Please show work.
QUESTION 11 Find the limit if it exists. lim 10x(x + 10)(x - 7) O a.-16,660 Ob. 2940 O C. -0 O d.-2940

Answer:

-168

Step-by-step explanation:

because  f(x) = 8 - 10xg(x) = 5x + 4

(fg)(x) = (8 - 10x)(5x + 4)(fg)(x) = 40x + 32 - 50x^2 - 40x(fg)(x) = 32 - 50x^2

(fg)(-2) = 32 - 50(-2)^2(fg)(-2) = 32 - 200(fg)(-2) = -168

The value that is minimized in the regression model using the least squares method is the sum of the squared residuals. The least squares method is a common approach for fitting a linear regression model to a set of data, and it is often used in statistical analysis to find the relationship between two variables.

When we use the least squares method in a regression model, we are trying to find the line of best fit that minimizes the sum of the squares of the differences between the predicted values and the actual values. In other words, we are trying to minimize the sum of the squared residuals.
The residuals are the differences between the predicted values and the actual values. Squaring the residuals ensures that they are all positive, which makes it easier to sum and analyze them. By minimizing the sum of the squared residuals, we are finding the line of best fit that is closest to the actual data points.
The value that is minimized in the regression model using the least squares method is the sum of the squared residuals. The least squares method is a common approach for fitting a linear regression model to a set of data, and it is often used in statistical analysis to find the relationship between two variables.

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Answer:

The probability that the dog is still lost at the end of the second day is 0.41

To solve this problem, we can use Bayes' theorem, which allows us to update the probability of an event based on new information.

Let A be the event that the dog is in forest A, and B be the event that the dog is in forest B. Let F be the event that the dog is found within two days.

We want to calculate P(F'), the probability that the dog is still lost at the end of the second day. We can use the law of total probability to express this as

P(F') = P(F'|A) × P(A) + P(F'|B) × P(B)

where P(F'|A) is the probability of not finding the dog within two days given that the dog is in forest A, P(F'|B) is the probability of not finding the dog within two days given that the dog is in forest B, and P(A) and P(B) are the prior probabilities of the dog being in forest A and forest B, respectively.

Using the information given in the problem, we can calculate

P(F'|A) = 1 - 0.5 = 0.5 (the probability of not finding the dog in forest A within two days is 1 - 0.5 = 0.5)

P(F'|B) = 1 - 0.8 = 0.2 (the probability of not finding the dog in forest B within two days is 1 - 0.8 = 0.2)

P(A) = 0.7 (the prior probability of the dog being in forest A)

P(B) = 0.3 (the prior probability of the dog being in forest B)

Plugging these values into the formula above, we get

P(F') = 0.5 × 0.7 + 0.2 × 0.3 = 0.41

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The given question is incomplete, the complete question is:

Oscar has lost his dog; there is a 70% probability it is in forest A and a 30% chance it is forest B. If the dog is in forest A and Oscar looks there for a day, he has a 50% change of finding the dog. If the dog is in forest B and Oscar looks there for a day, he has an 80% chance of finding the dog. what is the probability that the dog is still lost at the end of the second day?

The probability of getting all 7 answers correct is 0.00128%..

(a) To determine the number of possible answer sequences for the seven multiple-choice questions, each with five possible answers, we need to calculate the permutations.

Since there are 5 choices for each of the 7 questions, you will use the multiplication principle:
5 (choices for Q1) * 5 (choices for Q2) * ... * 5 (choices for Q7)

This can be simplified as:
5^7 = 78,125

So, there are 78,125 possible answer sequences for the seven questions.

(b) To find the probability of getting all seven answers correct when guessing, we need to consider that there is only one correct answer sequence out of the total possible sequences. The probability of guessing correctly can be calculated as follows:

Probability = (Number of correct sequences) / (Total number of sequences)

In this case, there is only one correct sequence, and we found there are 78,125 total sequences.

Probability = 1 / 78,125 = 0.0000128

So, the probability of getting all seven answers correct when guessing is approximately 0.0000128 or 0.00128%.

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Answer:

Roman numerals

Step-by-step explanation:

In a pedigree, Roman numerals are used to represent different generations, while Arabic numerals are used to represent individuals within each generation. For example, the first generation would be represented by Roman numeral I, the second generation by Roman numeral II, and so on. Within each generation, individuals are numbered sequentially using Arabic numerals, starting with 1 for the first individual in the generation.

Answer:

x=19

Step-by-step explanation:

Those two angles are vertical so they are congruent, equal the same thing. 8*19+2 = 154.

Answer:

x = 43

Step-by-step explanation:

3x + 7 = 136

3x = 129

x = 43

Answer:

A

Step-by-step explanation:

because i did the math and only got (2,1)

Answer:

The answer is C, both.

Step-by-step explanation:

y=mx+b

1=4(2)-7

1=8-7

1=1

9=4(4)-7

9=16-7

9=9

Answer:

41.75

Step-by-step explanation:

Answer: No, the triangle sum theorem is not true for a sphere surface.

