Is (x-7) a factor of (x2-5x+14)?
Yes or no

Answer:

83.6%

Step-by-step explanation:

Let's say the original price is x

x decreased by 12% means 88% of x is left.

0.88x decreased by 5% means 95% of 0.88x is left.

This means the answer is: 0.88x * 0.95 = 0.836

The percent of the total decrease is 83.6%

Hope this helps :)

Have a great day!

Answer:

x=3

Step-by-step explanation:

f(x)=2x+6

f(x)=12

Hence:

2x+6=12

2x+6-6=12-6

2x=6

x=6/2

x=3

We need to know about fraction to solve this problem. The amount Reshma spent on comic books is Rs 165 and the amount that is left with her is Rs 495.

We can solve this problem by calculating what 1/4th of 660 will be. In this question we know that Reshma spends 1/4th of her pocket money on comic books out of Rs 660. We can think of 660 being divided in 4 parts equally and that Reshma spends one part of it. The amount that will be left with Reshma is the rest three parts.

Reshma spends= 1/4x660=165

Amount left= 660-165=495

Therefore the amount Reshma spends on comic books is Rs 165 and the amount that is left with her is Rs 495.

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The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

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

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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The additional information needed to prove the triangles congruent by the SAS postulate is AC⊥BD,

To prove the triangles are congruent by the SAS postulate

we need to have two sides and the included angle of one triangle congruent to the corresponding sides and angle of the other triangle.

Given that a perpendicular AC is drawn to BD where C is midpoint of BC, we know that AC and BD are perpendicular and intersect at point D.

To apply the SAS postulate, we need to have two sides and the included angle of the triangles.

We know that AC is congruent to itself by the reflexive property of congruence.

So, we need to find two other congruent sides and an angle included between them.

Therefore, the additional information needed to prove the triangles congruent by the SAS postulate is AC⊥BD,

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The estimated probability of a success is 3/8.

Probability simply means the likelihood that a particular event will take place or occur based on the fact provided.

In this case, randomly generated list of integers from 0 to 7 is being used to simulate an event. Therefore, it means that there are 8 numbers.

Also, the numbers 1 and 3 representing a success.

Therefore, the probability that it's going to be a success will be:

= Number of success / Total number

= 3/8

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A sampling is a subset of an unit that is tested or examined in to make inferences about the larger population, whereas a census refers to the entire population, things, or information we're interested in analyzing.

Population pyramids that are expansive, constrictive, or stationary can be created using age-sex distributions.

The term "population" in the context of statistics means the whole set of individuals, objects, or metrics we're interested in investigating.

A sample, on the other hand, is a portion of a population that is actually measured or observed in order to draw conclusions about the full population.

Before we can determine the sample and population of a math issue, we must first select the topic we're interested in finding out.

For instance, if we were to look at worldwide average heights, the population would be made up of everyone alive today.

Choosing whether to investigate the whole population or simply a subset of it is the next stage.

If we are studying the overall community, no sample is necessary.

Hence, even if we are only looking at a small section of the population, we must collect a sample.

For instance, if we were to study the heights the people there, the population would be the whole of the United States.

We might measure the elevations of 1000 people randomly selected from the population, drawn from different regions of the United States, if we wished to sample this population.

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Answer:

440

Step-by-step explanation:

Answer:

B' (-3,11)

Step-by-step explanation:

B(2,3)  The rule is saying subtract 5 from x and 8 add to y

(2 -5, 3 + 8)

(-3,11)

For Tom's Pizza Restaurant where expenses for the restaurant include raw material for pizza, monthly rent and insurance, total 35 slices must be sold in a month to break even.

There is Tom has a Pizza Restaurant. Now, the Expenses for the restaurant include raw material for pizza = $7.02 per slices

Monthly rental = $ 121.00

Monthly insurance= $56.00

So, Monthly fixed expense = Rent + Insurance = 121+ 56 = $177

The sell rate of pizza = $12.02/slice.

We have to determine the number of slices restaurant sell in a month to break even.

Contribution margin per share = selling price per slice - variable cost per slice = 12.02 - 7.02 = $5.00

Number of slice to be sold to break even = Fixed cost divided by Contribution margin per slice = \(\frac{ 177}{5}\)

= 35.4

= 35 (rounded to whole number)

Hence, 35 slices must be sold for break even.

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The process capability, Cp is calculated by dividing the upper specification limit minus lower specification limit by 6 times the process standard deviation.

This is the formula for the process capability.

Cp = (USL - LSL) / (6 * Standard deviation)

Where, Cp is process capability USL is the Upper Specification Limit LSL is the Lower Specification Limit Standard deviation is the process standard deviation.

The extrudate is subsequently cut into individual parts, and the extruded parts have a critical cross-sectional dimension = 12.50 mm with standard deviation = 0.25 mm. The mean of this distribution is the center line of the control chart and the critical cross-sectional dimension 12.50 mm is the target or specification value.

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Answer:

Step-by-step explanation:

It can help to understand what the square of a binomial looks like when you are asked to solve a quadratic by completing the square.

