A storage container in the shape of a square-based prism has a volume of 120 ft. If the sides of the square base are 4 ft in length, determine the height of the container.​

Answer: B

Step-by-step explanation:

\((5x^2 -x-3)(2x+6)\\\\=2x(5x^2 - x-3)+6(5x^2 - x-3)\\\\=10x^3 - 2x^2 - 6x+30x^2 - 6x-18\\\\=\boxed{10x^3 +28x^2 - 12x-18}\)

Answer:

C, (x = 100, y = 10)

Step-by-step explanation:

hi again,

(2x - 70) = (x + 30), by the Alternate Exterior Angles

x - 70 = 30

x = 100

(2x - 70) + 5y = 180, by the Linear Pair Theorem

2(100) - 70 + 5y = 180

200 - 70 + 5y = 180

130 + 5y = 180

5y = 50

y = 10

The value of y is 48

y= kx

let's solve for k which is the constant

y= 8 , x= 4

k= 8/4

k= 2

Next is to calculate the value of y when x is 24

y = 2 × 24

y= 48

Hence the value of y is 48

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Answer:

Slope intercept form:y=mx+c

y=1/2x-7

Answer:

3.233

Step-by-step explanation:

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

Answer: True

Explanation: The domain of a quadratic function in standard format is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.

Linear function is almost always going to be all real numbers. The range of a non-horizontal linear function is all real numbers no matter how flat the slope might look.

Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

This causes the volume of the balloon to decrease, leading to an increase in the number of collisions between gas particles and the inside surface of the balloon, and causing the balloon to shrink and shrivel up.

Temperature is a measure of the average kinetic energy of the particles in a substance or system. In other words, it is a measure of how hot or cold something is relative to a standard reference point. The SI unit of temperature is the kelvin (K), but temperature is often measured in degrees Celsius (°C) or Fahrenheit (°F) in everyday life. Temperature plays a crucial role in many natural and man-made processes, and is a key factor in determining the behavior of matter at different states.

Here,

When a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy and slow down. As the temperature drops, the average kinetic energy of the gas particles decreases, causing them to move slower and collide less frequently. This results in a decrease in pressure inside the balloon.

According to the Ideal Gas Law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. As the pressure inside the balloon decreases, its volume also decreases, since the number of moles of gas and the gas constant remain constant.

Since the balloon is sealed, the gas particles cannot escape, so they continue to collide with each other and the inside surface of the balloon. As the volume of the balloon decreases, the gas particles become more crowded, increasing the number of collisions between them. This leads to a decrease in the distance between the gas particles and the inside surface of the balloon, causing the balloon to shrink and shrivel up.

In summary, when a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy, slow down, and collide less frequently, resulting in a decrease in pressure inside the balloon.

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Answer:

=3tn+4t

hope it helps...

Answer: 3nt + 4t.

Step-by-step explanation: Expand means distribute; there should be no parentheses or terms factored out.

t(3n + 4)

3nt + 4t <— multiply both terms in the parentheses by t.

Answer:

Step-by-step explanation:

Assume each player get x cards. Total number of cards now is 4x+24=52.

Therefore, 4x=52-24=28.

Then, x= 28/4=7.

The distance between Bloemfontein and Upington is a distance of 582 kilometers. The distance between two cities may vary depending on the route taken, traffic, and other factors. The distance between these two cities is measured in a straight line, which may not be the actual road distance.

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Answer:

8.5%

Step-by-step explanation:

Answer:

8.5%

Step-by-step explanation:

0.085

1: Ignore the 0 and take the numbers that is 85

2: Add a percent

3: Answer is 8.5%

Hope this helps.

Note that the notation   "∪C = {x : x ∈ for some S ∈ C} = ∪ { S:S ∈ C}" represents a mathematical statement involving sets.

∪C : This represents the  union (∪) of the sets in C.

{x : x ∈ for some S ∈ C}: This is the description or definition of the elements in the set formed by the union of sets in C.

It states that an element x belongs to the union of   sets in C if and only if x belongs to at least one set S that is an   element of the set C.

