Evaluate the expression

Answer:

x = 6

Step-by-step explanation:

cos 60° = JK/JL

cos 60° = 7 / (3x-4)

(1/2) = 7 / (3x-4)

(1/2) = 7 / (3x-4)

(3x-4) = (2)(7)

3x-4 = 14

3x = 14+4

3x = 18

x = 18/3

x = 6

Final answer:

To convert the tree's circumference from inches to centimeters, multiply 17 inches by the conversion factor of 2.54 cm per inch, resulting in 43.18 cm, which is not an exact match to the provided options but the closest option is 42.5 cm.

Explanation:

To convert James' measurement of the tree's circumference from inches to centimeters, we use the conversion factor that 1 inch equals 2.54 centimeters. Therefore, if the tree's circumference is 17 inches, we multiply 17 by 2.54 to get the circumference in centimeters.

The calculation is as follows:

Multiply the circumference in inches (17 inches) by the conversion factor (2.54 cm per inch).

The result is 17 inches × 2.54 cm/inch = 43.18 cm.

Therefore, the tree's circumference in centimeters is 43.18 cm, which rounds down to 43 cm when measuring to the nearest whole number, none of the options exactly match but option A is the closest. So, we must choose the closest option, which is A. 42.5 cm.

Answer:

Step-by-step explanation:

Let the no of cars be x and no of buses be y.

x + y = 60 -> y = 60 - x

6x + 30y = 600

with the available equations let us calculate the values of x and y.

6x + 30 * (60-x) = 600

6x + 1800 - 30x = 600

24x = 1200

x cars = 50

y buses = 10

maximum profit = 50 * 2.5 + 10 * 7.5 = $200

a) The objective function to maximize profit is: 2.5C + 7.5B using constraints 6C + 30B ≤ 600 and C + B ≤ 60. b) The parking lot should accept 50 cars and 10 buses to maximize profit. The maximum profit will be $200.

We need to set up a linear programming model to maximize profit from parking cars and buses.

A. Model Formulation:

Let C represent the number of cars and B represent the number of buses.

Objective Function: Maximize Profit = 2.5C + 7.5B

Constraints:

B. Solution:

First, we convert the inequalities to equations and solve:

We solve these equations simultaneously:

1. C + 5B = 100 (Equation 1)

2. C + B = 60 (Equation 2)

Subtract Equation 2 from Equation 1:

(C + 5B) - (C + B) = 100 - 60

⟶ 4B = 40 ⟶ B = 10

From Equation 2, we get:

C + 10 = 60 ⟶ C = 50

Maximum Profit Calculation:

Substituting C = 50 and B = 10 into the objective function:

Profit = 2.5(50) + 7.5(10) = 125 + 75 = 200

Therefore, to maximize profit, the attendant should accept 50 cars and 10 buses.

Maximum profit is $200.

Complete question:

The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50. How many of each should be accepted to maximize Profit?

a. Set up for the solution of this Linear Programming (LP) problem.

b. Using part (a), how many of each should be accepted to maximize Profit? What is the maximum profit?

Answer:

3 ft by 4/3 feet.

Step-by-step explanation:

We have been given that a card is 9 inches by 4 inches. A printing shop will enlarge it so that the longer side is any lengths up to 3 ft. We are asked to find the dimensions of biggest enlargement.

We will use proportions to solve our given problem.

[tex]\frac{\text{Card width}}{\text{Card length}}=\frac{\text{Enlarged width}}{\text{Enlarged length}}[/tex]

Upon substituting our given values, we will get:

[tex]\frac{\text{4 inches}}{9 \text{ inches}}=\frac{\text{Enlarged width}}{\text{3 ft}}[/tex]

[tex]\frac{4}{9}=\frac{\text{Enlarged width}}{\text{3 ft}}[/tex]

[tex]\frac{4}{9}\times \text{3 ft}=\frac{\text{Enlarged width}}{\text{3 ft}}\times \text{3 ft}[/tex]

[tex]\frac{4}{3}\times \text{ft}=\text{Enlarged width}[/tex]

Therefore, the dimensions of the biggest enlargement  would be 3 ft by 4/3 feet.

Answer:

Step-by-step explanation:

If the columns span R^6, this says that every b in R^6 is in the span of the columns, which is another way of saying that any b is a linear combination of the columns. Then the equation is consistent for some b or all b in R^6.

