What is the volume and the surface area of the right solid whose base is shown
if the sides are 1 foot high? What is the volume of a cone that has the same base
and the same altitude? Dimensions are in feet.

a) basis is  [ p , q , r . r ]

b) the dimension. P-2q 9p +2r -2q +4r -6p 12r p, q, rin R is 3 for subspace

since the two given equation are in three variable and constants

2q -r= p -----(1)

r= q -s -----(2)

p= q +2r -----(3)

From (2):

r +s= q (+s on both sides)

s= q -r -----(4) (-r on both sides)

Substitute. (3) into (1):

2q -r= q +2r

2q -q= 2r +r

q= 3r -----(5)

Substitute (5) into (4):

s= 3r -r

s= 2r (proved)

hence subspace is [ p , q , r . r ]

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Answer:

30.25

Step-by-step explanation:

All angles of a line must add up to 180. Since we already know that one angle is 90 degrees, we know that the other angles should add up to 90 degrees in order for all of the angles to add up to 180 degrees:

(3x-7)+(x+8)=90

4x+1=90

4x=89

x=22.25

22.25+8= 30.25

Answer:

3n - 4 = -19,    n = -5

Step-by-step explanation:

Primero tienes que sumar cuatro a ambos lados y obtener tres veces n es igual a menos quince. Luego, divide tres en ambos lados para obtener n es igual a -5

Answer:

The equations are the same. See Explanation for further detail.

Step-by-step explanation:

Starting out with the equation

5(x+2) = 5x + 10

Lets multiply both sides by 4

20(x+2) = 4(5x + 10)

Now we can add 31 to both sides of the equation.

20(x+2) + 31 = 4(5x+10) + 31

This is Elena's new equation.

By making the same change to both sides of the equation, the equation remains unchanged, and therefore will have the same results as the original equations. Thus, since the functions are equal, Elena can tell that her new equation is true.

Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)

The cost of each small charcuterie boards is $6 and one medium charcuterie boards is $7.

A mathematical statement known as an equation is made up of two expressions joined together by an equal sign. It is a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Let small charcuterie boards = c

Let medium charcuterie boards = m

Therefore, the equation will be:

10c + 12m = 144

5c + 9m = 93

Multiply equation i by 5

Multiply equation ii by 10

50c + 60m = 720

50c + 90m = 930

Subtract

30m = 210

m = 210/30

m = 7

Therefore, 5c + 9m = 93

5c + 9(7) = 93

5c + 63 =93

5c = 93 - 63

5c = 30

Divide both sides by 5

c =  30 / 5

c = 6

Therefore, based on the information the cost of each small charcuterie boards is $6 and one medium charcuterie board is $7.

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Answer:

m = 70°, n = 55°, p = 25°

Step-by-step explanation:

Start of with the 25 degree angle. It and angle p are vertical angles, and vertical angles are equal to each other. Now that we know the value of p we can solve for n. The 100° angle, n, and p are supplementary angles, meaning their total value equals 180 degrees. By subtracting p and 100 from 180, we get the value for n.

To find m, observe that the 110 degree angle and m also are supplementary angles. Simply subtract 110 from 180 to get the answer.

Answer: \(\boxed{\frac{1}{100}\ or\ 0.01}\)

Step-by-step explanation:

Determine the value of \(y^{12} \ when\ y=10^{-\frac{1}{6}\)

\(=(10^{-\frac{1}{6} })^{12}\)

\(=\frac{1}{100}\ or\ 0.01\)

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ y^{12}\hspace{5em}y=10^{-\frac{1}{6}}\qquad \implies \qquad \left( 10^{-\frac{1}{6}}\right)^{12}\implies 10^{-\frac{1}{6}\cdot 12} \\\\\\ 10^{-2}\implies \cfrac{1}{10^2}\implies \cfrac{1}{100}\)

Developing strategies for remembering facts is essential for children before they engage in drill and practice activities to develop fluency. By establishing these strategies, children can effectively learn, retain, and recall information, ultimately enhancing their performance during practice sessions.

Yes, it is important for children to develop strategies for remembering facts before engaging in drills and practice to develop fluency. By doing so, children can enhance their ability to recall information more quickly and accurately, making it easier for them to perform well on tests and assignments. Strategies such as visualizing, chunking, and using mnemonic devices can help children remember information more effectively. Once these strategies are established, drill and practice can then be used to further reinforce their understanding and speed up their recall time. This approach can ultimately lead to improved academic performance and a stronger foundation for learning.

