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What is the value of k?

A. −5
B. −3
C. 3
D. 5

Option A: [tex]28\sqrt{3}[/tex] is the expression equivalent to the expression [tex]4\sqrt{147}[/tex]

Explanation:

The expression is [tex]4\sqrt{147}[/tex]

To find the equivalent expression, let us solve the expression [tex]4\sqrt{147}[/tex]

The square root of 147 can be written as,

[tex]\sqrt{147} =\sqrt{49*3}[/tex]

Since, we know that 49 is a perfect square, we can write the above expression as,

[tex]\sqrt{147} =7\sqrt{3}[/tex]

Multiplying this value with the expression [tex]4\sqrt{147}[/tex], we have,

[tex]4\sqrt{147}=4(7\sqrt{3} )=28\sqrt{3}[/tex]

Thus, the expression which is equivalent to the expression [tex]4\sqrt{147}[/tex] is [tex]28\sqrt{3}[/tex]

Hence, Option A is the correct answer.

Answer:

Segment addition postulate justify the statement if D is between A and B then Ad plus DB equals Ab

Step-by-step explanation:

This postulate states that if two points A and B are given and third point D lies on line segment AB only if distance between the points satisfy the equations AD+DB=AB.

Answer:

Segment Addition Postulate

Step-by-step explanation:

The whole line segment would be AB. The midpoint of the line segment would be D. If we add AD (the first portion of the line segment), and DB (the second portion of the line segment), then we get AB (A-D-B)

Representation:

              (AD)                    (DB)

|--------------------------|---------------------------|

A                            D                             B

|------------------------------------------------------|

                   (line segment AB)

Answer:

64800 fluid ounces of juice.

Step-by-step explanation:

Given:

A factory can fill 225 bottles of orange juice each hour.

Each bottle of juice contains 24 fluid ounces of juice.

Question asked:

How many fluid ounces of juice are filled in each 12 hours shift ?

Solution:

By applying unitary method:

A factory can fill number of bottles in 1 hour =  225 (given)

A factory can fill number of bottles in 12 hours = [tex]12\times 225 = 2700\\[/tex]

Each bottle contains = 24 fluid ounces of juice (given)

2700 bottles contain = [tex]24 \times2700 = 64800[/tex] fluid ounces of juice.

Thus, 64800 fluid ounces of juice are filled in each 12 hours shift.

The least number of tabke that will seat all the bus members is 17.

To find the least number of tables needed to seat all 130 people, you can divide the total number of people by the number of people each table can seat (8).

Number of tables = Total number of people / Number of people per table

Number of tables = 130 / 8

Number of tables = 16 tables with 2 people left over

To seat all 130 people, you would need at least 17 tables.

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To find the least number of tables needed to seat all 130 people, you divide 130 by 8, and then round up to the nearest whole number. This gives you a total of 17 tables.

The subject of this question is a Mathematics problem, specifically a division problem involving the concept of rounding up. You are asked to determine the least number of tables needed to seat all 130 people, given that each table can seat 8 people.

In order to solve this problem, you need to divide the total number of people by the number of people that can be seated at each table (130 ÷ 8 = 16.25). Because you can't have a fraction of a table, you round this value up to the nearest whole number. Thus, you will need 17 tables to seat all 130 people.

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Answer:

his intrest rate is 7%

Step-by-step explanation:

294/1400=0.21

0.21/3 years = 0.07

0.07=7%

1400*0.07=98

98*3 years = 294

The rate of simple interest the account earned is 7%.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P = 1400, t = 3 and SI = 294.

∴ 294 = (1400×3×r)/100.

29400 = 4200r.

42r = 294.

r = 7%

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Answer:

m=63

Step-by-step explanation:

6=m/7-3

m/7=6+3

m/7=9

m=9*7

m=63

Yo sup??

we know that area of a triangle is given by the formula

A=1/2*b*h

where

b=lenght of base

h=height of the triangle

in the given figure

h=x

b=5x/6

plugging in the values, we get

A=1/2*x*5x/6

A=5x²/12

Please name the triangle as ABC and you will get full credit.

Hope this helps

Step-by-step explanation:

Let the width be x feet.

