2. Samuel used clay to make a diorama of the pyramids in Ancient Egypt. He made two triangular pyramids and three rectangular pyramids. How much clay did he use to create all the pyramids?

Answer:

$32

Step-by-step explanation:

Answer:

32 dollars

Step-by-step explanation:

20% of $40 is 8

so you subtract 8 to get your answer

40-8 = 32

Answer:

2/6 ??

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

DE + EF = DF

2x - 1 + 5x - 13 = 70

7x - 14 = 70

7x = 70 + 14

    = 84

x = 84 ÷ 7

x = 12

Answer: x=12

Step-by-step explanation:

2x-1+5x-13=70

Combine like terms

7x-14=70

Add 14 to both sides

7x=84

Divide both sides by 7

X=12

The probability that a family with 4 children has no more than 3 boys is 15/16.

To find the probability that a family with 4 children has no more than 3 boys, we can use the binomial distribution.

The binomial distribution is used to calculate the probability of obtaining a certain number of successes (boys in this case) in a fixed number of trials (children in this case), where each trial has only two possible outcomes (boy or girl) and the trials are independent.

Let X be the number of boys in the family. We want to find P(X ≤ 3), which is the probability of having no more than 3 boys. Since the probability of having a boy is 1/2 and the trials are independent, we can use the binomial distribution formula:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (1/2)⁴ + 4(1/2)⁴ + 6(1/2)⁴ + 4(1/2)⁴

= 15/16

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Answer:

36

Step-by-step explanation:

Given

3x + 2(y - 4) ← substitute x = 10 and y = 7 into the expression

= 3(10) + 2(7 - 4)

= 30 + 2(3)

= 30 + 6

= 36

The ordered pairs that defines the solutions of the system of equations f(x) = x² - 2x + 3; f(x) = -2x + 7 are

(2, 3) and (-2, 11)

Ordered pairs refers to the arrangement of 2 numbers in the form (a, b)

As used in the cartesian coordinates

a refers to a point in the x direction b refers to a point in the y direction

Solutions of the system of equation is the points where the straight line intersect the curve or where the two graphs intersect.

the point of intersection

x² - 2x + 3 = -2x + 7

x² - 2x + 2x + 3 - 7 = 0

x² + 3 - 7 = 0

x² - 4 = 0

solving for x

x² = 4

x = √4

x = 2 OR -2

solving for y

For x = 2, y = -2 * 2 + 7 = 3

For x = -2, y = -2 * -2 + 7 = 11

hence we have the points to be (2, 3) and (-2, 11)

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Answer:

SSS

Step-by-step explanation:

I can identify that these triangles are congruent by using the SSS (Side, Side, Side) postulate theorem. I know this because first, second, and home triangle share the same side as the third, second, and home triangle, meaning they are congruent, so are the other sides of the angle since the question states they are congruent.

The solution to the given proportion is \(x = \frac{96}{11}\). By cross-multiplying, we obtained the equation \(3x = 8(12-x)\). After simplifying, we had \(11x = 96\), and by dividing both sides by \(11\), we found that \(x = \frac{96}{11}\).

To solve the proportion \(\frac{x}{12-x} = \frac{8}{3}\), we can use cross-multiplication and algebraic manipulation. Let's go through the steps:

First, we cross-multiply the terms. This means we multiply the numerator of the first fraction (\(x\)) by the denominator of the second fraction (\(3\)), and we multiply the denominator of the first fraction (\(12-x\)) by the numerator of the second fraction (\(8\)):

\[3x = 8(12-x)\]

Next, we distribute the \(8\) to both terms inside the parentheses:

\[3x = 96 - 8x\]

Now, we want to isolate the \(x\) term on one side of the equation. To do that, we can add \(8x\) to both sides:

\[3x + 8x = 96\]

Combining like terms:

\[11x = 96\]

To solve for \(x\), we divide both sides of the equation by \(11\):

\[x = \frac{96}{11}\]

Therefore, the solution to the given proportion is \(x = \frac{96}{11}\).

In summary, to solve the proportion \(\frac{x}{12-x} = \frac{8}{3}\), we used cross-multiplication and algebraic manipulation. By cross-multiplying, we obtained the equation \(3x = 8(12-x)\). After simplifying, we had \(11x = 96\), and by dividing both sides by \(11\), we found that \(x = \frac{96}{11}\).

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The type of nonprobability design that is most likely to yield a representative sample is a stratified random sampling.

In stratified random sampling, the population is divided into distinct subgroups or strata based on certain characteristics or variables that are relevant to the research objective. Then, a random sample is selected from each stratum proportionally to the size or importance of that stratum in the population. This approach ensures that the sample reflects the diversity and heterogeneity of the population.

By stratifying the population and using random sampling within each stratum, the stratified random sampling design increases the likelihood of obtaining a representative sample. It allows for accurate representation of different groups within the population, which can help reduce sampling bias and provide more precise estimates of population characteristics.

