Divide. (5 1/4)÷(−2 1/2) Enter your answer as a mixed number, in simplified form, in the box.

Answer:

a

Step-by-step explanation:

THere are 52 students because there is 19 boys and 14 more girls than guys which means 19 + 19 + 14

There are 14 more girls than the 19 boys in the school orchestra, so there are 33 girls. Adding 33 girls and 19 boys, we find there are 52 students in the orchestra.

This question falls under the category of simple addition in mathematics. We are given there are 19 boys in the school orchestra and there are 14 more girls than the boys. To find out the total number of students, we add the number of boys to the number of girls.

First, understand that if there are 14 more girls than boys, the number of girls will be 19 (boys) + 14 = 33 girls. Next, adding the number of boys and girls together would give you 19 (boys) + 33 (girls) = 52 students. Hence, there are total 52 students in the school orchestra.

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A) The time to travel 45 miles at a speed of 30 mph can be found from ...

... time = distance / speed

... time = (45 mi)/(30 mi/h) = 3/2 h = 1 hr 30 min

B) The gas consumption can be found from ...

... (45 mi)/(54 mi/gal) = 5/6 gal

C) The cost of gas can be found from ...

... ($3.23/gal)×(5/6 gal) ≈ $2.69

For a 45 miles trip at 30 mph, it would take about 1.5 hours in a hybrid car that gets 54 mpg. It would use approximately 0.833 gallons of gas, costing about $2.69.

To solve this, we'll need to employ some basic math concepts. Starting off with the time it will take to get to your grandparents' house, you'll use the formula distance = speed x time. Given the speed is 30 mph and you're traveling 45 miles, that will be 45 miles / 30 mph = 1.5 hours.

Next, for the gallons of gas used on the trip, we'll use the car's mileage i.e., 54 miles per gallon. Hence, for a 45-mile trip, we have 45 miles / 54 mpg = 0.833 gallons of gas.

Finally, for the total cost of the trip, we'll multiply the amount of gas needed by the price per gallon. So, it will be 0.833 gallons x $3.23/gallon = $2.69. Thus the round trip will cost approximately $2.69 in gas.

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We simplify the equation to the form, which is simple to understand

r+31=-2(6r+4)

Reorder the terms in parentheses

r+31=+(-12r-8)

Remove unnecessary parentheses

+r+31=-12r-8

We move all terms containing r to the left and all other terms to the right.

+1r+12r=-8-31

We simplify left and right side of the equation.

+13r=-39

We divide both sides of the equation by 13 to get r.

r=-3

Answer: The number of pages in the U.S. tax code x=20000 and the number of pages in the King James Bible y = 1472

Step-by-step explanation:

Let the number of pages in the U.S. tax code be x and the number of pages in the King James Bible be y.

According to the given problem , we have the following system

x - y = 18528    ..............(1)

x + y = 21472     ..............(2)

Adding (1) and (2) , we get

2x = 18528 +21472 = 40000

⇒ 2x =40000

⇒ x =20000

Putting value of x = 20000 in (2) ,we get

20000 + y =21472

⇒ y = 1472

Ans  the number of pages in the U.S. tax code x=20000 and the number of pages in the King James Bible y = 1472

Final answer:

By setting up an equation and solving for B, which represents the number of pages in the Bible, it is determined that the King James Bible has 1,472 pages.

Explanation:

To determine how many pages are in the King James Bible, we need to set up an equation based on the information given in the problem. We know that the number of pages in the U.S. tax code exceeds the number of pages in the King James Bible by 18,528 and the combined total of pages in both the tax code and the Bible is 21,472.

Let's let B represent the number of pages in the Bible. Then the number of pages in the U.S. tax code would be B + 18,528. The total number of pages in both is given to be 21,472, so we can write the following equation:

B + (B + 18,528) = 21,472

Simplifying the equation, we get:

2B + 18,528 = 21,472

Subtract 18,528 from both sides to get the number of pages in the Bible:

2B = 2,944

Divide by 2 to solve for B:

B = 1,472

Therefore, the King James Bible has 1,472 pages.

The answers are in slope-intercept form, so you can see that the slope (coefficient of x) is only correct for choices b and c.

When you substitute x=3/2 into those equations, you find that b gives y=6 (correct) and c gives y=0 (incorrect).

The appropriate choice is ...

... b.) y = 2x+3

√61 ≈ 7.8

√101 ≈ 10.05

The integers between these numbers are 8, 9, 10. The product of these is 720.