If an augmented matrix can be transformed by elementary row operations into reduced echelon form, then the equation Ax = b is consistent.

Any matrix can be transformed by elementary row operations into reduced echelon form, but not every matrix equation Ax = b is consistent

For example, after echelon reduction we have

1 6. 7. 8. 8.

0 1. 5. 4. 9

0. 0. 1. 3. 6

0. 0. 0. 1. 6.

0. 0. 0. 0. 1

0. 0. 0. 0. 0

In this case, the matrix doesn't have a solution, then the matrix is inconsistent

But if the matrix echelon reduction gives

1 6. 7. 8. 8.

0 1. 5. 4. 9

0. 0. 1. 3. 6

0. 0. 0. 1. 6.

0. 0. 0. 0. 1

0. 0. 0. 0. 1

Then, the system have a solution but not unique, the system have a solution for some b in R^6.

Then, the solution is II and III

So the correct option is D.

Answer:

Final Answer -$50

Step-by-step explanation:

The account balance of Clare can be calculated using negative value. To solve the given problem we have to assume that her bank account has a negative value

Now Clare's account balance is $0.

Given:

Clare has $150 in her bank account.

She buys a bike for $200.

Determine the amount balance in Clare account.

Since the price of the bike is more than the account balance of Clare, we can assume that her bank account has a negative value, although since the bank account cannot go past 0, except for loans and debts, and it is not stated whether Clare has taken a loan.

Therefore we can state that the account balance of,

$0=$100 - $150= -$50

Thus, Now Clare's account balance is $0

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The instantaneous velocity of the baseball 3 seconds after it is hit is [tex]\( 24 \)[/tex] feet per second.

To find the instantaneous velocity of the baseball 1 second and 3 seconds after it is hit, we need to differentiate the height function [tex]\( s(t) \)[/tex] with respect to time [tex]\( t \)[/tex] to get the velocity function [tex]\( v(t) \).[/tex]

The height function is given by:

[tex]\[ s(t) = -16t^2 + 88t + 4 \][/tex]

1. Find the Velocity Function:

[tex]\[ v(t) = s'(t) \][/tex]

Differentiate [tex]\( s(t) \)[/tex] with respect to [tex]\( t \)[/tex]:

[tex]\[ v(t) = -32t + 88 \][/tex]

2. Evaluate the Instantaneous Velocity at [tex]\( t = 1 \)[/tex] second:

[tex]\[ v(1) = -32(1) + 88 = 56 \][/tex]

The instantaneous velocity of the baseball 1 second after it is hit is [tex]\( 56 \)[/tex] feet per second.

3. Evaluate the Instantaneous Velocity at [tex]\( t = 3 \)[/tex] seconds:

[tex]\[ v(3) = -32(3) + 88 = 24 \][/tex]

The answer is [tex]\( 24 \)[/tex] feet per second.

So, after differentiating the height function to get the velocity function, we substituted the given values of time [tex](\( t = 1 \)[/tex] and [tex]\( t = 3 \))[/tex] into the velocity function to find the corresponding instantaneous velocities.

The instantaneous velocity provides information about the speed and direction of the baseball at a specific moment in time. In this case, 1 second after being hit, the baseball is moving upward with an instantaneous velocity of [tex]\( 56 \)[/tex] feet per second, and 3 seconds after being hit, it is still moving upward but with a reduced instantaneous velocity of[tex]\( 24 \)[/tex] feet per second.

The complete question is given here :

A foul tip of a baseball is hit straight upward from a height of 4 feet with an initial velocity of 88 feet per second. The function [tex]s(t) = -16t^2 + 88t + 4[/tex] describes the ball's height above the ground, s(t), in feet, t seconds after it was hit. What is the instantaneous velocity of the ball 1 second after it is hit? 3 seconds after it is hit?

Answer:

Alex has 110 shells

Benji has 132 shells

Carmen has 66 shells

Step-by-step explanation:

In this question, we are tasked with calculating the number of shells each of the friends have.

