Tyler collects 1242 cans of pet food. He gives 150 cans to the vet. Then he packs 9 cans in each box to give to the animal shelter. How many cans of pet food are not in a box?

The rate of change for Modis building stairwell is 0.68 feet per step.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Part A: In the Modis building, he climbs 22 steps for every 15 ft of horizontal travel.

Now, rate = 15/22

= 0.68 feet per step

In Sears Tower, he climbs 17 steps for every 7 ft of horizontal travel

Here, rate 7/17

= 0.41 feet per step

Part B: Sears Tower steps are easy to climb, because rate is lesser than Modis building steps.

Therefore, the rate of change for Modis building stairwell is 0.68 feet per step.

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Answer:

25 minutes

Explanation:

Subtract the two times to find the duration.

(i) The function that predicts your expected payroll for the day is,

For first person; y = $50 + $10.50x

For second person; y = $60 + $10.50x

Where, y is total amount and x is number of working hours.

(ii) In Wednesday; The amount expect to pay your employees is,

For first person;

⇒ y = $102.50

For second person;

⇒ y = $112.50

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The first employee scheduled to work next Wednesday makes $10.50 per hour and averages $50 per day for commission.

And, The other person that is scheduled earns $10.50 per hour and averages $60 per day for commission.

Let total amount earn = y

And, Number of working hours = x

Hence, We can formulate;

The function that predicts your expected payroll for the day is,

For first person;

⇒ y = $50 + $10.50x

For second person;

⇒ y = $60 + $10.50x

And, For 5 hours, the amount is,

For first person;

⇒ y = $50 + $10.50x

⇒ y = 50 + 10.50 × 5

⇒ y = 50 + 52.50

⇒ y = $102.50

For second person;

⇒ y = $60 + $10.50x

⇒ y = 60 + 10.50 × 5

⇒ y = 60 + 52.50

⇒ y = $112.50

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After 3 years the rate of simple interest charged at this to Chloe bank is  7%

We can start by using the formula for simple interest:

Simple Interest = Principal * Rate * Time

where the principal is the amount borrowed, the rate is the interest rate as a decimal, and the time is the duration of the loan in years.

Plugging in the given values, we get:

168 = 800 * Rate * 3

Solving for the rate, we get:

Rate = 168 / (800 * 3) = 0.07

Hence,

The rate of simple interest charged at this bank is 0.07, or 7% as a percentage.

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The value of x for the similar triangles is equal to 13.

We have the triangles to be similar, this implies that the length 8 of the smaller triangle is similar to the length x - 1 of the larger triangle

and the length 10 of the smaller triangle is similar to the length x + 2 of the larger triangle

so;

10/(x + 2) = 8/(x - 1)

10(x - 1) = 8(x + 2) {cross multiplication}

10x - 10 = 8x + 16

10x - 8x = 16 + 10 {collect like terms}

2x = 26

x = 26/6 {divide through by 6}

x = 13.

Therefore, the value of x for the similar triangles is equal to 13.

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Answer:

$2,000

Step-by-step explanation:

The initial investment price is given by the y-value where the graph intersects the y-axis

This is at y = 2

Since the scale is in thousands of $, that would mean $2,000 as the original price

Answer: 159 bpm

Step-by-step explanation:

if his rate is 53 beats in 1/3 of a minute, in 3/3 of a minute, (1 full minute), it will be 53 x 3 = 159 beats

so we can say his heart rate is 159 beats/minute, or 159 bpm

Kingsley knows that 1 inch is about 2. 54 centimeters.6 inches is equivalent to 15.24 centimeters.

To convert any given length in inches (I) to centimeters (c), Kingsley can use the following equation:

c = I * 2.54

This equation works because we know that 1 inch is equal to 2.54 centimeters. So, to convert any given length in inches to centimeters, we simply multiply the number of inches by 2.54. The result gives us the equivalent length in centimeters.

For example, if we want to convert a length of 6 inches to centimeters, we can use the equation:

c = 6 * 2.54 = 15.24

So, Kingsley knows that 1 inch is about 2. 54 centimeters. 6 inches is equivalent to 15.24 centimeters.

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The number of wires that cut from of 200 meters is 66 meters 66 centimeters.

What are the nearest two places?

The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

Given the length of the wire is 200 meters.

Assume that he cuts n pieces of length 3 meters.

The length of n pieces is 3n.

Therefore the equation is

3n = 200

n = 200/3

n= 66.66

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The probability that the first n coupons which you collect do not form a complete set is (c^n - (c-1)^n) / c^n.

To find the probability that the first n coupons collected do not form a complete set, we need to count the number of ways in which the first n coupons can be collected so that they do not form a complete set and divide it by the total number of ways in which n coupons can be collected, which is c^n.

Let S be the set of all possible complete sets of coupons. The number of ways in which the first n coupons can form a complete set is the number of ways to choose any one of the complete sets in S, multiplied by the number of ways to order the coupons within that set. There are (c choose n) ways to choose n coupons out of c, and for each complete set of n coupons, there are n! ways to order them. Therefore, the number of ways to choose n coupons that form a complete set is (c choose n) * n!.

The total number of ways to choose n coupons out of c is c^n.

So, the probability that the first n coupons collected do not form a complete set is:

P = 1 - [(c choose n) * n! / c^n]

Alternatively, we can count the number of ways in which the first n coupons can be collected so that they do form a complete set. There are (c-1)^n ways to choose n coupons out of c-1 types of coupons, and for each set of n coupons, there is exactly one way to add the missing coupon to form a complete set. Therefore, the number of ways to choose n coupons that form a complete set is c^n - (c-1)^n.

So, the probability that the first n coupons collected do not form a complete set is:

P = (c^n - (c-1)^n) / c^n

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The number of children and adults that swam at the public pool are 247 and 208 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent the number of children by x and the number of adult by y

this means;

x+y = 455 equation 1

1.75x + 2.5y = 952.25 equation 2

using substitution method,

x = 455-y

substitute 455-y for x in equation 2

1.75(455-y) + 2.5y = 952.25

796.25-1.75y+2.5y = 952.25

0.75y = 952.25-796.25

0.75y = 156

divide both sides by 0.75

y = 156/0.75

y = 208

substitute 208 for y in equation 1

x = 455-208

x = 247

therefore the number of children and adults in the pool are 247 and 208 respectively.

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Answer:

Step-by-step explanation:

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Answer:

Below

Step-by-step explanation:

rate X time = distance

rate  = distance / time    <=====we want minimum of this so make denominator as large as possible and numerator as small as possible

      distance = 595  KM    ( rounds up to 600 km)

        time = 8 hr 44 min  rounds down to 8 :40    you could make it 8:44.99)

595 km / (8 + 44.99/60) hr  = 68 km/hr

Answer:

The equation is:

8x + 4 = 68

and the solution is:

x = 8

Step-by-step explanation:

The equation is:

8 time x and 4 is 68

8x+4 = 68

Solve:

8x + 4 - 4 =  68 - 4

8x + 0 = 64

8x = 64

x = 64/8

x = 8

Check:

8*8 + 4 = 68

The equation is y = (-0.5)x + 34 and it will take 16 days for the water level to be 26 feet.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let the number of days = x, and the water level = y.

Given that,

Water level of river = 34 ft (initial value/y-intercept)

Rate of change = -0.5 ft per day (slope)

The equation of the line is given as:

y = mx + c

where, m is the slope

c is the y-intercept.

Substituting the values we have:

y = (-0.5)x + 34

The number of days in which the water level will reduce to 26 ft is:

26 = (-0.5)x + 34

26 - 34 = -0.5x

x = 16 days.

Hence, it will take 16 days for the water level to be 26 feet.

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Point H is located at 6 on the number line, which is 6 units to the right of the zero point.

We know that Point G is located at-18 on the number line, and that Point H is 24 further than Point G. To find the position of Point H, we need to add 24 to the position of Point G

Point H = Point G + 24

Substituting the position of Point G, we get

Point H = -18 + 24

Simplifying the expression, we get

Point H = 6

thus, Point H is located at 6 on the number line.

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The probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.

To calculate the probability that all four of the selected bolts are torqued to the proper limit, we need to find the number of combinations of 4 bolts out of 20 that have been torqued to the proper limit.

Let's call the number of proper bolts n = 20 - 5 = 15.

The number of combinations of 4 proper bolts out of 15 is given by the binomial coefficient nCk, where n is the number of bolts and k is the number of bolts selected.

nCk = n! / (k! (n - k)!).

So, the number of combinations of 4 proper bolts out of 15 is:

15C4 = 15! / (4! (15 - 4)!) = 15! / (4! 11!) = 1365.

Therefore, the probability of selecting all 4 proper bolts out of 20 is:

P = number of combinations of 4 proper bolts / number of combinations of 4 bolts = 1365 / 20C4 = 1365 / 4845 = 0.28

So, the probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.

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The value of the equation is A = 6ab - 2bc + 12ac - b²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2b ( 3a - c ) + 12ac - b²   be equation (1)

On simplifying the equation , we get

A = 2b ( 3a ) - 2b ( c ) + 12ac - b²

On further simplification , we get

A = 6ab - 2bc + 12ac - b²

Hence , the equation is A = 6ab - 2bc + 12ac - b²

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Answer:

k = 48.4

Step-by-step explanation:

[tex] \frac{k - 16}{6} = 5.4 \\ 6 \times \frac{(k - 16)}{6} = 5.4 \times 6 \\ k - 16 = 32.4 \\ k = 32.4 + 16 \\ k= 48.4 [/tex]

John can buy any amount of chocolate between 0 and 2.2 pounds (rounded to one decimal place) and still have enough money to buy the jelly beans.

John brings $15 to the candy store and buys a bag of jelly beans for $4. He plans to buy some chocolate that costs $5 per pound. Let x be the number of pounds of chocolate John could buy.

The cost of the chocolate John plans to buy is $5 per pound, so the total cost of x pounds of chocolate is 5x. John's total budget is $15, so he must have enough money to buy the jelly beans and the chocolate. Therefore, the inequality that represents this situation is:

4 + 5x ≤ 15

To solve for x, we can begin by isolating the variable on one side of the inequality. We can do this by subtracting 4 from both sides of the inequality:

5x ≤ 11

Next, we can isolate x by dividing both sides of the inequality by 5:

x ≤ 11/5

Therefore, the possible values of x, the number of pounds of chocolate John could buy, are all real numbers less than or equal to 11/5. However, since John cannot buy a negative amount of chocolate, we must also restrict x to be greater than or equal to 0. Therefore, the solution to the inequality is:

0 ≤ x ≤ 11/5

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The total time that tammy sent in total playing games is; 4.5 hours

The parameters given for Tammy in playing the game are;

Number of games played = 12 games

Time spent per game = ³/₈ hours

Thus;

Total time she spent playing game will be gotten by multiplying the time per game by number of games played to get;

Total time spent = ³/₈ * 12

= 9/2

= 4.5 hours

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Complete question is;

A game lasts 3/8 hours. Tammy played 12 of these games. For how long did she play in total? Write your answer in simplest form.

The volume is 3315 cubic feet.

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.

The given polynomial function is V(x)=x³-4x.

Here, W(x)=V(3x)

Replace x by 3x in the function V(x)=x³-4x, we get

V(3x)=(3x)³-4(3x)

V(3x)=27x³-12x

W(x)=27x³-12x

Replace x by 5 in the function W(x)=27x³-12x, we get

Now, W(5)=27(5)³-12(5)

= 27×125-60

= 3375-60

= 3315 cubic feet

Hence, the volume is 3315 cubic feet.

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"Your question is incomplete, probably the complete question/missing part is:"

A polynomial function V(x)=x³-4x that represents the volume of the right triangle pyramid when measured in cubic feet.

The function (x) =(3x) gives the volume (in cubic feet) of the pyramid when x is measured in yards.

Find a function W(x) that gives us the volume when measured in yards also to find W(5).

A solution to this system of linear equations is (1, -2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

4x - 2y = 8     ......equation 1.

y = -2     ......equation 2.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).

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Function g(x) is function f(x) translated 3 units to the left and 2 units down.

Here we know that the function f(x) = (x − 2)³ is transformed to g(x) = (x + 1)³ − 2.

Remember that:

A vertical translation of N units is written as:

g(x) =f(x) + N

if N > 0, the translation is up.

If N < 0, the translation is down.

A horizontal translation of N units is written as:

g(x) =f(x) + N

if N > 0, the translation is left.

If N < 0, the translation is right.

Here we can see that:

g(x) = f(x + 3) - 2

Then we have a translation of 3 units to the right and 2 units downñ.

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The equation that describes the graphed function is -

g(x) = - f(x) - 3.

A root function in mathematics is given as -

y = [tex]$\sqrt[n]{x}[/tex]

We can further write the function as -

y = [tex]$x^{\frac{1}{n} }[/tex]

Given is the graph of the function as shown in the image attached.

We can write the function f(x) as -

f(x) = √x

Inverting the f(x) across the {x} axis, we can write -

- f(x) = - √x

After downward translation, we can write g(x) as -

g(x) = - f(x) - 3

Therefore, the equation that describes the graphed function is -

g(x) = - f(x) - 3.

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