C

let y = f(x)

Then rearrange making x the subject

y = - [tex]\frac{2}{3}[/tex] x - 18 ( add 18 to both sides )

y + 18 = - [tex]\frac{2}{3}[/tex] x

multiply both sides by -  [tex]\frac{3}{2}[/tex]

- [tex]\frac{3}{2}[/tex] (y + 18) = x

x = - [tex]\frac{3}{2}[/tex] y - 27

change y to x for inverse function

[tex]f^{-1}[/tex](x) = - [tex]\frac{3}{2}[/tex] x - 27 → C

Answer:

4m+12$$, squared 12/34+10566

Step-by-step explanation:

the quotient should be 2x² + x - 3 not 2x² + x + 3

the error was made in the division of x² into the line -3x² + 6x - 3

where it goes in - 3 times not + 3 times ← error

-2.5 is the best approximation.  Putting this into the equation we get:

-2.5*-2.5*-2.5  -4*-2.5 +6

-15.625 + 10 + 6 = .375

Answer:  D  or  -2.5

Step-by-step explanation:

By using a graphing calculator, we can see that there is only one rational x intercept, -2.525. By simply rounding this value to the nearest tenth we get -2.5

If you divide by 8, you can put the equation into intercept form. That form is ...

... x/a + y/b = 1

where a and b are the x- and y-intercepts, respectively.

Here, your equation would be

... x/(-2) + y/(-4) = 0

The graph with those intercepts is not shown with your problem statement here. See the attachment for the graph.

The answer is 1, 2, 3, 4, 5, 6, 10 .

Have a good day!!! <3

When you have a linear equation of the form y = mx, such as this one, you know immediately that the line passes thru the origin (0,0).  Were the form y = mx + b, then the y-intercept would be (0,b) and the x-intercept ( [-b/m, 0).

The distributive property tells you the product is found by multiplying each term inside parentheses by the factor outside.

... 4 -6n = 8n +8·7

... 4 = 14n +56 . . . . . . . add 6n to both sides

... -52 = 14n . . . . . . . . . subtract 56 from both sides

... -52/14 = -26/7 = n . . . divide by 14, reduce the fraction

The solution is ...

... n = -26/7 = -3 5/7

The answer is c because the amount of money you have 37 minus the amount you can spend ( at most 34) has to be more than or equal to 3.

Answer:

C. 37 - m ≥ 3

Let's solve your equation step-by-step.

4−x=11−8

Step 1: Simplify both sides of the equation.

4−x=11−8

4+−x=11+−8

−x+4=(11+−8)(Combine Like Terms)

−x+4=3

−x+4=3

Step 2: Subtract 4 from both sides.

−x+4−4=3−4

−x=−1

Step 3: Divide both sides by -1.

−x /-1=-1/-1

x=1

Answer:

x=1

51° 29' + 32° 46' = (51+32)° (29+46)'

= 83° 75' . . . . . there are 60' in 1°, so 75' = 1° + 15'

= 84° 15'

Answer:

$75.19

Step-by-step explanation:

Let 'x' be the cost of remote keyless entry.

And [tex]8x[/tex] be the cost of 4-way power front passenger seat.

Total cost = destination charge + title fee + taxes

So we have the equation:

[tex]20,000 = (17,980+x+8x)+0.072(17,980+x+8x)[/tex]

Now solving for 'x', we get:

[tex]20,000 = (17,980+9x)+0.072(17,980+9x)[/tex]

[tex]20,000=17,980+9x+1294.56+0.648x[/tex]

[tex]20,000=19274.56+9.648x[/tex]

[tex]725.44=9.648x[/tex]

[tex]x=\frac{725.44}{9.648} =75.19[/tex]

Therefore, the cost of remote keyless entry is $75.19.

Answer:

$601.53

Step-by-step explanation:

just do what the person did but all they forgot to do was to multiple for the "8 times" so take 75.19*8 to get 601.53.

Answer: The answer is 17.87. However the answer including all the numbers you put in your question is 17.92. I used only the first 2 numbers after the decimal point.

Step-by-step explanation: Consider how many numbers are behind the decimal points as they will help you know where to put the decimal point in your answer.

Hope this helps!

Jack drives an 18 wheeler. The truck's gas tank holds 105 gallons of gasoline. The driver begins the trip with a full tank.

Tank holds 105 gallons

65% of gasoline is 0.65 * 105 = 68.25

so 68.25 gallons left in the tank

Tank holds 105 gallons  and left out with 68.25 gallons

So gasoline used = 105 - 68.25= 36.75

36.75 gallons of gasoline used

Answer:

Change

Step-by-step explanation:

Here there are two variables a and b.

a is causing variable b.

In other words, a is an independent variable which can take any values, and b takes values depending on the value of a.

Examples are:  b=ma+k or b =2a^2 etc.

Whenever we change a there is a change in b.

