Subtract the expressions.

(7.43n − 2.2) − (6 + 10.5n)

−30.70n − 4.5
−3.07n − 8.2
9.63n − 4.5
17.93n + (−8.2)

Answer:

It'd be $4,700

Step-by-step explanation:$500 + $2,400 + $1,800 = $4,700. Minus that amount from her savings account total and that's how much money she has left.

The expression that represents the height of the triangular base of the pyramid is given by: Option B: (5/2)√3 untis

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

\(|AC|^2 = |AB|^2 + |BC|^2\)

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

The question is incomplete, and the upper part of the completed question is:
"The base of a solid oblique pyramid is an equilateral triangle with an edge length of 5 units. A solid oblique pyramid has an equilateral triangle base with an edge length of 5 units. "

The diagram of the base of the considered pyramid is attached below.

The perpendicular from A to BC is touching BC at C, and is bisecting it (it can be proved).

Consider the triangle ADB. It is a right angled triangle.

We need the length of AD which represents the height of the triangle ABC.

This is obtained using Pythagoras theorem as:

\(|AB|^2 = |AD|^2 + |DB|^2\\\\|AD|^2 = |AB|^2 - |DB|^2\\\\|AD| = \sqrt{5^2 - \left( \dfrac{5}{2}\right)^2}\)

(took positive root because of |AD| being length, which is a non-negative quantity).

SImplifying it, we get:

\(|AD| = \sqrt{5^2 - \left( \dfrac{5}{2}\right)^2}\\\\|AD| = \sqrt{\dfrac{5^2(4-1)}{4}} = \dfrac{5\sqrt{3}}{2} = \dfrac{5}{2} \times \sqrt{3} \: \rm units\)

Thus,  the expression that represents the height of the triangular base of the pyramid is given by: Option B: (5/2)√3 untis

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Trigonometric functions, rational functions, hyperbolic functions, and log functions are some examples of having inverse.

The inverse of a function is basically a reverse function or undo of the function.

For example y = f(x) then the inverse will be x = f(y).

It means in the inverse function we need to interchange x and y.

Suppose a function,

y = sinx here x is the angle while y is the real number.

Now, x = sin⁻(y) here sin⁻(y) is a function of x as inverse.

Another example y = 2x

x = 2/y if x is output then it will be inverse.

Hence "Trigonometric functions, rational functions, hyperbolic functions, and log functions are some examples of having inverse".

For more information about the inverse of a function,

brainly.com/question/2541698

#SPJ1

a) The probability of a randomly selected diner waits less than 8 minutes for a table is 0.4

b) The probability of a randomly selected diner waits more than 1.5 minutes is 0.925

Given, wait times of between 0 and 20 minutes at a local restaurant follow a uniform distribution.

The probability density function of a uniform distribution is given by

f(x) = {1/(b-a)} where a ≤ x ≤ b

where a = 0 and b = 20

Therefore, the probability density function of f(x) = 1/20 for 0 ≤ x ≤ 20

For the  probability that a randomly selected diner waits between 2 and 7.5 minutes for a table, we need to find the area under the curve from x = 2 to x = 7.5

∴ P(2 ≤ x ≤ 7.5) = ∫₂⁷.⁵(1/20) dx

= 5.5/20 ⇒ 0.275

a) We need to find the area under the curve from x = 0 to x = 8

∴ P(x < 8) = ∫₀⁸(1/20) dx

= 8/20 ⇒ 0.4

b) We need to find the area under the curve from x = 1.5 to x = 20

∴ P(x > 1.5) = ∫₁.₅²⁰(1/20) dx

= 18.5/20 ⇒ 0.925

To know more about the "probability" of a randomly selected: https://brainly.com/question/30044489

#SPJ11

The value of A is 114.

The value of B is 46.

The value of C is 64.

The value of D is 200.

statistics, the science of collecting, analyzing, presenting, and interpreting data.

To find the value of A will be = Total for cell phone - No of Mp3 player

= 154 - 40

= 114

To find B = Mp3 Player + Non Mp3 Player

= 24 + 22

= 46

To find C = Mp3 Player with cellphone + Mp3 Player without cellphone

= 40 + 24

= 64

To find D = 136 + C

= 136 + 64

= 200

To learn more on statistics, visit https://brainly.com/question/15525560

#SPJ1

The sampling distribution of sample proportions have a standard deviation of 0.09 when the sample size is 18.

The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Standard Deviation is calculated by

Each number's deviation from the mean must be determined, and then squared.

Next, add up all of these values.

Divide the result by the quantity of numbers.

Then calculate its square root.

σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²

Given data,

To determine the sample size, n, that will result in a sampling distribution of sample proportions with a standard deviation of 0.09, we can use the formula for the standard deviation of a sample proportion:

σ = √((p (1 - p)) / n)

Given that the standard deviation (σ) is 0.09 and the success rate (p) is 0.18, we can rearrange the formula and solve for n:

0.09 = √((0.18 * (1 - 0.18)) / n)

Squaring both sides of the equation, we get:

0.0081 = (0.18 (1 - 0.18)) / n

Simplifying further:

0.0081 = 0.1476 / n

Multiplying both sides by n:

n x 0.0081 = 0.1476

Dividing both sides by 0.0081:

n = 0.1476 / 0.0081

n ≈ 18

Therefore, the sample size, n, required for the sampling distribution of sample proportions to have a standard deviation of 0.09 is 18.

To learn more about standard deviation click :

https://brainly.com/question/28189061

#SPJ6

Answer:

15/2/(9/2-41/8)=15/2(36/8-41/8)=15/2/-5/8=60/8/-5/8=60/-5=-12

Step-by-step explanation:

Answer: The correct answer is A)

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Answer:

\(y=2(x+6)^2+7\)

\((-6,7)\)

Step-by-step explanation:

\(y=2x^2+24x+79\)

Completing the square is a process of converting a quadratic equation in standard form into vertex form.

The first step in completing the square is grouping the quadratic and linear terms of the quadratic equation.

\(y=(2x^2+24x)+79\)

Factor out the coefficient of the quadratic term,

\(y=2(x^2+12x)+79\)

Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.

\(y=2(x^2+12x+36-36)+79\)

Simplify,

\(y=2(x^2+12x+36)+79+(2)(-36)\)

\(y=2(x+6)^2+79-72\)

\(y=2(x+6)^2+7\)

The x-coordinate of the vertex of the equation is equal to (-1) times the numerical part of the quadratic term, and the y-coordinate is equal to the constant.

\((-6,7)\)

Answer

Explanation

Debby has 15 yards in total to make pillow cases.

Each pillow case requires (8/9) yard.

How much yard is left after she makes as many pillowcases as she can.

1 pillowcase = (8/9) yard

We need to obtain how many pillowcases 15 yards can make.

That is obtainable by dividing 15 by (8/9).

Hence, 16.875 pillowcases of (8/9) yards each, are obtainable from 15 yards.

Since pillowcases cannot exist in fraction, the 0.875 pillowcase has to be extra yards of fabric.

1 pillowcase = (8/9) yard

0.875 pillowcase = 0.875 × (8/9) = (7/8) × (8/9) = (7/9) or 0.778 yards.

Hence, the number of yards that will be left after making as many

Answer:

x = 12

Step-by-step explanation:

Given the expression \(x \div 4 + 5 = 8.\) we are to find the value of x;

Step 1; Rearrange the equation:

\(\frac{x}{4} + 5 = 8\\\)

Step 2: subtract 5 from both sides of the equation:

\(\frac{x}{4}+5-5 = 8-5\\\frac{x}{4} + 0 = 3\\\frac{x}{4} = 3\\)

Step 3: Find the value of x:

\(x = 4*3\\x = 12\)

Hence the solution to the equation is 12 not -72

Answer:

x=-12

Step-by-step explanation:

Given the expression  we are to find the value of x;

Step 1; Rearrange the equation:

Step 2: subtract 5 from both sides of the equation:

Step 3: Find the value of x:

Hence the solution to the equation is 12 not -72

Answer:

y = −3x + 2

Step-by-step explanation:

It slopes down so it must be B or C

It drops 3 in y for every increase of 1 in x

so m = -3

Answer:

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

Step-by-step explanation:

Let be \(x\) and \(y\) the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:

i) She found that 4 cylinders and 5 prisms weigh 32 ounces:

\(4\cdot x +5\cdot y = 32\,oz\) (Eq. 1)

ii) And that 1 cylinder and 8 prisms weigh 35 ounces:

\(x + 8\cdot y = 35\,oz\) (Eq. 2)

Now we solve the system of linear equations algebraically:

From (Eq. 2):

\(x = 35 - 8\cdot y\)

(Eq. 2) is (Eq. 1):

\(4\cdot (35-8\cdot y) + 5\cdot y = 32\)

\(140-32\cdot y +5\cdot y = 32\)

\(32\cdot y - 5\cdot y = 140-32\)

\(27\cdot y = 108\)

\(y = 4\,oz\)

From (Eq. 2):

\(x = 35 - 8\cdot (4)\)

\(x = 35 - 32\)

\(x = 3\,oz\)

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

If the p-value is less than or equal to the selected significance level, the null hypothesis is rejected; otherwise, it is not. In other words, if p, reject\(H_{0}\); if p>, do not reject \(H_{0}\).

In null hypothesis testing, this criterion, also known as (alpha), is frequently set to 05. If there is less than a 5% chance that the null hypothesis would be accepted and a result as spectacular as the effects that result would occur, the null hypothesis is rejected. When this happens, the result is said to be statistically significant.

The null hypothesis would be rejected if a statistical test was conducted with a threshold of relevance = 0.1, 0.05, & 0.01.

If the P value is smaller than alpha, the preset level of statistical significance, the alternative hypothesis is considered instead of the null hypothesis.

Learn more about the null hypothesis at

https://brainly.com/question/16945299?referrer=searchResults

#SPJ4

If Allie spins the spinner 2 times. the probability that Allie spins A on the first spin and & on the second spin is: B. 1/16.

Based on the information provided, the spinner has four possible outcomes: K, S, A, and %, each with equal probability of 1/4.

To find the probability that Allie spins A on the first spin and & on the second spin, we need to multiply the probability of spinning A on the first spin (1/4) by the probability of spinning & on the second spin (1/4), because the two events are independent.

Therefore, the probability is:

P(A on first spin and & on second spin) = P(A) × P(&) = (1/4) × (1/4) = 1/16

So the probability that Allie spins A on the first spin and & on the second spin is 1/16.

Learn more about probability here:https://brainly.com/question/24756209

#SPJ1

Answer:

The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph.

I hope it helps.

Answer:

34.65 mi²

Step-by-step explanation:

Area of parallelogramam = b · h

b = 6.3 mi

h = 5.5 mi

Let's solve

6.3 · 5.5 = 34.65 mi²

So, the area of the shape is 34.65 mi²

The weight of the compact car, which is approximately 1,354 kilograms, can be converted to 1,354,000 grams.

In the metric system, "kilo" means thousand, so 1 kilogram is equal to 1000 grams. To convert from kilograms to grams, we simply multiply the weight in kilograms by 1000.

In this case, the weight of the compact car is given in kilograms as 1,354. To convert to grams, we multiply by 1000 to get:

1,354 kg x 1000 g/kg = 1,354,000 g

Therefore, the weight of the compact car in grams is approximately 1,354,000 grams.

The weight of an object is a measure of the force with which gravity pulls on the object. The unit of weight in the metric system is the newton (N), but kilograms (kg) are commonly used as a unit of mass and weight in everyday life. The conversion between mass and weight depends on the local acceleration due to gravity, which is approximately 9.81 m/s^2 at the Earth's surface.

Learn more about kilograms here:

https://brainly.com/question/11593892

#SPJ4

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

In conclusion, the set {0} ∪ {1/n | n∈ℤ} is not an open set.

Explanation:

You are asking whether the set {0} ∪ {1/n | n∈ℤ} is an open set.

Step 1: Define the set
First, let's define the set in question. The set can be written as {0} ∪ {1/n | n∈ℤ, n≠0}, which means the union of two sets: {0} and {1/n | n∈ℤ, n≠0}. The second set contains all the elements of the form 1/n, where n is an integer, and n is not equal to 0.

Step 2: Determine if the set is open
An open set is a set in which for every point x, there exists some ε > 0 such that the open interval (x-ε, x+ε) is entirely contained within the set. Now, let's see if our set meets this criterion.

For any non-zero integer n, the point 1/n is in the set. However, there is no ε > 0 such that the open interval (1/n - ε, 1/n + ε) is entirely contained within the set, since the interval will contain points that are not of the form 1/n. This means that the set is not open, as there is no suitable ε for these points.

Since {0} is a singleton set and singleton sets are always closed, and {1/n | n∈ℤ} is a set of real numbers, the union "{0} u {1/n | n∈ℤ}" is not an open set. This is because it contains points on the boundary (0) as well as points that are not interior points (such as 1 and -1) due to the nature of the set {1/n | n belongs to z}.

In conclusion, the set {0} ∪ {1/n | n∈ℤ} is not an open set.

Know more about the open set click here:

https://brainly.com/question/31480826

#SPJ11

Answer: x+12

We know that the area is length * width. Since length is x+4, we know

(x+4) * something = x^2+16x+48.

To find that something, note that 48 (from the right side) = 4 (from the left side) * 12. Why is this important? Well, then we know that the something is x+12.

This is because (x+4) * (x+12) = x^2 + 16x + 48. But just focus on this part: 48. Even if we put like 3x+12 or something, that would work out to 3x^2+28x+48. It's 48 every time.

Hope that helped,

-sirswagger21

Answer:

\(m\widehat{VU}=120^{\circ}\)

Step-by-step explanation:

The angle \(\angle TUV\) forms arc \(\widehat{TV}\). The measure of this arc is twice the measure of angle \(\angle TUV\), since \(U\) is a point on the circle. Since \(\overline{TU}\) forms an arc \(\widehat{TU}\), we can set up the following equation:

\(\widehat{TV}+\widehat{VU}=\widehat{TU}\).

Since arc TU represents half of a circle and there are 360 degrees in a circle, we can substitute the following values and solve for the measure of arc VU:

\(\\2\cdot 30^{\circ}+\widehat{VU}=180^{\circ},\\60^{\circ}+\widehat{VU}=180^{\circ},\\m\widehat{VU}=\boxed{120^{\circ}}\)

To solve this problem, we can use the normal approximation to the binomial distribution. Given that 65% of murders are committed with a firearm, we can assume that the probability of a murder being committed with a firearm is 0.65.

To apply the normal approximation, we need to calculate the mean (μ) and the standard deviation (σ) of the binomial distribution. The mean is given by μ = n * p, where n is the sample size and p is the probability of success. In our case, μ = 150 * 0.65 = 97.5. The standard deviation is calculated as σ = √(n * p * (1 - p)), which gives us σ = √(150 * 0.65 * 0.35) ≈ 5.46. Next, we need to convert the problem into a standard normal distribution by using z-scores. The z-score is calculated as z = (x - μ) / σ, where x is the number of murders committed with a firearm that we want to find the probability for. In this case, we want to find the probability of having 100 or more murders committed with a firearm, so we use x = 100. The corresponding z-score is z = (100 - 97.5) / 5.46 ≈ 0.458. Using a standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of 0.458, which is approximately 0.6736. This can be done by subtracting the probability from 1, giving us 1 - 0.6736 ≈ 0.3264. Therefore, the probability that 100 or more murders out of a sample of 150 are committed with a firearm is approximately 0.3264, which is not one of the given options.

Learn more about probability here: brainly.com/question/15573695

#SPJ11

Answer: Choice D (lower right corner)

A transition or translation is where we shift a figure sliding it up, down, left or right. The upper "7" shaped figure slides down to get the other "7", or the bottom figure is slid up to match the top figure.

Step-by-step explanation:

Reread the underlined sentence on page 4.

What does the figurative language in this

sentence suggest about the narrator?

He feels that people should have used better tools

to help them detect advanced life forms on other

planets.

He sympathizes with people for not apprehending

that there was advanced life on other planets.

He is unable to believe that there could be any

form of life more advanced than humans.

He blames people's exaggerated idea of their

superiority for their failure to imagine life more

advanced than themselves.