Therefore, length = 2x - 10

Perimeter of rectangle = 52

[tex]2(2x - 10 + x) = 52 \\ 2(3x - 10) = 52 \\ \therefore \: 3x - 10 = \frac{52}{2} \\ \therefore \: 3x - 10 = 26\\ \therefore \: 3x = 26 + 10\\ \therefore \: 3x = 36 \\ \therefore \: x = \frac{36}{3} \\ \therefore \: x = 12 \\ \purple{ \boxed{\therefore \: width \: of \: rectangle = 12 \: feet }}[/tex]

Answer:

awnser b

Step-by-step explanation:

Answer:

544 units^2

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

202 times with a remainder of 5 but if you need an exact number that i would go with 203 because if you round it up

Step-by-step explanation:

Volume of the hexagonal prism = 1732.7772 ft³

Solution:

Height of the prism (H) = 15.4 ft

Side of the hexagon base (b) = 6.58 ft

Height from center to the side length (h) = 5.7 ft.

Let us first find the area of the base.

Area of the base (B) =  [tex]6\times\frac{1}{2}\ bh[/tex]

                                 [tex]$=6\times\frac{1}{2}\times 6.58 \times 5.7[/tex]

Area of the base (B) = 112.518 ft²

To find the volume of the hexagonal prism:

Volume of the hexagonal prism = Area of the base × Height

                                                     = 112.518 × 15.4

                                                     = 1732.7772 ft³

The volume of the hexagonal prism is about 1732.7772 ft³.

Answer:

Rajeev walked at 3.5 miles per hour of speed

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Distance Rajeev walked = 7/8 of a mile = 0.875 miles

Time of walking = 1/4 of an hour = 15 minutes

2. What was the speed in miles per hour?

Let's use the Direct Rule of Three for answering this question, as follows:

Distance in miles     Time in minutes

           0.875                      15

              x                           60

*************************************************

15x = 0.875 * 60

15x = 52.5

x = 52.5/15

x = 3.5

Rajeev walked at 3.5 miles per hour of speed

Please, find attached the picture with the whole question.

Answer:

              [tex]9.8gallons\leq x\leq 10.2gallons\\ \\ \ [9.8gallons,10.2gallons][/tex]

Both are different forms to represent the same: the amount of gas is between 9.8 gallons and 10.2 gallons, including the borders.

Explanation:

1. Relation between the number of gallons of gas pumped and the total amount paid:

[tex]Number\text{ }of\text{ }gallons=amount\text{ }paid(\$)/price(\$/gallon)[/tex]

2. Conversion

The amount paid is said to be $ 25 ± $0.50

To transform that into number of gallons, divide by the price of the regular gas: $2.50/gallon

[tex]Number\text{ }of\text{ }gallons=\$25/(\$2.50/gallon)\pm$0.50/(\$2.50/gallon)[/tex]

[tex]Number\text{ }of\text{ }gallons=10gallons\pm0.2gallon[/tex]

3. Absolute value equation (inequality)

              [tex]|x-10gallons|=0.2gallons[/tex]

Solution:

[tex]-0.2\leq x-10\leq 0.2[/tex]

[tex]-0.2+10\leq x\leq 0.2+10[/tex]

[tex]9.8\leq x\leq 10.2[/tex]

Hence, the solution is:

           [tex]9.8gallons\leq x\leq 10.2gallons\\ \\ \ [9.8gallons,10.2gallons][/tex]

The absolute value equation that represents how many gallons of gas Hugo will pump, assuming a cost of $1.60 per gallon, is |1.6g - 25| ≤ 0.50. Solving this, we find Hugo will pump between approximately 15.31 and 15.94 gallons of gas based on his budget of $25 plus or minus $0.50.

Given that Hugo is pumping regular gas into his truck and the total amount he is willing to spend varies between $24.50 and $25.50, we can create an absolute value equation to model this. Assuming the cost per gallon is $1.60, we want to find the number of gallons, represented by 'g', such that the absolute difference between the cost of g gallons and $25 is not more than $0.50.

The absolute value equation would, therefore, be: |1.6g - 25| ≤ 0.50. We can solve this as a compound inequality: -0.50 ≤ 1.6g - 25 ≤ 0.50.

Solving for 'g' in this inequality, we find: 15.3125 ≤ g ≤ 15.9375. This means Hugo will pump between approximately 15.31 and 15.94 gallons of gas.

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Answer:

She wanted to persuade others that women should not ride bicycle

Answer:

B.

Step-by-step explanation:

Answer:

x = sqrt(273)/2 - 1/2 or x = -1/2 - sqrt(273)/2

Step-by-step explanation:

Solve for x:

x - 3 = 56/(x + 4)

Cross multiply:

(x - 3) (x + 4) = 56

Expand out terms of the left hand side:

x^2 + x - 12 = 56

Add 12 to both sides:

x^2 + x = 68

Add 1/4 to both sides:

x^2 + x + 1/4 = 273/4

Write the left hand side as a square:

(x + 1/2)^2 = 273/4

Take the square root of both sides:

x + 1/2 = sqrt(273)/2 or x + 1/2 = -sqrt(273)/2

Subtract 1/2 from both sides:

x = sqrt(273)/2 - 1/2 or x + 1/2 = -sqrt(273)/2

Subtract 1/2 from both sides:

Answer:  x = sqrt(273)/2 - 1/2 or x = -1/2 - sqrt(273)/2

To solve the equation x - 9/3 = 56/x + 4 for x, multiply both sides by x, distribute and simplify, factor out x, set each factor equal to zero, and solve for x to get the solutions 0 and 63.

To solve the equation x - 9/3 = 56/x + 4 for x:

Therefore, the solutions for x are 0 and 63.

Answer: No.

Step-by-step explanation:

If you divide 54183 by each number, it would be in decimal form.

Answer:

No

Step-by-step explanation:

Amount spent for food = $5850, housing = $4680, clothing = $2340, savings = $2600, taxes = $5850, expenses = $2080.

Step-by-step explanation:

Step 1:

Given details are Total Income = $23,400

Step 2:

Amount spent for food, F= 1/4th of 23,400 = [tex]1/4 \times 23400[/tex]

= $5850

Step 3:

Amount spent for housing, H = 1/5th of 23,400 = [tex]1/5 \times23400[/tex]

= $4680

Step 4:

Amount spent for clothing, C = 1/10th of 23,400 = [tex]1/10 \times 23400[/tex] = $2340

Step 5:

Amount spent for savings, S = 1/9th of 13,400 = [tex]1/9\times 23400[/tex] = $2600

Step 6:

Amount spent for taxes, T = 1/4th of 23,400 =  [tex]1/4 \times 23400[/tex] =$5850

Step 7:

Find amount spent on other expenses by totaling all expenditures and subtracting from the annual income.

Annual Income = F + H + C + S + T + E

Amount spent on other expenses, E = 23400 - (5850 + 4680 + 2340 + 2600 + 5850)

E = 23400 - 21320

E = $2080

Answer:

The correct option is 7.5

Therefore the length of BE is 7.5 units

Step-by-step explanation:

Given:

AB || CD

AE = 5

DE = 2

EC = 3

DC = 1.5

To Find:

BE = ?

Solution:

In Δ ABE and Δ DCE

∠ABE ≅ ∠DCE …………..{ Alternate angles are equal since AB || CD }  

∠AEB ≅ ∠DEC ……….....{Vertical opposite angles are equal}  

Δ ABE ~ Δ DCE….{Angle-Angle Similarity test}  

If two triangles are similar then their sides are in proportion.  

[tex]\dfrac{BE}{CE} =\dfrac{AE}{DE}=\dfrac{AB}{DC} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Substituting the values we get

[tex]\dfrac{BE}{CE} =\dfrac{AE}{DE}[/tex]

[tex]\dfrac{BE}{3}=\dfrac{5}{2}\\\\BE=\dfrac{15}{2}=7.5[/tex]

Therefore the length of BE is 7.5 units

Answer:

%120

Step-by-step explanation:

Step 1:  Divide the new weight by the original weight.

24/20 = 1.2

Step 2:  Change 1.2 into percent

To make a percent, multiply the number by 100

1.2 * 100 = %120

Answer:  %120

Answer:

32

Step-by-step explanation:

4 elephants = 1 blue whale

4 blue whales = 1 tree = 16 elephants

2 trees = 1 monument = 32 elephants

The Washington Monument is 32 elephants tall.

To determine how many elephants tall the Washington Monument is, we need to set up a proportion using the given comparisons between elephants, blue whales, Redwood trees, and the Washington Monument.

First, let's establish the individual proportions:

1 blue whale = 4 elephants in length.

1 Redwood tree = 4 blue whales in height.

1 Washington Monument = 2 Redwood trees in height.

Now we can combine these proportions to find out how many elephants equal the height of one Washington Monument:

1 Washington Monument = 2 (Redwood trees) = 2 * 4 (blue whales) = 2 * 4 * 4 (elephants) = 8 * 4 elephants = 32 elephants.

Thus, the Washington Monument is 32 elephants tall.

the car trave after 12 minute in mile

the car travels 8 miles after 12 minutes.

To find out how far the car travels after 12 minutes, we first need to determine the time interval that includes 12 minutes. From the table, we see that the time intervals are spaced by 10 minutes each.

Since 12 minutes falls between 10 and 20 minutes, we need to find the corresponding distance for this time interval.

Given that the car travels at a constant speed, we can see that the distance traveled in each time interval is constant.

From the table:

- From 0 to 10 minutes, the car travels 8 miles.

- From 10 to 20 minutes, the car also travels 8 miles.

Therefore, if the car travels 8 miles in the first 10 minutes, it would also travel 8 miles in the next 2 minutes (from 10 to 12 minutes).

So, the car travels 8 miles after 12 minutes.

The complete Question is given below:

A car travels at a constant speed. The table shows the distance y (in miles) that the car travels after x minutes. How far does the car travel after 12 minutes?

Time(minutes),  x  0 | 10 | 20 | 30

Distance(miles), y 0 | 8   | 16  | 24

Answer:

11/6

Step-by-step explanation:

6/3+(-1/6)

2+(-1/6)

2-1/6

12/6-1/6

11/6

Answer: 11/6

Step-by-step explanation:

Margo will pay $1.5 in interest after borrowing $100 at an annual interest rate of 6% for 6 months, using the simple interest formula I = PRT.

To calculate the interest Margo will pay after 6 months on a $100 loan with an annual interest rate of 6%, we have to first convert the annual rate to a semiannual rate because interest is being calculated for half a year. The formula for simple interest is I = PRT, where I is the interest, P is the principal amount ($100), R is the rate of interest per period, and T is the time the money is borrowed for, in years.

In this case, R would be 6% per year, or 0.06 (when converted to a decimal). However, since only half a year (which is 6/12 or 0.5 years) has passed, we will need to adjust this interest rate by half, resulting in R = 0.03 for 6 months. We then calculate the interest I using the formula:

I = PRT = $100 * 0.03 * 0.5 = $1.5

Therefore, Margo will pay $1.5 in interest after 6 months.

Answer:

After 2 hrs canoe rentals and kayak rentals cost would be same.

Step-by-step explanation:

Let the number of hours be 'x'.

Given:

Set up fee for Kayak rental = $5

Hourly rate for Kayaks rental = $8

Solution:

First we will find the total cost of Kayak rentals.

total cost of Kayak rentals can be calculated by sum of Set up fee for Kayak rental and Hourly rate for Kayaks rental multiplied by number of hours.

framing in equation form we get;

total cost of Kayak rentals = [tex]5+8x[/tex]

Now Given:

Set up fee for Canoe rental = $9

Hourly rate for Canoe rental = $6

Now we will find the total cost of Canoe rentals.

total cost of Canoe rentals can be calculated by sum of Set up fee for Canoe rental and Hourly rate for Canoe rental multiplied by number of hours.

framing in equation form we get;

total cost of Canoe rentals = [tex]9+6x[/tex]

Now to find the number of hours when both rentals would cost same we will make both the equation equal we get;

[tex]5+8x=9+6x[/tex]

Combining like terms we get;

[tex]8x-6x=9-5\\\\2x=4[/tex]

Now Dividing both side by 2 we get;

[tex]\frac{2x}{2}=\frac{4}2\\\\x=2\ hrs[/tex]

Hence After 2 hrs canoe rentals and kayak rentals cost would be same.

Final answer:

To find when the cost of renting a canoe equals the cost of renting a kayak, we set up an equation for each rental's cost, equalize them, and solve for the number of hours. It takes 2 hours for both to cost the same.

Explanation:

To determine the number of hours it takes for canoe rentals and kayak rentals to cost the same amount, we can set up an equation based on the cost structures provided:

If we let h be the number of hours, the costs for both rentals can be expressed as $5 + 8h (kayak) and $9 + 6h (canoe). To find when they cost the same, we can set these expressions equal to each other:

5 + 8h = 9 + 6h

Now, let's solve for h:

Subtract 6h from both sides to get the terms involving h by themselves:

5 + 8h - 6h = 9 + 6h - 6h

5 + 2h = 9

Next, subtract 5 from both sides to solve for h:

2h = 9 - 5

2h = 4

Finally, divide both sides by 2:

h = 4 / 2

h = 2

The number of hours it takes for the cost of renting a canoe and a kayak to be the same is 2 hours.

Answer: [tex]diameter=38\ in[/tex]

Step-by-step explanation:

Based on the picture I assume that the exercise asks for the diameter of the sphere.

So, it is necessary to remember the following:

1.  the volume of a sphere can be calculated with the following formula:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where "r" is the radius.

2. The radius is twice the diameter.

So, knowing that the volume of the sphere is:

[tex]V=9,145.33\pi\ in^3[/tex]

You can substitute them into the equation and then solve for "r" in order to find its value:

[tex]9,145.33\pi\ in^3=\frac{4}{3}\pi r^3\\\\\frac{(3)(9,145.33\pi\ in^3)}{4\pi}=r^3\\\\\sqrt[3]{\frac{(3)(9,145.33\pi\ in^3)}{4\pi}}=r\\\\r=19\ in\\\\[/tex]

Then, the diameter is:

[tex]d=2r\\\\d=2(19\ in)\\\\d=38\ in[/tex]

f(x) = 3x + 3

Solution:

Let us take f(x) = y.

The points indicated in the graph are (0, 3) and (–2, –3).

Slope(m) of the line passing through two points formula:

[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points in the above formula,  

[tex]$m=\frac{-3-3}{-2-0}[/tex]

    [tex]$=\frac{-6}{-2}[/tex]

m = 3

constant is the y-intercept which implies c = 3.

The equation of a line standard form is y = mx + c.

y = 3x + 3

The equation of a line is

f(x) = 3x + 3

Answer: 143

Step-by-step explanation: 19 x 7.5 = 142.5 rounds to 143

Hope this helps

Answer:

C)  [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given:

Number of freshmen = 3

Number of sophomores =3

Number of juniors =3

Number of seniors = 3

The team's captain is randomly selected from any grade level.

To find the the probability that a freshman will not be selected as captain.

Solution:

Total number of members in the team = [tex]3+3+3+3[/tex] = 12

Probability that a freshman will be selected as captain will be:

⇒   [tex]\frac{Number\ of\ freshmen}{Total\ members}[/tex]

⇒ [tex]\frac{3}{12}[/tex]

Reducing to simple fraction by dividing numerator and denominator by 3.

⇒ [tex]\frac{3\div3}{12\div 3}[/tex]

⇒ [tex]\frac{1}{4}[/tex]

Thus, probability that a freshman will not be selected as captain will be given as:

⇒ [tex]1-\frac{1}{4}[/tex]

Taking LCD.

⇒ [tex]\frac{4}{4}-\frac{1}{4}[/tex]

Subtracting the numerators.

⇒ [tex]\frac{3}{4}[/tex]     (Answer)

Answer:

c

Step-by-step explanation:

∠A = 90°, ∠B = 60° and ∠C = 30°

Step-by-step explanation:

⇒ 12² + (12√3)² = 144 + 432 = 576

⇒ √576 = 24 = a.  This shows that the triangle is a right angled triangle.

So ∠A = 90°

⇒ cos B = AB/BC = 12/24 = 1/2

⇒ ∠B = 60°

⇒ ∠C = 180° - (90° + 60°) = 180° - 150°

⇒ ∠C = 30°

The angle measures of triangle ABC is therefore;

mZA= 90°, m ZB = 60°, m ZC = 30°

By testing for Pythagoras triple;

Hence, the triangle is a right-angled triangle.

We can then evaluate mZC as follows;

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