Explanation:

Consider 3 cities A,B,C at the following locations

The placement of C is important because this then allows angle ABC to be 90 degrees. Angles BAC and BCA are also 90 degrees each because B is directly north of both A and C (all northerly roads lead to the north pole at point B). This bizarre triangle has all three angles of 90 degrees. The angles here sum to 90+90+90 = 270 degrees.

No, the triangle sum theorem is not true on the surface sphere.

The triangle sum theorem states that, the sum of the three interior angles of any triangle is always 180°.

Given that, is the triangle sum theorem true on the surface sphere or not, so in relation to Euclid's geometry,

A statement that is equivalent to the parallel postulate is that there exists a triangle whose angles add up to 180°. Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere. The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.

Hence, there exists no such triangle on the surface of a sphere.

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Answer:

The answer is -20.

Step-by-step explanation:

To evaluate the expression, plug x= -3 and y= -5 into the expression. By plugging in the information given from the problem, the expression will look like 4(-3) + 3(-5) + 7.

Next, solve the expression, and the answer will be -20.  

The equation in slope-intercept form of the line that passes through (6, −1) and (3, −7) is:y = 2x − 13.

To write an equation in slope-intercept form of the line that passes through (6, −1) and (3, −7), you will use the point-slope form, as follows:

y − y1 = m(x − x1),

where:

m = slope (or gradient) of the line, and

(x1, y1) = the coordinates of a point on the line.

Let us calculate the slope (gradient) of the line using the given points:

(6, −1) and (3, −7).

m = (y2 − y1)/(x2 − x1)

m = (−7 − (−1))/(3 − 6)

= −6/−3

= 2

Thus, the slope of the line is 2.

Using the coordinates of one of the points, say (6, −1), in the point-slope form, we obtain:

y − y1 = m(x − x1)y − (−1)

= 2(x − 6)y + 1

= 2x − 12

Subtracting 1 from both sides, we get:

y = 2x − 13

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....................

Answer:

42

Step-by-step explanation:

6+4(12-15)^2

Order Of Operations: Parantheses

6+4(-3)^2

Exponent next:

6+4(9)

Multiplication:

6+36

=42

Hope this helps :)

The output of the function can be calculated by plugging in 2 for x and evaluating the equation:\(f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.\)

The Common Core standards for Pre-Calculus focus on the study of functions and their applications, as well as the development of a deeper understanding of the algebraic and geometric principles in the mathematical field. One of the core concepts covered in Pre-Calculus is the concept of polynomial functions. A polynomial function is an expression made up of terms that involve only constants, variables, and exponents. It is represented by the equation \(f(x) = ax^n + bx^n-1 + cx^n-2 + … + z\), where a, b, c, …, z are constants and n is a non-negative integer. To find the value of a polynomial function at a given value of x, the equation can be evaluated by plugging in the x value and calculating the output. For example, if a polynomial function is represented by the equation f(x) = 2x^3 + 5x^2 - 7x + 4, and the x value is 2, then the output of the function can be calculated by plugging in 2 for x and evaluating the equation: \(f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.\)

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Complete question:

What is the output of the polynomial function f(x) = 2x^3 + 5x^2 - 7x + 4 when x = 2?

Answer:

Rate is 2%

Step-by-step explanation:

Step one:

given data

Principal= $7500

Simple interest= $450

time=3 years.

Applying the simple interest formula which is

SI=PRT/100

Step two:

substitute we have

450=7500*R*3/100

cross multiply we have

45000=22500R

divide both sides by 22500

R=45000/22500

R=2%

The trigonometric ratios are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

5 is the hypotenuse length, while for angle A, we have that the sides are given as follows:

Hence the ratios are given as follows:

For angle B, we have that 4 is now the adjacent side, while 3 is the opposite side, hence:

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Answer:

yes

Step-by-step explanation:

so first you would convert pounds into ounces (It's easier for me)

and there are 16 ounces in one pound so for 3 pounds you would have 48 ounces then add the 15 ounces to get 63 ounces and if she needs twice as much to make a vase she would need 126 ounces for a vase then you would add the other 63 to that to get a total of 189 ounces of clay in order to create the bowl and vase, and in order to find out how many ounces are in a 12 pound bag you would just multiply 12 by 16 to get 192 ounces. So yes she does have enough clay to make a bowl and a vase.

The simple interest for a deposit of $ 5,000 at 3 % rate of interest for 1 year would be $ 150

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as S

Now , the value of S is

The principal amount = $ 5,000

The rate of interest R = 3 %

The time period T = 1 year

So , the Simple Interest is given by the equation

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

Simple Interest S = ( 5000 x 3 x 1 ) / 100

On simplifying the equation , we get

Simple Interest S = 150000 / 100

Simple Interest S = $ 150

Therefore , the value of S is $ 150

Hence , the simple interest for the deposit is $ 150

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The range in which 95% of the scores lie is between 75 and 95.

According to the Empirical Rule: For a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% of the data falls within 2 standard deviations of the mean, and approximately 99.7% of the data falls within 3 standard deviations of the mean.

So, about 95% of the scores lie between 75 and 95. T

This is because the mean score is 85 and one standard deviation is 5, so one standard deviation below the mean is 80 (85-5) and one standard deviation above the mean is 90 (85+5).

