Question 5 of 25
Which of these operations is not closed for polynomials?
A. Subtraction
B. Division
C. Addition

step 1

Find the hypotenuse of the right triangle

Applying Pythagorean Theorem

c^2=7^2+24^2

c^2=625

c=25 ft

therefore

the height is equal to

h=25+24=49 ft

Answer:

4x+2=22

4x+2-2=22-2

4x=20

4x/4=20/4

x=5

In order to find the percentage that 13 represents from 25, we can use the following rule of three, knowing that 25 students represent 100%:

So 13 students is 52% of 25 students.

An odd function is a function where f(-x) = -f(x) for all x.

Given the function \(f(x) = -3x5 + 5x³ - 2x\), we want to prove that it is an odd function. Let's test the definition of an odd function by plugging in -x for x in the given function:

f(-x) =\(-3(-x)5 + 5(-x)³ - 2(-x)f(-x)\)

= \(3x5 - 5x³ + 2xf(-x)\)

=\(-(-3x5 + 5x³ - 2x)\) .

We can see that f(-x) is equal to -f(x), thus we can prove that the function f(x) is an odd function.  

we can prove mathematically that the function \(f(x) = -3x5 + 5x³ - 2x\)  is an odd function.

An odd function is symmetric with respect to the origin. If the function f(x) satisfies the equation f(-x) = -f(x) for all values of x, then f(x) is an odd function. Now, we are given the function\(f(x) = -3x5 + 5x³ - 2x\).

To prove that f(x) is an odd function, we need to show that f(-x) = -f(x). Let's substitute -x for x in the equation \(f(x) = -3x5 + 5x³ - 2x\)

to obtain f(-x):

\(f(-x) = -3(-x)5 + 5(-x)³ - 2(-x)f(-x)\)

= \(-3(-x⁵) + 5(-x³) + 2x\)

We can simplify this expression as follows: \(f(-x) = 3x⁵ - 5x³ + 2x\)  Now, we need to show that f(-x) = -f(x).

Let's substitute the expression for f(x) into the right-hand side of this equation:-\(f(x) = -(-3x5 + 5x³ - 2x)f(-x) = 3x⁵ - 5x³ + 2x\)

We can see that f(-x) is equal to -f(x), which is the definition of an odd function.

we have proven mathematically that the function \(f(x) = -3x5 + 5x³ - 2x\) is an odd function.

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The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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The given question is to prove that the vector n = ai + bj is perpendicular to the line whose equation is ax + by + c = 0. The given hint is to let P1(x1, y1) and P2(x2, y2) be distinct points on the line.

We need to prove that vector n = ai + bj is perpendicular to the line whose equation is ax + by + c = 0.Since P1(x1, y1) and P2(x2, y2) are distinct points on the line. So, the direction vector of the line is = (x2-x1)i + (y2-y1)j

Let vector be v = (x2-x1)i + (y2-y1)j. The given line equation is ax + by + c = 0. So, normal vector n of the line = a i + b j.Now, we need to show that the dot product of vector n and v is equal to zero, i.e., n . v = 0 (as the dot product of two perpendicular vectors is always zero).n . v = a (x2-x1) + b (y2-y1) = 0, which shows that vector n = a i + b j is perpendicular to the line whose equation is ax + by + c = 0.

Hence, the given statement is proved.
To prove that the vector n = ai + bj is perpendicular to the line with the equation ax + by + c = 0, we can use the hint given and consider two distinct points P1(x1, y1) and P2(x2, y2) on the line.

Since P1 and P2 lie on the line, they satisfy the equation of the line:
1) ax1 + by1 + c = 0
2) ax2 + by2 + c = 0

Now, let's find the vector connecting P1 and P2:
P2 - P1 = (x2 - x1)i + (y2 - y1)j

To show that the vector n is perpendicular to the line, we must show that the dot product of n and (P2 - P1) is zero. The dot product of two vectors is zero if they are perpendicular.