However, it's important to note that even with stratified random sampling, there may still be limitations and potential sources of bias. Factors such as nonresponse rates and the accuracy of the population data used for stratification can impact the representativeness of the sample. Nevertheless, when properly implemented, stratified random sampling is a valuable nonprobability design for achieving representativeness in a sample.

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The average is the arithmetic mean of all the observations of a set of numbers. The number of times Brandon rolls above the average is 7.

The average is the arithmetic mean of all the observations of a set of numbers. it is found by dividing the sum of all the observations of the set by the number of observations in the set.

\(\rm{Average=\dfrac{Sum\ of\ observations}{Number\ of\ observations}\)

In order to know the number of times Brandon rolls the dice above the average, we first need to calculate the average of the twenty rolls.

The average of the 20 times dice rolls,

\(\rm Average = \dfrac{6+1+3+4+4+4+6+5+5+3+6+4+4+5+2+3+5+4+4+2}{20}\)

\(\rm Average = \dfrac{80}{20} = 4\)

Thus, the average of the 20 rolls of the dice is 4.

Now, the number of times the result of the dice roll is above 4(x>4) is 7.

Hence, the number of times Brandon rolls above the average is 7.

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Answer:

(-5, 1)

Step-by-step explanation:

Eliminate the equal sides of each equation and combine.

\( - x - 4 = \frac{3}{5} x + 4\)

Solve − x −4 =35x + 4 for x.

\(x = - 5\)

Evaluate y when x = −5.

\(y = 1\)

hence, the system of this equation is (-5, 1).

The "Assume Non-Negative" option in Excel Solver is helpful when the solution to a problem appears to depend on the starting values for the decision variables.

This option is particularly useful when working with linear programming problems where the solution depends on the values of the decision variables, and there is no clear starting point.

The "Assume Non-Negative" option instructs Solver to assume that all decision variables have non-negative values. This means that the solution will only be searched for in the non-negative space, which can help to narrow down the solution space and make the search more efficient.

In other words, Solver will not search for solutions that violate the non-negative constraint, which can save time and computational resources.

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Answer:

(2,9) , (3,8) , (4,7) , (5,6)

Step-by-step explanation:

ab+ba = 10a+b+10b+a = 11a+11b = 11(a+b)

if a+b = 11 then ab+ba = 11²

(a,b) or (b,a) : (2,9) , (3,8) , (4,7) , (5,6)

check: 29+92 = 121 = 11²

56+65 = 121 = 11²

With a water flow rate of 2 gallons per minute (gpm), the volume of water after 4 minutes will be 8 gallons of water.

Gallons per minute (gpm) is a measurement of the flow rate of the liquid. Gpm measures how much volume of water is flowing out (in imperial measurement of gallon) of the pipe, shower head, taps, pumps, etc in a given time.

Given that a drum is being filled with a flow rate of 2 gpm and the time given is 4 minutes, we need to figure out the volume of water using a water flow rate gallons per minute (gpm) we will then calculate with the following formula:

Volume = flow rate × time

Volume = 2×4

Volume = 8 gallons

Therefore the drum will be filled with 8 gallons of water after 4 minutes of filling.

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Mateo takes 20 minutes to run around the track once.

The rate at which an object goes from one location to another is known as its speed. It is described as the distance that an object covers in a certain amount of time. The distance traveled in one unit of time is typically used to express speed, such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph) (mph).

\(Speed = \frac{distance}{time }\)

Here we assume that the distance around the track is 'd', Adrian's speed is 'a' (in distance per minute) and Mateo's speed is 'm' (also in distance per minute).

Since Adrian takes 15 minutes to run around the track once, we have:

a = d/15

Let's use the formula: time = distance/speed

to write two equations for the total distance traveled by each boy.

For Adrian: 2d = a × 30

For Mateo: 2d = m × t

where 't' is the time it takes Mateo to run around the track once.

Since we know that Mateo runs faster than Adrian, we have:

m > a

Substituting the expression we found for 'a' into the equation for Adrian, we get:

2d = (d/15) × 30

d = 225

Now, we can solve for Mateo's speed using the equation for the total distance traveled by Mateo:

2d = m × t

2(225) = m × t

m = 450/t

Substituting this expression for 'm' into the inequality m > a, we get:

450/t > d/15

15×450 > d×t

6750 > d×t

Substituting d = 225, we get:

6750 > 225t

t < 30

Since Mateo takes less than 30 minutes to run around the track once, and we know that Adrian takes 15 minutes, the possible value for t is 20 minutes: t = 20.

Therefore, Mateo takes 20 minutes to run around the track once.

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Answer:

6.6

Step-by-step explanation:

Answer:

6.6

Step-by-step explanation:

not to scale

the answer should be

\(14x + 2\)

The perimeter of triangle is \((14x+2)\) unit.

