Solve the equation using synthetic division: x^(3)-11x^(2)+40x-50=0

Using the zero product, the solutions to the equation x² + x - 30 = 12 are  A. x=-7 or x=6

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

x^2 + x - 30 = 12

Express the exponent as a proper superscript

So, we have the following representation

x² + x - 30 = 12

Subtract 12 from both sides

This gives

x² + x - 42 = 0

Expand

x² + 7x -6x - 42 = 0

When the equation is factored, we have

(x +_7)(x - 6) = 0

Solve for x

x = -7 and x = 6

Hence, the solutions are x = -7 and x = 6

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Answer:

12 sides

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

since the polygon is regular then the exterior angles are congruent

number of sides = 360° ÷ 30 = 12

Answer:

12.

Step-by-step explanation:

Answer:

Logic puzzles use grids to help you make eliminations based on deciphering the truth in the clues provided.

We can use the method to solve a logic puzzle is;

''Logic puzzles use grids to help you make eliminations based on deciphering the truth in the clues provided.''

Here,

We have to find a method to solve the logic puzzle.

What is Logic puzzle?

A problem that can be solved through the deductive reasoning is called Logic puzzle.

Now,

To solve a logic puzzle we can use grids which help to make eliminations based on deciphering in providing the truth in the clues.

Hence,

We can use the method to solve a logic puzzle is;

⇒ 'Logic puzzles use grids to help you make eliminations based on deciphering the truth in the clues provided.'

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Answer:

equation is 29x+32=90

answer x=2

Step-by-step explanation:

29x+32=90

29x=90-32

29x=58

x=58/29

x=2

Our students selected 50 residences at random. We discovered that owners live in 26 homes. By the way, we might use this to calculate our sample proportion. The result will be 26 out of 50 and.52. We're going to do an experiment to see if the proportion of owner-occupied homes in your neighbourhood is different from the national average using hypotheses.

The test result will be the null hypothesis. The true percentage being 69 is the null hypothesis. A distinct theory serves as the alternative. According to the inquiry, we are attempting to ascertain whether the community differs from the country. I will admit that 0.69 is not the true proportion. The test statistic must be located. Since this is an example Z test, we are able to use the calculator function in the tests. Sure, window. If we went to the tests and clicked the stat, we would find the single proportion Z. It's a test, really. The Christmas portion cost 69. We have 26 successes out of 50 samples. Since the genuine percentage is different from.69 in our alternative, proportion does not equal no proportion. Our final result will be a negative Z score of 2.599. We receive a p value of 9 from the window. We'll decide on a conclusion. We will contrast our significance level with the p value. It does not provide a relevance level for this issue. We'll only apply 5%. So, we would reject the null hypothesis if our p value is lower than the significance level, correct? Obtaining the sample proportion is necessary. If the null hypothesis is correct, it's a very uncommon occurrence, and we have evidence that the proportion of owner-occupied homes in our community is higher than the national average.

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Therefore, we can conclude that approximately 68% of the oranges from the orchard weigh between 3.5 oz. and 5.5 oz. using the empirical rule.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, we want to find the percentage of oranges that weigh between 3.5 oz. and 5.5 oz., which is one standard deviation below and above the mean, respectively.

First, we need to standardize the values using the z-score formula:

z = (x - μ) / σ

where:

x is the value we want to standardize (in this case, 3.5 oz. and 5.5 oz.)

μ is the mean (4.5 oz.)

σ is the standard deviation (1 oz.)

For 3.5 oz.:

z = (3.5 - 4.5) / 1 = -1

For 5.5 oz.:

\(z = (5.5 - 4.5) / 1 = 1\)

Now, we can use a standard normal distribution table or calculator to find the area under the curve between z = -1 and z = 1. The area between two z-scores represents the percentage of data that falls between those values.

According to the table, the area between \(z = -1\)and \(z = 1\)is approximately 0.6827 or 68.27%.

Therefore, we can conclude that approximately 68% of the oranges from the orchard weigh between 3.5 oz. and 5.5 oz. using the empirical rule.

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Answer:

Correct: Option a. negative reciprocals

Step-by-step explanation:

Perpendicular lines are defined as those who intersect at an angle of 90°.

There is an easy way to find out if two equations of lines correspond to perpendicular lines or not.

If line 1 is

y=m1x+b1

And line 2 is:

y=m2x+b2

The condition for the lines to be perpendicular is that:

m1*m2=-1

Solving for m2:

\(\displaystyle m2 = -\frac{1}{m1}\)

As seen, both slopes are negative reciprocals.

Correct: Option a. negative reciprocals

Answer:

It is just .55*12,400

Step-by-step explanation:

thats literally all it is

Answer:

If you Meant (12,400) then around 6,820 planned to travel again

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

i got it right

Answer:true

Step-by-step explanation:

is true if you don’t believe me check the picture

The integral ∫[0 to 1] x² dx evaluates to 1/3.

To evaluate this integral, we can use the power rule for integration. Applying the power rule, we increase the power of x by 1 and divide by the new power. Thus, integrating x² gives us (1/3)x³.

