4. Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint,
1 1/2 cups
of red paint, and 1/2 of a cup of white paint. Elena has 2/3 of a cup of white paint.
a. Assuming she has enough red paint and blue paint, how much purple paint can
Elena make?

Answer:

B

Step-by-step explanation:

MOVE TO THE RIGHT 9 TIMES!!

Elizabeth will practice piano for 252 minutes in one week by solving function f(x)=504x where x = time in multiple of 2years.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

As given

f(x)=504x where x = time in multiple of 2 years

For 1 year x=1/2

Hence,

y=504*1/2

y=252 minutes

Elizabeth will practice piano for 252 minutes in one week.

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When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.

A cube is a solid shape with six square faces. Each side of a square  has the same side length, so all  faces are the same size.

A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.

Shape Properties of  Cube  

Thus, when edge D connects with edge X, this net is folded into a cube.

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The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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The hospital can get 4.15 milligrams from these three companies.

A linear equation is one in which the highest power of any variable is not more than 1. A linear equation in 2 variables can be solved by substitution method, if we have two simultaneous equations.

Here, we know that

Company A's supply of medicine = 1.7 mg

also, company A's supply = 2( B's supply - C's supply)

⇒ 1.7 = 2( B - C)

⇒ 1.7 = 2B - 2C .... (1)

Moreover, we are given that

A's supply = C's supply + 0.9

⇒ 1.7 = C + 0.9

⇒ 1.7 - 0.9 = C

⇒ 0.8 = C

Now, substituting the value of C in (1), we get,

1.7 = 2B - 2(0.8)

1.7 = 2B - 1.6

1.7 + 1.6 = 2B

⇒ B = 3.3/2

B = 1.65

Thus, the total supply from all three companies is (1.7 + 1.65 + 0.8) = 4.15 mg

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Answer: 2048

Step-by-step explanation:

(25+(2×7)+3×(6-3)+2000​

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Ophelia's commission for that week's sales of $13,330 is $1,499.40.

To calculate Ophelia's commission, we need to find the amount of sales that exceeds $5,000 and then apply the commission rate of 18% to that excess amount.

First, we subtract $5,000 from the total sales of $13,330 to find the excess amount:

Excess amount = $13,330 - $5,000 = $8,330

Next, we apply the commission rate of 18% to the excess amount:

Commission = 18% of $8,330

To find 18% of $8,330, we multiply $8,330 by 0.18:

Commission = $8,330 * 0.18 = $1,499.40

Therefore, Ophelia's commission for that week's sales of $13,330 is $1,499.40.

Ophelia earns a commission of 18% on the portion of sales that exceeds $5,000. Since her total sales were $13,330, the excess amount is $8,330. Multiplying this excess amount by the commission rate of 18% gives us the commission earned. It's important to note that commission is calculated only on the amount that exceeds $5,000, not on the entire sales amount.

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Answer:

-5

Step-by-step explanation:

100 - 121 + 16

Power of 2 just means to multiply the number by iteself. So 10×10, 11×11, 4×4.

Answer: Irrigation water can come from groundwater, through springs or wells, surface water, through rivers, lakes, or reservoirs, or even other sources, such as treated wastewater or desalinated water. As a result, it is critical that farmers protect their agricultural water source to minimize the potential for contamination.

Step-by-step explanation:

Answer:

Total pipes = 692 pipes

Step-by-step explanation:

Now we have to,

→ find the amount of pipes he use.

Forming the expression,

→ 610 plastic pipes + 82 metal pipes

Let's solve the problem,

→ 610 plastic pipes + 82 metal pipes

→ 610 + 82

→ 692 pipes

Hence, the farmer used 692 pipes.

Lets draw a picture:

where a is the side opposide to 60 and b is the side opposide to 30.

Since we have a right triangle, we can apply a trigonometric function. For instance, if we apply sine function, we get

then, a is given by

since sin60=0.866, then a is equal to

therefore, the answer is a = 50.23.