The perimeter of triangle is sum of length of all three sides of triangle.

From figure, sides of triangle are,

                \(3x+2,5x,6x\)

Now, find perimeter of given triangle,

                \(Perimeter=3x+2+5x+6x\\\\Perimeter=8x+6x+2\\\\Perimeter=14x+2\)

Thus, the perimeter of triangle is \((14x+2)\) unit.

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Answer:

n>=-4

Step-by-step explanation:

(0 -  5 • (n - 2)) -  30  ≤ 0

-5n - 20  =   -5 • (n + 4)

 -5 • (n + 4)  ≤ 0

Divide both sides by  -5

Subtract  4  from both sides which is n ≥ -4

Answer:

Step-by-step Solution:

Check:

Hence, this is correct.

Answer:

6:10

Step-by-step explanation:

Answer:

Trinomial

Binomial

and monomial

Step-by-step explanation:

Answer:

Step-by-step explanation:

choices:

W c Z

R c W

0 E Z

∅ c R

{0, 1, 2, ...} c_ W

-2 E W

Answer:

b

Step-by-step explanation:

The inscribed angle 36°m is half the measure of its intercepted arc, that is

b = 2 × 36 = 72

c = 360 - (108 + 72) = 360 - 180 = 180 ( total sum of arcs in a circle )

The angle between a tangent and the radius of a circle at the point of contact is 90° , then

d = 90

Thus b = 72, c = 180, d = 90 → b

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Answer: 18

Step-by-step explanation:

9 kids each have two bags

9 x 2 = 18

9 + 9 = 18

Answer:

The half of 6 is 3 the half of 3 is 1.5 the half of 1.5 is 0.75

Answer: <1 = 26°

Step-by-step explanation:

given that:

• <ABD = 66°

• <2 = 14° + <1 (since ''more than' means we add)

• Find <1

Since it is obvious that <ABD is a sum of <1 and <2:

⇒ <ABD = <1 + <2

now we know that <2 is 14° more than <1 and that <ABD = 66°

⇒ 66° = <1 + (14° + <1)

⇒ 66° = <1 + 14° + <1

⇒ <1 = (66° - 14°) ÷ 2

⇒ <1 = 26° ...Answer...

hope that helps...

The first law of thermodynamics, mathematically expressed as:

ΔU = Q - W

Where:

ΔU represents the change in internal energy of the system,

Q represents the heat added to the system, and

W represents the work done by the system.

The first law of thermodynamics, also known as the law of energy conservation, states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

The term "internal energy" (ΔU) refers to the total energy possessed by the system, including the kinetic and potential energy of its molecules. It is a measure of the system's thermal energy.

The term "heat" (Q) represents the transfer of energy between the system and its surroundings due to temperature difference. It is a form of energy transfer that occurs spontaneously from higher temperature regions to lower temperature regions.

The term "work" (W) represents the energy transfer resulting from forces applied to the system, causing displacement. It can take different forms, such as mechanical work, electrical work, or expansion work.

For different scenarios, the explicit form of the energy balance equation can be derived by considering the specific types of work and heat involved in the system. By drawing appropriate schematics, one can identify the relevant forms of work and heat transfer. Examples include:

Adiabatic Process: In this scenario, no heat transfer occurs (Q = 0). The energy balance equation simplifies to ΔU = -W, where the work done by the system contributes to the change in internal energy.

Isothermal Process: In this case, the temperature remains constant (ΔU = 0). The energy balance equation becomes Q = W, indicating that the heat added to the system is fully converted into work.

Isobaric Process: Here, the pressure remains constant. The energy balance equation can be written as ΔU = Q - PΔV, where P is the constant pressure and ΔV is the change in volume. This equation accounts for both heat transfer and work done against the constant pressure.

Therefore, by applying appropriate schematics and considering the specific conditions of a given scenario, one can deduce the explicit form of the energy balance equation and understand the interplay between heat, work, and the change in internal energy.

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Answer: See explanation

Step-by-step explanation:

The sequence is gicen as 6,11,16,21,26. Here, the first term (a) = 6, common difference = 11 - 6 = 5

Therefore, since it's an arithmetic progression, the algebraic expression for the general term of the sequence will be given as:

= a + (n-1)d

= 6 + (n-1)5

= 6 + 5n - 5

The 25th term in the sequence would be:

= 6 + 5n - 5

= 6 + 5(25) - 5

= 6 + 125 - 5

= 126

Answer:

8

Step-by-step explanation:

Billy started with 15 apples.

Lost 2, and another 5, In total 7 apples were taken.

" Lost " Indicates subtraction.

The equation would look like this: 15 - 7.

Subtract.

Hence, your answer should be 8.

Hopes this helps!

Have a good day :).

Answer: 8

Step-by-step explanation: 15 - 2 = 13 and 13 - 5 = 8.

(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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