Which mathematical word describes both 2.25
and 6.75
in the expression 2.25x+6.75x−5.5
?

Answer:

Because in the left-hand case the incoming ray is perpendicular to the surface so it is not refracted.

Step-by-step explanation:

Short answer: Because in the left-hand case the incoming ray is perpendicular to the surface so it is not refracted. In other words the angle of incidence is zero in contrast to the right-hand case.

240 full glasses of juice can be poured from the large can of juice.

Calculating the volume of the large can of juice and the volume of the tiny glass is necessary to answer this problem. The volume of the can must then be divided by the volume of the glass to determine how many glasses can be filled.

The formula V = r2h, where r is the radius and h is the height, determines the volume of a cylinder.

The radius for the large juice can is equal to half the diameter, or r = 6 inches. It is 15 inches tall. Hence, the huge can's volume is as follows:

V large is equal to (1620)(6)2(15) cubic inches.

The radius for the little glass is equal to half its diameter, or 1.5 inches. It is 3 inches tall. Hence, the little glass's volume is as follows:

V small is equal to 1.5 x 2 x 3 or 6.75 cubic inches.

We divide the volume of the large can by the volume of the tiny glass to determine how many glasses can be filled:

V large/V small is equal to (1620)/(6.75), or 240.

As a result, the enormous can of juice can be used to fill 240 glasses to the brim.

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The time to reach 125 feet is 1.3 seconds, the time to reach a maximum height of 147.52 ft is 2.5 seconds

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

h(t) = -16t^2 + 79t + 50

To do this, we set h(t) = 125

So, we have

-16t^2 + 79t + 50 = 125

Using a graphing tool, we have

t = 1.3

So, the time taken is 1.3 seconds

We have

h(t) = -16t^2 + 79t + 50

Differentiate and set to 0

-32t + 79 = 0

So, we have

32t = 79

This gives

t = 2.46875

t = 2.5

Next, we have

h(2.46875) = -16 * 2.46875^2 + 79 * 2.46875 + 50

Evaluate

h(2.46875) = 147.52

Hence, the maximum height is 147.52 ft

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Answer:

D-The data in Sample B is clustered around the center where Sample A is more spread out

Step-by-step explanation:

maybe sorry if wrong

122 degrees Fahrenheit is equal to 50 degrees Celsius.

Fahrenheit is a temperature scale where water freezes at 32 degrees and boils at 212 degrees under standard atmospheric pressure.

It is primarily used in the United States, the Bahamas, Belize, and the Cayman Islands.

For example, a typical comfortable room temperature of 72 degrees Fahrenheit would be 22.2 degrees Celsius on the Celsius scale.

Using the formula F = (9/5 x C) + 32, we can find the temperature in Fahrenheit when the temperature is 50 degrees Celsius.

F = (9/5 x C) + 32

F = (9/5 x 50) + 32

F = (90) + 32

F = 122

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Answer:

terms:  'k' and '-3d'

coefficient of 'k' is 1

coefficient of '-3d' is -3

Step-by-step explanation:

if a variable exists by itself then its coefficient is 1, otherwise

whatever value precedes a variable is its coefficient

a. Slope of RS = [tex]-\frac{7}{5}[/tex] and slope of adjacent to RS =  [tex]-\frac{5}{7}[/tex]

b. Length of RS  = [tex]\sqrt{74}[/tex] and Length of adjacent to RS = [tex]\sqrt{74}[/tex]

c. The parallelogram PQRS is Rhombus.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

[tex]Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}[/tex]

a. for the points R (-6, 6) and S (-1, -1)

Slope of RS = [tex]\frac{-1 - (+6)}{-1 - (-6)}[/tex] = [tex]-\frac{7}{5}[/tex]

Slope of RS = [tex]-\frac{7}{5}[/tex]

Slope of adjacent side (RQ, SP) to RS = [tex]\frac{6-1}{-6-1}[/tex] = [tex]\frac{5}{-7}[/tex]