To evaluate the definite integral from x = 0 to x = 1, we substitute the upper limit (1) into the antiderivative and subtract the result when the lower limit (0) is substituted.

Using the Fundamental Theorem of Calculus, the area under the curve is given by the expression A = ∫[0 to 1] f(x) dx. For this case, f(x) = x².

To approximate the area using right endpoints, we can use a Riemann sum. Dividing the interval [0, 1] into subintervals and taking the right endpoint of each subinterval, the Riemann sum can be expressed as lim[n→∞] Σ[i=1 to n] f(xᵢ*)Δx, where f(xᵢ*) is the value of the function at the right endpoint of the i-th subinterval and Δx is the width of each subinterval.

In this specific case, since the function f(x) = x² is an increasing function on the interval [0, 1], the right endpoints of the subintervals will be f(x) values.

Therefore, the area under the curve from x = 0 to x = 1 can be expressed as lim[n→∞] Σ[i=1 to n] (xi*)²Δx, where Δx is the width of each subinterval and xi* represents the right endpoint of each subinterval.

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Labor productivity is an important measure of economic growth, and there are several factors that can affect it. These include the amount of physical capital available, the education and training of workers, and the use of advanced technology. Overall, while falling prices can be a positive factor for economic growth, it is not directly tied to labor productivity, making option B the correct answer.

Option B, "the speed with which prices fall," is not directly related to labor productivity. While falling prices can indicate a decrease in inflation and potentially stimulate economic growth, they do not directly impact the efficiency of workers or the production process.

In contrast, the other options are all important factors that can affect labor productivity. A higher saving rate can lead to greater investment in physical capital and technological advancements, which can improve productivity. Similarly, increasing the growth rate of physical capital and labor productivity can both lead to increases in overall productivity.

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Answer:

A

Step-by-step explanation:

the other options have a common difference

Answer:

A is not arithmetic series

Step-by-step explanation:

In B,C and D there is arithmetic series as a2-a1=a3-a2

In A. there is no such series.....

To say that two variables are negatively correlatted means that when one variable increases, the other variable decreases.

Negative correlation refers to a relationship between two variables where they tend to move in opposite directions. When one variable increases, the other variable tends to decrease, and vice versa. This negative relationship indicates an inverse association between the two variables.

Option A, "When one variable increases, the other decreases," accurately describes negative correlation. As one variable increases, the other variable decreases, reflecting the negative relationship between them.

Negative correlation does not imply that both variables change at the same rate (Option D). In negative correlation, the relationship is characterized by the opposite direction of change, not necessarily the same magnitude or rate of change.

Option B, "When variable increases, the other also," suggests a positive correlation, where both variables move in the same direction. This is not the case in negative correlation.

Option C, "When one variable decreases, the other also decreases," is a misinterpretation of negative correlation. In negative correlation, when one variable decreases, the other variable tends to increase, not decrease.

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9514 1404 393

Answer:

Step-by-step explanation:

It looks like you want to simplify the sums.

1. (3r -4) -(-5b -3) = 3r -4 +5b +3 = 5b +3r +(-4+3)

  = 5b +3r -1

__

2. (-4k -1) -(-6k -6) = -4k -1 +6k +6 = (-4+6)k +(-1+6)

  = 2k +5

__

3. (-6k +7) -(7k +5) = -6k +7 -7k -5 = (-6-7)k +(7-5)

  = -13k +2

Answer:

£368.94

Step-by-step explanation:

The multiplier for 43% is 0.43

0.43 x 258 = 110.94 which is 43%

But if you are increasing 258 by 43% you must add on 258 as well

Or instead you can just do 258 x 1.43= 368.94

If there are 342 more trees bearing red apples than trees bearing green apples, then the number of trees with green apples are 1336.

The 3/5 of fruit trees are orange trees, then 2/5 of the fruit trees are apple trees.

Let the total number of fruit trees be = x. Then we can write two equations based on the given information that, there are 4515 orange trees and there are 342 more red apple trees than green apple trees,

The equations are :

⇒ 3/5 x = 4515         ...equation(1)

⇒ x - 4515 = (G + 342) + G   ...equation(2)

Where G is the number of trees bearing green apples.

From equation(1), we can solve for x:

x = (4515)/(3/5) = 7525

Substituting this value of "x" into equation(2),

We get,

⇒ 7525 - 4515 = (G + 342) + G

⇒ 3010 = 2G + 342

⇒ 2668 = 2G

⇒ G = 1334.

Therefore, there are 1336 trees with green apples.

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The given question is incomplete, the complete question is

A fruit plantation has two types of fruit trees: apple trees and orange trees. 3/5 of the fruit trees are orange trees. There are 4515 orange trees on the plantation. The apple trees bear apples of two different colors. There are 342 more trees bearing red apples than trees bearing green apples.

How many trees with green apples are there?