  (x -a)² = x² -2ax +a²

In this form, the constant term a² is the square of half the x-coefficient. The x-coefficient and the constant in the binomial have the same sign.

Your quadratic is ...

  x² -12x +21 = 0

It can be easier to complete the square if the given constant term is subtracted from both sides:

  x² -12x = -21

Now, the square can be completed by adding the square of half the x-coefficient: (-12/2)² = (-6)² = 36.

  x² -12x +36 = -21 +36

  (x -6)² = 15 . . . . . . . . the form you want for your answer template

__

Taking the square root gives ...

  x -6 = ±√15

  x = 6 ± √15 ≈ {2.13, 9.87} . . . . solutions to the equation

_____

Additional comment

The form we use for solving by completing the square is only one step away from "vertex form." That is, knowing the vertex of the function graph, we can write the vertex form equation, and find a solution immediately using the complete the square procedure.

  vertex form equation: (x -6)² -15 = 0

  form used for "complete the square" solution: (x -6)² = 15

Answer:

X =4

Step-by-step explanation:

The solution is in the attached file

Answer:

A

Step-by-step explanation:

Answer:

On the y-axis line

Step-by-step explanation:

Given the location (a,b) of the point P on the coordinated plane.

If a=0

Then the location of P on the x-axis is at x=0

Since b is not equal to zero, b could be positive or negative.

Therefore, the point P could be located on the positive y-axis or the negative y-axis,

It must be exactly on the line.

The area of the sector is approximately 23.24 m^2.

To find the area of the sector, we first need to find the central angle of the sector.

The entire circumference of the circle is given by 2πr, where r is the radius of the circle. In this case, the circumference is 2π(3) = 6π m.

The arc length given is 47 m, which we can use to find the central angle of the sector:

central angle = (arc length / circumference) × 360°

central angle = (47 / 6π) × 360°

central angle ≈ 299.02°

Now that we have the central angle, we can use the formula for the area of a sector:

area of sector = (central angle / 360°) × πr^2

area of sector = (299.02 / 360) × π(3)^2

area of sector ≈ 7.43π m^2

Rounding to two decimal places, the area of the sector is approximately 23.24 m^2.

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The response times observed in the two experiments suggest that the cognitive demands of the two tasks differ, with the second task being more cognitively demanding than the first.

The very short response times of less than 100 milliseconds observed in the lab might be due to several factors. One possibility is that the participant has developed a prepotent response that is initiated almost automatically upon presentation of the stimulus. This means that the participant has become so familiar with the task that their response is almost reflexive, requiring little cognitive processing. Another possibility is that the stimulus presented was so salient or intense that it elicited an immediate and involuntary response from the participant. In the second experiment where participants say the word "now" as soon as they detect the green circle, the response times were between 100 and 200 milliseconds. This suggests that the cognitive tasks involved in this version of simple detection may require more conscious effort and attention than the tasks in the first experiment. Participants in the second experiment had to actively detect the presence of the green circle and make a conscious decision to say "now", whereas in the first experiment their response may have been more automatic. Therefore, the response times observed in the two experiments suggest that the cognitive demands of the two tasks differ, with the second task being more cognitively demanding than the first.

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Answer:

A=38.24

Step-by-step explanation:

Compound Area

The figure shows a shape formed by two shapes: Half a circle and a trapezium.

The circle has a radius of r=5.2/2=2.6 and the trapezium has a height of h=6.5 and bases b1=5.2 and b2=3.3.

The area of half a circle is:

\(\displaystyle A_c=\frac{\pi r^2}{2}\)

Using pi = 3.14:

\(\displaystyle A_c=\frac{3.14\cdot 2.6^2}{2}=10.6132\)

The area of the trapezium is:

\(\displaystyle A_t=\frac{b_1+b_2}{2}.h\)

\(\displaystyle A_t=\frac{5.2+3.3}{2}\cdot 6.5=27.625\)

The total area of the figure is:

\(A=10.6132+27.625=38.2382\)

Rouning to the nearest hundredth:

A=38.24

Answer:

The opening price of the stock in the beginning of the day was $4.

Step-by-step explanation:

To be able to calculate the price of the stock at the beginning of the day, you have to consider that the equation to calculate the final price is equal to the opening price multiply for the result of one plus the increase or decrease percentage, which is:

final price=opening price*(1+0.04)

Now, you know that the final price is $4.16, so you can replace this value in the formula and solve for the opening price:

4.16=opening price*1.04

opening price=4.16/1.04

opening price=4

According to this, the answer is that the opening price of the stock in the beginning of the day was $4.

Answer: A.) For these data, as the number of at bats increases, the number of hits tend to increase.

This is because the points seem to trend upward as we move from left to right. This makes sense because the more attempts you get, the more hits you're expected to get.

Assume that someone has a batting average of 0.300; this means that if they got 1000 attempts, then we expect about 0.300*1000 = 300 hits. Now if they got 2000 at bats this time, then we expect about 0.300*2000 = 600 hits.