Answer:

(15+3d)/6 = c

2 1/2 + 1/2d = c     (more simplified)

Step-by-step explanation:

15 = -3(2c +d)

15 = -6c -3d

+3d       +3d

15 +3d = -6c

/-6          /-6

(15+3d)/6 = c

2 1/2 + 1/2d = c

Answer:

\((0.518,0.790)\)

Step-by-step explanation:

Use the formula \(CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }\) where \(\hat{p}\) is the sample proportion, \(n\) is the sample size, and \(z^*\) is the corresponding z-value for a given confidence level.

We know that \(\hat{p}=\frac{53}{81}\), \(n=81\), and \(z^*=2.5758\) for a 99% confidence level.

Therefore, the 99% confidence interval is \((0.518,0.790)\)

The number of boxes that Amanda can cover with W square inches of wallpaper will be equal to W/2(lw + lh + wh).

Let's assume that Amanda wants to build n wooden storage boxes. All of these boxes are shaped like rectangular prisms, as shown in the image below.

She wants to cover all the sides of each box with special wallpaper. If she has a total of W square inches of wallpaper, we need to find out how many boxes she can cover. Let's solve this problem mathematically.

Mathematical Solution:

Each rectangular prism has six sides (faces). If we want to cover all the six sides of a rectangular prism with special wallpaper, we need to find the total surface area of that rectangular prism. Therefore, the surface area of each rectangular prism can be calculated by the formula:

Surface Area = 2lw + 2lh + 2wh,

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

We know that Amanda has W square inches of wallpaper to cover all the boxes. Therefore, the total surface area of n boxes will be:

n × Surface Area = W.

Substituting the value of the Surface Area, we have:

n × (2lw + 2lh + 2wh) = W

2n(lw + lh + wh) = W

n(lw + lh + wh) = W/2

n = W/2(lw + lh + wh).

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The possible values for the discriminant include the following:

A. -1

D. -18

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.

Discriminant, D = b² - 4ac

In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.

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Complete Question:

The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.

A. -1

B. 3

C. 0

D. -18

Answer: D

Step-by-step explanation:

9514 1404 393

Answer:

  (a)  216

Step-by-step explanation:

Put 5 where n is in the formula to find the 5th term. Do the arithmetic.

  a5 = (5 +1)^3 = 6^3 = 216

The 5th term is 216.

The domain is {-8, -12, 1, -2} and the range is {5, -11, -1, -4}

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

The graph

On the graph, we have

(-8,5) (-12,-11)  (1-1) (-2,-4)

The domian is the set of the input values

Using the ordered pairs as a guide, we have

Domain = {-8, -12, 1, -2}

For the range, we have

The range is the set of the output values

So, we have

Range = {5, -11, -1, -4}

Hence, the range is  {5, -11, -1, -4}

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Answer:

16 per hour

Step-by-step explanation:

12/45         x/60 cross multiply

45x=720 divide by 45 from each side

x=16

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Step-by-step explanation:

substituting values and solving the equation,we get,

1) y= 4

2) x=4

3)x=10

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Answer:

Bias for the estimator = -0.56

Mean Square Error for the estimator = 6.6311

Step-by-step explanation:

Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.

To find - Determine the bias and the mean squared error for this estimator of the mean.

Proof -

Let us denote

X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)

Now,

An estimate of mean, μ is suggested as

\(\mu = \frac{3X_{1} + 4X_{2} }{8}\)

Now

Bias for the estimator = E(μ bar) - μ

                                    = \(E( \frac{3X_{1} + 4X_{2} }{8}) - 4.5\)

                                    = \(\frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5\)

                                    = \(\frac{3(4.5) + 4(4.5)}{8} - 4.5\)

                                    = \(\frac{13.5 + 18}{8} - 4.5\)

                                    = \(\frac{31.5}{8} - 4.5\)

                                    = 3.9375 - 4.5

                                    = - 0.5625 ≈ -0.56

∴ we get

Bias for the estimator = -0.56

Now,

Mean Square Error for the estimator = E[(μ bar - μ)²]