Slope of adjacent to RS =  [tex]-\frac{5}{7}[/tex]

b. Length of a line = [tex]\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}[/tex]

points R (-6, 6) and S (-1, -1)

Length of RS = [tex]\sqrt{({-1- (-6))^{2} } + ({-1-6})^{2}}[/tex] = [tex]\sqrt{74}[/tex]

Length of RS  = [tex]\sqrt{74}[/tex]

Length of adjacent to RS = [tex]\sqrt{({-6- 1))^{2} } + ({6-1})^{2}}[/tex] = [tex]\sqrt{74}[/tex]

Length of adjacent to RS = [tex]\sqrt{74}[/tex]

c. All sides are equal

PQ=QR=RS=SP=√74

So, diagonal PR = [tex]\sqrt{({-6- 6))^{2} } + ({-6-6})^{2}}[/tex] = [tex]12\sqrt{2}[/tex]

and  diagonal QS = = [tex]\sqrt{({-1- 1))^{2} } + ({-1-1})^{2}}[/tex] = [tex]2\sqrt{2}[/tex]

Diagonals are unequal then parallelogram PQRS is Rhombus.

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Answer:

Midpoint of AB is (-2,-2)

Step-by-step explanation:

thats the answer

The area that was used for planting peas is given as follows:

2.6675 feet².

The area that was used for planting peas is obtained applying the proportions in the context of the problem.

The total area of the garden is given as follows:

10 and (2/3) feet².

Hence the decimal representation of the area is given as follows:

10 + (2/3) = 10.67 feet².

(conversion from mixed number to decimal).

The area that was used for planting is one fourth of the total area of the garden, hence it is given as follows:

1/4 x 10.67 = 2.6675 feet².

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The present value is $9,824.56.

Future value is the sum of the present value and the interest earned. When an amount earns a simple interest, it means that the present value grows at a linear rate.

Future value = simple interest + present value

Present value = future value - simple interest

Simple interest in a linear function of the present value, the interest rate and the duration of the investment.

Simple interest = present value x interest rate x time

14,000 - p = p x 0.085 x 5

14,000 - p = 0.425p

14,0000 = 1.425p

p = 14,000 / 1.425

p = $9,824.56

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Answer: what's so urgent?

Step-by-step explanation:

The equation of the ellipse is (x - 6)² / 4 + (y - 1)² / (16/9) = 1, the center is (6,1), and the directrices are x = 0 and x = 12.

The center of the ellipse is the midpoint of the major axis. The midpoint of the line segment connecting (4,1) and (8,1) is ((4+8)/2, (1+1)/2) = (6,1). Therefore, the center of the ellipse is (6,1).

The distance between the center and one of the vertices (say, (8,1)) is the length of the semi-major axis, a. This distance is (8-6) = 2. Therefore, the semi-major axis is a = 2.

The eccentricity, e, is given as 1/3.

The distance between the center and one of the foci, c, is related to the semi-major axis and eccentricity by the equation c = ae. Plugging in the values we know, we get c = (1/3)(2) = 2/3.

We can write the equation of the ellipse in standard form:

(x - 6)² / 2² + (y - 1)^2 / b² = 1

where b is the semi-minor axis. We can solve for b using the relationship between the semi-major axis, semi-minor axis, and eccentricity:

So the equation of the ellipse is:

(x - 6)² / 4 + (y - 1)² / (16/9) = 1

The directrices are located a distance of a² / c = (2²) / (2/3) = 6 units away from the center along the major axis. These are the lines x = 6 - 6 = 0 and x = 6 + 6 = 12.

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Answer:

2/(1/4) = 8 1/4th gallons to fill the container and 1/8 * x = 8/8 (x=8) times you can fill the tank with 1/4th gallon

Step-by-step explanation:

First let's answer the first part of the question: what fraction of the container is filled?

If there is 1/4 a gallon of water in the container which holds 2 gallons, we can show this by adding 0/4 to 1/4 to get 1/8 as the fraction of the container filled. (Or just double the denominator for both gallons instead of 1)

To represent this with a multiplication equation, we will take the holding of the container which is 2 gallons

1/8 times x = how many times you can fill the container with 1/4 gallon of water (which is 8 total)

and then our division which is

2 divided by 1/4 = how many shares of water can fit in the container

I hope this helps :)

Answer:

Step-by-step explanation:

You want the measures of the angles (5x+10°) and (10x+50°) that are divisions of an angle marked as a right angle.

The angle addition theorem tells you the whole is the sum of its parts. Here, the right angle in the diagram is divided into two parts, marked 5x+10° and 10x+50°. The measure of the right angle is the sum of these parts:

  90° = (5x +10°) +(10x +50°)

  30° = 15x . . . . . . . subtract 60°

  2° = x . . . . . . . . . divide by 15

Using this value for x, we find the angle measures to be ...

  5x+10° = 5(2°) +10° = 10° +10° = 20°

  10x+50° = 10(2°) +50° = 20° +50° = 70°

In summary, ...

In response to the query, we can state that As a result, $1,154.74 is the interest response to the original query.

To calculate simple interest, divide the principal by the interest rate, the duration, and other variables. The marketing formula is simple return = capital + interest + hours. The easiest way to compute interest is with this method. The most common method for calculating interest is as a percentage of the principal amount. For instance, if he borrows $100 from a buddy and promises to pay it back at 5% interest, he will only pay his portion of the 100% interest. $100 (0.05) = $5. Interest must be paid when you borrow money and must be added to any loans you make. The annual percentage of the loan amount is frequently used to calculate interest. This percentage represents the loan's interest rate.

Now we can apply the following calculation to figure out how much a mortgage will cost each month:

(P x I / (1 -)

[tex]$1,575 = ($150,000 x 0.003875) / (1 - (1 + 0.003875)^(-360))[/tex]

After calculating the unknown variable, we obtain:

[tex]1 - (1 + 0.003875)^(-360) = ($150,000 x 0.003875) / $1,575\s(1 + 0.003875)^(-360) = 0.9900162785\s1 + 0.003875 = (0.9900162785)^(-1/360)[/tex]

0.003162 is the monthly interest rate.

In the second month, the following principle was paid:

Principal payment is $1,575 less $576.61 to equal $998.39.

Hence, at the end of the second month, the total interest paid is:

Total interest paid equals the sum of the first month's interest and the second month's interest.

Total interest paid equals $1,154.74 ($578.13 + $576.61).

As a result, $1,154.74 is the response to the original query.

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The terms in the numerator and simplify the fraction, giving us: -2x² - 1/(2x + 1)

A numerator is the part of a fraction that is above the line and indicates how many parts of a whole are being considered. It is the number that is being divided.

The first step in solving this problem is to factor out the numerator. Using the distributive property, we can rewrite the numerator as:

(-3x² + 6x³ - 4 - x) = (-3x² + 6x³ - 4) - x

Now, we can factor out -3x² from the first two terms, giving us:

(-3x² + 6x³ - 4) - x = -3x²(1 + 2x - 4/3x²) - x

We can now divide the numerator and denominator by the common factor of -3x², giving us:

(-1 - 2x + 4/3x²) - (x/(-3x²)) ÷ (2x + 1)

By dividing the numerator and denominator by -3x², we can now cancel out the -3x² terms, leaving us with:

(-1 - 2x + 4/3x²) - (1/3) ÷ (2x + 1)

The next step is to simplify the fraction. To do this, we must multiply the numerator and denominator by the reciprocal of the denominator. In this case, the reciprocal is -1/(2x + 1) giving us:

[(-1 - 2x + 4/3x²) - (1/3)] × (-1/(2x + 1))

Simplifying the numerator yields:

(2x + 1 - 4/3x² + 1/3) × (-1/(2x + 1))

Finally, we can combine the terms in the numerator and simplify the fraction, giving us: -2x² - 1/(2x + 1).