Answer: 0.8

Step-by-step explanation:

Answer:

f

Step-by-step explanation:

Answer: falseeeeeee

Step-by-step explanation:

Step-by-step explanation:

Given:

To find:

Solution:

(multiplication of digits give a larger number compared to addition, subtraction and division)

= (12 × 7) × (4 + 1)

∴ The biggest number Tony can make is 420.

In testing the hypotheses the p-value is 0.0071.

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

To find the p-value, we need to determine the probability of getting a z-score of 2.45 or higher if the null hypothesis is true (i.e. if the population mean is really 34).

Since this is a one-tailed test (Ha: μ > 34), we look up the area to the right of z = 2.45 in the standard normal distribution table.

Using a standard normal distribution table, the area to the right of z = 2.45 is approximately 0.0071.

Therefore, the p-value is 0.0071.

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Answer:

4, 6, 10, 12 I think are the sides the perimeter=32

Step-by-step explanation:

Answer:

(3, 5)

Step-by-step explanation:

It would be (3, 5) because since Juans house is in the same quadrant as the school there wouldn't be any negative numbers in the coordinates. The only coordinate that doesn't have negative numbers is (3, 5). That's your answer.

Options a, b, d, and g are the correct conditions for a Binomial Distribution.

The four conditions necessary for X to have a Binomial Distribution are:

a. There are n set trials: In a binomial distribution, the number of trials, denoted as "n," must be predetermined and fixed. Each trial is independent and represents a discrete event.

b. The trials must be independent: The outcomes of each trial must be independent of each other. This means that the outcome of one trial does not influence or affect the outcome of any other trial. The independence assumption ensures that the probability of success remains constant across all trials.

d. There can only be two outcomes, a success and a failure: In a binomial distribution, each trial can have only two possible outcomes. These outcomes are typically labeled as "success" and "failure," although they can represent any two mutually exclusive events. The probability of success is denoted as "p," and the probability of failure is denoted as "q," where q = 1 - p.

g. The probability of success, p, is constant from trial to trial: In a binomial distribution, the probability of success (p) remains constant throughout all trials. This means that the likelihood of the desired outcome occurring remains the same for each trial. The constant probability ensures consistency in the distribution.

The remaining options, c, e, and f, are not conditions necessary for a binomial distribution. Option c, "Continue sampling until you get a success," suggests a different type of distribution where the number of trials is not predetermined. Options e and f, "You must have at least 10 successes and 10 failures" and "The population must be at least 10x larger than the sample," are not specific conditions for a binomial distribution. The number of successes or failures and the size of the population relative to the sample size are not inherent requirements for a binomial distribution.

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Answer: The radius of the circle is 3 units, the standard form of the equation is (x – 1)² + y² = 3, and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

To determine the properties of the circle whose equation is x^2 + y^2 - 2x - 8 = 0, we can complete the square as follows:

x^2 - 2x + y^2 - 8 = 0

(x^2 - 2x + 1) + y^2 = 9

(x - 1)^2 + y^2 = 3^2

The last expression is in the standard form of the equation for a circle with center (1, 0) and radius 3. Therefore, the center of the circle is (1, 0), which does not lie on either the x-axis or the y-axis.

We can also see that the radius of the circle is 3 units because the equation is in the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.

Finally, we can see that the radius of this circle is the same as the radius of the circle whose equation is x^2 + y^2 = 9, which is the equation of a circle with center (0, 0) and radius 3.

Answer:

56 meters

Step-by-step explanation:

when calculating the perimeter, you need to take into account every side of the figure.

i will start at the top and go clockwise showing you my calculations

5 + 5 + 11 + 7 + 16 + 7 + 5

= 56

The surface area of a sphere can be found by drawing a net and adding the area of all their respective two-dimensional surfaces. Use the formula 4π r² to find the surface area of a sphere, where r is the radius of the figure.

When finding surface area, one need to calculate the total area of the surfaces that make up a shape, such as a sphere, cone, or cylinder. Formula for surface area of sphere: 4π r², where "r" is radius, accounting for its consistent curved surface.

For a cone, surface area is found by adding the curved lateral surface area to the base area. The lateral surface area of a cone is π rℓ, where "r" is the radius of the base and "ℓ" is the slant height.

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See full text below

How is finding the surface area of a sphere different from finding the surface area of a cone or cylinder? Drag the correct shapes to complete the sentence. cylinder cone or sphere cone or cylinder

cone

sphere

cylinder or sphere

The surface area of a ---------- can be found by drawing a net and adding the area of all their respective two-dimensional surfaces. Use the formula 4π r² to find the surface area of a -------, where r is the radius of the figure.

The mean amount for the three bills is  $100  .

In the question ,

it is given that

the electricity bill for June is = $75

the electricity bill for July is = $75

the electricity bill for August is = $150

Sum of the electricity for three months = 75 + 75 + 150 = 300

number of months =  3

The mean of the three months can be calculated using the formula ,

mean = (sum of bill for three months )/( number of months)

Substituting , the  values

we get

mean = 300/3

= 100

Therefore , the mean amount is $100 .

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Answer:

615.44

Step-by-step explanation:

If diameter = 28, then radius is 14

Area = 3.14 x (14x14) =615.44