100 Points! Algebra question. Photo attached. Only looking for an answer to C and D. Thank you!

The formula used to calculate the variance of a set of data is Variance = [tex]s^2[/tex]=1n−1n∑i=1(xi−¯x[tex])^2[/tex].(Option-A)

To calculate the variance, each data point is subtracted from the mean, squared, and then added together. This gives the sum of the squared deviations from the mean. This sum is then divided by the total number of data points to get the average squared deviation from the mean, which is the variance.

Variance is a measure of the spread or variability of a set of data. It is useful in statistical analysis to understand how much the data points differ from the mean, and to compare different sets of data. Lower variance values indicate that the data is more tightly clustered around the mean, while higher variance values indicate that the data is more spread out.(option-A)

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1) the value of the expression is 48.

2) The value of the expression is 5 mg.

3) The total cost for 12 labour hours is R2940.

Now, Let's "M" represent Mukhari age.

Then, "Five years older than Mukhari" can be written as,

"M + 5".

And, If Mukhari is 43 years old, we can substitute M with 43:

M + 5 = 43 + 5 = 48

Therefore, the value of the expression is 48.

2.1.2 Let's "R" represent the recommended daily allowance of iron.

"25% of the recommended daily allowance of iron" can be written as 0.25R.

And, If the recommended daily allowance of iron is 20 mg, we can substitute R with 20:

0.25R = 0.25(20) = 5

Therefore, the value of the expression is 5 mg.

2.1.3 Let's "C" represent the total cost, "P" to represent the cost of parts, and "L" to represent the number of labour hours.

"The total cost of the repair is R1500 for parts plus R120 per hour of labour" can be written as:

C = P + 120L

If the total cost for 12 labour hours is required, we can substitute L with 12:

C = P + 120(12) = P + 1440

We know that P (the cost of parts) is R1500:

C = 1500 + 1440 = 2940

Therefore, the total cost for 12 labour hours is R2940.

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Answer: the perimeter of the shape is 31 centimeters.

Step-by-step explanation:

To find the perimeter of the shape with the given side lengths, we need to add up all the sides. The given side lengths are 6 cm, 6 cm, 11 cm, and 8 cm.

Perimeter = 6 cm + 6 cm + 11 cm + 8 cm

Perimeter = 31 cm

Therefore, the perimeter of the shape is 31 centimeters.

The equation for g(x) representing the exponential function f(x) = 2^x after a vertical stretch by a factor of 6 and a reflection across the x-axis is g(x) = -6 * 2^x.

To find the equation for the function g(x) that represents the exponential function f(x) = 2^x after a vertical stretch by a factor of 6 and a reflection across the x-axis, we need to apply these transformations step by step.

Vertical Stretch by a factor of 6:

Multiply the function f(x) by 6: 6 * 2^x

Reflection across the x-axis:

Take the negative of the function obtained from the previous step: -6 * 2^x

Therefore, the equation for g(x) is:

g(x) = -6 * 2^x

To graph both functions, you can plot the points for f(x) using the original exponential function f(x) = 2^x, and then plot the points for g(x) using the transformed equation g(x) = -6 * 2^x. By comparing the two graphs, you will see the effect of the vertical stretch and reflection across the x-axis.

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The limit of the trigonometry function cosec(2x) - xcosec³(x) as x approaches 0 is undefined

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

cosec(2x) - xcosec³(x) as x approaches 0

Substitute 0 for x in the above expression, so, we have the following representation

cosec(2 * 0) - 0 * cosec³(0)

This gives

cosec(0) - 0

So, we have

cosec(0)

Evaluate

cosec(0) = undefined

Hence, the limit of the trigonometry function cosec(2x) - xcosec³(x) as x approaches 0 is undefined

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Answer:

12,782.5, 722.5, 1,392.5, 8,092.5

Step-by-step explanation:

The expression can be converted into function form at f(x) = 52.50 + yx, where y is the charge per mile and x is the number of miles. You gave me 3 values, and I'm assuming the last two could be 12, so here are the four possibilities.
y = 19: 52.50 + (670)(19) = 12,782.5

y = 1: 52.50 + (670)(1) =  722.5

y = 2: 52.50 + (670)(2) = 1,392.5

y = 12: 52.50 + (670)(12) = 8,092.5

Line A:

y=4

Line B:

x = 8

Answer: P(even) = 1/2

Step-by-step explanation:

in the data set, 1 2 3 4, only 2 are even out of the 4

2/4 = 1/2

P(even) = 1/2

Relative frequency = (individual value/total values) * 100

For the value "20": 20/10 + 15 + 20 + 10 + 20 + 30 + 10 + 50 +60 + 70) * 100 = 7.14%

For the value "60": 60/10 + 15 + 20 + 10 + 20 + 30 + 10 + 50 +60 + 70) * 100 = 21.43%

For the value "50": 50/10 + 15 + 20 + 10 + 20 + 30 + 10 + 50 +60 + 70) * 100 = 17.86%

For the value "10": 10/10 + 15 + 20 + 10 + 20 + 30 + 10 + 50 +60 + 70) * 100 = 3.57%

Since none of these values are 30%, the answer is no value in the given data set will produce a relative frequency of 30%.

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

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Renee’s layaway fee is $15.95, her down payment is $31.90, and her weekly payments are $7.98 each.

We are given that;

Combined price of the items = $318.95

Layaway fee=5%

Down payment=10%

Now,

A percentage is a minimum number or ratio that is measured by a fraction of 100.

The layaway fee by multiplying the item price by 5%. The formula is: layaway fee=item price×0.05

The down payment by multiplying the item price by 10%. The formula is: down payment=item price×0.1

Calculate the weekly payment by multiplying the item price by 15% and dividing it by 6. The formula is: weekly payment=6item price×0.15​

Plugging in the given values and simplify the expressions. Here are the calculations:

layaway fee=318.95×0.05=15.95

down payment=318.95×0.1=31.90

weekly payment=6318.95×0.15​=7.98

Therefore, by percentage the answer will be $15.95, $31.90, and $7.98

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The  equation to hold true, the value of n is 0.18074.

To find the value of n in the equation:

[tex]\(\frac{{216^n - 2}}{{\left(\frac{1}{{36}}\right)^{3n}}} \)[/tex]

we need to set the numerator and denominator to have the same base.

First, let's simplify the denominator:

[tex]\(\left(\frac{1}{36}\right)^{3n} = \left(\frac{1}{36}\right)^3 \cdot n \)\\\(\left(\frac{1}{36}\right)^3 = \frac{1}{36^3} = \frac{1}{46656} \)[/tex]

Now we can rewrite the equation as:

[tex]\(\frac{{216^n - 2}}{{\frac{1}{46656} \cdot n}} \)[/tex]

To simplify further, we can multiply the numerator by 46656 and divide the denominator by n:

[tex]\(\frac{{46656 \cdot (216^n - 2)}}{n} \)[/tex]

Now we can see that the numerator is divisible by n:

[tex]\(46656 \cdot \frac{{216^n - 2}}{n} \)[/tex]

For the equation to hold true, the numerator must be divisible by n. Since 46656 is divisible by n, we can find the value of n by setting the numerator equal to zero:

[tex]\(216^n - 2 = 0 \)[/tex]

Solving this equation for n, we find:

[tex]216^n[/tex] = 2

Taking the logarithm of both sides:

log(216) = log(2)

Simplifying further:

[tex]\(n = \frac{{\log(2)}}{{\log(216)}} \)[/tex]

Using a calculator to evaluate this expression, we find:

=0.18074

Therefore, for the equation to hold true, the value of n is 0.18074.

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There are 7776 possible roll combinations when a die is rolled 5 times.

To determine the number of possible roll combinations when a die is rolled 5 times, we need to consider the total number of outcomes for each roll and multiply them together.

When rolling a fair six-sided die, there are six possible outcomes for each roll, which are the numbers 1, 2, 3, 4, 5, and 6.

Therefore, there are 6 possible outcomes for the first roll.

Since each roll is independent of the others, the total number of possible roll combinations can be found by multiplying the number of outcomes for each roll together.

In this case, we need to multiply 6 (the number of outcomes for the first roll) by 6 (the number of outcomes for the second roll) by 6 (the number of outcomes for the third roll) by 6 (the number of outcomes for the fourth roll) by 6 (the number of outcomes for the fifth roll).

Therefore, the total number of possible roll combinations is:

6⁶ = 7776

So, there are 7776 possible roll combinations when a die is rolled 5 times.

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The ratios 3 : 5 and 2 : 4 do not form a proportion

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

Ratios = 3 : 5 and 2 : 4

Express the ratios as fractions

So, we have the following representation

Ratios = 3/5 and 2/4

Evaluate the quotients

Ratios = 0.6 and 0.5

The fractions are not equivalent

Hence, the ratios do not form a proportion

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The experimental probability is 0.6 or 60%.

Looking at the given sample of 20 coin tosses, let's identify the sequences that have exactly one "heads":

HTTH, HHTT, HTTT, HHHH, HHHT, HTHT, HTHH, HHTH, HTHH, HTHT, THHH, HTHH.

There are 12 sequences that meet the criteria.

Since we have a total of 20 coin tosses, the total number of possible outcomes is 20.

Therefore, the experimental probability that only 1 of 4 children in a family is a boy is:

P(1 boy) = Number of favorable outcomes / Total number of possible outcomes

= 12 / 20

= 0.6

So, the experimental probability is 0.6 or 60%.

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It will take approximately 4 minutes for all 200 lamps to be lit.

In this scenario, the lighting of lamps follows a pattern where each person who receives the lit lamp from the guruji goes on to light two more lamps. This process continues until all 200 lamps are lit.

Starting with the guruji, in the first round, he lights one lamp. In the second round, two new people are lit by the guruji and the first person. Therefore, there are a total of 1 + 2 = 3 lamps lit by the end of the second round.

In each subsequent round, the number of newly lit lamps is doubled compared to the previous round. So, in the third round, four new lamps are lit, making the total number of lit lamps 1 + 2 + 4 = 7.

This doubling pattern continues until all 200 lamps are lit. We can represent this pattern mathematically: 1 + 2 + 4 + 8 + ... + 2^(n-1), where n represents the number of rounds required to light all 200 lamps.

To determine the number of rounds, we can solve the equation 2^(n-1) ≥ 200. By solving this equation, we find that n ≥ 8. Therefore, it will take at least 8 rounds to light all 200 lamps.

Since each round takes 30 seconds, the total time required will be 8 rounds × 30 seconds = 240 seconds or 4 minutes.

Hence, it will take approximately 4 minutes for all 200 lamps to be lit.

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Answer: c

Step-by-step explanation:

The volume of the pyramid include the following: C. 240 ft³.

In Mathematics and Geometry, the volume of a square pyramid can be calculated by using the following formula:

Volume of a square pyramid, V = 1/3 × a² × h

Where:

By substituting the given side lengths into the formula for the volume of a square pyramid, we have the following:

Volume of square pyramid = 1/3 × 6² × 20

Volume of square pyramid = 12 × 20

Volume of square pyramid = 240 ft³.

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The matrix that shows the change in snow amount from Year 1 to Year 2 by month for each city is,

City                      January                     February

A                             23                             23

B                             - 1                               - 6

C                             - 13                              - 8

We have to given that,

The table shows the amount (in inches) of snow that each of three cities received in January and February of two years.

Now, By the data using two matrices, one for each year, find a matrix that gives the change in the amount (in inches) of snow from Year 1 to Year 2 by month for each city as,

Table for year 1,

City                      January                     February

A                             19                             16

B                             10                              11

C                             15                              12

Table for year 2,

City                      January                     February

A                             42                             39

B                             9                                5

C                             2                                4

Hence, the matrix that shows the change in snow amount from Year 1 to Year 2 by month for each city is,

City                      January                     February

A                             23                             23

B                             - 1                               - 6

C                             - 13                              - 8

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The range of users that access the website each day can be represented by the inequality 95 < u < 155.

To determine the range, we need to consider the two cases:

Case 1: 125 - u < 30

Solving this inequality:

- u < -95

u > 95

Case 2: 125 - u > -30

Solving this inequality:

- u > -155

u < 155

Combining the two cases, we find that the range of users that access the website each day is:

95 < u < 155

Therefore, the range of users that access the website each day can be represented by the inequality 95 < u < 155.

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Picking neither is the opposite of picking a rose or a lily.

We know that [tex]P(A)=1-P(A')[/tex].

Therefore:

[tex]P(\text{Neither})=1-(P(\text{Rose})+P(\text{Lily}))\\P(\text{Neither})=1-\left(\dfrac{1}{4}+\dfrac{5}{9}\right)\\P(\text{Neither})=1-\left(\dfrac{9}{36}+\dfrac{20}{36}\right)\\P(\text{Neither})=1-\dfrac{29}{36}\\P(\text{Neither})=\dfrac{7}{36}[/tex]

Answer:

3<x<6

Step-by-step explanation:

x²-9x<-18

x²-9x+18<0

(x-3)(x-6)<0

3<x<6

Answer: 3/10, 1/3, 8/9, 4/5

Answer:

The cement that is needed to build the monument will be 7 m³. Thus, the correct option is B.

What is the volume?

The volume of the rectangular prism is calculated as,

V = LWH

V = 4 m x 0.5 m x 4 m

V = 8 m³

The volume of the triangular prism is calculated as,

V = (BHL) / 2

V = (2 m x 1 m x 0.5 m) / 2

V = 0.5 m³

Since there are two triangular prisms, the total volume of both triangular prisms is:

⇒ 2 x 0.5 m³

= 1 m³

The total amount of cement is calculated as,

⇒ (Volume of rectangular prism - Total volume of both triangular prisms)

⇒ (8m³ - 1m³)

⇒ 7 m³

Thus, the correct option is B.

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Answer:

Yes, that’s correct! Periodic tightening of nuts and bolts is a common type of maintenance for all exercise equipment. This helps to ensure that the equipment remains stable and safe to use.

Step-by-step explanation:

Approx. 68.27% of uncooked hotdogs weigh between 1.24 ounces and 1.46 ounces.

Now, For the values of 1.24 ounces and 1.46 ounces using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, σ is the standard deviation, and z is the corresponding z-score.

Hence, We get;

For 1.24 ounces:

z = (1.24 - 1.35) / 0.11

z = -1

For 1.46 ounces:

z = (1.46 - 1.35) / 0.11

z = 1

Now, For standard normal distribution table (or a calculator) to find the area under the standard normal curve between z = -1 and z = 1.

This area represents the proportion of uncooked hotdogs that weigh between 1.24 ounces and 1.46 ounces.

Hence, From the table, we find that the area between z = -1 and z = 1 is 0.6827.

Therefore, 68.27% of uncooked hotdogs weigh between 1.24 ounces and 1.46 ounces.

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The length of the major axis of the ellipse is, 8

Since, We know that;

Standard form of equation of ellipse is,

⇒ (x - h)²/a² + (y - k)²/b² = 1

If a < b

Then, Major axis = 2b

Here, The  equation of ellipse is,

⇒ (x - 1)²/9 + (y + 5)²/16 = 1

⇒ (x - 1)²/3² + (y + 5)²/4² = 1

Here, 3 < 4

Hence, Major axis is,

= 2b

= 2 x 4

= 8

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The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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The surface area of the rectangular prism is 396 square inches

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

7 in by 12 in by 6 in

The surface area of the rectangular prism is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the area is 396 square inches

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The number of square feet needed to cover the hole is 44ft²

To find this, we need to find the area of the green region and subtract the little square that it has inside.

Remember that for a rectangle, the area is the product between the dimensions, then the area of the green region is:

A = 12ft*4ft = 48ft²

The little square has an area:

a = 2ft*2ft = 4ft²

Then the area needed is:

area = 48ft² - 4ft² = 44ft²

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