John read 7 and 1/2 pages in 2/5 of an hour at what rate in pages per hour did he read?

The average skid mark for the car is 98.5 feet.

The average skid mark can be calculated by the formula -

S = ✓30Dfn, where s is speed of car, D is skid distance, f is drag factor and n is braking efficiency. Keep the values in formula to calculate the value of D.

57 = ✓30 × D × 1.1 × 1

Performing multiplication on Right Hand Side of the equation

57 = ✓D × 33

Taking square on both sides of the equation

D = 57² ÷ 33

Taking square on numerator on Right Hand Side of the equation

D = 3249 ÷ 33

Performing division on Right Hand Side of the equation

D = 98.45 feet

Rounding to the nearest tenth of a foot

D = 98.5 feet

Hence, the average skid mark is 98.5 feet.

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Using the angle of elevation, the height of the tower is 9.2 ft.

He is  5 ft tall. The angle of elevation of the tower is 23 degree.

He is standing 10 feet away from the base of the tower.

The height of the tower can be found as follows;

The situation forms a right angle triangle.

The height of the tower can be found using trigonometric ratios.

Hence,

tan ∅ = opposite / adjacent

where

tan 23° = h / 10

cross multiply

h = 10 tan 23°

h = 4.2447481621

h = 4.2 ft

Therefore,

height of the tower = 4.2 + 5 = 9.2 ft

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Step-by-step explanation:

the answer is Y=-1/2×+5

Explanation:

You put the gradient in M for Y=M×+C (substitute) then you substitute the coordinates it has given you into the X and Y part of linear equation. (x,y)

There are 180 three-digit numbers that leave a remainder of 2 when divided by 5 and 128 three-digit numbers that leave a remainder of 6 when divided by 7.

The smallest 3-digit number to leave a remainder of 2 when divided by 5 is 102.

The next number will be 107, and then 112,

The last 3 digit number to leave a remainder 2 when divided by 5 is 997

Therefore here we get an Arithmetic Progression

102, 107, 112, ..., 997

We know that for any term of an A.P

aₙ = a + (n - 1)d

where,

a = first term

n = the order number of that particular value

d = common difference

Here,

a = 102

d = 107 - 102

= 5

The number of 3 digit number for the above problem will be the value of n for 997

Hence we get

997 = 102 + (n - 1)5

or, 102 + 5n - 5 = 997

or, 5n + 97 = 997

or, 5n = 997 - 97

or, 5n = 900

or, n = 900/5

or, n = 180

Next, we need to find the no. of three-digit numbers that leave the remainder of 6 when divided by 7

The smallest 3-digit number to leave the remainder of 6 when divided by 7 is 104

The largest is 993

Therefore, just like before, we get the A.P

104, 111, 118, ..., 993

here,

a = 104

d = 7

aₙ = 993

Hence we get,

993 = 104 + (n - 1)7

or, 104 + 7n - 7 = 993

or, 97 + 7n = 993

or, 7n = 993 - 97

or, 7n = 896

or, n = 128

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The transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

The given functions are f(x)=-1/4 x-2 and r(x)=4f(x).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

r(x)=4f(x)

So, r(x)=4(-1/4 x-2)

⇒ r(x)=-x-2

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Vertical: stretch

The graph of the functions is given below.

Therefore, the transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

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The system of inequalities that best represent the shaded feasible region shown on the graph is

information gotten from the question include

inequality graph showing shaded regions

some interpretation on the information from the question include

This interpretation removes the first and the last options since they contain the equal to sign

positive slope moves from bottom left to top right

y < x + 1

negative slope moves from top left to down right

y < -x - 2

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Answer:

18x−33−f(x)=0

Solve for f by simplifying both sides of the equation, then isolating the variable.

The fault with Jerome's approach as required in the task content is; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.

Commutative property of addition is a property of addition which posits that Changing the order of addends does not change the sum.

On this note, the use of the commutative property of addition on the given expression; 3 - 6 + 5 would yield the expression; 3 + 5 - 6.

Consequently, the fault with Jerome's approach is that; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.