Of course things won't fit this perfectly since everything in life has random statistical error, but this gives a good idea of the upward trending data. The two variables (at bats and hits) are strongly related. We can say the variables have strong positive correlation.

To find σg(X)^2, we need to calculate the variance of the function g(X) = 4X^2 + 2, where X is a random variable with a given density function. The density function is defined as f(x) = (3/2)(x + 1) for 0 ≤ x and 0 elsewhere. By calculating the variance of g(X), we can determine the value of σg(X)^2.

To calculate the variance of g(X), we first need to find the mean of g(X), denoted as E[g(X)]. For a continuous random variable, the mean is calculated as the integral of the function multiplied by the density function. In this case, we have:

E[g(X)] = ∫(4X^2 + 2) * f(x) dx

Substituting the given density function, we have:

E[g(X)] = ∫(4X^2 + 2) * (3/2)(X + 1) dx

After simplifying and evaluating the integral, we can find the value of E[g(X)].

Next, we calculate the variance of g(X), denoted as Var[g(X)]. The variance is calculated as the expectation of the squared difference between g(X) and its mean, E[g(X)]^2. In mathematical terms:

Var[g(X)] = E[(g(X) - E[g(X)])^2]

By substituting the values of g(X) and E[g(X)], we can evaluate this expression and find the value of Var[g(X)].

Finally, to find σg(X)^2, we take the square root of Var[g(X)], i.e., σg(X) = √Var[g(X)]. After calculating Var[g(X)], we can determine the value of σg(X) to three decimal places as needed.

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(2,4)

Step-by-step explanation:

I'm not sure in the slightest but with the formula I learned I think this is correct

The formula for finding the standard deviation for a binomial distribution is σ2=npq. f.

What means binomial distribution?

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution.

For each random variable X, the binomial distribution formula is given by;

P(x:n,p) = nCx px (q)n-x

Where,

n = the number of experiments

x = 0, 1, 2, 3, 4, …

p = Probability of Success in a single experiment

q = Probability of Failure in a single experiment = 1 – p

formula for finding standard deviation of a binomial distribution is npq. f.

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Answer:

perimeter = 16x+9x+8x+11

simplified perimter = 33x+11

Step-by-step explanation:

this isnt even close to 100 pts but okay

Answer:

a. 16x + 9x + 8x + 11

b. 33x + 11 (or 11(3x + 1) if this is asking for a factored expression)

Step-by-step explanation:

Looking at the directions, part a tells us to use all 4 side lengths, so the equation for part a is 16x + 9x + 8x + 11.

Now to simplify that expression.

16x + 9x + 8x + 11

Step: Combine 16x, 9x, and 8x. I'll go from left to right.

25x + 8x + 11

33x + 11

(What you see above this statement is my answer, but work is below if this is asking for a factored expression.)

11: 1, 11

33: 1, 3, 11, 33

Now divide both 33x and 11 by 11 and put the 11 outside the parentheses.

33x/11 = 3x

11/11 = 1

11(3x + 1)

The modified Reynolds analogy, also known as the Chilton-Colburn analogy, is expressed mathematically as Nu = f * Re^m * Pr^n. It relates the convective heat transfer coefficient (h) to the skin friction coefficient (Cf) in fluid flow. This equation is widely used in heat transfer analysis and design applications involving forced convection.

The modified Reynolds analogy is a useful tool in heat transfer analysis, especially for situations involving forced convection. It provides a correlation between the heat transfer and fluid flow characteristics. The Nusselt number (Nu) represents the ratio of convective heat transfer to conductive heat transfer, while the Reynolds number (Re) characterizes the flow regime. The Prandtl number (Pr) relates the momentum diffusivity to the thermal diffusivity of the fluid.

The equation incorporates the friction factor (f) to account for the energy dissipation due to fluid flow. The values of the constants m and n depend on the flow conditions and geometry, and they are determined experimentally or by empirical correlations. The modified Reynolds analogy is widely used in engineering calculations and design of heat exchangers, cooling systems, and other applications involving heat transfer in fluid flow.

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Answer: John is 12, Fred is 6.

Step-by-step explanation:

12/2=6

12-4=8

6-4=2

8/2=4

Answer:

John: 10

Fred: 5

Step-by-step explanation:

We can solve this like a system of equations.

Set Variables:

John: j

Fred: f

Given Info:

2f = j

j - 4 = 6(f - 4)

Use the distributive property, a(b+c) = ab+ac to simplify.

j - 4 = 6f - 24

Use info from the first equation and substitute.

j - 4 = 6f - 24

2f = j

6f = 3j

j - 4 = 3j - 24

Add 24 on both sides.

j - 4 + 24 = 3j - 24 + 24

j + 20 = 3j

Subtract j on both sides.

j - j + 20 = 3j - j

20 = 2j

Divide 2 on both sides.

\(\frac{20}{2} = \frac{2j}{2}\)

j = 10

Because j is twice f, divide 10 by 2 to get f.

10/2 = 5

Answer:

First you would have to multiply 15 times 19.50. Then, subtract 11.50 from the product.

Step-by-step explanation: