USING YOUR MATH
4. A semi-truck is being loaded with boxes of varying weights. The total weight of boxes loaded is shown below as a function of the number of boxes loaded into the truck.
(a) For each interval below, find the average rate of change. Do not round. Include units with your answers.
5 to 11 boxes:
11 to 20 boxes:
20 to 25 boxes:
(b) Over which interval was the average weight per box the greatest?
5. A hot liquid was placed in a freezer and its temperature was recorded. The data for the first 8 minutes is shown below.
At what average rate is the temperature changing from 2 to 8 minutes? Use proper units.

Answer:

3 6/7

Step-by-step explanation:

divide 6/7 by 2/9 and that equals 3 6/7 and since you cant simplify that the answer stays the same which the answer is 3 6/7

The expression −(4b)(4b)(4b) using positive exponents is -(4b)³

From the question, we have the following parameters that can be used in our computation:

−(4b)(4b)(4b)

Express properly

So, we have

−(4b) * (4b) * (4b)

5⁻¹² * 32⁻³ * 9⁻¹⁵

By using the definition of positive exponents, we have

−(4b) * (4b) * (4b) = -(4b)³

So, the solution is -(4b)³

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Answer:

495cm^2

Step-by-step explanation:

First of all get the total ratio which is (5+12+13)=30 then use it to find the length of each side that is to say

EACH SIDE RESPECTIVELY AS PER THE RATIO

side 1

(5/30) × 150cm = 25cm

base

(12/30) × 150cm = 60cm

side 2

(13/30) × 150cm = 65cm

My triangle will have one side 25cm, side one 65cm and the base 60cm then you are going to use pythagoras theorem to find out the height of the triangle using the formula

a^2 + b^2 = c^2

the height will be 'a', 25cm will be 'b' then inorder to create a right angle we will divide the baseinto two that is to say (60cm / 2= 30cm) therefore the 30cm will be 'c'

In conclusion

HEIGHT

= a^2 + (25cm)^2 = (30cm)^2

= a^2 + (25cm × 25cm) = (30cm × 30cm)

= a^2 + 625cm^2 = 900cm^2

= a^2 = 275cm^2

= √a^2 = √275cm^2

= a = 16.5cm

therefore the height is 16.5cm

AREA

Height = 16.5cm

Total base = 60cm

Area = 1/2 × basearea × height

= 1/2 × 60cm × 16.5cm

= 495cm^2

This triangle is not possible.

A triangular field has sides of lengths 29, 35, and 51 miles. The largest angle of the triangle can be calculated using the Law of Cosines, which is a generalization of the Pythagorean Theorem.

Law of Cosines:The Law of Cosines is a mathematical tool used to calculate the length of a side or the size of an angle of a non-right triangle. It states that the square of any side of a triangle is equal to the sum of the squares of the other two sides,

minus twice the product of these two sides and the cosine of the angle between them.Mathematically, the law of cosines is expressed as: `a^2 = b^2 + c^2 - 2bc cos A`,

where `a` is the unknown side, and `b` and `c` are the known sides of the triangle, and `A` is the angle between sides `b` and `c`.We can use the Law of Cosines to find the largest angle in the triangle as follows:Let `A` be the largest angle,

which is opposite the longest side `51 mi`.Using the Law of Cosines, we have:`

a^2 = b^2 + c^2 - 2bc cos A``51^2 = 29^2 + 35^2 - 2(29)(35) cos A``2601 = 1681 + 1225 - 2030 cos A``2030 cos A = 1225 + 920``cos A = (1225 + 920)/2030``cos A = 2145/2030``cos A ≈ 1.057139``A = cos^-1 (1.057139)`

Since the cosine function is only defined for values between -1 and 1, `1.057139` is not a valid value for `cos A`.

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The needed number of days at 10 degrees is given as follows:

11 days.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:

m = -2/5

m = -0.4.

Hence the time needed for a temperature of 10 degrees is given as follows:

9 + 2 = 11 days.

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The resulting value of the division of x²+x-4 by (x+3),

Quotient = x - 2

Remainder = 2

Division:

The process of division means the process of breaking a number up into equal parts, and finding out how many equal parts can be made.

Given,

Here we have the expression x²+x-4.

Now, we need to divide by the expression (x + 3).

Here we have to use the long division method in order to solve it.

The following steps are followed to solve this:

1. Divide the first term of the dividend by the first term of the divisor

2. Write down the calculated result x in the upper part of the table.

3. Multiply it by the divisor

4. Subtract this result from the dividend

This steps is repeated until no further division.

Thus process will be showed on the attached figure.

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Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

y = - 0

The line is horizontal.

Answer:

1  i think i looked it up on mathaway

Step-by-step explanation:

1

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Step-by-step explanation:

As the cards are being drawn with replacement, the events are independent. Thus we can find the probability by multiplying the probability of individual events.

There are 4 queens in a pack of 52 cards. So, probability of drawing a queen= 4/52=1/13

There are 26 red cards. So, probability of drawing a red card= 26/52=12

Required probability= 1/13×1/2=1/26

Answer:

1/26

Step-by-step explanation:

For probability, the numerator is the number of options for the specified property (red card/drawing a queen) and the denominator is the total number of options (in this case 52).

There are 26 red cards in a deck, the the probability of choosing a red card is \(\frac{26}{52}\) or \(\frac{1}{2}\).

There are 4 queens in a deck, so the probability of choosing a queen is \(\frac{4}{52}\) or \(\frac{1}{13}\).

To find the probability of getting these both, multiply the results, giving \(\frac{1}{26}\).

Answer: A,B,E,F

Step-by-step explanation:

Answer:

The answer is A, B, E, F

Step-by-step explanation:

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

9514 1404 393

Answer:

  g(x) = f(x -1)

  h(x) = f(x) +4

Step-by-step explanation:

We notice that the output values correspond to the output values of f(x), but the input to f(x) is 1 less than the corresponding input to g(x). For some given value of x, ...

  g(x) = f(x -1)

__

The input values correspond to those for f(x), but the output values are all 4 more than for f(x).

 h(x) = f(x) +4

Answer:

$42.00

Step-by-step explanation:

We can represent the given information as a ratio:

% of original price : price

                          5% : $2.00

Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.

5%      :  $2.00

↓ × 20   ↓ × 20

100%  :  $40.00

Now that we know the original price, we can add $2.00 to get the new price.

$40.00 + $2.00 = $42.00

Answer:

14 minutes

Step-by-step explanation:

For every two minutes the temperature increases by 15 c. since 8 equals 55, 10 is 70, 12 is 85, and 14 is 100.

Answer:

14

Step-by-step explanation:

Answer:

  m∠X ≈ 29°

Step-by-step explanation:

The hypotenuse and the side adjacent to angle X are given. The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(X) = XW/XV = 7/8

The inverse cosine function is used to find the angle.

  X = arccos(7/8) ≈ 29°

Answer:

66.69

Step-by-step explanation:

You start off with -3.9 x -5.7 which gives you a positive, and that positive is 22.23, then you multiply that number by 3, and you get 66.69.

(y-18)(y+x)

u have been provided with:

so for solving it u have to make a equation first so choose wisely now make the equation but how?

first of all take

(y-18)(y+x)

this will be ur equation as both the variables x and y given to u r positive(+) so this can be one equation.

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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Answer:

No is something worng

Step-by-step explanation:

y= 9/8 * x - 1

Answer:

C

Step-by-step explanation:

Tyler, because his money is increasing exponentially.

I finished taking the test and got it right :)

The person who will have more money by year 20 is given by: Option C: Tyler, because his money is increasing exponentially

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

For example, \(y = a.b^x\) , where a is a and b are constants is an exponential function.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

\(I = \dfrac{P \times R \times T}{100}\)

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

\(CI = P(1 +\dfrac{R}{100})^T - P\)

The final amount becomes:

\(A = CI + P\\A = P(1 +\dfrac{R}{100})^T\)

Usually these two rates are used on money. The compound interest is exponential as it has power T as a variable, but for simple interest, there is no variable exponent.

Both are positive, and growth of exponential function is always going to surpass the growth of linear function (can be proven by derivatives).

Since we are not given the function's equation, we cannot correctly calculate the value just from graph, but as in 14 years, the blue line is already close to red line so it will likely cross it after 6 more years (thus total 20 years) because of good growth.

Thus, the person who will have more money by year 20 is given by: Option C: Tyler, because his money is increasing exponentially

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Answer:

  17 years

Step-by-step explanation:

The formula for the value of an account earning compound interest can be used to find the number of years. That formula is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r compounded n times per year for t years.

__

Solving for t, we find ...

  A/P = (1 +r/n)^(nt) . . . . . . divide by P

  log(A/P) = nt·log(1 +r/n) . . . . take logarithms

  t = log(A/P)/(n·log(1 +r/n)) . . . . . divide by the coefficient of t

For the given values, the time required is ...

  t = log(1740/670)/(365·log(1 +0.055/365)) ≈ 17.353

It would take about 17 years for the account value to reach $1740.

_____

Additional comment

The time-value-of-money (TVM) apps of your calculator or spreadsheet can be used to find the time period of interest. Here, setting P/Y = 1 gives N in years.

Using proportions, it is found that the equivalent cost in U.S. dollars per gallon would be of 5.11.

In September 2016, the cost of gasoline in Berlin was around 1.21 euros per liter. Hence, per gallon, that is, per 3.785 liters, we use a rule of three to find the cost.

1.21 euros - 1 liter

x euros - 3.785 liters

Applying cross multiplication:

\(x = 1.21(3.785) = 4.57985\)

Cost of 4.57986 euros per gallon. Since 1 U.S dollar is equivalent to approximately 0.896 euros, we have that:

1 dollar - 0.896 euros

x dollars - 4.57986 euros

Applying cross multiplication again:

\(0.896x = 4.57986\)

\(x = \frac{4.57986}{0.896}\)

\(x = 5.11\)

The equivalent cost in U.S. dollars per gallon would be of 5.11.

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\(n=7t\).

Linear equations are those that contain constants of proportionality, and they have the following form:

\(y=mx+b\); where "m" represents the constant of proportionality and "b" is the y-intercept.

We are being asked to make a function whose n value (number of trees) varies directly with time (t). This means that the independent variable is time, because it determines the number of trees. Hence, we know that "t" is going to be our "x" value and "n" is going to be our "y". Finally, we know that the constant of proportionality "m" is 7.

Edit the previously presented model and adapt it to this case:

\(y=mx+b\\ \\n=7t\)

Note: The value of the y-intercept was removed since the problem didn't give a value for it.

\(n=7t\); where "n" is the number of trees that the average American uses in paper products and "t" is time in years.

Complete Question:

Leslie placed this ad in Collector Car Monthly.

1957 Chevrolet Nomad station wagon. Tropical

Turquoise, 6 cyl. auto, PS, PW, AM/FM, repainted,

rebuilt transmission, restored two-tone interior.

Mint! Moving, sacrifice, $52,900. 555-4231

(a) If the publication charges $48 for the first three lines and $5 for each extra  line, how much will this ad cost Leslie?  

(b) b. Ruth buys the car for 8% less than the advertised price. How much does she pay?

(c) Ruth must pay her state 6% sales tax on the sale. How much must she pay in sales tax?

Answer:

\(Total = \$53\)

\(Ruth = \$48668\)

\(Sales\ Tax = \$2920.08\)

Step-by-step explanation:

Given

\(Ad = 4\ lines\)

\(Charges: \$48\) --- First 3 lines

\(Additional: \$5\) -- Extra lines

Solving (a) : Determine the total charge

The ad has 4 lines. This means that 3 of the 4 lines will be charged at $48 (in total) while the extra line will be charged at $5 per line

So, the total charge is calculated as:

\(Total = 3\ lines + 1\ line\)

\(Total = \$48 + 1 * \$5\)

\(Total = \$48 + \$5\)

\(Total = \$53\)

Solving (b): How much does Ruth pay?

From the ads, the price of the car is:

\(Price = \$52,900\)

And Ruth pays 8% less.

This means that she pays 92% (i.e. 100% - 8% = 92%)

So, the calculation is:

\(Ruth = 92\% * Price\)

\(Ruth = 92\% * \$52900\)

\(Ruth = \$48668\)

Solving (c): The sales tax

\(Sales\ Tax = Sales\ Tax\% * Amount\ Paid\)

\(Sales\ Tax = 6\% * \$48668\)

\(Sales\ Tax = \$2920.08\)

The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

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(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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