What expression represents "eight more than a number cubed and 2"?

Possible Answers:

Answer:

$ 38.17

Step-by-step explanation:

Answer: B. [tex]26x+270\leq1,325[/tex]

Step-by-step explanation:

Let 'x' denote the amount of money Annie can spend lunch for each person.

Given: The cost of renting the meeting room = $270

The number of people attend the meeting = 26

Then, the expression for total amount spent on lunch will be :-

[tex]\text{Total amount on lunch}=26x[/tex]

The expression for total spent by Annie will be:-

[tex]26x+270[/tex]

Since, the budget  for renting a meeting room at a local hotel and providing lunch= $1325

Thus, the inequality shows how to find the amount, x, Annie can spend lunch for each person will be :-

[tex]26x+270\leq1,325[/tex]

Final answer:

To solve for the length and width of the garden, we set up a quadratic equation based on the given area and the relation between length and width. Upon solving the quadratic equation, we find the width to be 5 feet and the length to be 10 feet.

Explanation:

The problem states that the length of a rectangular garden is 5 feet longer than its width and that the area of the garden is 50 square feet.

To find the length and width, let's define the width as w feet. Therefore, the length will be w + 5 feet. The area of a rectangle is found by multiplying the length and width, so we have the equation:

w × (w + 5) = 50

Expanding this we get:

w^2 + 5w - 50 = 0

Now we need to solve this quadratic equation for w. Factoring the quadratic, we find that (w + 10)(w - 5) = 0, which gives us two possible solutions for w: -10 and 5.

Since a width can't be negative, we discard -10 and take w = 5 feet. So, the width of the garden is 5 feet and the length is 5 + 5 = 10 feet.

Answer:

The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 5.2, \sigma = 0.08, n = 20, s = \frac{0.08}{\sqrt{20}} = 0.0179[/tex]

Find the interval that contains 95.44 percent of the sample means.

0.5 - (0.9544/2) = 0.0228

Pvalue of 0.0228 when Z = -2.

0.5 + (0.9544/2) = 0.9772

Pvalue of 0.9772 when Z = 2.

So the interval is from X when Z = -2 to X when Z = 2

Z = 2

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]2 = \frac{X - 5.2}{0.0179}[/tex]

[tex]X - 5.2 = 2*0.0179[/tex]

[tex]X = 5.2358[/tex]

Z = -2

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-2 = \frac{X - 5.2}{0.0179}[/tex]

[tex]X - 5.2 = -2*0.0179[/tex]

[tex]X = 5.1642[/tex]

The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches

Final answer:

To calculate 1/x divided by 1/y, you multiply 1/x by the reciprocal of 1/y, which is y, resulting in y/x.

Explanation:

The question asks us to find the value of 1/x divided by 1/y. This is a division problem involving fractions and can be solved using the rules of division for fractions.

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second. In this case, the reciprocal of 1/y is y/1 which simplifies to y. Therefore, the division 1/x ÷ 1/y becomes 1/x × y.

When we multiply these together, we get:

So, the answer is y/x.

The equation of the parabola in vertex form is f(x) = -7x^2 + 4

To write the equation of a parabola in vertex form, we use the formula f(x) = a(x - h)^2 + k where (h, k) represents the vertex. In this case, the vertex is (0,4) so our equation becomes f(x) = a(x - 0)^2 + 4 which simplifies to f(x) = ax^2 + 4. To find the value of a, we substitute the coordinates of the point (1,-3) into the equation and solve for a. Plugging in these values, we get -3 = a(1)^2 + 4, which simplifies to -3 = a + 4. Solving for a, we find that a = -7. Therefore, the equation of the parabola in vertex form is f(x) = -7x^2 + 4.

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Answer:

C.

Step-by-step explanation:

Final answer:

A teacher will require 1200 square inches of fabric to cover the surface area of two foam cubes, with each side measuring 10 inches.

Explanation:

The question involves finding the total surface area of two foam cubes to determine how much fabric a teacher needs to cover both cubes. To solve this, we must calculate the surface area of one cube and then multiply by two because there are two identical cubes. Each face of a cube measures 10 inches on a side.

The area of one face is given by:

Area of one face = side × side = 10 in × 10 in = 100 square inches

Since a cube has 6 faces, the total surface area of one cube would be:

Total surface area of one cube = 6 × Area of one face = 6 × 100 square inches = 600 square inches

Therefore, for two cubes, we need:

Total surface area for two cubes = 2 × 600 square inches = 1200 square inches

The teacher will require 1200 square inches of fabric to cover the two cubes.

See the attached figure.

E direction is a line which is parallel to x-axis. (blue line).

NW direction lies on a line that is at an angle of 135 degrees to the positive direction of the x axis. (red lines).

Intersection between red line and blue line will give the coordinates of the vessel in distress location which is point C (3,2)

Answer:

Her goal is to read 150 pages each day.

Step-by-step explanation:

Let p represent the number of pages she wants to read each day.

Then 136% of that number is 204 pages, or, in an equation,

         1.36p = 204

Solving for p, we get:  p = 204/1.36 = 150 pages

Her goal is to read 150 pages each day.

Answer:

p-8

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

30+30+30+30+30=150

Also 5*30=150

Answer:

Decigrams to Decagrams/Dekagrams

Step-by-step explanation:

1 decigram is equal to 0.01 Deca/Dekagrams

Decigrams have less value than Decagrams.

Therefore,

You divide 1 decigram by 100 to get 0.01 decagrams.

Answer:

The correct tabe is here,

let take f(x)=y

then if

x=1,f(x)=7

x=2,f(x)=11/2

x=3,f(x)=5

x=4,f(x)=19/4

and so on so so far

To match the units of distance in feet and time in seconds, the units of the gravitational constant g must be feet per second squared (ft/s^2). On Earth, g is roughly 32.17 ft/s² in U.S. Customary units.

When Emily drops a coin from rest, the distance traveled by the coin (s) can be used to calculate the acceleration due to gravity (g) when the time (t) the coin took to fall is known. The formula provided suggests that distance is equal to 0.5 times gravity acceleration times the square of time (s = 0.5 * g * t²).

Given that Emily measured the distance in feet and the time in seconds, the units for g must be compatible with these measurements. Since distance is in feet and time is squared in seconds, the unit for g must be feet per second squared (ft/s²) to ensure that all units cancel out correctly, leaving us with the unit of distance in feet. On Earth's surface, the value of g using U.S. Customary units is approximately 32.17 ft/s².

Answer:

8/3 is between 2 and 3 above 2.5

11.3 is between 3 and 4 above 3.5

Step-by-step explanation:

8/3 converts to the decimal 2.666666... which means its located on the number line between 2 and 3 above 2.5.

11/3 converts to 3.6666.... which means its located on the number line between 3 and 4 above 3.5.

Draw a horizontal number line. Mark the point 8/3 at approximately 2.67 and the point 11/3 at approximately 3.67 to visually represent these values.

To plot the points 8/3 and 11/3 on a number line.

Draw a Horizontal Number Line

Start by drawing a horizontal line on a piece of paper or a whiteboard. This line will serve as your number line.

Make sure it's long enough to accommodate the range of values working with.

Mark the Point for 8/3 (approximately 2.67)

To plot the point 8/3 on the number line, need to find its approximate location.

To do this, you can divide 8 by 3 to calculate its decimal value:

8 ÷ 3 ≈ 2.67 (rounded to two decimal places).

Now, locate the point approximately at 2.67 on the number line, and make a small mark or dot to represent this point.

Mark the Point for 11/3 (approximately 3.67)

To plot the point 11/3 on the number line, calculate its approximate location in a similar way:

11 ÷ 3 ≈ 3.67 (rounded to two decimal places).

Locate the point approximately at 3.67 on the number line and make a small mark or dot to represent this point.

Label the Points (Optional)

label these points to indicate what they represent.

label the point at 2.67 as "8/3" and the point at 3.67 as "11/3" to provide context for the values you've plotted.

Therefore, the plotting of the points 8/3 and 11/3 on the number line is on the right side of zero between 2 and 4.

Learn more about number line here

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Answer:

Prime factors of 24 is 2× 3×2×2

Step-by-step explanation:

Given : Number  24.

To find: Write 24 as a product of its prime factors.

Solution : We have given that number 24

Prime number : numbers which are divisible by 1 or itself only

Example = 2, 3, 5, 7,....etc

So we will find the factor of 24 by prime factorization

24 is divisible by 1

24 ÷ 3 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

Hence we can write 24 as 2× 3×2×2

Therefore, Prime factors of 24 is 2× 3×2×2

y = 0 . . . . is the equation of the line.

_____

The line shows y to have the same value for every value of x. Thus the value of y is a constant, and there is no dependence on x at all. This is true for any horizontal line. Here, the constant value is zero, so the equation is ...

... y = 0

The correct answer is C) (5m^50 - 11n^8) (5m^50 + 11n^8)

We can tell this because of the rule regarding factoring the difference of two perfect squares. When we have two squares being multiplied, we can use the following rule.

a^2 - b^2 = (a - b)(a + b)

In this case, or first term is 25m^100. So we can solve that by setting it equal to a^2.

a^2 = 25m^100 -----> take the square root of both sides

a = 5m^50

Then we can do the same for the b term.

b^2 = 121n^16 ----->take the square root of both sides

b = 11n^8

Now we can use both in the equation already given

(a - b)(a + b)

(5m^50 - 11n^16)(5m^50 + 11n^16)

To decide which random sample has a higher probability, we need to consider the sample size. As the sample size increases, the sample mean tends to approach the population mean more closely. We can use the properties of the normal distribution and the formula for the standard error of the mean to calculate the probabilities for each random sample size.

To decide which has a higher probability, we need to consider the sample size of each random sample. In general, as the sample size increases, the sample mean tends to approach the population mean more closely.

Given that each sample is from a population that is normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution to calculate the probabilities.

(a) For a random sample of size n = 10, the probability of the sample mean being between 90 and 110 can be calculated using the formula for the standard error of the mean:

Standard error of the mean = standard deviation / sqrt(sample size)

Using this formula, the standard error of the mean for n = 10 is 15 / sqrt(10) = 4.74.

Since the sample mean follows a normal distribution, we can use the properties of the normal distribution to find the probability:

p(90 ≤ sample mean ≤ 110) = p((90 - 100) / 4.74 ≤ (sample mean - 100) / 4.74 ≤ (110 - 100) / 4.74)

We can look up the probabilities for the z-scores using a standard normal distribution table or a calculator to find the probability for the given range.

(b) For a random sample of size n = 20, we can follow the same steps as above to calculate the probability of the sample mean being between 90 and 110.

The standard error of the mean for n = 20 is 15 / sqrt(20) = 3.35.

p(90 ≤ sample mean ≤ 110) = p((90 - 100) / 3.35 ≤ (sample mean - 100) / 3.35 ≤ (110 - 100) / 3.35)

We can again use a standard normal distribution table or a calculator to find the probability for the given range.