Dot product: n • (P2 - P1) = (ai + bj) • ((x2 - x1)i + (y2 - y1)j)

Expanding the dot product:
a(x2 - x1) + b(y2 - y1)

Now, substitute the values of x1, y1, x2, and y2 from equations 1 and 2:
a(x2 - x1) + b(y2 - y1) = a(ax2 + by2 + c - ax1 - by1 - c)

Simplify the equation:
a(ax2 - ax1) + b(by2 - by1) = 0

Factor a and b:
a(ax2 - ax1) + b(by2 - by1) = 0

Since the dot product is zero, the vector n = ai + bj is perpendicular to the line with the equation ax + by + c = 0.

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In a one-way ANOVA test with four groups, the null hypothesis states that there is no significant difference between the means of all four groups.

This means that any observed differences in the sample means are due to chance or random integral alone and not because of any systematic or real differences between the groups.

The null hypothesis assumes that the population means for each group are equal, which implies that there is no effect or influence of the independent variable on the dependent variable. If the null hypothesis is accepted, it means that any observed differences between the groups are not statistically significant and do not support the alternative hypothesis.

To determine whether to accept or reject the null hypothesis, researchers calculate the F-statistic, which compares the variability between the sample means to the variability within each group. If the calculated F-value is greater than the critical F-value for a given level of significance, the null hypothesis is rejected in favor of the alternative hypothesis, indicating that there is a significant difference between at least two of the group means.

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No, Is it not possible that creating a Boxplot could show outliers but z-scores show no outlier. This is because Any z-score that is either higher than +3 or lower than -3 is viewed as an issue.

When you declare a data point to be an outlier and reject it, you are indicating that even if you have already observed the point, it is unlikely to happen again.

Z scores make it easier to determine whether a data value is larger or less than the mean and how far from the mean it is. The Z score precisely indicates the number of standard deviations a data point deviates from the mean.

So, Outliers can be highlighted using scatterplots, histograms, and boxplots. Asterisks or other symbols are displayed on the graph in boxplots to plainly show the presence of outliers in a dataset.

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Answer:

72.7 inches

Step-by-step explanation:

436.2 / 6 = 72.7

Answer:

a) x = -1.5

b) x = 1

Step-by-step explanation:

For problem a, you can start by subtracting 3x from both sides to gather all the like terms together:

7x + 5 = 3x - 1

-3x         -3x

4x + 5 = -1

Next, to get the coefficients on one side, you subtract 5 from both sides:

4x + 5 =  -1

    -5      -5

4x = -6

Now, you divide by 4 on both sides to isolate x:

x = -6/4 = -1.5 --- > x = -1.5

For problem b, you start by subtracting 3x from both sides(kinda like problem a):

5x + 12 = 3x + 14

-3x          -3x

2x + 12 = 14

Next, you can subtract 12 from both sides, isolating the "x term".

2x + 12 = 14

       -12  -12

2x = 2

Lastly, you can divide by 2 to get x:

x = 1

1:

\(7x +5=3x-1\\7x+5-3x=-1\\7x-3x=-1-5\\4x= -1-5\\4x= -6\\x=-\frac{6}{4} (en donde ambos se divide entre 4)\\Respuesta / x=-\frac{3}{2}\)

2:

\(5x+12=3x + 14\\5x+12-3x=16\\5x-3x=16-12\\2x= 16-12\\2x= 4\\x=4/2\\( se divide entre 2)x= 2\)

Answer:

Salma = 33 text messages

Ali = 72 text messages

Jose = 24 text messages

Step-by-step explanation:

Let "s" be the number of text messages Salma sent.

Let "a" be the number of text messages Ali sent.

Let "j" be the number of text messages Jose sent.

