evaluate ( 6^2 - 4^2 ) x ( 1/4 )^2

The rectangular blocks with the measure of 7 cm by 8 cm by 9 cm will not fit in the smallest cylindrical cup with the radius of 5cm.

Rectangular block with the least dimensions, 7cm by 8cm side.

Circle with radius r is x² + y² = r²

∴ x² + y² = 5² or x² + y² = 25

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

Its observed that the block cannot fit inside the cup. We can confirm this if

y >4 when x = 3.5

3.5² + y² = 25

12.25 + y² = 25

y² = 12.75

taking positive square root, y≈3.57

Since this is <4, the block cannot fit the 5 cm radius cup.

equation for the cup with r = 6cm,

x² + y² = 6² or x² + y² = 36

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

it is observed the block will fit inside the cup as y>4 when x = 3.5

3.5² + y² = 36

12.25 + y² = 36

y² = 23.75

taking positive square roots, y≈4.87

Since this is >4, the block can fit the 6 cm radius cup.

equation for the cup with r = 7cm,

x² + y² = 7² or x² + y² = 49

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

it is observed the block will fit inside the cup as y>4 when x = 3.5

3.5² + y² = 49

12.25 + y² = 49

y² = 36.75

taking positive square roots, y≈6.06

Since this is >4, the block can fit the 7 cm radius cup.

∴ the block will not fit the smallest cup

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The percentage of expenditure which goes towards salaries is 78%

Company's expenditure:

Salaries: R105 000 000

Equipment: R10 000 000

Marketing: R2 000 000

Other: R8 000 000

Total expenditure= R105 000 000 + R10 000 000 + R2 000 000 + R8 000 000

= R135,000,000

percentage of the expenditure is salary= R105 000 000 / R135,000,000 × 100

= 0.78

= 78%

Therefore, 78% of the company's expenditure goes towards salary.

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The game with 8 minutes of time-outs is 98 minutes long.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division.

In this case, the algebraic expression that represents the length of the soccer game would be:

m = 90 + x

where m represents the total length of the game in minutes, 90 represents the fixed length of the game, and x represents the variable length of time-outs in minutes.

To find the length of the game with 8 minutes of time-outs, we substitute x = 8 into the expression:

m = 90 + 8 = 98

Therefore, the game with 8 minutes of time-outs is 98 minutes long.

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Answer:

cant see it clearly

Step-by-step explanation:

bc it's to far

Answer:

the answer is c

Step-by-step explanation:

Divide 198.00 by 100, multiply 1.98 by 40, 198.00 minus 79.20, 118.80

The code from solving the expressions is MGWMGWW

1. 7b

2. 6y - 1

3. -m + 0.5

4. 9x - 2y

5. 4j

6. -12x + 22

7. 6m - 8

Algebraic expressions are expressions that are composed of coefficients, variables, terms, factors and constants.

They also consist of mathematical operations, such as;

Given the expression;

b + b + b + b + 3b

collect the like terms

7b

2(4y-  3) - 2x + 5

collect like terms

6y - 1

Hence, the code is MGWMGWW

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Answer: all points are a solution except for (4, 2) (and (2, 0) i think)

Step-by-step explanation:

Answer:

15

_

2

Step-by-step explanation:

hope you get it since I don't know how to do it under __

The second segment crosses the x-axis at (1.5, 0), and the slope of the segment is -1

The area under any probability density curve is always 1 and it is used for finding out the probabilities for any random variable X taking a certain range of values.

Let the second segment crosses at (a,0) on the X-axis:

The area under the density curve is 1.

the given fig can be divided into a rectangle and a triangle by dropping a line from the point (0.5, 1) in the x-axis.

The coordinate point of the second segment at the x-axis:

Now,

1*0.5+1/2*1*(a-0.5)=1

1+(a-0.5)=2

a-0.5=2-1

a=1+0.5

a=1.5

Thus the second segment crosses the x-axis at (1.5, 0)

The slope of that segment c:

The slope  of that segment=y₂-y₁/x₂-x₁

By considering the points (0.5, 1) and (1.5, 0)

We will have the slope as:

m=0-1/1.5-0.5

m=-1/1

m=-1

the equation of the line containing this segment:

The line passes from the point (0.5, 1)

y=mx+b is used to find the value of the intercept

so, substitute the values in the equation:

1=(-1)*0.5+b

1=-0.5+b

b=1.5

so, the equation for that line segment is

y=-x+1.5

x+y=1.5

To calculate the probability P(X > 1):

[tex]P(X > 1)=\int\limits\limits^1_1 {y} \, dx \\P(X > 1)=\int\limits^1_1 {(-x+1.5)} \, dx[/tex]

[tex]P(X > 1)=[\frac{-x^2}{2}+1.5x]_1^1^.^5\\\\P(X > 1)= (\frac{(-1.5)^2}{2} +1.5*1.5)-(\frac{-1^2}{2}+1.5*1)\\[/tex]

P(X>1)=-1.125+2.25+0.5-1.5

P(X>1)=0.125

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The required value of angle x for a given hexagon is 20°.

