Martina is recording the percentages she earned on each quiz in her math class. Here are her results for the last 7 quizzes.
74, 64, 90, 74, 92, 68, 71
Find the range of the data set.

=___

Answer:

Martin family: 20 hours

Lewis family: 35 hours

Step-by-step explanation:

Let's say that the Lewis family sprinklers were out for L hours and the Martin family's sprinklers were out for M hours. We know that for each hour that the Lewis family sprinkler was on, 30L of water was put out. We can thus write the Lewis family sprinkler water output as 30L per each hour of L = 30 * L. Similarly, the Martin family sprinkler water output = 15 * M .

We know that the total hours for the sprinklers is 55, so L + M = 55. The total water output for the sprinklers is the sum of the sprinkler outputs, so 30 * L + 15 * M = 1350

L + M = 55

30 * L + 15 * M = 1350

One way to solve this would be to solve for L in the first equation and substitute that into the second

subtract M from both sides in the second equation

55 - M = L

30 * (55-M) + 15 * M = 1350

30 * 55 - 30 * M + 15 * M = 1350

1650 - 15M = 1350

subtract 1650 from both sides to isolate the M and its coefficient

-15M = -300

divide both sides by -15 to isolate M

M = 20

L = 55-20 = 35

Answer:

8.1 = LM

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

13 * 5 = LM^2

65 = LM^2

sqrt(65) = LM

8.06225 = LM

To one decimal place

8.1 = LM

Answer:

7.5 Imperial Gallons = 30 Imperial Quarts

Hi there!  

»»————-　★　————-««

I believe your answer is:  

30 qt.

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

7.5 * 4 = 30

7.5 gal. = 30 qt.

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: x = 7

Step-by-step explanation:

6(2x-11)+15=3x+12

1) Distribute 6 (distributive-property)

12x - 66 + 15 = 3x + 12

12x - 51 = 3x + 12

Subtract 12 from both sides; what ever you do to one side, you need to do to ther other.

12x - 63 = 3x

Subtract 3x from both sides.

9x - 63 = 0

Add 63 to both sides.

9x = 63

Divide by 9 to getx by itself.

63/9 = 7

x = 7

Answer:

I think it is 0.909090909090. Hope this helped.

Step-by-step explanation:

Answer:

Residual value

Answer:

D

Step-by-step explanation:

the first term is 8, the ratio is 1/2 ( 8*1/2 = 4, 4*1/2 = 2, 2*1/2 = 1)

the formula for an explicit geometric formula is :

[tex]a_{n} = a_{1} * r^{(n-1)}[/tex]

plug in your numbers :

[tex]a_{n} = 8 * (\frac{1}{2}) ^{(n-1)}[/tex]

Answer:

Step-by-step explanation:

Answer:

angle 1 = 80

angle 2 = 80

Step-by-step explanation:

in rhombus all sides are equal and also diagonals bisects each other

so

Answer:

The total price is $9.30

Step-by-step explanation:

Price of the orders of popcorn= $5.25

Price of the drinks= $4.05

After finding the equation of the line, it is found that:

Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear  equation.

------------------------

Equation of a line:

The equation of a line is given by:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

------------------------

Finding the slope:

Given two points (x,y), the slope is given by change in y divided by change in x.

Thus:

[tex]y = 3x + b[/tex]

------------------------

To find the y-intercept, we replace one of the points into the equation. I will replace (3,6). Thus:

[tex]6 = 3(3) + b[/tex]

[tex]b = 6 - 9 = -3[/tex]

Thus, the equation of the line is:

[tex]y = 3x - 3[/tex]

------------------------

Is (4,8) a solution of the same linear  equation?

We have to replace x by 4 and y by 8, and see if it results in an identity. So

[tex]8 = 3(4) - 3[/tex]

[tex]8 = 12 - 3[/tex]

[tex]8 \neq 9[/tex]

Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear  equation.

A similar problem is given at https://brainly.com/question/16024991

Answer:

x=3

Step-by-step explanation:

I suggest getting this app called photo math, it will help you soo much.

Answer:

x = 3

Step-by-step explanation:

4 (x - 1 ) + 4x -1 = 19

solve the brackets first

4x - 4 + 4x -1 = 19

4x + 4x -4 -1 = 19

8x -5 = 19

8x = 19+5

8x = 24

x = 24/8

x = 3

The question given is incomplete as the information about the headphones isn't given.

However, we can solve the problem by using hypothetical values.

Answer:

Kindly check explanation

Step-by-step explanation:

Given

Write the ratio of detective headphones to total headphones in the sample. Then write the ratio as a decimal and as a percent.

Let :

The number of defective headphones = 10

The total number of headphones on the sample = 50

To express as a ratio :

Defective headphones : total headphones

10 : 50 = 1 : 5

To express as a percentage ;

1 / 5 * 100% = 20%

Answer:

It is not because the half the perimeter is not only one side but another half side of the triangle, and the distence between two points in a triangle can never become longer then the length of one side.

Step-by-step explanation:

The math part I am unsure of because you did say prove but let me know if this helps. Thanks!

Answer:

24+p=t

Step-by-step explanation:

If he scored 24 points in the first half, and p in the next half, he scored a total of t points.

Given:

The graph of a scatter plot.

To find:

The function that best fits the given points.

Solution:

From the given graph it is clear that the linear function is the best fit for the given points because the points lie on a straight line or near to it.

So, options B and C are incorrect because they represent exponential and quadratic function respectively.

Let as assume the two points on the graph are (0.80,-12.82) and (2,-12.79).

Using this two points, the equation of line is:

[tex]y-(-12.82)=\dfrac{-12.79-(-12.82)}{2-0.80}(x-0.80)[/tex]

[tex]y+12.82=\dfrac{-12.79+12.82}{2-0.80}(x-0.80)[/tex]

[tex]y+12.82=0.025(x-0.80)[/tex]

[tex]y+12.82=0.025x-0.02[/tex]

[tex]y=0.025x-0.02-12.82[/tex]

[tex]y=0.025x-12.84[/tex]

[tex]y=-12.84+0.025x[/tex]

It is the approximate function to the function that is in option A.

Therefore, the correct option is A.

Answer:

42 units^2

Step-by-step explanation:

Break this into a rectangle and a triangle

The rectangle is 12 by 1

A = l*w = 12*1 =12

The triangle has a base of 6-1 =5  and a height of 12

A = 1/2 bh = 1/2 (5)*12 = 30

Add the areas together

12+30 =42

Answer:

[tex]42 \: {units}^{2} [/tex]

Step-by-step explanation:

First divide the shape into triangle and a rectangle

then find the Area of the triangle and the rectangle separately

Area of the rectangle

[tex]area = l \times b \\ = 12 \times 1 \\ = 12 \: \: {units}^{2} [/tex]

Area of the triangle

[tex]area = \frac{1}{2} \times bh \\ = \frac{1}{2} \times 5 \times 12 \\ = \frac{60}{2} \\ = 30 \: \: {units}^{2} [/tex]

Area of the shape

[tex]12 + 30 = 42 \: {units}^{2} [/tex]

Answer:

2*sqrt(5)

Step-by-step explanation:

By using Pythagoras theorem, we have

4^2+2^2=(the third side)^2

16+4=(the third side)^2

Third side=sqrt(20)=2*sqrt(5)

Answer:

x=11

Step-by-step explanation:

5x+7=62

5x=62-7

5x=55

x=11

Answer:

A = 79°

Step-by-step explanation:

CosA = adjacent ÷ hypoteneous

A = Cos^-1(6÷32)

A. =. 79.19°

A= 79°

the answer to this question is the slope is 43

Answer:

Therefore, the slope is 3/4

Step-by-step explanation:

An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)

Likewise, an

y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)

Now we have two points(4,0) (0,-3)

To find the slope given two points, we use the formula

rise÷run , or y2−y1÷x2−x1 .

Plug in the given points into the formula

-3-0/0-4

-3/-4

3/4

Therefore, the slope is 3/4

Hope this helps!

Answer:

Total=(0.25(p))+(0.05(r))

replace the letter value with the # of items and solve using equation

Answer:

think this one

Step-by-step explanation:

the answers there

i think

real numbers, integers, rational numbers

=========================================================

Explanation:

So far in your studies, every number is a real number. This is assuming your teacher hasn't introduced complex or imaginary numbers yet.

So that's why -12 is a real number.