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x=-3, y=5

2х + Зу = 9

3х + 5y = 16

6x + 9y = 27

6x + 10y = 32

-y = -5

y = 5

2x + 3(5) = 9

2x = 9-15

2x = -6

x=-3

The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 9 5/8, where 9 is the quotient and 5 is the remainder.

Remain length = 13.2' = 13' 2 2/5 ".

Length of black steel pipe is 21'-0".

7' 9 5/8" =7.8 '

Remain length = 13.2' = 13' 2 2/5 ".

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Answer:

Revolution traveled by me = 30π ft.

Revolution traveled by my friend = 20π ft.

Difference between revolutions = 10π ft.

Step-by-step explanation:

In one revolution, I travel 2π(15) = 30π ft., and my friend travels 2π(10) = 20π ft., so my revolution is 30π - 20π, or 10π, ft. longer than my friend's revolution.

Jason's exam score was 1.41 standard deviations above the mean, and we need to determine what percentile he falls in. A normal distribution is used to solve the problem because we know that exam scores were normal. The mean of the exam scores is zero, while the standard deviation is one.

The area under the normal distribution curve can be determined using the standard normal distribution table. Jason's exam score is located 1.41 standard deviations above the mean. As a result, the proportion of students that scored lower than Jason is the same as the area under the normal distribution curve to the left of his exam score. This proportion can be found in the standard normal distribution table.

The standard normal distribution table provides the area to the left of a given Z-score or number of standard deviations from the mean. Jason's Z-score is 1.41, so we'll need to look up the area to the left of 1.41 in the standard normal distribution table. According to the standard normal distribution table, the area to the left of 1.41 is 0.9207. This means that 92.07% of students scored lower than Jason in the exam, so Jason is in the 92.07th percentile. He performed better than 92.07% of the students who took the exam in the class.

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Answer:

task b

Step-by-step explanation:

The area of an obtuse triangle can be found using the formula: Area = (1/2) * base * height.

To find the base and height of the triangle, we need to identify a right angle within the triangle. One way to do this is by drawing an altitude from one vertex to the opposite side.

Once we have the right angle, we can determine the base and height. The base is the length of the side to which the altitude is drawn, and the height is the length of the altitude itself.

Unfortunately, the given information does not provide any measurements or angles of the triangle. Therefore, we cannot calculate the area of the obtuse triangle accurately.  Hence, the answer cannot be determined with the given information.

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Answer:

5t≥900

Step-by-step explanation:

Answer:

More than 1 (2.5 is the answer)

Step-by-step explanation:

more than 1.

Step-by-step explanation:

5/8 ÷ 2/8 is 40/16. when simplified, you get 5/2. change it to decimals and you get your answer

Answer:

take the dots and either put them together or rake them away

Step-by-step explanation:

Example: .....+..=....... five dots plus two dots equals seven dots.

......-...=... six dots minus three dots equals three since you are taking away three

i hope u found this helpful.

The largest possible area of such a trapezoid rounded down to the nearest integer is  108.

The two parallel facets are the bases, and top, as constantly, is the perpendicular distance from one base to the opposite. The place of this parallelogram is its peak (half-peak of the trapezoid instances its base

Area of a trapezoid is = 1/2 * sum of the two parallel side * height

                                    =  1/2 * (12 + 10 ) * 8

                                    =  88

Area of a trapezoid is = 1/2 * sum of the two parallel side * height

                                    =  1/2 * (12 + 8) * 10

                                    = 100

Area of a trapezoid is = 1/2 * sum of the two parallel side * height

                                    =  1/2 * (8+ 10 ) * 12

                                    =  108

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Explanation

The equation of a circle with center (h,k) and radius r units is given by:

then

Step 1

find the diameter of the cirlce:

to do this, we can use the distance between two points formula:

if

the distance from A to B is

so,let

distance CD=

hence, the diameter of the circle is

Step 2

find the center of the circle:

the center of the circle is the midpoint of CD

so

replace

so, the center of the circle is (-3,-1)

Step 3

finally, replace in the formula to get the equation of the circle

let

replace

therefore, the answer is

I hope this helps you

The expected number of rolls until all faces have appeared in some order in six consecutive rolls is 1 / [1 - (5/6)^6].