What is a hexagon?

In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. Six vertices and six angles make up a hexagon. The words "hexa" and "gonio" both refer to six.

A hexagon's internal angles add up to 720°. All of the sides and interior angles of a regular hexagon are the same lengths.

Given, the interior angles of a hexagon are 7x°, 7x°, 4x°, 7x°, 7x°, and 4x° respectively.

So, the sum of interior angles = 720°

or, 7x° + 7x° + 4x° + 7x° + 7x° + 4x° = 720°

or, 36x° = 720°

or, x = 720/36

or, x =20°

Hence, the required value of x is 20°.

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The four possible times that car B could take to complete one lap are: 120 seconds, 90 seconds, 60 seconds, and 30 seconds.

The equation used to solve this problem is (150 - 30) = N * B, where N is the number of laps and B is the total number of seconds for car B to complete one lap. Therefore, the four possible times for car B to complete one lap are 120 seconds, 90 seconds, 60 seconds, and 30 seconds.

When solving for the total time, it is important to remember that the two cars start the race together and that their speeds remain constant. This means that the time it takes for car B to complete one lap must be a factor of 150 seconds. If car B takes a time that is not a factor of 150, then it will not be able to finish the race in 150 seconds.

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The value of p such that the matrix M does not have an inverse is given as follows:

p = -5.

The matrix M for this problem is given as follows:

M = [7 2

       p -1].

As it is a 2 x 2 matrix, the determinant is obtained with the multiplication of principal diagonal subtracted by the multiplication of the secondary diagonal, hence:

|M| = -7 - 2p.

The matrix does not have an inverse if the determinant assumes a value of zero, hence the value of p is obtained as follows:

-7 - 2p = 0

2p = -7

p = -7/2

p = -5.

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Answer:

Genesis has 126 different outfits to choose from.

Step-by-step explanation:

To calculate the total number of different outfits Genesis can choose, we need to multiply the number of choices available for each article of clothing. So we have:

7 choices for pants

2 choices for t-shirts

3 choices for sweaters or hoodies

3 choices for shoes

To find the total number of outfits, we multiply the number of choices for each category:

7 x 2 x 3 x 3 = 126

Therefore, Genesis has 126 different outfits to choose from.

126 different combination does Genesis have to choose.

We have,

Pants = 7

T shirts = 2

Sweaters or Hoodies = 3

Shoes = 3

So, the number of different combination is

= C(7, 1) x C( 2, 1) x C(3, 1) x C(3, 1)

= 7 x 2 x 3 x 3

= 126 ways

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The solution is, the retail price of the mattress, before the discount is $2,400. & the wholesale price, before the markup was $960

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Part A:

Given that the mattress is sold for 50% off of the retail price, let the retail price of the mattress be x, then

50% of x = 1200

⇒ 0.5x = 1200

⇒ x = 1200 / 0.5 = 2400

Therefore, the retail price of the mattress, before the discount is $2,400.

Part B:

Given that the store marks up the retail price to 150% of the wholesale price. Let the whole sale price be p, then

(100% + 150%) of p = 2400

250% of p = 2400

2.5p = 2400

p = 2400 / 2.5 = 960.

Therefore, the wholesale price, before the markup was $960.

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The equation we need is[tex]P(3 < =x < =5) = (x^3 - 3x^2 + 5x - 3)/24[/tex]. We can solve this in R by using the dbinom() function. The code is: dbinom(3:5, size=4, prob=0.25) which yields an answer of 0.3125. This means that the probability of 3 to 5 bicycle accidents occurring in the next four months is 0.3125.

The equation for the probability of a certain number of bicycle accidents occurring in the next four months is [tex]P(x) = (x^3 - 3x^2 + 5x - 3)/24[/tex], where x is the number of accidents. To solve this equation with R, we can use the dbinom() function which is used to calculate the binomial cumulative distribution function. We set the size parameter to 4 (the number of months) and the probability parameter to 0.25 (the probability of a bicycle accident occurring at the intersection in a single month). The code is dbinom(3:5, size=4, prob=0.25). This yields an answer of 0.3125, meaning that the probability of 3 to 5 bicycle accidents occurring in the next four months is 0.3125. This calculation is useful for understanding the likelihood of certain numbers of bicycle accidents occurring in a given time period, and can be used to inform decisions about safety at intersections.

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Marianne's withholding tax if her monthly gross earnings are $3,270 is $305.00.

The correct option is A.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Brittany works as a medical office assistant.

She is married and claims 2 withholding allowances.

Her monthly gross earnings are $3,270.

So, 3270 - 2(666.5) = $1937.3

So,

(1937.3 x 0.15) + 14.49 = $305.00

Therefore, the value is $305.00.

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A bar chart or a histogram might be suitable if all the sample sizes are the same and the team is worried about the amount of flaws.

Consider comparing the quantity of defects across several production lines, departments, or time periods.

The number of faults would be the continuous variable in this instance, and the bars would represent the number of samples that included a particular number of defects.

