate plane in mathematics. The third quadrant in a coordinate plane is the bottom-left quadrant, where both the x and y coordinates are negative.

Looking at the options: A) (0,6), B) (-6,2), C) (2,-6), and D) (-6,-2); we can clearly see that option D) (-6,-2) is the point in the third quadrant, as both coordinates are negative. The pair (-6,-2) meets this description, with -6 on the x-axis and -2 on the y-axis. So, the correct answer is option D).

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8 times 2/3 is 16/3, which when simplified is 5 1/3

To evaluate 8(2/3), you need to multiply 8 by 2/3. The value of 8(2/3) is 16/3.

To evaluate 8(2/3), you need to multiply 8 by 2/3. To do this, you can simplify 2/3 by dividing both the numerator and denominator by their greatest common factor, which is 1.

This simplifies 2/3 to 2/3. Then, multiply 8 by 2/3 to get the final answer.

Therefore, the value of 8(2/3) is 16/3.

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Answer:

2541 peanut cookies were sold

Step-by-step explanation:

A system of equations can be written to match the problem description. Let p and c represent the initial numbers of peanut and chocolate cookies, respectively. Then we have ...

p - c = 1820 . . . . Lyn had 1820 more peanut cookies

After selling 35% of her peanut cookies, Lyn had 1-0.35 = 0.65 of the original number left. Likewise, after selling 15% of her chocolate cookies, she had 1-0.15 = 0.85 of the original number left. Then after the sales, the difference in cookie count was 95:

0.65p -0.85c = 95

We only need to know the original number of peanut cookies (p), so we can use Cramer's rule to find the solution for p.

p = (-95 +0.85·1820)/(-0.65+0.85) = 1452/0.20 = 7260

The original number of peanut cookies Lyn had was 7260, so the number she sold is ...

0.35 · 7260 = 2541

_____

Cramer's rule says the solution to ...

ax +by =c

dx +ey =f

is given by ...

x = (ec-bf)/(ea-bd)

y = (fa-cd)/(ea-bd)

Answer:

2541 cookie were sold

Step-by-step explanation:

Answer:

slope = 5

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 - 3 = 5(x - 4) ← is in point- slope form

with slope m = 5

Answer:

B.. skewed left

Step-by-step explanation:

Answer:

Option B. skewed left.

Step-by-step explanation:

In the figure attached maximum frequency of the data is at the 45. Distribution on the right side of the maximum frequency is upto 48 and in the left it is upto 36.

As we can see point 36 is more distant from peak point 45 as compared to point 48.

Therefore, distribution of the data is more in the left than in the right.

Therefore, the shape of this distribution is skewed left.

Option B. skewed left is the correct answer.

The answer for this question is 3

Answer:

B. 3

Step-by-step explanation:

x=1 ; y = 2

x=3; y =8

the average rate of change = (8-2)/(3-1) =  6/2 = 3

Answer

B. 3

Answer:

The answer is 7/8 chance.

Step-by-step explanation:

To find this answer, you have to divide the blue marbles by red marbles. Then, you will get 28/32.

You can simplify it, so simplify it to the smallest possible number, therefore getting 7/8.

Answer:

12.5, not 100% sure though.

Answer:

Step-by-step explanation:

12.5 is right.  Because it say similar to triangle XYZ

Answer:

12

Step-by-step explanation:

We know that 15/20 students voted in the StuCo election on the first go around.

Using this ratio for 16 student is as simple as multiplying 15/20 by 16

(15/20)*16=12

Based on the voting ratio of 3:4 from Monday's election, we predict that 12 out of the 16 students present on Tuesday voted.

The question asks to predict the number of students who voted in Tuesday's election based on the ratio of students who voted on Monday. On Monday, 15 out of 20 students voted, which establishes a voting ratio of 15:20, or 3:4 when simplified. To predict Tuesday's voter turnout, we apply this ratio to the 16 students present on Tuesday.

Using the simplified ratio of 3:4, for every 4 students, 3 vote. Since 16 students were in class on Tuesday:

Therefore, we predict that 12 students voted in Tuesday's election.

Answer:

The perimeter is equal to [tex]16\ units[/tex]

Step-by-step explanation:

we have that

[tex]A(-1,1),B(2,5),C(5,1)[/tex]

The perimeter of triangle ABC is equal to

[tex]P=AB+BC+AC[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance AB

[tex]A(-1,1),B(2,5)[/tex]

[tex]AB=\sqrt{(5-1)^{2}+(2+1)^{2}}[/tex]

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

[tex]AB=\sqrt{25}[/tex]

[tex]AB=5\ units[/tex]

step 2

Find the distance BC

[tex]B(2,5),C(5,1)[/tex]

[tex]BC=\sqrt{(1-5)^{2}+(5-2)^{2}}[/tex]

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

[tex]BC=\sqrt{25}[/tex]

[tex]BC=5\ units[/tex]

step 3

Find the distance AC

[tex]A(-1,1),C(5,1)[/tex]

[tex]AC=\sqrt{(1-1)^{2}+(5+1)^{2}}[/tex]

[tex]AC=\sqrt{(0)^{2}+(6)^{2}}[/tex]

[tex]AC=\sqrt{36}[/tex]

[tex]AC=6\ units[/tex]

step 4

Find the perimeter

[tex]P=5+5+6=16\ units[/tex]

Answer:

The answer is 16 untis

Step-by-step explanation:

Answer:

[tex]b=40.01\ units[/tex]

Step-by-step explanation:

we know that

Applying the law of sines

[tex]\frac{b}{sin(B)}=\frac{a}{sin(A)}[/tex]

[tex]b=\frac{a}{sin(A)}(sin(B))[/tex]

we have

[tex]a=25\ units[/tex]

[tex]A=32.5\°[/tex]

Find the measure of angle B

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so

[tex]A+B+C=180\°[/tex]

substitute the given values

[tex]32.5\°+B+26.8\°=180\°[/tex]

[tex]B=180\°-59.3\°=120.7\°[/tex]

Find the length side b

[tex]b=\frac{a}{sin(A)}(sin(B))[/tex]

substitute the values

[tex]b=\frac{25}{sin(32.5\°)}(sin(120.7\°))[/tex]

[tex]b=40.01\ units[/tex]

Answer:

The probability that there were 3 males is 1/4.

Step-by-step explanation:

Total Number of kitten = 4

Probability of a kitten to be male = 1/2

Probability of a kitten to be female = 1/2

Probability that out of 3 were male = 4 × 1/2 × 1/2 × 1/2 × 1/2

                                                          = 1/4

Therefore, The probability that there were 3 males is 1/4.

Answer:

[tex]\large\boxed{z=\dfrac{15\sqrt3}{2}[/tex]

Step-by-step explanation:

Lookat the picture.

We have

[tex]2a=15\to a=\dfrac{15}{2}\to a\sqrt3=\dfrac{15\sqrt3}{2}[/tex]

small triangle:

[tex]x=2a=\dfrac{15}{2}\to a=\dfrac{15}{4}\to y=\dfrac{15\sqrt3}{4}[/tex]

[tex]a+b=15\to b=15-\dfrac{15}{4}=\dfrac{60}{4}-\dfrac{15}{4}=\dfrac{45}{4}[/tex]

[tex]a=\dfrac{15}{4}\\\\b=\dfrac{45}{4}\\\\x=\dfrac{15}{2}\\\\y=\dfrac{15\sqrt3}{4}\\\\z=\dfrac{15\sqrt3}{2}[/tex]

Answer:

[tex]\frac{901}{999}[/tex]

Step-by-step explanation:

we know that

A Recurring Decimal, is a decimal number with a digit (or group of digits) that repeats forever.

In this problem we have

0.901 recurring

that means

0.901901901..

Let

[tex]x=0.901901901..[/tex]

Multiply x by a power of  [tex]10[/tex], one that keeps the decimal part of the number the same:  

[tex]1,000x=901.901901..[/tex]

Subtract [tex]x[/tex] from [tex]\\1000x[/tex]

[tex]1,000x-x=901.901901..-0.901901..=901[/tex]

The repeating decimals should cancel out

[tex]\\999x=901[/tex]

solve for x

Divide by [tex]999[/tex] both sides

[tex]990x/990=135/990[/tex]

[tex]x=\frac{901}{999}[/tex]

Answer:  D. 2x4+x3–x+2 is prime

Step-by-step explanation:

Answer:

Option D)

Step-by-step explanation:

Given:

x= {2,3,4}

y={49,343,2401}

Points with coordinates (x,log(y)) are required to be plotted

Finding (x,log(y)):

log(y)= {log(49),log(343),log(2401)}

Log(49)=1.69020

log(343)=2.53529

log(2401)=3.38039

Now the transformed data set will be written in coordinates form:

(2,1.690),(3,2.535),(4,3.380)

Which is option D !