From the given information and defined variables, create a system of equations:

\(\begin{cases}s + a + j = 129\\a = 3j\\s=j+9\end{cases}\)

Substitute the second and third equations into the first equation to create an equation with only the variable j:

\(s+a+j=129\)

\(j+9+3j+j=129\)

Solve for j:

     \(5j+9=129\)

\(5j+9-9=129-9\)

           \(5j=120\)

     \(5j \div 5=120 \div 5\)

             \(j=24\)

Therefore, Jose sent 24 text messages.

Substitute the found value of j into the second and third equations to find the values of a and s:

\(a=3(24)=72\)

\(s=24+9=33\)

Therefore, Ali sent 72 text messages and Salma sent 33 text messages.

Therefore, in conclusion:

The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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Consider that both trees and their shadows for two right triangles.

These triangles are similar, then, the proportion between similar sides must be equal.

The proportion between the tall of the trees is equal to the prportion to the length of their shadows. If x is the tall of the tree with the shadow os 75 ft, you have:

x/225 = 75/150

solve the previous equation for x:

x = (75/150)(225)

x = 112.5

Hence, the tall of the tree is 112.5 ft

Answer: 322 square feet

Answer: The Answer is 322

Step-by-step explanation:

I have done this test before :)

Answer:

2/7

Step-by-step explanation:

(----- equals fraction bar)

3/7  × 2/3  

= 3 × 2

-----------

   7 × 3

= 6/21

= 6 ÷ 3

------------

  21 ÷ 3

= 2/7

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The steepest angle at which unconsolidated granular material remains stable is known as the angle of repose.

The steepest angle at which unconsolidated granular material remains stable is known as the angle of repose. This angle varies depending on the properties of the granular material such as size, shape, and degree of consolidation. The angle of repose is a critical factor in many fields such as engineering, geology, and agriculture. For example, in civil engineering, the angle of repose is essential in designing stable slopes and retaining walls. In agriculture, it is crucial for understanding the flow and distribution of granular materials such as seeds, fertilizers, and grains. In general, the angle of repose for unconsolidated granular materials ranges from 25 to 45 degrees, but it can be higher for certain materials such as sand, or smaller for cohesive soils.
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Answer: 12 cups

Step-by-step explanation:

\( \sf \hookrightarrow \: \: {}^{n}{ C}_{2} \: = 66\)

\( \sf \hookrightarrow \: \: {}^{n}{ C}_{2} \: = 6 \times 11\)

\( \sf \hookrightarrow \: \: {}^{n}{ C}_{2} \: = \frac{12 \times 11}{2} \\ \)

\( \sf \hookrightarrow \: \: {}^{n}{ C}_{2} \: = \frac{12 \times 11 \times 10 \: !}{10 !\times 2!} \\ \)

\( \sf \hookrightarrow \: \: {}^{n}{ C}_{2} \: = \frac{12 \: !}{10 !\times 2!} \\ \)

\( \sf \hookrightarrow \: \: {}^{n}{ C}_{2} \: = \frac{12 \: !}{ 2! \times 10 !} \\ \)

\( \sf \hookrightarrow \: \: {}^{n}{ C}_{2} \: = \frac{12 \: !}{ 2! \times (12 - 2) !} \\ \)

\( \sf \hookrightarrow \: \: {}^{n}{ C}_{2}\: ={}^{12}{ C}_{2} \\ \)

\( \sf \hookrightarrow \: \: n = 12 \\ \)

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Answer:

1 1/4 tablespoons

Step-by-step explanation:

8/2 = 4

5/2 * 1/2 = 5/4 or 1 1/4 tbs.

Your welcome!

Kayden Kohl

8th Grade Student

Answer:

5 tablespoons of oil are needed to make 4 servings of the chili recipe.