Two standard deviations below the mean are 75 (85-2*5) and two standard deviations above the mean is 95 (85+2*5).

Therefore, the range in which 95% of the scores lie is between 75 and 95.

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Answer:

isosceles acute

Step-by-step explanation:

two side the same isosceles and all angles less then 90

Yes, the number 9 is a perfect square

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

Is 9 a perfect square

As a general rule

Perfect square numbers are numbers that have integer square roots

Using the above as a guide, we have the following:

√9

Using a calculator, we have

√9 = ±3

±3 is an integer

Hence, 9 is a perfect square

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Answer:

-13

Step-by-step explanation:

3x-5x+10=35

-2x+10=36

-2x=36-10

-2x\-2=26\-2

x=-13

To calculate the energy of the resulting explosion when a 10,000 kg UFO made of antimatter crashes with a 40,000 kg plane made of matter, we can use Einstein's famous equation, E=mc², which relates energy (E) to mass (m) and the speed of light (c).

In this case, we'll need to calculate the total mass of matter and antimatter involved in the collision and then use the equation to find the energy released. The equation E=mc² states that energy is equal to the mass multiplied by the square of the speed of light (c). In this scenario, we have a collision between a UFO made of antimatter and a plane made of matter. Antimatter and matter annihilate each other when they come into contact, resulting in a release of energy.

To calculate the energy of the resulting explosion, we need to determine the total mass involved in the collision. The total mass can be calculated by adding the masses of the UFO and the plane together. In this case, the UFO has a mass of 10,000 kg and the plane has a mass of 40,000 kg, so the total mass is 50,000 kg.

Next, we can use the equation E=mc² to calculate the energy. The speed of light (c) is a constant value, approximately 3 x 10^8 meters per second. Plugging in the values, we have E = (50,000 kg) x (3 x 10^8 m/s)². Simplifying the equation, we have E = 50,000 kg x 9 x 10^16 m²/s².Multiplying the numbers, we get E = 4.5 x 10^21 joules. Therefore, the energy of the resulting explosion when the UFO and plane collide is approximately 4.5 x 10^21 joules.

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To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.

Given:

a = [1, 3, 5]

b = [1, 3, 5]

To find a · b, we multiply the corresponding components and sum them:

\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)

So, a · b equals 35.

Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.

On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.

First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.

Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).

The graph paper would show a single point labeled 35 on the number line.

Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.

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We want to find how much Janice spends on her last purchase.

The correct option here is C, she must have spent $50 on the last store.

Let's see how to get the correct answer:

We know that the average is $30 per store, and we know that she goes to 5 stores, then the total amount spent in the 5 stores is:

5*$30  = $150

Notice that average is just given by the total amount of money she spent divided the number of stores she visited, this does not mean that she spent $30 in each of these stores.

Now, we also know that in the first 4 stores she spents a total of $100.

We want to know how much does she spend on the last store, this will be given by the difference between the total amount and $100, this is:

$150 - $100 = $50

So she must have spent $50 on the last store, meaning that the correct option is C.

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The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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The probability that the mean height of 64 dogs is between 27 and 28.5 inches is approximately 0.8531.

We can use the central limit theorem to approximate the distribution of the sample mean. The central limit theorem states that if we take a large enough sample from a population, the sample mean will be approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, we have:

Population mean (μ) = 28 inches

Population standard deviation (σ) = 4 inches

Sample size (n) = 64

a) To find the probability that the mean height of 64 dogs is less than 27 inches, we need to standardize the sample mean and find the corresponding area under the standard normal distribution. We have:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

z = (27 - 28) / (4 / sqrt(64))

z = -2

Using a standard normal distribution table or calculator, we find that the probability of z being less than -2 is approximately 0.0228. Therefore, the probability that the mean height of 64 dogs is less than 27 inches is approximately 0.0228.

b) To find the probability that the mean height of 64 dogs is greater than 28.5 inches, we standardize the sample mean and find the area to the right of the standardized value. We have:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

z = (28.5 - 28) / (4 / sqrt(64))

z = 1

Using a standard normal distribution table or calculator, we find that the probability of z being greater than 1 is approximately 0.1587. Therefore, the probability that the mean height of 64 dogs is greater than 28.5 inches is approximately 0.1587.

c) To find the probability that the mean height of 64 dogs is between 27 and 28.5 inches, we need to find the area under the standard normal distribution between the two standardized values. We have:

z1 = (27 - 28) / (4 / sqrt(64))

z1 = -2

z2 = (28.5 - 28) / (4 / sqrt(64))

z2 = 1

Using a standard normal distribution table or calculator, we find that the probability of z being between -2 and 1 is approximately 0.8531. Therefore, the probability that the mean height of 64 dogs is between 27 and 28.5 inches is approximately 0.8531.

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Answer:

Slope/m=1/2, y-intercept=-4

Step-by-step explanation:

Y=mx+b is slope-intercept form. So in the equation y=1/2x-4, m stands for the slope, and in the equation 1/2 is in the place of m. B stands for the y-intercept, and in its place is -4.

Ahem, I'm writing with a mouse, excuse the scraggly lines and writing on the graph.