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The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2

The given equation of the line is

5x - 2y = -6

Ax + By = C1

Bx - Ay = C2

are perpendicular.

Then the perpendicular to the line 5x - 2y = -6 is 2x + 5y = C2

We have to find the value of C2

The line is passing through the point (5, -4)

Substitute the values in the equation and find the value of C2

2(5) + 5(-4) = C2

C2 = 10 -20

= -10

The equation will be 2x + 5y = -10

Rearrange the terms and make it slope intercept form

2x + 5y = -10

5y = -10 -2x

5y = -2x - 10

y = (-2/5)x - 2

Hence,  equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2

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The required number maximum number of copies can be afforded x < 24.28.

Given that,
We have $8.50 and you need to make copies of a flyer at a store that charges $0.35 per copy.

Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the number of copies be x,
According to the question,

0.35x < 8.50
x < 8.50 / 0.35
x < 24.28

Thus, the required number maximum number of copies can be afforded x < 24.28.

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Answer:

  A, B, F

Step-by-step explanation:

You want to know the errors made in graphing y = -3x +2 by plotting the y-intercept of 2 and then plotting another point 3 down and 2 left of that.

The appropriate graph would be created by plotting the y-intercept at 2, then moving down 3 units and 1 unit right from there, because the slope is -3.

The y-intercept is correctly plotted at y=2.

The next point is incorrectly plotted down 3 units and 2 units left of the y-intercept. It should be plotted down 3 units and 1 unit right.

The slope is -3, or -3/1. For a negative slope, the rise or run, but not both, will be negative. We don't know the student's rationale for using 2 as the "run" in ...

  slope = rise/run

The best error descriptors seem to be ...

A)  The student used the y-intercept, 2, for the denominator of the slope. The slope should be −3 or −3/1 .

B)  The student said that, because the slope is negative, both rise and run are negative. When the slope is negative, either the numerator is negative or the denominator is negative, not both.

F) After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 1 unit, because the slope is −3/1, not −3/−2.

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Answer:

2<y<6

Step-by-step explanation:

12 < 8y-y^2

y^2 -8y +12 <0

(y-6)(y-2)<0

y < 6

y < 2

 2.       6

-       -        +

-       +.       +

+.      -         +

2<y<6

The correct number in the function f (3) will be;

⇒ f (3) = 2

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The graph is shown in figure.

Now,

Clearly, By the image of the graph;

At x = 3,

The function is defined as;

⇒ f (3) = 2

Thus, The correct number in the function f (3) will be;

⇒ f (3) = 2

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The missing values in the ratio table include the following:

A = 2

B = 6

In Mathematics, a proportional relationship can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order for the ratio of the number of people to liters of ginger ale needed to have a proportional relationship, the variables x and y must have the same constant of proportionality.

Next, we would calculate the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 24/4

Constant of proportionality (k) = 6.

Now, we can determine the value of A and B:

A = x/k

A = 12/6

A = 2

For the value of B, we have:

B = x/k

B = 36/6

B = 6.

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Answer: A=2 and B=6

Step-by-step explanation: I hope this helped you

:D

Answer: 3x+19

Step-by-step explanation:

The distance traveled by the car in 2hours is 120miles

Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

from the definition speed= distance/time

since the train has constant speed,therefore the speed of the car = 150/2 1/2

= 60miles/hour

Distance= speed×time

Therefore for a time of 2hours the train will cover

60×2= 120 miles

Therefore the distance covered in 2hours is 120miles

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Answer:-454/539

Step-by-step explanation:32.34(s+1)=5.1

                                            32.34s+32.34=5.1

                                            32.34s=5.1-32.34

                                            32.34s=-27.24

                                            s=-454/539

The amount of tax paid per tonne of sand is $14.835 as the sand costs $98.90 per tonne.

In mathematics, a percentage is a value or ratio expressed as a fraction of 100.

The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.

Given,

The cost of one Tonne of sand=$98.90

The tax on one Tonne=15%

The  amount of tax per Tonne of sand is,

=(15/100)×98.90

=$14.835

Hence, the amount of tax paid per tonne of sand is $14.835.