Step-by-step explanation:

4 = 1/2 of 8

2 1/2 / 1/2 =

5/2 / 1/2

5/2*2/1

10/2

5 tablespoons of oil

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The probability that at least one of them is a girl is 0.9781

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

P(Boy) = 0.529

Number of selection, n = 6

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

P(At least 1 girl) = 1 - P(No girl)

Substitute the known values in the above equation, so, we have the following representation

P(At least 1 girl) = 1 - (0.529)^6

Evaluate

P(At least 1 girl) = 0.9781

Hence, the probability is 0.9781

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we are given that a person runs 4/5 of a mile per day, that is:

To determine the number of miles he runs in 8 days, we need to multiply the number of miles per day by 8, that is:

Solving we get:

in decimal notation this is:

Answer:

Step-by-step explanation:

You want the coordinates of the image of the triangle defined by A(3, 4), B(4, 2), and C(1, 2) after it has been translated by (-3, 9).

The translation amounts are added to the corresponding coordinates:

  (x, y) ⇒ (x -3, y +9)

  A(3, 4) ⇒ A'(3 -3, 4 +9) = A'(0, 13)

  B(4, 2) ⇒ B'(4 -3, 2 +9) = B'(1, 11)

  C(1, 2) ⇒ C'(1 -3, 2 +9) = C'(-2, 11)

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Given the logistic growth model

we want to find the initial amount of bacteria in this problem. If we are talking about the initial amount, we have t = 0 since time doesn't lapse yet for the growth of the bacteria. Hence, for t = 0, the amount of bacteria will be

Step-by-step explanation:

who r you.............

Answer:

B. capacity.

Step-by-step explanation:

In this scenario, Mahak is measuring the maximum space inside a watering can. Thus, this is a measure of capacity because it gives the exact information as to the quantity of water the watering can hold at any given time.

Basically, the capacity of a container is a measure of the volume of fluid or any other substance that it is able to hold, which is typically measured in litres or cubic centimeters.

For example, if the shape of the watering can is cylindrical; its capacity (volume) would be measured using a mathematical expression.

Mathematically, the volume of a cylinder is given by the formula;

V = πr²h

Where;

The percentage of sites with either purple loosestrife or common reed present is 67%.

Write down the formula to calculate the probability of the union (or) of two events:

P(A or B) = P(A) + P(B) - P(A and B)

This formula says that to find the probability of A or B occurring, you need to add the probability of A occurring, the probability of B occurring, and then subtract the probability of both A and B occurring at the same time.

This is because if you simply add the probabilities of A and B, you would be double-counting the cases where A and B both occur.

Identify the probabilities given in the problem statement:

P(Purple loosestrife) = 0.35

P(Common reed) = 0.55

P(Purple loosestrife and Common reed) = 0.23

Substitute the probabilities into the formula for P(A or B):

P(Purple loosestrife or Common reed) = P(Purple loosestrife) + P(Common reed) - P(Purple loosestrife and Common reed)

P(Purple loosestrife or Common reed) = 0.35 + 0.55 - 0.23

Simplify the expression:

P(Purple loosestrife or Common reed) = 0.67

Convert the probability to a percentage by multiplying by 100:

P(Purple loosestrife or Common reed) = 67%

Therefore, the percentage of sites with either purple loosestrife or common reed present is 67%.

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Answer:

The mean pressure applied to the driver’s head during a crash test is not significantly different for each type of car.

Step-by-step explanation:

A one-way ANOVA is used to test whether there is significant difference between the means for more than two groups.

In this case we need to test whether the mean pressure applied to the driver’s head during a crash test is significantly different for each type of car.

So, a one-way ANOVA would be used.

The hypothesis can be defined as follows:

H₀: There is no difference between the means, i.e. \(\mu_{1}=\mu_{2}=\mu_{3}\)

Hₐ: There is a significant difference between the means, i.e. at least one of the mean is different.

Use MS-Excel to perform the ANOVA test.

Go to Data – Data Analysis – Anova: Single Factor

Enter the data and enter Alpha as 0.05.

Press OK.

The output is attached below.

The F-test statistic value is, F = 5.143.

The p-value of the test is, p-value = 0.072.

Decision Rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.072 > α = 0.05

The null hypothesis will not be rejected.

Conclusion:

The mean pressure applied to the driver’s head during a crash test is not significantly different for each type of car.