We proceed as follows;

Since Alex is the linking point between the other two friends, we say that let the number of shells Alex has be A

Now, Benji has 20% more shells

This mathematically means that the number of shells owned by Benji = (20% × A) + A = 0.2A + A =  1.2A

Carmen has 40% fewer shells than Alex;

Mathematically, this means that the number of shells owned by Carmen is A - (40% × A) = A - 0.4A = 0.6A

To find A, we simply add all together and equate to 308

Mathematically, we have;

A + 1.2A + 0.6A = 308

2.8A = 308

Divide both sides by 2.8

A = 308/2.8

A = 110

This means Alex has 110 shells

Benji has 1.2A = 1.2 × 110 = 132 shells

Carmen has 0.6A = 0.6 × 110 = 66 shells

Answer:

  84.5 cubic meters

Step-by-step explanation:

You want the volume of a pyramid with a base area of 42.25 m² and a height of 6 m.

The formula for the volume of a pyramid is ...

  V = 1/3Bh

Using the given values, we find the volume to be ...

  V = 1/3(42.25 m²)(6 m) = 84.5 m³

The volume of the pyramid is 84.5 cubic meters.

Answer:

2/3

Step-by-step explanation:

To know the fraction of men over women, we just need to divide the total number of men in the academy by the total number of women in the academy. So, we have that:

Fraction = men / women = 24 / 36 = 2/3

So the fraction we want to know is 2/3, that is, for every 2 men, there are 3 women in the academy.

Answer

y = 2(x - 8)(x + 2)

Step-by-step explanation:

A(x - 8)(x + 2)

A × -8 × 2 = -32

-16A = -32

A = 2

y = 2(x - 8)(x + 2)

Answer:

11

Step-by-step explanation:

8.7A+10=105.7

8.7A=95.7

A=11

Answer: (A) The longer side in the rectangle is 45 units.

(B) The line LP measures 14 cm.

Step-by-step explanation: In the rectangle, two sides are given as 2x and 3x + 3, respectively. The perimeter is also given as 146 units. The formula to determine the perimeter is

Perimeter = 2(L + W)

We can now substitute for the values

146 = 2(2x + 3x + 3)

146 = 2(5x + 3)

146 = 10x + 6

Subtract 6 from both sides of the equation

140 = 10x

Divide both sides of the equation by 10

14 = x

With the value of x now known as 14, the sides of the rectangle are,

L = 2x

L = 2 x 14

L = 28

And the other side is

W = 3x + 3

W = 3(14) + 3

W = 42 + 3

W = 45

Therefore the longer side is 45 units.

In question B;

The rhombus has all sides congruent as one of its properties. This simply implies that the diagonal from point M to point O, is the same length as the diagonal from point L to point N. Hence, at point P, where both diagonals intersect, both diagonals are divided into two equal lengths each. If line LN is 28 cm, then line LP which is half of LN shall be 28 divided by 2, and that gives us 14 cm.

Answer:

4 5/6 (the last option)

Step-by-step explanation:

to ensure and find out you can dive 5/6 then add 4 and you get 4.833333333333

The median is [tex]\(55\)[/tex], Q1 is approximately [tex]\(19.5\)[/tex], Q3 is [tex]\(79\)[/tex], and the interquartile range is [tex]\(59.5\).[/tex]

To find the median, first quartile (Q1), third quartile (Q3), and interquartile range (IQR) for the given set of numbers, you first need to arrange them in ascending order:

[tex]\[ 14, 25, 28, 38, 55, 66, 92, 94, 97 \][/tex]

Now, let's find each of the required values:

1. **Median (Q2)**: The median is the middle value of the dataset when arranged in ascending order. Since there are 9 numbers, the median will be the value at the [tex]\(\frac{9+1}{2} = 5\)[/tex]-th position, which is the 5th number in the sorted list: [tex]\(55\)[/tex].

2. **First Quartile (Q1)**: Q1 is the median of the lower half of the dataset. Since there are an odd number of data points in the lower half (4 points), Q1 will be the median of the first four numbers: [tex]\( \frac{14 + 25}{2} = 19.5 \).[/tex]

3. **Third Quartile (Q3)**: Q3 is the median of the upper half of the dataset. Similarly, since there are an odd number of data points in the upper half (also 4 points), Q3 will be the median of the last four numbers: [tex]\( \frac{66 + 92}{2} = 79 \).[/tex]

4. **Interquartile Range (IQR)**: IQR is the difference between Q3 and Q1. So, [tex]\( IQR = Q3 - Q1 = 79 - 19.5 = 59.5 \).[/tex]

So, the median is [tex]\(55\)[/tex], Q1 is approximately [tex]\(19.5\)[/tex], Q3 is [tex]\(79\)[/tex], and the interquartile range is [tex]\(59.5\).[/tex]

Answer:

67,500 residents

Step-by-step explanation:

The population density is defined as the average number of people living per square unit area.