Answer:

x=61

Step-by-step explanation:

X=61

Because (52+67)-180=61

when the two books were published

Answer: It would be (B) because you don't actually have to know the date unless it is a part of the equation which you dont have to know in this question :)

Hope this will help you out :)

Answer:

a.0

Step-by-step explanation:

The exponential function levels at 0

Please give brainliest

The answer to your question is this:

[tex]y + 5\leq 28\\y\leq 23[/tex]

D

the answer is D. dilation cannot be used to prove this

The answer is D since dialation only beating to increase in size

Answer:

81% of 403 is.....326.43! (Rounding it to the nearest hundred gives '326')

Step-by-step explanation:

(P= Percentage / X= The number your finding the percentage of...)

Formula : X = P% * X

X = 81% * 403

Converting percent to decimal:

Converting percent to decimal:p = 81% ÷ 100 = 0.81

X = 0.81 x 403

X = 326.43

Answer:

The length of the formed by these vertices is 11 units.

Step-by-step explanation:

We are given the following coordinates of two vertices of a right angled triangle and we are to find the length of the side formed by these vertices:

[tex](-2, 5)[/tex] and [tex](9,5)[/tex]

Using the distance formula to find the side length:

Side length = [tex] \sqrt { ( 9 - ( - 2 ) ) ^ 2 + ( 5 - 5 ) ^ 2 } [/tex] = [tex]\sqrt{121}[/tex] = 11 units

Answer:

11

Step-by-step explanation:

Note that the horizontal line y = 5 goes through both vertices, and that the length of the side formed by those vertices is the distance between the vertices in this case.  That distance would be 9 - (-2), or 11.

Answer:

8x² + 4x - 5

Step-by-step explanation:

M - N

= 5x² - (- 3x² - 4x + 5) ← distribute parenthesis by - 1

= 5x² + 3x² + 4x - 5 ← collect like terms

= 8x² + 4x - 5

Answer:

Step-by-step explanation:

When x<-2, f(x)=5

When -2<x<3, f(x)=2x+2

When x>3, f(x)=-3

Answer:

Step-by-step explanation:

Given is a graph of piecewise function.

We are given a horizontal line for

[tex]x<-2[/tex]

Hence [tex]f(x) = 5, x<-2[/tex]  ... I

Whenever

[tex]-2\leq x<3[/tex], the graph is a line passing through (-2,-2) and (3,8)

Hence using two point equation we get

[tex]\frac{y+2}{8+2} =\frac{x+2}{3+2}\\5(y+2)=10(x+2)\\y=2x+2[/tex]...II

Again for

[tex]x>3\\y=-3[/tex]... III

I,II and III together give the piecewise funciton

Answer:16

Step-by-step explanation:

original price

100

=  

new price

new percent

;

64.5

100

=  

75

x

64.5x = 7500 → x ≈ 116.3

Subtract 100 from the new percent (116.3 − 100 = 16.3) → 16%

The approximate percentage of the tip is 14%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Dinner at your favorite restaurant cost $64.50 with tax for you and your family.

You give the waiter $75 to pay the bill and a tip.

That means,

the tip amount = 75 - 64.50

= 10.50

The tip percentage,

= 10.50 x 100 / 75

= 14%

Therefore, 14% is the required percentage.

To learn more about the percentage;

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Answer:

A. 60+x°=90

Step-by-step explanation:

Complementary angles add up to 90°.

Answer:

x = 12

Step-by-step explanation:

Given

4(x - 5) = 8x + 4 - 6x ← distribute left side and simplify right side

4x - 20 = 2x + 4 ( subtract 2x from both sides )

2x - 20 = 4 ( add 20 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Given the point (9,2) is on the graph of f(x), the corresponding point for the function f(-3/4x) is found by multiplying the x-coordinate of the given point by -3/4. This yields the corresponding point (-6.75, 2).

The given point is (9,2). In the function f(-3/4x), the variable is multiplied by the factor -3/4. We apply this factor to the x-coordinate of the given point to find the x-coordinate of the corresponding point in the function f(-3/4x).

Therefore, the x-coordinate of the corresponding point is 9×-3/4 = -27/4 = -6.75. The y-coordinate remains the same because the transformation corresponds only to the x-coordinates of points. So, the corresponding point in the function f(-3/4x) is (-6.75,2).

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