Choice A is one of the answers

---------------

The set of whole numbers is {0,1,2,3,4,...} so we aren't including negative values here, which rules out choice B. However, the set of integers does include negative values

{..., -3, -2, -1, 0, 1, 2, 3, ...}

That makes -12 an integer

Choice C is one of the answers

----------------

The value -12 is not irrational because we can write it as a fraction of two integers. Eg: -12 = -12/1

This shows that -12 is rational and why choice F is one of the answers and allows us to rule out choice D.

------------------

We can rule out choice E because the set of natural numbers is {1,2,3,4,...} basically the set of whole numbers but we kicked out 0.

The requried, -12  is an element of sets of real numbers, integers, and rational numbers. Options A, C, and F are correct.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

Here,

Only sets that consist of negative values are, real numbers, integers, and rational numbers.

So - 12 is a negative number that belongs to the set of real numbers, integers, and rational numbers.

Thus, the requried, -12  is an element of sets of real numbers, integers, and rational numbers. Options A, C, and F are correct.

Learn more about the number system here:

https://brainly.com/question/22046046

#SPJ2

Answer:

The slope is -3/4 and the y intercept is 5

Step-by-step explanation:

- 3x - 4y= -20

Slope intercept form is

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

Solve for y

Add 3x to each side

- 3x - 4y+3x=3x -20

-4y = 3x-20

Divide by -4

-4y/-4 = 3x/-4  -20/-4

y = -3/4 x+5

The slope is -3/4 and the y intercept is 5

Answer:

Slope: [tex]\displaystyle-\frac{3}{4}[/tex]

Y-intercept: 5

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.

[tex]-3x-4y=-20[/tex]

To find the slope and y-intercept of the given line, rearrange the equation into slope-intercept form. We can do this by isolating y.

Add 3x to both sides:

[tex]-3x-4y+3x=-20+3x\\-4y=3x-20[/tex]

Divide both sides by -4:

[tex]y=\displaystyle -\frac{3}{4} x+5[/tex]

Now, we can identify [tex]\displaystyle-\frac{3}{4}[/tex] to be in place of m, the slope, and 5 to be in place of b, the y-intercept. Here is a comparison:

[tex]y=\displaystyle -\frac{3}{4} x+5[/tex]

[tex]y=mx+b[/tex]

I hope this helps!

Answer:

x = 2

Step-by-step explanation:

0.3 (4 - x) = x - 1.4

1.2 - 0.3x = x - 1.4

-0.3x - x = -1.4 - 1.2

-1.3x = -2.6

x = 2

Answer:

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{} 0,3(4-x)=x-1,4 \\\\1,2-0,3x=x-1,4 \\\\x+0,3x=1,2+1,4\\\\1,3x=2,6 \\\\\underline{x=2 \ \ \ \ \ \ \ } \\\\0,3(4-2)=2-1,4 \\\\2\cdot 0,3=0,6 \\\\0,6=0,6[/tex]

Answer:

[tex]y=2x^2+1[/tex]

Step-by-step explanation:

The general equation for a parabola in vertex form is the following:

[tex]y=a(x-h)^2+k[/tex]

Where ([tex]h,k[/tex]) is the parabola's vertex and (a) is the stretch and compression factor. As one can see in the given graph, the parabola has a vertex at (0, 1), moreover, it passes through the point (1, 3). Substitute these points into the equation for the parabole, and simplify,

[tex]y=a(x-h)^2+k[/tex]

Vertex: (0, 1)

[tex]y=a(x-0)^2+1[/tex]

A point on the parabola: (1, 3)

[tex]3=a(1-0)^2+1[/tex]

[tex]3=a1+1\\3 = a + 1\\[/tex]

Inverse operations,

[tex]3=a+1[/tex]

[tex]2 = a[/tex]

Substitute back into the original expression:

[tex]y=a(x-h)^2+k[/tex]

[tex]y=2(x-0)^2+1[/tex]

Simplify to put in standard form:

[tex]y=2(x-0)^2+1[/tex]

[tex]y=2(x)^2+1[/tex]

[tex]y=2x^2+1[/tex]

Answer: f(x) = -(x-1)^2+5

Explanation:

f(x) = h(x) + 6

f(x) = -(x-1)^2 - 1 + 6

f(x) = -(x-1)^2+5

Must click thanks and mark brainliest