-Given the density is 225res/sq mile and the area is 300 sq mile, the area's population is:

[tex]\rho=\frac{Population}{Area}\\\\Population=Area \times \rho\\\\=300 \ mi^2\times 225\ res/mi^2\\\\=67500\ residents[/tex]

Hence, there are 67,500 residents in Flint county.

To calculate the population of Flint County, the population density (225 residents/mile2) is multiplied by its area (300 mile2), resulting in a population of 67,500 residents.

To find the population of Flint County, we need to multiply the population density by the area of the county. The population density is given as 225 residents per square mile, and the area of Flint County is 300 square miles. By multiplying these two values together, we can determine the total population.

Population of Flint County = Population Density × Area = 225 residents/mile2 × 300 mile2

Population of Flint County = 225 × 300 = 67,500 residents

Therefore, the population of Flint County is 67,500 residents.

Answer:

17.5  yds =r

Step-by-step explanation:

Circumference is given by

C = 2*pi*r

35pi = 2 *pi*r

Divide each side by 2pi

35pi/2pi = 2*pi*r/2pi

17.5 =r

Answer:

24 inches

Step-by-step explanation:

The area of the square is 36 in2. The area of square can be represented as side x side or side squared. So, the sides must be 6 inches in length since 6x6 is 36. If one side is 6, 4 sides are 24.

Final answer:

The percentage increase in the perimeter of the rectangle is 6%.

Explanation:

To find the percentage increase in the perimeter of the rectangle, we need to calculate the new perimeter and compare it to the original perimeter.

The original length is 20 and the width is 30. The original perimeter is 2(20+30) = 100.

When the length is increased by 10%, it becomes 20 + 10% of 20 = 20 + 2 = 22. The width is increased by 5%, so it becomes 30 + 5% of 30 = 30 + 1.5 = 31.5.

The new perimeter is 2(22+31.5) = 106. The percentage increase in the perimeter is (106-100)/100 * 100 = 6%.

Answer:

8 × 7

Step-by-step explanation:

(4 × 2) × 7

We can multiply what is inside the parentheses

(8) × 7

Answer:

8*7

Step-by-step explanation:

Multiply what is inside the parentheses first, (PEMDAS)

(4*2)*7

8*7

Hope this helps! :)

Answer:

10 Yards

Step-by-step explanation:

In every yard there is 3 feet

If you have 30 feet you have ____ yards

Divide 30 by 3 to get 10 yards!

Hope this Helps!

Answer: The modes of that set of data are both 8 and 2

Step-by-step explanation: The mode is the number that appears most often in a data set and 8 and 2 are the only number that appear more than once in that set of data

Answer:

8 and 2

Step-by-step explanation:

I got this for a quiz and the answer was 8 and 2.

Answer:

The sum of negative one - sixth and three times x minus 2 times y.

The required translation of the given expression is the sum of negative one-sixth and three times x minus 2 times y.  Option C is correct.

Given that,
To choose the translation that best fits the expression: − 1/6 + 3x − 2y

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression.
=− 1/6 + 3x − 2y
we can write such as,
-1/6 = negative one-sixth,
3x = three times x
2y = two times y
− 1/6 + 3x − 2y =  the sum of negative one-sixth and three times x minus 2 times y

Thus, the required translation of the given expression is the sum of negative one-sixth and three times x minus 2 times y.  Option C is correct.

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Answer:

The confidence level of the study is 99.9%

The confidence level is 99.9% of the margin error is 8%

Step-by-step explanation:

Explanation:-

Candy has observed 250 sports cars

The sample size 'n' = 250

Sample proportion 'p' = 15% = 0.15

The margin of error = 8% = 0.08

The margin of error  is determined by   = [tex]\frac{z_{\alpha }\sqrt{p(1-p)} }{\sqrt{n} }[/tex]

                                                 [tex]0.08 X \sqrt{250} = z_{\alpha } \sqrt{0.15 (1-0.15)}[/tex]

                                                    [tex]\frac{ 0.08 X \sqrt{250}}{ \sqrt{0.15 (1-0.15)}} = z_{\alpha }[/tex]

                                                    [tex]z_{\alpha }= \frac{ 0.08 X \sqrt{250}}{ \sqrt{0.15 (1-0.15)}} = \frac{1.2649}{0.35707}[/tex]

                                                    [tex]z_{\alpha } = 3.5431[/tex]

Conclusion:-

The z- score of 99.9% level of significance = 3.54 for two tailed test

Hence the confidence level is 99.9% of the margin error is 8%.

Answer: the first one

Step-by-step explanation:

Answer:

The first one graph

Step-by-step explanation:

I think

Answer: I believe the answer is 9 days.

Step-by-step explanation: 16 divided by 1.75 (1 and three-fourths) is equal to 9.143, which is only enough to feed him 9 full days.

Answer:

The answer to your question is 9 days.

Step-by-step explanation:

Data

Food needed = 1 3/4 cups

Total food = 16 cups

Number of days = ?

Process

1.- Convert the mixed fraction into an improper fraction

              1 3/4 = (4 + 3)/4 = 7/4

2.- Divide the total food by the food needed

              16/1 ÷ 7/4 = 64/7

-Simplify                     9        Quotient

                          7   64

                                 1          Remainder

3.- Mark can feed his dog 9 days and there will be 1/7 of the bag left.

Answer:

Here we have the table for the 8 students that said yes.

a) Out of the 8 students, 5 purchased their favorite food more than four times a month.

The proportion will be p = 5/8, and this can not be simplified anymore because 5 is a prime number and 5 is not a factor of 8.

b) The mean time will be equal to the amount of each of the 8 purchased their favourite food divided by the total sample (8)

This is:

m = (6 + 4 + 3 + 8 +6 + 9 + 4 + 7)/8 = 5.875

c) Out of a sample of 20, 8 buy lunch regularly, this is; p1 = 8/20

The amount of students that regularly buy food will be:

p1*1000 = (8/20)*1000 = 400

And of those 400, 5/8 buy their favourite lunch more than 4 times per month:

(5/8)*400 = 250

d: The mean number of times that a student regularly buys salad.

We have 3 students that regularly buy salad (so we only do the math with those 3)

The mean is (8 + 6 + 7)/3 = 7

So for the students that regularly buy salad, the mean of times that the buy salad in a month is 7 times.

Answer: Yes and No

When the longest side is not longer than the sum of the two shorter

Step-by-step explanation:

Let first convert mile to kilometre

1 mile = 1.609km

AB = 0.5mile = 0.8045 km

BC = 1/3 miles = 0.53633 km

DE=0.205 kilometer

EF=0.01 kilometer

AC=1/4 mile = 0.40225

DF=0.02 kilometer

When the longest side is not longer than the sum of the two shorter sides , then a triangle can be made

Let's first consider AB, BC and AC Each set of line segments AB, BC and AC can form a triangle

Also DE, EF and DF

Each set of line segments DE, EF and DF can't form a triangle because the longest side is greater than the sum of the two shorter sides.

Answer: 260 downloads of the standard version were there.

Step-by-step explanation:

Let x represent the number of downloads of the standard version.

Let y represent the number of downloads of the high-quality version.

Yesterday, the high-quality version downloaded four times as often as the standard version. It means that

y = 4x

The size of the standard version is 2.9 megabytes (MB). the size of the high-quality version is 4.6 MB. the total size downloaded for the two versions was 5538 MB. It means that

2.9x + 4.6y = 5538- - - - - - - - - - - -1

Substituting y = 4x into equation 1, it becomes

2.9x + 4.6 × 4x = 5538

2.9x + 18.4x = 5538

21.3x = 5538

x = 5538/21.3

x = 260

Final answer:

To determine the number of standard version song downloads, we set up and solved a system of linear equations. We found that the standard version was downloaded 260 times.

Explanation:

The student's question involves solving a system of linear equations to find out how many times the standard version of a song was downloaded. We have two versions of a song: a standard version (2.9 MB) and a high-quality version (4.6 MB). We are told that the high-quality version was downloaded four times as often as the standard version and that the total size downloaded was 5538 MB. To solve this, we set up two equations:

Let x represent the number of standard version downloads, and 4x represent the number of high-quality version downloads.

The total size equation would be 2.9x + 4.6(4x) = 5538

Combining like terms and solving for x, we have:

2.9x + 18.4x = 5538

21.3x = 5538

x = 5538 / 21.3

x = 260

So, there were 260 downloads of the standard version of the song.