All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday. 25% of students brought their lunch. 50 students brought their lunch. How many students in total are in Ridgewood Junior High School?

The percentage of students age 15 and above travel to school by bus is 47%

The table of values is given as:

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15                            18                 165

Age 15 and above    65                                 195

Column totals          152          110        98      360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above  = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15           87              18      60        165

Age 15 and above    65          92        38        195

Column totals          152          110        98      360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

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The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let x represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, V, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

[tex] \frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0[/tex]

Which gives;

[tex] \frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0[/tex]

6•x² - 106•x + 315 = 0

[tex]x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6} [/tex]

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

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Answer:

(4,-1) (4,0) (4,1)

Step-by-step explanation:

If you graph this, it will be a straight vertical line.  No matter what y is, x will always be 4.

Using proportions, it is found that the total percentage increase in the investor's stock account was of 6.2%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The values of the stocks of Company A and Company B, after the increase are given, respectively, by:

The total values are given as follows:

The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:

P = (8668 - 8160)/8160 x 100% = 6.2%.

The total percentage increase in the investor's stock account was of 6.2%.

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Answer:

B: 8.3

Step-by-step explanation:

We will substitute 600 to the y, since our final answer will be a number that makes the value of the stock reach $600.

log (y) = 0.30x + 0.296

Replacing y with 600, the equation becomes:

log (600) = 0.30x + 0.296

2.78 = 0.30x + 0.296

To move all the x and real numbers to different sides, we take 0.296 away from both sides to form:

2.78 - 0.296 = 0.30x

2.484 = 0.30x

x = 8.28

The approximation of 8.28 will be rounded to 8.3.

Then our final answer will be B: 8.3

If the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16 then the price of one umbrella is $8 and price of one cap is $4.

Given that the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16.

We have to find the price of one umbrella and one cap.

We have to form equations first to find the price of umbrella and cap.

Equation of two variables look like ax+by=c. It can be a linear equation, quadratic equation or a cubic equation.

let the price of umbrella be x and price of cap is y.

We know that total cost is equal to price of one unit multiplied by the units.

According to question.

2x+y=20----------1

x+2y=16-----------2

Multiply equation 2 by 2 and then subtract resulted equation from equation 1.

2x+y-2x-4y=20-32

-3y=-12

y=-12/-3

y=4

put the value of y in equation 2 to get the value of x.

x+2y=16

x+2*4=16

x+8=16

x=16-8

x=8

Hence the price of one umbrella is $8 and the price of one cap is $4.

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Answer:

13/8

Step-by-step explanation:

4 2/8 - 2 5/8

34/8 - 21/8 = 13/8

1 5/8 as a mixed fraction

The dimensions of the rectangle as described in the task is; 12.4 by 5.7 yd.

Since the area, length and breadth of the rectangle are as described, it follows that;

66 = x(2x+1)

66 = 2x² + 1

x² = 32.5

x = 5.7

Therefore, the dimensions are 5.7 and 12.4.

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Answer:

  150 cm

Step-by-step explanation:

The total of exterior angles is 360°. We can use this fact to find the number of sides. The perimeter is the total length of all of the congruent sides.

The measure of an exterior angle of the regular polygon is the supplement of the adjacent interior angle:

  exterior angle = 180° -156° = 24°

The total of n of these angles is 360°, so n is ...

  24°×n = 360°

  n = 360°/24° = 15

The polygon has 15 exterior angles, hence 15 sides

The perimeter is the total length of the 15 congruent sides:

  P = 15×(10 cm) = 150 cm

The perimeter of the regular polygon is 150 cm.

Answer:

b = (a - 6)/2h

Step-by-step explanation:

a = 2bh + 6 (subtract 6 from both sides)

a - 6 = 2bh (divide both sides by 2)

(a - 6)/2 = bh (divide both sides by h)

(a - 6)/2h = b

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We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.  

Let x = number of gallons of 3% milk

Thus;

336 - x = number of gallons of 7% milk

Therefore;

0.03x + 0.07(336 - x) = 0.06(336)

0.03x + 23.52 - 0.07x = 20.16

-0.04x = -3.36

x = 84 gallons

We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.  

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The total cost to laminate the table top is $128.

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides.

The first step is to determine the area of the table top.

Area of a trapezoid = 0.5  x (sum of the lengths of the parallel sides) x height

0.5 x (6 + 10) x 4 = 32 square foot

Now, multiply the area by the cost per square foot

32 x 4 = $128

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Answer: [tex]\frac{3}{c^2}[/tex]

Step-by-step explanation:

This uses the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex].

The number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5

From the information given;

The bricklayer needs = 100 pieces of angle

The number of cuts = 54

Length of cuts = 3/ 16'' Inches

a. To determine the number of cuts form a 20% length, we have to multiply the length by the percentage and by the initial number of cuts

= 20/ 100 × 3/ 16 × 54

= 0. 2 × 0. 1875 × 54

= 2. 0

The number of cuts would be 2

b. To determine the number of pieces of 20' angle to have 100 pieces we would divide the initial number of pieces by the angle

= 100/ 20

= 5 pieces

The number of pieces of 20' angle is 5

Thus, the number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5

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Based on the profit function given, the level of production that yields the maximum profit is 55 units. The maximum profit is $2,025.

With a profit function:

=-x² + 110x - 1,000

Using a parabola function, we know:

= -b / 2a

The maximum units is:

= -110 / (-2 x 1)

= 55 units

The maximum profit is:

= -(55)² + (110 x 55) - 1,000

= $2,025

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Using the z-distribution, it is found that a sample of 171 should be selected.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]z = 1.96, \sigma = 40, M = 6[/tex]

Hence we solve for n to find the needed sample size.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]6 = 1.96\frac{40}{\sqrt{n}}[/tex]

[tex]6\sqrt{n} = 40 \times 1.96[/tex]

[tex]\sqrt{n} = \frac{40 \times 1.96}{6}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{40 \times 1.96}{6}\right)^2[/tex]

n = 170.7.

Rounding up, a sample of 171 should be selected.

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Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,

In order to determine whether x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35, we will show that f(5) = 0

Substitute x = 5 into the function to have;

f(5) = 5^3 – 5(5)^2 + 7(5) – 35

f(5) = 125 - 125 + 35 - 35

f(5) = 0

Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,

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We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.

In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and weighted averages offers a method that is easy to apply:

70 · 140 = 55 · x + 80 · (140 - x)

70 · 140 = 80 · 140 - 25 · x

25 · x = 10 · 140

x = 56

We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.

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Answer:

There are about 80 students age 15 and above take a car to school.

Step-by-step explanation:

1. For all the columns the total has been given.

2. Bus is taken as 60 as walk/bike has been given 65 under age 15.

3. 195 row total Age 15 and above has been provided and updated.

4. Walk/Bike 152, 65 is already given Age 15 and above difference is 87.

5. Bus 60 under age 15 is already given total 110 difference is 50.

6. Age 15 and above 65,50,195 (Total) is already given row difference is 80.

7. Car is Age 15 and above is 80 and Total column is 98 difference is 18.

8. Age 15 and above take car is 80.

Answer:

its 41%

Step-by-step explanation:

i took the test

Answer:

sin (- 135°)= – sin 135°= – sin (1 × 90°+ 45°) = – cos 45° = – 1√2

cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = – sin 45°= – 1√2

tan (- 135°) = – tan 135° = – tan ( 1 × 90° + 45°) = – (- cot 45°) = 1

csc (- 135°)= – csc 135°= – csc (1 × 90°+ 45°)= – sec 45° = – √2

sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= – csc 45°= – √2

cot (- 135°) = – cot 135° = – cot ( 1 × 90° + 45°) = – (-tan 45°) = 1

Step-by-step explanation:

hope this helps

Answer:

7/16

Step-by-step explanation:

(2+5)/(2+3+5+6) = 7/16

The probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.

According to the given question.

Numnber of yellow balls = 2

Number of green balls = 3

Number of red balls = 5

Number of black balls = 6

So,

The total number of balls in a bag = 2+ 3+ 5 + 6 = 16

And,

The sum of yellow and red ball = 2 + 5 = 7

Therefore,

The probability of either a yellow or a red ball being drawn if only one ball is drawn

= [tex]\frac{total\ number\ of \ red \ and \ yellow\ balls }{Total\ number\ of \ balls}[/tex]

[tex]= \frac{7}{16}[/tex]

Hence, the probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.

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The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of hamburger sold and y represent the number of cheeseburgers sold, hence:

x + y = 460    (1)

Also:

y = 3x       (2)

From both equations:

x = 115, y = 345

The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.

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The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13

y = -14x² + 1035x - 10266

-14x² + 1035x - 10266 = 0

x = -b ± √b² - 4ac / 2a

= -1035 ± √1035² -4(-14)(-10266) / 2(-14)

= -1035 ± √1071225 - 574896 / -28

= -1035 ± √496329 / -28

x = 1035 / 28 ± √496329 / 28

x = 11.80 or 62.13

The maximum value of x is 62.13

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Answer:

Width = 5.5ft, Length = 8ft.

Step-by-step explanation:

Area of Rectangle = Length x Width

Let w be the Width of the rectangle.

From the information given from the question,

Length = 2w - 3 (3ft less than twice the width)

Area of Rectangle = [tex](2w-3)w\\=2w^{2} -3w[/tex] = 44

Now we can solve for w to find the dimensions.

[tex]2w^{2} -3w-44=0[/tex] (Quadratic Equations)

We can use the Quadratic formula to find w.

[tex]w=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

Since a = 2, b = -3 and c = -44,

[tex]w=\frac{-(-3)+/-\sqrt{(-3)^{2}-4(2)(-44) } }{2(2)} \\= 5.5 or -4 (reject)[/tex]

We reject negative values here.

Therefore, the width of the Rectangle = 5.5ft

While the length of the rectangle = 2(5.5) - 3 = 11 - 3 = 8ft

110 postcards Xiulin had at first.

Algebric equation is a mathematical statement in which two equation set equal to each other.

Let the number of postcards belonging to Xiulin and Meifang be x.

Let the number of postcard Meifang gave to Xuilin be 'a'

Number of postcard left with meifang

=> x-a = 72                                                              

=> x = 72+a

Meifang had 76 fewer postcards than Xiulin.

so, (x+a)-72=76

   72+a+a-72=76

   2a = 76

   a = 38

meifang give 38 cards to xuilin

x = 72+38

 = 110

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Answer:I beleive the answer is c-3600

Step-by-step explanation:

90$ a month for 48 months=4320

Plus the interest rate of 8.33  so 4320x0.833=3598.56

Then you have to round up from 3598.56 to the nearest 100 dollars, so it would be 3600.

Answer:

She does not get bonus points and she ends up at level 5.

Equation: 4 - 6 + 8 -1 = 5

Equation using only addition: 4 + -6 + 8 + -1 = 5

I hope this helps!

Answer:

Answer:the answer is zero

Answer:the answer is zero Step-by-step explanation:

Answer:the answer is zero Step-by-step explanation:when we add -42 and -54 the answer we get is -96. -96and +96 cut each other and then the answer is zero

[tex] - 42 - 54 + 96 = 0[/tex]