= ∪{ S:S ∈ C}   : This means that the union (∪) of sets in C is equal to the union of all sets S that belong to the set C.

In summary,  the statement is saying that the union of sets in C consists of all elements that belong to at least one set in C. It is the combined collection of elements from all sets in C.

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Answer:

d

Step-by-step explanation:

The inverse of a conditional statement, makes both the hypothesis and conclusion or "p" and "q" negative. In other words, it adds a not to both sides.

So the inverse of "If p, then q" would be "If not p, then not q."

"If the measure of angle 1 does not equal 60 degrees, then angle 1 is not acute."

Answer:

Should be x coordinate of point C, hope this helps

Step-by-step explanation:

Answer:

71

Step-by-step explanation:

The measure of angle WXY will be thee ame as the measure of the intercepted arc, 109°.

W and Y are both tangent to the circle; this means angle XWZ and angle XYZ are both 90°.

Every quadrilateral has a total measure of 360°; to find the measure of WZY, we subtract:

360-90-90-109 = 71°

The measure of angle WZY (∠WZY) is; 71°

From the attached image, we can say that the measure of ∠WXY will be the same as the measure of the intercepted arc, 109°.

Now, W and Y are both tangent to the circle and this means that ∠XWZ and ∠XYZ are both equal to 90°.

Now, every quadrilateral has a total internal sum of angles as 360°.

Thus,  ∠WZY is gotten from;

∠WZY = 360 - (90 + 90 + 109)

∠WZY = 71°

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Answer:

z= 6

Step-by-step explanation:

You check it by plugging the value, z, into the equation.

11(6)-5=9(6)+7

61=61

Answer:

z=6

Step-by-step explanation:

11z-9z=7+5

2z=12

z=6

a) Approximately 77.94% of possums have heads less than 95.4 mm.

b) Approximately 96.93% of possums have heads more than 85.8 mm.

c) Approximately 74.93% of possums have heads between 85.8 and 95.4 mm.

d) The maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.

a) We can use the normal distribution to answer this question. Let X be the head length of a brushtail possum. Then X has a normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm. We want to find P(X < 95.4 mm).

Using the standard normal distribution table or a calculator, we can find the z-score corresponding to a head length of 95.4 mm:

\(z = \frac{(95.4 - 92.6)}{3.6} = 0.78\)

Then, using the standard normal distribution table, we can find the probability that a standard normal variable is less than 0.78:

P(Z < 0.78) = 0.7794

Therefore, approximately 77.94% of possums have heads less than 95.4 mm.

b) Again, using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find P(X > 85.8 mm).

Finding the corresponding z-score:

\(z = \frac{(85.8 - 92.6)}{3.6} = -1.89\)

Using the standard normal distribution table, we find:

P(Z > -1.89) = P(Z < 1.89) = 0.9693

Therefore, approximately 96.93% of possums have heads more than 85.8 mm.

c) To find the percentage of possums with heads between 85.8 and 95.4 mm, we can subtract the probability of heads less than 85.8 mm from the probability of heads less than 95.4 mm:

P(85.8 < X < 95.4) = P(X < 95.4) - P(X < 85.8)

Using the same calculations as in parts (a) and (b), we get:

P(85.8 < X < 95.4) = 0.7794 - 0.0301 = 0.7493

Therefore, approximately 74.93% of possums have heads between 85.8 and 95.4 mm.

d) We want to find the maximum head length of the shortest 10% of possum heads. This is equivalent to finding the 10th percentile of the distribution. Using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find the head length x such that P(X < x) = 0.1.

Using the standard normal distribution table or a calculator, we can find the z-score corresponding to the 10th percentile:

P(Z < z) = 0.1

z = -1.28

Then, we can find the corresponding head length x:

x = μ + zσ = 92.6 + (-1.28)(3.6) = 87.68

Therefore, the maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.

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The answers are:

27. P(6) = 0.2 , 28. P(even number) = 0.6 , 29. P(6) = 1/10 , 30. P(even number) = 5/10 = 0.5

The experimental probability of getting a 6 is 0.2, because 2 out of 50 displays were 6s.

The experimental probability of getting an even number is 0.6, because 30 out of 50 displays were even numbers.

The theoretical probability of getting a 6 is 1/10, because there is 1 chance out of 10 that the calculator will display a 6.

The theoretical probability of getting an even number is 5/10, because there are 5 chances out of 10 that the calculator will display an even number.

As you can see, the experimental probabilities are close to the theoretical probabilities. This is because the calculator was programmed to randomly display a digit from 0 to 9, so the results should be evenly distributed. However, there is always some chance of variation, so the experimental probabilities may not be exactly equal to the theoretical probabilities.

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Answer:

vssguudgebseisiehjejsieheusssushsbddjdhfbbfjfjfnfnfnfnfnnfjfngjfjfjfjfjfjfjfjf

Answer:

13.1833333 hours

Step-by-step explanation:

Answer:

13 hours 11 minutes.

Step-by-step explanation:

Adding the hours we get

7 + 5 = 12 hours

Adding the minutes:

= 53 + 18

= 71 minutes

= 1 hours 11 minutes

So the answer is

13 hours 11 minutes.

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

We cannot conclude that there are more than 70,000 defined words in the dictionary.

To test the claim that there are more than 70,000 defined words in the dictionary, we can set up the null and alternative hypotheses as follows:

Null Hypothesis (H0): The mean number of defined words on a page is 48.0 or less.

Alternative Hypothesis (H1): The mean number of defined words on a page is greater than 48.0.

So, sample mean

= (59 + 37 + 56 + 67 + 43 + 49 + 46 + 37 + 41 + 85) / 10

= 510 / 10

= 51.0

and, the sample standard deviation (s)

= √[((59 - 51)² + (37 - 51)² + ... + (85 - 51)²) / (10 - 1)]

≈ 16.23

Next, we calculate the test statistic using the formula:

test statistic = (x - μ) / (s / √n)

In this case, μ = 48.0, s ≈ 16.23, and n = 10.

test statistic = (51.0 - 48.0) / (16.23 / √10) ≈ 1.34

With a significance level of 0.05 and 9 degrees of freedom (n - 1 = 10 - 1 = 9), the critical value is 1.833.

Since the test statistic (1.34) is not greater than the critical value (1.833), we do not have enough evidence to reject the null hypothesis.

Therefore, based on the given data, we cannot conclude that there are more than 70,000 defined words in the dictionary.

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After answering the given query, we can state that Marty decided to put equation $2500 in bonds as a result.

Using the equals sign (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical formulas through a mathematical assertion. The equal symbol, for example, puts a space between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two lines that are printed on opposite sides of a letter. Most of the time, the emblem and the particular program match. e.g., 2x - 4 = 2 is an example.

Assume that x represents the amount invested in bonds and y represents the amount invested in equities.

The issue statement informs us that:

x + y = 9000 (Equation 1)

Since the assets generate $525 in yearly income, we can write:

0.05y + 0.08x = 525 (Equation 2)

We must answer for x in Equation 2 in order to determine the value of x (the sum spent in bonds).

Let's first rephrase Equation 1 in terms of x as follows:

y = 9000 - x

We can now enter the following equation in place of y in Equation 2:

0.05(9000 - x) + 0.08x = 525

450 - 0.05x + 0.08x = 525

0.03x = 75

x = 2500

Marty decided to put $2500 in bonds as a result.

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The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

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Answer:

probably 145.15ft^2 but who really knows good luck

Step-by-step explanation:

we're gonna have to find the area of the square and circle and then subtract the square area to see the remaining shaded area's value. if the square has side of length 16 then we know it's area is 16ftx16ft=256ft^2. Now the area of the circle requires us to know its radius. we see the diagonal dashed line travels the diameter of the circle. you can use pythagoras theorem to find its length so sqrt(16^2+16^2)=22.63ft. but this is diameter and we want radius so 22.63/2=11.3ft. the formula for the area of a circle is pi*r^2 so pi*11.3^2=401.15ft^2. now we can say 401.15-256=145.15ft^2