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Kayla has to purchase [tex]6[/tex] packs of cupcakes, and the dressmaker can make [tex]5[/tex] copies of the pattern.

Provide a discount on a third element in exchange for the first item's purchase, also known as purchase with purchase. Although it may also encourage sales of the side product, its primary goal is to increase sales of the main products.

The purchase accounts is a nominal account, and as per nominal account rules, business costs are debited. All purchases made on credit are noted in the purchase diary, whilst purchases made with cash are noted in the cash book.

number of packs [tex]=[/tex] (total number of cupcakes) / (number of cupcakes in each pack)

We know that there are [tex]34[/tex] people attending the party

total number of cupcakes [tex]= 34[/tex]

Plugging this into the formula above, we get:

number of packs [tex]= 34 / 6 = 5.67[/tex]

Therefore, Kayla should buy [tex]6[/tex] packs of cupcakes.

number of pattern cuts [tex]=[/tex] (total amount of material) / (amount of material used for each pattern)

We know that the seamstress has [tex]4.5m[/tex] of material and each pattern uses [tex]0.8m[/tex] of material, so we can plug these values into the formula above:

number of pattern cuts [tex]= 4.5 / 0.8 = 5.625[/tex]

Therefore, the seamstress can cut out the pattern [tex]5[/tex] times.

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Answer:

[tex]{ \tt{2x + 3y = 27x}} \\ { \tt{27x - 2x = 3y}} \\ { \tt{25x = 3y}} \\ \\ { \tt{x = \frac{3}{25}y }}[/tex]

The Area of Composite figure is 131cm² we can find it by dividing the figure in two parts.

Rectangle is a plane which one side is long and other side is short and and all angle between these sides are 90° and opposite sides are parallel to each other.

We can divide this figure in two part Rectangle and Triangle.

The Rectangle having length = 10 cm and breadth = 5 cm.

Whereas, Triangle have sides having length 6cm (Base) and 3 cm (Perpendicular).

[tex]Area\ of\ Rectangle = Length (l) * Breadth (b)[/tex]

= 10 x 5 cm²

= 50 cm².

[tex]Area\ of\ Triangle =\frac{1}{2} *b*h[/tex]

For this we have to find third side,

[tex]Third\ Side = \sqrt{(First\ Side)^{2} +(Second\ Side)^{2} }[/tex] ( Using Pythagoras Theorem)

[tex]Third\ Side = \sqrt{(6)^{2} +(3)^{2} }[/tex]

Third Side = 6.7 cm

[tex]s= \frac{a + b + c}{2}[/tex] , where a, b, c are three sides

[tex]= \frac{6.7 + 6 +3}{2}[/tex]

= 7.85 cm.

Now we use Heron's formula to find the area of triangle,

Area of Triangle = [tex]\sqrt{s\ (s-a)\ (s-b)(\ s-c)}[/tex][tex]=\sqrt{7.85\ (7.85-6.7)\ (7.85-6)\ (7.86-3)}[/tex]

= 81 cm²

So the Area of Composite figure = (50 + 81) cm²

= 131 cm²

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Answer:

y(x)= -2x - 2

Step-by-step explanation:

If we assume that your mass is m kilograms, then you would need to eat 80 times your mass in food each day. Therefore, you would eat:

80m kilograms of food per day

To find how much you would eat in a month, we need to multiply the amount of food you eat in a day by the number of days in a month. We'll assume a month has 30 days.

Number of kilograms of food eaten per month = Number of kilograms of food eaten per day x Number of days in a month

= 80m x 30

= 2400m

Therefore, you would eat 80m kilograms of food per day and 2400m kilograms of food per month.