When illustrating the distribution of a count variable, such as the number of defects, bar charts and histograms can be used to visually spot patterns and trends in the data.

Therefore, the number faults would be the continuous variable in this instance, and the bars would represent the number of samples that included a particular number of defects.

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The scale factor was applied to the first diamond is 2.5

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

The diamonds

The scale factor is calclated as

scale factor = Diamond 2/Diamond 1

Substitute the known values in the above equation, so, we have the following representation

scale factor = 1.5/0.6

Evaluate

scale factor = 2.5

Hnce, the scale factor is 2.5

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The number of terms in the sequence is given as follows:

135 terms.

The general notation of a sequence is given as follows:

[tex]\sum_{m = a}^{k} f(m)[/tex]

The parameters are given as follows:

Hence the number of terms in the sequence is obtained as follows:

n = k - a + 1.

The parameter values for this problem are given as follows:

a = 1, k = 135.

Considering the parameter values above, the number of terms of the sequence is given as follows:

n = 135 - 1 + 1

n = 135.

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Answer:

angle 1 = 26 degrees angle 2 is 154 degrees

DONT FORGET TO PUT THE DEGREES SIGN IN YOUR ANSWER

Step-by-step explanation:

Since the angles add up to a straight line, or 180 degrees, the equation is

(x+4)+7x=180 degrees

8x+4=180

8x=176

x=22

so, angle 1 is 26, angle 2 is 154 degrees

The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.

Assume L is the length and W is the width. Then the area is given as,

A = L × W

And the perimeter is given as,

P = 2(L + W)

A rectangle has a width-to-height ratio of 8:5. The perimeter of the rectangle is 208 inches. Then the equations are given as,

208 = 2(W + H)

H + W = 104                ...1

H / W = 8 / 5              ....2

From equations 1 and 2, then we have

(8/5)W + W = 104

(13/5)W = 104

W = 40 inches

Then the height is given as,

H = (8/5) x 40

H = 64 inches

Then the area of the rectangle is given as,

A = 40 x 64

A = 2,560 square inches

The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.

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Answer: 40%

Step-by-step explanation:

Answer:

The volume of the rectangular prism can be calculated by multiplying its length, width, and height: 8 x 4.12 x 3.12 = 128.064 cubic inches.

Answer:

V=342,784in

Step-by-step explanation:

V=1/3(L×W×H)

where v=volume of rectangular prism,L=length.W=width or breadth,H=height

V=1/3×8×412×312

V=342,784in

The possible value for the original number is 30

Represent the number with n

So, we have

Lacey = 10 * (n/10 + 1/2)

Euan = 100 * (n/100 + 1/2).

Also, Lacey's new number is 3/4 of Euan's new number, so we have:

10 * (n/10 + 1/2) = (3/4) * (100 * (n/100 + 1/2))

Solving for n, we have:

100 * (n/100 + 1/2) = (4/3) * (10 * (n/10 + 1/2))

Divide through by 100

n/100 + 1/2 = (4/30) * (n/10 + 1/2)

Evaluate

(n + 50)/100 = 4n/300 + 2/30

So, we have

n + 50 = 4n/3 + 20/3

Multiply through by 3

3n + 50 = 4n + 20

Evaluate the like terms

n = 30

Hence, the original number is 30

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Answer:

Step-by-step explanation:

1.  ΔONG≅ΔLMI

2.  1:2

3. ON = 12

   NG = 30

4.  P-ONG = 6+7.5+12 = 25.5

    P-LIM = 12+15+24 = 51

5.  1:2

Answer:

Step-by-step explanation:

I gotchu.

sin70 = x/3.6

x = 3.6sin70

x = 3.4

Answer:

x = 3.4

Step-by-step explanation:

As the given triangle is a right triangle we can use trigonometric ratios to solve for x.

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the triangle:

As we know the angle and the hypotenuse, and wish to find the side opposite the angle, substitute the values into the sine ratio and solve for x:

[tex]\implies \sin(70^{\circ})=\dfrac{x}{3.6}[/tex]

[tex]\implies x=3.6\sin(70^{\circ})[/tex]

[tex]\implies x=3.382893...[/tex]

[tex]\implies x=3.4\; \sf (nearest\;tenth)[/tex]

Therefore, x = 3.4 to the nearest tenth.

According to the information in the table, the histogram would be as shown in the attached image.

To graph the information in the table we must take into account the relationship of the data. On the one hand we have the frequency, which is the data that varies, and the different variations of time.

In accordance with the above, what we want to demonstrate with this table are the different frequencies of time that students take to do their math homework. Additionally, most students take between 10 and 25 minutes to do their math homework.

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•Mr Bradford lunged at his wedding ring as it fell into the WHIRLPOOL of the bathtub drain.

•Sarah's morher CALMED her screaming baby by giving her a teddy bear to hold.

Answer: whirlpool, calmed

Step-by-step explanation:

A vortex looks like a whirlpool

Since the baby is scream giving a teddy bear will probably calm it