To find the probability that all faces have appeared in some order in six consecutive rolls of a 6-sided die, we can use the principle of inclusion-exclusion.

Let's calculate the probability of the complement event first, which is the probability that at least one face is missing from the sequence in six consecutive rolls.

In the first roll, there are 6 possibilities for the face that appears. In the second roll, there are 5 possibilities remaining, and so on. Therefore, the probability of missing a face in one roll is (5/6).

Since we want to find the probability of missing a face in six consecutive rolls, we multiply the probabilities together: (5/6)^6.

Now, to find the probability of all faces appearing in some order in six consecutive rolls, we can subtract the probability of the complement event from 1.

Probability = 1 - (5/6)^6.

For the expected number of rolls until such a sequence appears, we can use the concept of geometric distribution. The expected number of rolls for a geometric distribution is equal to 1 divided by the probability of success.

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Answer:

t ≤ − 4

Step-by-step explanation:

Answer: t ≤ -4

Step-by-step explanation:

rearrange the problem 24-(-6*t)≤0  Pull out like factors :24 + 6t  =   6 • (t + 4)

Divide both sides by 6    Subtract  4  from both sides t ≤ -4

Answer:

Step-by-step explanation:

Use a distributive property.

Distributive property:

\(\Longrightarrow: \sf{A(B+C)=AB+AC}\)

⇒ 6(x-4)=10

First, divide by 6 from both sides.

⇒ 6(x-4)/6=10/6

Solve.

⇒ x-4=5/3

Add by 4 from both sides.

⇒ x-4+4=5/3+4

Solve.

5/3+4

4*3/3+5/3

4*3+5/3

4*3=12

12+5=17

x=17/3

Dividing is another option.

17/3=5.6

x=17/3=5.6

I hope this helps you! Let me know if my answer is wrong or not.

The result is obtained by using the formula for a triangle.

Simply we count the number of grids representing a certain unit.

We have a flag in coordinate system can be seen in the picture.

Each grid represents a foot. Kenna will make five flags.

The flag is a triangle with the base at y-axis.

The base length is 3 ft and the height is 2. The area of the triangle is

Area of a flag = ½ bh

Area of a flag = ½(3)(2)

Area of a flag = 3 ft²

Area of five flags = 5(3 ft)

Area of five flags = 15 ft²

Hence, Kenna will need the material of 3 ft² for one flag and 15 ft² for five flags.

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An equilibrium phase diagram can be used to determine phase transitions, phase presence, and phase compositions at different conditions.

An equilibrium phase diagram can be used to determine the below mentioned parameters:

A) It can determine where phase transitions will occur. Phase transitions refer to changes in the state or phase of a substance, such as solid to liquid (melting) or liquid to gas (vaporization). The phase diagram provides information about the conditions at which these transitions take place, such as temperature and pressure.

B) It can determine what phases will be present for each condition of chemistry and temperature. The phase diagram shows the different phases or states of a substance (such as solid, liquid, or gas) under different combinations of temperature and pressure. It provides a visual representation of the stability regions for each phase, indicating which phase(s) will be present at a given temperature and pressure.

C) It can determine the chemistry and amount of each phase present at any condition. The phase diagram gives information about the composition (chemistry) and proportions (amount) of different phases present under specific conditions. It helps identify the coexistence regions of multiple phases and provides insight into the equilibrium compositions of each phase at various temperature and pressure conditions.

In summary, an equilibrium phase diagram is a valuable tool in understanding the behavior of substances and can provide information about phase transitions, phase stability, and the chemistry and amounts of phases present at different conditions.

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Answer:

x = 5

Step-by-step explanation:

5(x + 4) - 8 = x + 32

5x + 20 - 8 = x + 32

5x + 12 = x + 32

5x - x + 12 = 32

5x - x = 32 - 12

4x = 32 - 12

4x = 20

x = 5

Hope this helped! :)

Answer:

x=0

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

\(3+11t-9u\\\\\rightarrow\boxed{t = 9; u = 11}\\\\3+11(9)-9(11)\\\\3+99-99\\\\102-99\\\\\boxed{3}\)

Hope this helps.