Therefore, the family drank juice at a rate of 0.8 gallons per week.

Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.

Here,

To find the rate at which the family drank juice, we need to divide the total amount of juice consumed by the time it took to consume it.

The total amount of juice consumed is 4 gallons. The time period is 5 weeks.

So, the rate at which the family drank juice is:

4 gallons ÷ 5 weeks = 0.8 gallons per week

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Answer:

34ft

Step-by-step explanation:

Area1=5*2=10ft

Area2=4*6=24ft

Total Area=Area1+Area2=24+10=34ft

Scott's age is 11x

Georgia's age is 6x = 4y

therefore y=1.5x

Fiona's age is 7x

Oscar's age is 3y

therefore 3(1.5x)=4.5x

Fiona's age: Oscar's age

7x : 4.5x

7 : 4.5

Answer:

Step-by-step explanation:

[tex]27=3\times 3 \times 3=3^3[/tex]

ordered: [tex]3^3[/tex]

52 applicants apply, 30 employees will be hired and at least 30 of them will pass the background test.

To determine how many applicants need to apply to meet the hiring target, we need to work backwards from the desired number of hires.

Let X be the total number of applicants needed to hire 30 new employees.

Out of all applicants, 10% do not meet the base business requirements. Therefore, the number of applicants who do meet the base business requirements is:

[tex]$0.9X$[/tex]

Out of these applicants who meet the base business requirements, 12% do not pass the pre-screening assessment. Therefore, the number of applicants who pass the pre-screening assessment is:

[tex]$0.88(0.9X) = 0.792X$[/tex]

Out of these applicants who pass the pre-screening assessment, 23% do not show up for the interview. Therefore, the number of applicants who show up for the interview is:

[tex]$0.77(0.792X) = 0.6108X$[/tex]

Out of these applicants who show up for the interview, 5% fail the background test. Therefore, the number of applicants who pass the background test is:

[tex]$0.95(0.6108X) = 0.58026X$[/tex]

Since we need to hire 30 new employees, we can set this equal to 30 and solve for X:

[tex]$0.58026X = 30$[/tex]

[tex]$X \approx 51.74$[/tex]

Therefore, Company B needs approximately 52 applicants to apply to meet their hiring target.

To meet the hiring target, Company B will need to ensure that at least 30 employees pass the background test. From the above calculations, we know that 0.58026X applicants pass the background test. Therefore, we can solve for X:

[tex]$0.58026X = 30$[/tex]

[tex]$X \approx 51.74$[/tex]

This means that if 52 applicants apply, 30 employees will be hired and at least 30 of them will pass the background test.

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Telling Marvin the number 18 should get us into the museum.

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse of multiplication, and is used to find out how many times one number is contained within another number.

To get into Marvin's Magic Museum, we need to figure out which number Marvin likes based on the given information.

Marvin likes the number 14, but not 15. This suggests that he likes even numbers, since 14 is even and 15 is odd.

Marvin likes the number 21, but not 26. This suggests that he likes numbers that are divisible by 3, since 21 is divisible by 3 and 26 is not.

Marvin likes the number 35, but not 39. This suggests that he likes numbers that are not divisible by 4, since 35 is not divisible by 4 and 39 is.

Putting these clues together, we can see that the number Marvin likes must be even, divisible by 3, and not divisible by 4. The only number in the list that meets these criteria is 18, since it is even, divisible by 3 (6 times), and not divisible by 4.

Therefore, telling Marvin the number 18 should get us into the museum.

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Answer:

  g(x) = 2x²

Step-by-step explanation:

You want the vertical dilation of function f(x) = x² by a factor of 2.

Any function is dilated vertically by a factor of k by multiplying the function value by k:

  g(x) = k·f(x) . . . . . . dilates f(x) vertically by a factor of k

  g(x) = 2x² . . . . . . dilates f(x) = x² vertically by a factor of 2