                                                             = Var(μ bar) + [Bias(μ bar, μ)]²

                                                             = \(Var( \frac{3X_{1} + 4X_{2} }{8}) + 0.3136\)

                                                             = \(\frac{1}{64} Var( {3X_{1} + 4X_{2} }) + 0.3136\)

                                                             = \(\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})] }) + 0.3136\)

                                                             = \(\frac{1}{64} [{3(57.76) + 4(57.76)}] } + 0.3136\)

                                                             = \(\frac{1}{64} [7(57.76)}] } + 0.3136\)

                                                             = \(\frac{1}{64} [404.32] } + 0.3136\)

                                                             = \(6.3175 + 0.3136\)

                                                              = 6.6311

∴ we get

Mean Square Error for the estimator = 6.6311

Answer: \(h'(x) = \frac{1}{x}.\)

Step-by-step explanation:

By the chain rule,

\(h'(x) = \frac{d}{dx}(\log(4x)) = \frac{1}{4x} \cdot 4 = \boxed{\frac{1}{x}}.\)

Answer:

10

8.4

5

Step-by-step explanation:

Answer:

117.5 cm that the answer on your question

It is just a way of describing a set.

You put the set in braces (sometimes called curly brackets), {}, which is a typical way to show that you are talking about sets.

Here are a few examples:

{x| x > 0} This is read: The set of all x such that x is greater than 0.

Reading it character by character:

{ — shows you that we are talking about a set, and it sort of opens up, or starts the set

x — tells you that we are talking about a set of elements x

| (and a : is also used sometimes) — such that (this is just notation). This says that you are about to be given to rule to see what “rule” or characteristic the x’s will have.

x > 0 — This just says what characteristics x must have to be in this set. So 7, 1/2, .3 and pi are all in this set, while -1, 0, -radical(2) are not.

So this example is just how you would use set builder notation to talk about the set “the positive real numbers”

So why use it? Because it can describe more complicated sets much more succinctly.

2. {3n + 1 | n is an element of the natural numbers} (and this could be written more succinctly if I used certain symbols) would be the set {4, 7, 10, 13, …}

3. {n^2 + n + 1 | n is an element of the natural numbers} would be the set {3, 7, 13, 21, …} and notice here, if you didn’t see the set builder notation, you might have trouble knowing what the next term in the set was.

Answer:

37/50

Step-by-step explanation:

So 37 out of 50 who finished the class, so 37/50 .

And you can't simplify it.

Answer: Width = 8ft, Length = 12 ft

Step-by-step explanation:

irst, let'Fs express the width of the garden as w (the unknown that we are trying to solve), since the length is 4 feet longer than it's width, we can express this as 4+w. Since the flowerbed is rectangular, the formula for the area is A=lw where l is it's length and w is it's width, replacing l with 4+w, then replace A for 96 sq.ft and we can begin solving for the unknown w. Multiplying 4+w and w, using the distributive property where a(b+c)=ab+ac, we will wind up with w^2 + 4w = 96, subtracting 96 and moving it to the other side, we end up with w^2 + 4w -96 = 0, now let's use the quadratic formula for the x intercepts where \(x = \frac{-b +/- \sqrt{b^2-4ac}}{2a}\) , remember the quadratic equation has the form \(ax^2+bx+c\), therefore our a value is 1, our b value is 4, and our c value is -96 (remember to put that negative!), we will get 2 answers, 8 and -12, a negative width is unreasonable and so 8 is the correct width, and since the length is 4 extra feet, this makes the length 12 feet for a total area of 96 feet. hope this helps! Its helpful to draw and visualize the problem!  

Answer:

175

I hope this helps and is the right answer

Answer:

it will take 4 weeks just multiple 24 x 4 +55

Answer: 10

Step-by-step explanation:

9 1/6 x 1 1/11

55/6 x 12/11

cross reduce

5/1 x 2/1

10