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The factory produced 1.404 x 10⁶ sweets in a year

Standard form is a way of writing very large numbers or very small numbers in a simpler form. It is also called scientific notation

Given that: The factory produces 270000000 sweets every

week.

To know how many sweets the factory produces in a year, we will multiply the quantity produced in a week by 52 since there are 52 weeks in a year. Thus:

Number of sweet in a year = Weekly production x 52

                                 = 270000000 x 52 = 14040000000 sweets

To express 140400000000 in standard form, we will move the position of the decimal point to the back of the first number(1) and take note of the number of steps we take to get there. The  number of steps will then be  used as the power of 10:

14040000000 = 1.404 x 10⁶

Therefore, the number of sweets produced by the factory in a year in standard form is 1.404 x 10⁶ sweets

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Dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).

Three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given,

A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top

Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.

Let the cut squares will have side h then h is the height of the box and the two lengths are (25-2h) and (20-2h).

The dimensions of the box are (25-2h) and (20-2h)..

Volume of the box will be V=h(25-2h)(20-2h)

Hence, dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).

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This is an example of Cluster random sampling.

Cluster sampling refers to probability sampling when the population is divided into multiple smaller groups, also called clusters, and then further sampling is performed to check the data.

Here we can see that the principal had selected 222 boxes randomly over here. This implies that she had taken a group of boxes randomly. Then she proceeded to check every t-shirt in this box.

Therefore here we see that the population i.e the boxes were divided into smaller groups. The 222 boxes are the clusters here. Therefore we can conclude that the principal uses the cluster random sampling method.

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The value of the 48 cm will be equal to 480 mm.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that the number is 48 cm. Here 48 cm is the length of any object the value of 48 cm in the unit mm will be calculated as below,

1 cm = 10 mn

48 cm = 48 x 10 mm

48 cm = 480 mm

Therefore, the value of the 48 cm will be equal to 480 mm.

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Answer:

11.6666666 (infinitely)

[tex]\huge\mathcal {♨Answer♥}[/tex]

Answer is on the attachment...

☆...Hope this helps...☆

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Answer:

length is 20 yards, width is 15 yards

Step-by-step explanation:

Length = width + 5

2(W + 5) + 2(W) = 70

2W + 10 + 2W = 70

4W + 10 = 70

4W = 60

W = 60 ÷ 4

W = 15 yards

L = 15 + 5

L = 20 yards

Answer:

Step-by-step explanation:

Yes, of course!

A parabola's direction is based on whether its "a" value is positive or negative and whether it is opening vertically or horizontally (y= or x =)!

The equation that can be used to find the price of one tire patch is 22.20 - 4x = 1.90 and 4x + 1.90 = 22.20

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

Rhyan paid using a gift card that had $22.20 on it.

Let x represent the cost of each tire patch needed for the mountain biking trip. Rhyan bought four tire patches and had $1.90 remaining. Hence:

22.20 - 4x = 1.90

4x + 1.90 = 22.20

The equation is 22.20 - 4x = 1.90

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Answer:

10t + 20

Step-by-step explanation:

Assuming it is a standard deck of 52 cards and a standard dice of 6 faces.

There are 13 heart cards in a standard deck, therefore the odd of getting a heart is 13 : 52 = 1/4.

There is only 1 six in a standard dice, therefore the odd of getting a six is 1/6.

For these events to happen simultaneously, we multiply the chances.

Therefore, the chance of getting a heart in a deck of cards and a six on a dice is 1/4 x 1/6 = 1/24.

Answer:

heart from a deck of cards= 13/52 = 1/4

getting a six on a dice= 1/6 = 1/6

Step-by-step explanation:

heart from a deck of cards :

In the context of ordinary maths questions the answer is so obvious as to almost not be worth mentioning. There are 52 cards in an ordinary deck and 13 of them have heart pips, so 13/52 = 1/4.

six from a dice :

There is a 1/6 chance of rolling a 6. There are only 6 sides on a die, and only 1 of them is 6, so there is a 1/6 chance of rolling a 6.

at the same time is:

13/15 + 1/6 = 31/30 = 1/30