But it should be noted when there is a change in b, there is a change in a also.

However, normally a is changed first and b is derived from a.

Hence the statement

In order to show that variable a causes variable b, you need to change_____ variable

a.

To show that variable a causes variable b, you need to establish a cause-and-effect relationship between the two variables.

To show that variable a causes variable b, you need to establish a cause-and-effect relationship between the two variables. This can be done through experimentation or observation. By manipulating variable a and observing its effect on variable b, you can determine if there is a causal relationship between them.

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Answer:

The answer is 6(3 + 4)

Step-by-step explanation:

In order to find this, we must find the greatest common factor of both numbers. Below are the factors for each number.

18: 1, 2, 3, 6, 9, 18

24: 1, 2, 3, 4, 6, 12, 24

You'll notice that the highest number on both lists is 6. So we divide each number by 6 and then express as a distribution.

6(3 + 4)

The expression 18 + 24 can be expressed using the distributive property as 6(3 + 4)

To express using the distributive property, we take following steps :

Find the greatest common factor of the values 18 and 24

Factors of :

Divide, the values by the 6 and express in the form a(b + c) :

Therefore, the required expression is 6(3 + 4)

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slope of JK:    -3/7

slope of LK:    1/2

slope of ML:   -3/7

slope of MJ:   2

Quadrilateral JKLM is   a parallelogram because both pairs of opposite sides are parallel

calculate the slope m using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = J(- 3, 2 ) and (x₂, y₂ ) = K(4, - 1 )

[tex]m_{JK}[/tex] = [tex]\frac{-1-2}{4+3}[/tex] = - [tex]\frac{3}{7}[/tex]

with (x₁, y₁ ) = L(2, - 5 ) and (x₂, y₂ ) = K(4, - 1 )

[tex]m_{LK}[/tex] = [tex]\frac{-1+5}{4-2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Similarly

[tex]m_{ML}[/tex] = [tex]\frac{-2+5}{-5-2}[/tex] = - [tex]\frac{3}{7}[/tex]

[tex]m_{MJ}[/tex] = [tex]\frac{-2-2}{-5+3}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2

JKLM is a parallelogram because both pairs of opposite sides are parallel

The diameter is a vertical line (x=3) and is of length 9 (= 5-(-4)). The radius is half the diameter (so is 4.5), and the center is 4.5 units above the bottom end of the diameter, so is at (3, 0.5). The square of the radius will be 4.5² = 20.25.

A circle with center (h, k) and radius r has formula

... (x -h)² +(y -k)² = r²

The equation of this circle can be written as

... (x -3)² +(y -0.5)² = 20.25

The equation of the line with slope m and passing through the point [tex](x_0,y_0)[/tex] is

[tex]y-y_0=m(x-x_0).[/tex]

Since m=6 and the coordinates of the point are (8,3), then the equation is

[tex]y-3=6(x-8).[/tex]

Answer: correct choice is B.

Since, there are 6 science fiction stories, 4 adventure stories, 3 historical stories and 2 sport stories.

So, total number of stories = 6+4+3+2 = 15 stories

Probability that Artie selects a science fiction story = [tex]\frac{6}{15}[/tex]

Probability that Artie selects an adventure story = [tex]\frac{4}{15}[/tex]

Probability that story selected is either a science fiction or adventure fiction = P(Science) + P(Adventure)

= [tex]\frac{6}{15} + \frac{4}{15}[/tex]

= [tex]\frac{10}{15}[/tex]

= 0.66

=0.67

Therefore, the probability that the story Artie selects is either a science fiction story or an adventure story is 0.67.

Answer:Probability of selecting either A or B P(A∩B)=2/3.

Step-by-step explanation:

Total number of story books=6+4+3+2=15

Let A be the event of selecting science fiction story

then its probability P(A)=number of science stories/total stories=6/15

Now let B be the event of selecting adventure story P(B)=number of adventure stories/total stories

=4/15

thus Probability of selecting either A or B P(A∩B)=P(A)+P(B)=6/15+4/15=10/15=2/3.

Answer: option. y=-1.33x; 2.67

Solution:

If y varies directly with x, the relation between y and x is:

y=kx

where k is a constant of proporcionality.

We know y=8 when x=-6. Replacing these values in the equation above:

8=k(-6)

8=-6k

Solving for k: Dividing both sides of the equation by -6:

8/(-6)=-6k/(-6)

-1.33=k

k=-1.33

Then the relation between y and x is:

y=kx→y=-1.33x

What is the value of y when x=-2?

Replacing x by -2 in the formula:

y=-1.33x→y=-1.33(-2)→y=2.66

Answer:

20%

Step-by-step explanation:

i did it and got it right

the picture is my evidence.