which expression is a cube root of -2i?

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

Answer:

3<x<6

Step-by-step explanation:

x²-9x<-18

x²-9x+18<0

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

3<x<6

Answer: c

Step-by-step explanation:

Answer:

The answer is 7.1cm to 1d.p

Step-by-step explanation:

Area of square =L²

25=L²

√L²=√25

L=5cm

hyp²=opp²+adj²

x²=5²+5²

x²=25+25

x²=50

√x²=√50

x=7.1cm to 1d.p

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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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 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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Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

[tex]\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}[/tex]

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

[tex]\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}[/tex]

[tex]\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4[/tex]

[tex]\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}[/tex]

[tex]\textsf{Step 4:} \quad y+2=-4x+24[/tex]

[tex]\textsf{Step 5:} \quad y+2-2=-4x+24-2[/tex]

[tex]\textsf{Step 6:} \quad y=-4x+22[/tex]

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

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 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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Answer:

Step-by-step explanation:

The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:

Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ​

where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35​=−0.75

This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35​=0.5

This means that 36 psi is 0.5 standard deviations above the mean.

Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.

Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649

This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.

Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%

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 solutions to the systems of equations graphically are (-2, 3) and (3, 8)

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

f(x) = x + 5

g(x) = x² - 1

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (-2, 3) and (3, 8)

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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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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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We can see here that the total weight of candy in a 5/6 pound bag site is 377 grams.

Weight is a measure of the force exerted by gravity on an object. It is the measure of how heavy an object is. Weight is typically expressed in units such as pounds or kilograms. The weight of an object can vary depending on the gravitational force acting on it.

There are 16 ounces in a pound.

Thus, a 5/6 pound bag of candy weighs

5/6 × 16 = 13.3 ounces.

If you want to know the weight in grams, 13.3 ounces is equal to 377 grams.

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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]

The calculated volume of the solid figure is 421.08 cubic feet

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

Base area = 38.28 square feet

Height = 11 feet

Using the above as a guide, we have the following:

Volume = Base area * Height

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

Volume = 38.28  * 11

Evaluate

Volume = 421.08

Hence, the volume of the solid figure is 421.08 cubic feet

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Based on the formula of Venn Diagram, the number of customers at the supermarket who purchased both shirts and pants is 26.

A Venn Diagram is a pictorial representation of data such that the relationships between two or more data sets are highlighlighted for similarities and differences.

A Venn Diagram may use overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, we can conclude that 26 customers purchased both shirts and pants, using the formula of Venn Diagram.

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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

The equivalent expression in the form [tex]x^2 + rx + sx + 6[/tex] is:

[tex]x^2 + 2x + 3x + 6[/tex], which can be further factored as (x + 2)(x + 3).

To rewrite the expression [tex]x^2 + 5x + 6[/tex] in the form [tex]x^2 + rx + sx + 6[/tex], we need to find values for r and s such that the coefficients of the x terms match.

Given expression: [tex]x^2 + 5x + 6[/tex]

To factorize this expression, we need to find two numbers that multiply to give 6 and add up to 5. The numbers that satisfy these conditions are 2 and 3.

Now, let's rewrite the expression using these values:

[tex]x^2 + 2x + 3x + 6[/tex]

By grouping the terms, we can rewrite it as:

[tex](x^2 + 2x) + (3x + 6)[/tex]

Factoring out the common terms in each group:

x(x + 2) + 3(x + 2)

Now, notice that (x + 2) appears as a common factor in both terms. We can further simplify the expression:

(x + 2)(x + 3)

Thus, the equivalent expression in the form [tex]x^2 + rx + sx + 6[/tex] is:

[tex]x^2 + 2x + 3x + 6[/tex], which can be further factored as (x + 2)(x + 3).

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The probability that Julie will be a captain, given that she makes the team, is 1/10.

To find the probability that Julie will be captain given that she makes the team, we need to consider the number of possible outcomes where Julie is a captain, and divide it by the total number of outcomes where she makes the team.

Given that there are 40 students trying out for the soccer team and 16 of them will make the team, the probability of Julie making the team is 16/40, which can be simplified to 2/5.

Out of the 16 students who make the team, we know that 4 of them will be captains.

Therefore, the probability of Julie being a captain among those who make the team is 4/16, which can be simplified to 1/4.

To calculate the probability that Julie will be a captain given that she makes the team, we multiply the probability of making the team (2/5) by the probability of being a captain among those who make the team (1/4):

(2/5) [tex]\times[/tex] (1/4) = 2/20 = 1/10.

So, the probability that Julie will be a captain, given that she makes the team, is 1/10.

This means that out of all the students who make the team, there is a 1 in 10 chance that Julie will be selected as a captain.

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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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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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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 yearly interest rate of Karl's account is 0.02, which is equivalent to 2% (since 0.02 multiplied by 100 gives the percentage value).

The function f(x) = 1,000 * 1.02^t represents the amount in Karl's savings account over t years. The number 1.02 is the growth factor, which is equal to (1 + r), where r is the yearly interest rate.

To find the yearly interest rate, we need to solve the equation:

1.02 = 1 + r

Subtracting 1 from both sides of the equation:

0.02 = r

Therefore, the yearly interest rate of Karl's account is 0.02, which is equivalent to 2% (since 0.02 multiplied by 100 gives the percentage value).

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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: