300x7065
A tough one can you solve it without looking the answer up or not cheating in any way

Answer: The differential equations is

y3 3x3logx = 8x3.

Step-by-step explanation:

break the given original- value problem. The DE is homogeneous. xy2dy/ dx = y3- x3; y( 1) = 2.

result

Given a homogenous discriminational equation, xy2 dy/ dx = y3- x3

xy2dy/ dx = y3- x3

dy/ dx = ( y3- x3)/ xy2

dy/ dx = (( y/ x) 3- 1)/( y2/ x2)---( 1)

Put y/ x = v ⇒ y = xv

separatew.r.t x

dy/ dx = x.dv/ dx v

Equation( 1) becomes,

⇒ dv/ dx v = ( v3- 1)/ v2

⇒ dv/ dx = (( v3- 1)/ v2)- v

⇒ dv/ dx = ( v3- 1- v3)/ v2

v2. dv = -1/x.dx

Integrate on both sides, we get

∫ v2. dv = ∫- 1/x.dx

v3/ 3 = - logx C

1/3( y3/ x3)) log x = C( 2)

Now, given that y( 1) = 2

Substituting y = 2 and x = 1 in equation( 2)

(1/3) ×(23/13)) log 1 = C

C = 8/3

From equation( 2), we get

⇒( y3/ 3x3) logx = 8/3

thus, the needed differential equation is y3 3x3logx = 8x3.

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Answer:

From top to bottom:

A, J, E, B, I, C, D, G, F, H

See below for more clarification.

Step-by-step explanation:

We are given that AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. And we want to prove that ΔAEB ≅ ΔDEC.

Statements:

1) XY is perpendicular to AB.

Definition of perpendicular bisector.

2) XY ⊥ CD.

In a plane, if a transveral is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

3) m∠AXE = 90°, m∠DYE = 90°.

Definition of perpendicular lines.

4) ∠AXE ≅ ∠DYE.

Right angles are congruent.

5) XE ≅ YE

Definition of a midpoint.

6) ∠A ≅ ∠D.

Alternate Interior Angles Theorem

7) ΔAEX ≅ ΔDEY

AAS Triangle Congruence*

(*∠A ≅ ∠D, ∠AXE ≅ ∠DYE, and XE ≅ YE)

8) AE ≅ DE

Corresponding parts of congruent triangles are congruent (CPCTC).

9) ∠AEB ≅ ∠DEC

Vertical Angles Theorem

10) ΔAEB ≅ ΔDEC

ASA Triangle Congruence**

(**∠A ≅ ∠D, AE ≅ DE, and ∠AEB ≅ ∠DEC)

Answer:

Step-by-step explanation:

the 2nd and 4th answers look good.  the 1st answer is correct as well.

To solve this look at the x axis and y axis,  the x axis is in inches, the y axis is in pounds.  So you know that as the distance increase per inch,  the force in pounds is increasing too.  

so the force applied is going up,   0.73 pounds , for each inch of travel ( or stretch) of the spring.  

Answer:

Hello. How's your day been so far?

Step-by-step explanation:

Answer:

Ya

Step-by-step explanation:

In the one-way ANOVA, the within-groups variance estimate is equivalent to the within-cells variance estimate in the two-way ANOVA.

Option B is right choice.

In the one-way ANOVA, the within-groups variance estimate is equivalent to the within-cells variance estimate in the two-way ANOVA.

This is because both types of variance estimates measure the variation within groups or cells of the independent variable(s).
In a one-way ANOVA, the independent variable has only one factor or level, and the within-groups variance estimate measures the variation within each group or level of the factor.

This estimate reflects the extent to which the data points within each group deviate from the group mean.
In a two-way ANOVA, there are two independent variables or factors, and the within-cells variance estimate measures the variation within each combination of levels of the two factors.

This estimate reflects the extent to which the data points within each cell (or combination of factor levels) deviate from the mean of that cell.
Therefore, the within-cells variance estimate in the two-way ANOVA plays a similar role as the within-groups variance estimate in the one-way ANOVA.

Both estimates reflect the degree of variability within the groups or cells of the independent variable(s) and both are used to calculate the F-statistic and determine the statistical significance of the effects of the independent variable(s) on the dependent variable.

Option B is right choice.

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A 90% confidence interval for the average speed of all drivers on interstate 94 is (73.69, 76.31)

Given that,

Imagine asking a sample of 16 people how quickly they travel on Interstate 94. You determine the average speed to be 75 mph and the variance to be 9 mph after gathering your sample.

Solution is as given below :

90% Confidence Interval for μ is

μ = X ± tₐ/2 (n-1) 5/\(\sqrt{n}\)

μ = 75  ± (1.75) * 3/\(\sqrt{16}\)

μ = (73.69, 76.31)

Consequently, a 90% confidence interval for the interstate 94 average speed of all drivers is μ = (73.69, 76.31)

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Answer: 0

Step-by-step explanation:

To find the coefficient of x in the equation:

x/8 + 4 = 6

We can begin by isolating x on one side of the equation. We can do this by subtracting 4 from both sides:

x/8 = 2

Next, we can multiply both sides by 8 to get rid of the fraction:

x = 16

Since there is no x-term on one side, the coefficient of x is 0.

Therefore, the coefficient of x in the given equation is 0.

The probability that all 3 balls land in different cans is 12/25.

The probability that all 3 balls land in different cans can be calculated using the multiplication rule of probability. The multiplication rule states that the probability of two or more independent events occurring together is the product of their individual probabilities.

Step 1: Calculate the probability of the first ball landing in any of the 5 cans. This probability is 5/5 = 1.

Step 2: Calculate the probability of the second ball landing in a different can than the first ball. There are now only 4 cans left that the second ball can land in, so the probability is 4/5.

Step 3: Calculate the probability of the third ball landing in a different can than the first two balls. There are now only 3 cans left that the third ball can land in, so the probability is 3/5.

Step 4: Multiply the probabilities from steps 1, 2, and 3 to get the probability that all 3 balls land in different cans. The probability is 1 * 4/5 * 3/5 = 12/25.

Therefore, there is a probability of 12/25 that all 3 balls will land in different cans.

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Given that 4 judges agreed, the probability that the panel made the correct decision depends on the distribution of correct decisions among the remaining 3 judges.

To determine the probability that the panel makes the correct decision, we need to consider the number of judges required for a majority vote. Since there are seven judges in total, four judges must agree for a majority decision. To find the probability of this scenario, we need to consider the different ways in which exactly four, five, six, or all seven judges can make the correct decision.

Given that four judges agreed, we calculate the probability as follows:

1) Four judges agree, and three judges disagree: The probability is calculated as \((0.7)^4 * (0.3)^3\) * (the number of ways to choose 4 judges out of 7).

2) Five, six, or seven judges agree: The probability is calculated as\((0.7)^5 * (0.3)^2 *\)(the number of ways to choose 5 judges out of 7) +\((0.7)^6 * (0.3)^1\)* (the number of ways to choose 6 judges out of 7) +\((0.7)^7 *\) (the number of ways to choose 7 judges out of 7).

By calculating these probabilities and summing them up, we can find the overall probability that the panel makes the correct decision.

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Answer:

AngleASZ Is-congruent-to AngleZSB

Step-by-step explanation:

The incenter of a triangle is a point inside a triangle that is equidistant from all the sides of a triangle. The incenter is the point formed by the intersection of all the three angles of the triangle bisected. The lines drawn from the incenter to the sides of the triangle forming right angles to the sides are congruent.

If Point Z is equidistant from the sides of ΔRST, point Z is the incenter of triangle RST. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. This lines are therefore congruent to each other, i.e. ZA = ZB = ZC.. Since the angles of the sides of the triangles are bisected to form the incenter, therefore:

AngleASZ Is-congruent-to AngleZSB

Answer:

AngleASZ Is-congruent-to AngleZSB

Step-by-step explanation:

D is the correct answer

By using the concept of probability, it can be calculated that

a)  P(X \(\leq\) 1) = 0.25

b) P(0.5 \(\leq\) X \(\leq\) 1)  = 0.1875

c) P(X > 1.5) = 0.4375

d) Median = 1.414

e) F'(X) = 0.5x , 0 \(\leq\) x \(\leq\) 2

           0, otherwise

f) E(X) = 1.33

g) V(X) = 0.2311, SD(X) = 0.4807

h)  E(h(X)) = 2

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

The cdf is

f(x) = \(\left \{ {\frac{x^2}{4}},{ 0 \leq x \leq 2} \atop {1, x=2}} \right.\)

Now,

a) P(X \(\leq\) 1) = \(\frac{1^2}{4} = 0.25\)

b) P(0.5 \(\leq\) X \(\leq\) 1)

= \(\frac{1^2}{4} - \frac{0.5^2}{4}\\\\\frac{3}{16}\\\\0.1875\)

c) P(X > 1.5) = 1 - P(X \(\leq\) 1.5)

                      \(1 - \frac{1.5^2}{4}\)

                       0.4375

d) Let \(\mu\) be the median

P(x \(\leq \mu\)) = 0.5

\(\frac{\mu^2}{4} = 0.5\)

\(\mu^2 = 0.5 \times 4 =2\\\mu = \sqrt{2}\\\mu = 1.414\)

e) F'(x) =

\(\frac{2x}{4}, 0 \leq x \leq 2\\0, otherwise\)

F'(X) = 0.5x , 0 \(\leq\) x \(\leq\) 2

           0, otherwise

f) E(x) =

\(\int_0^2 x \times 0.5 xdx\\=0.5 \times \frac{x^3}{3} |_0^2 \\=0.5 \times \frac{2^3}{3}\\=\frac{4}{3}\\=1.33\)

g) V(X) = E(\(X^2\)) -\((E(X))^2\)

    E(X^2) =

                   \(\int_0^2x^2(0.5x)dx \\0.5 \times \frac{x^4}{4}|_0^2\\2\)

\(V(X) = 2 - (1.33)^2\)

V(X) = 0.2311

SD(X) = \(\sqrt{0.2311} = 0.4807\)

h) h(X) = \(X^2\)

   E(h(X)) = \(\int_0^2X^2({0.5X)dx\)

               = \(0.5 \frac{x^4}{4}|_0^2\)

               = \(0.5 \times \frac{2^4}{4}\)

               = 2

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Answer:

For question 6 there are 3 steps, and for question 7 there are 2 steps

Step-by-step explanation:

Question 6:

step 1. 89 x 2=178

step 2. 89 x 3=267

step 3. 267 + 178=445

Question 7:

step 1. 35 x 3= 105

step 2. 25 x 5= 12

Your're welcome :)

A binomial probability distribution with p = 0.3 is c. positively skewed.

A binomial probability distribution with p = 0.3 is positively skewed. This means that the distribution is skewed to the right. In a binomial distribution, the skewness is determined by the value of p, which represents the probability of success in each trial. When p is less than 0.5, as in this case (p = 0.3), the distribution tends to be positively skewed.

The correct answer is c. positively skewed.

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The number of pre-sale tickets must she sell to make her goal is (c) 200

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

These parameters can be represented using the following system of equations

10x + 15y = 3500

x + y = 300

The graph that completes the question is added as an attachment

From the graph, we have

(x, y) = (200, 100)

The variable y represents the number of pre-sale ticket

So, we have

x = 200

Hence, the number of pre-sale ticket is (c) 200

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Answer:

C, 200

Step-by-step explanation:

An easier way to get the answer in this case would be to see where the 2 lines meet, which is at 200 pre-sale tickets :))

Info given

We have a total of people given (82). We also know that we have 54 children of under 12 years and under some children were under 3 years

We define x as the number of children under 3 years.

We want to find C for the total cost. We don't have the unitary prices but we can assume it as C1 (over 3 and lower than 12) and C2(adults) for children and adults.

Solution:

With C the total amount collected and C1 and C2 described above.

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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The inferential statistics would employ the probability to predict how many miles one should be able to drive a 2000 Toyota Celica during its lifetime.

The inferential statistics are calculated by using analytical tools such as test-statistic values, degree of freedom, sample size, and the rejection criteria(assumption or hypothesis).

Thus, the given information is about predicting the miles. So, according to the probability theory, it needs a sample of data about 2000 Toyota Celica.

Hence, it falls under the inferential branch of statistics. So, option C is correct.

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Disclaimer: The given question on the portal was incomplete. Here is the complete question.

Question: Which branch of statistics would employ probability to predict how many miles one should be able to drive a 2000 Toyota Celica during its lifetime?

A. Predictive statistics

B. Descriptive statistics

C. Inferential statistics

D. Differential statistics

Answer:

5x - 13y + 2

Step-by-step explanation:

Given: 2x – 4y + 6 + 3x – 9y – 4

Combine all like terms:

5x - 13y + 2

The solution of expression after simplification is,

⇒ 5x - 13y + 2

We have to given that,

An expression to simplify as,

⇒ 2x - 4y + 6 + 3x - 9y - 4

Now, We can simplify the expression by combining the like terms as,

⇒ 2x - 4y + 6 + 3x - 9y - 4

⇒ 2x + 3x - 4y - 9y + 6 - 4

⇒ 5x - 13y + 2

Therefore, The solution of expression after simplification is,

⇒ 5x - 13y + 2

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The first scenario described is an example of a retrospective cohort study.  The second scenario suggests a retrospective cohort study as well. The third scenario represents a cross-sectional study, where researchers conduct a survey among high school students to assess the prevalence of obesity and diabetes.

1. In the first scenario, a retrospective cohort study is conducted by tracking individuals over a 20-year period. The study begins in 1960 and collects data on cigar smoking practices. After 20 years, the participants are followed up to determine if they developed any cancers. This type of study design allows researchers to examine the long-term effects of smoking Cuban cigars.

2. The second scenario involves a retrospective cohort study as well. The objective is to study the long-term neurological effects of a discontinued anesthetic agent. The researchers identify patients who received the drug before it was discontinued and then assess the occurrence of subsequent neurological disorders. This study design allows for the examination of the relationship between exposure to the anesthetic agent and the development of neurological disorders.

3. The third scenario represents a cross-sectional study. Researchers aim to assess the prevalence of obesity and diabetes among high school students during their junior year. They conduct a survey to gather information on the students' current weight, diabetes status, and other relevant factors. A cross-sectional study provides a snapshot of the population at a specific point in time, allowing researchers to examine the prevalence of certain conditions or characteristics.

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Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

The graph of the polynomial function f(x) = x^4 + x^3 - 2x^2 will depend on the behavior of the function as x approaches infinity and negative infinity, as well as the location and behavior of any local extrema.

To determine the behavior of the function as x approaches infinity and negative infinity, we can look at the leading term of the polynomial, which is x^4. As x becomes very large (either positive or negative), the x^4 term will dominate the expression, and f(x) will become very large in magnitude. Therefore, the graph of the function will approach positive or negative infinity as x approaches infinity or negative infinity, respectively.

To find any local extrema, we can take the derivative of the function and set it equal to zero:

f(x) = x^4 + x^3 - 2x^2

f'(x) = 4x^3 + 3x^2 - 4x

Setting f'(x) equal to zero, we get:

4x(x^2 + 3/4x - 1) = 0

The solutions to this equation are x = 0 and the roots of the quadratic expression x^2 + 3/4x - 1. Using the quadratic formula, we can find these roots to be:

x = (-3 ± sqrt(33))/8

Therefore, the critical points of the function are x = 0 and x = (-3 ± sqrt(33))/8.

To determine the behavior of the function near each critical point, we can use the second derivative test. Taking the second derivative of f(x), we get:

f''(x) = 12x^2 + 6x - 4

Evaluating f''(0), we get:

f''(0) = -4

Since f''(0) is negative, we know that x = 0 is a local maximum of the function.

Evaluating f''((-3 + sqrt(33))/8), we get:

f''((-3 + sqrt(33))/8) = 11 + 3 sqrt(33)/2

Since f''((-3 + sqrt(33))/8) is positive, we know that x = (-3 + sqrt(33))/8 is a local minimum of the function.

Evaluating f''((-3 - sqrt(33))/8), we get:

f''((-3 - sqrt(33))/8) = 11 - 3 sqrt(33)/2

Since f''((-3 - sqrt(33))/8) is also positive, we know that x = (-3 - sqrt(33))/8 is another local minimum of the function.

Based on this information, we can sketch the graph of the function as follows:

Therefore, the statement that describes the graph of this polynomial function is: "The graph of the function has a local maximum at x = 0 and two local minima at x = (-3 ± sqrt(33))/8. As x approaches infinity or negative infinity, the graph of the function approaches positive or negative infinity, respectively."

Answer:

  y = 130(24/13)^(x -10)

Step-by-step explanation:

The y-value changes by a factor of 240/130 = 24/13 for a unit change in the x-value. This means we can write the function as though it had an initial value of 130 and a growth factor of 24/13, translated 10 units to the right.

  y = 130(24/13)^(x -10)

_____

Additional comment

This can also be written in the form ...

  y = a·e^(kx)

where a=130·(24/13)^(-10) ≈ 0.28266, and k=ln(24/13) ≈ 0.61310

Each morning Daniel runs 5 miles in 45 minutes. If he keeps the same pace, it will take Daniel 1 hour and 22.5 minutes to run 8.5 miles.

To begin, we know that daniel runs 5 miles in 45  minutes, which means he runs at a rate of 1 mile in 9 minutes. to determine how long it will take him to run 8.5 miles, we need to calculate how long it will take him to run 3.5 miles( which is the difference between 5 and 8.5.

To do this, we multiply 9 minutes (the rate at which he runs 1 mile) by 3.5 ( the number of miles he needs to run).  this gives us a result of 31.5 minutes. we then add this to the 45 minutes it takes him to run 5 miles, giving us a total of 1 hour and 22.5 minutes to run 8.5 minutes.

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The domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation for the function is:

f(x) = 3x⁵

The domain of the function: D = all real number

The range of the function: R = all real number

x-intercept = 0

y-intercept = 0

Increasing interval: x ∈ [0, ∞)

Decreaing interval: x ∈ (-∞, 0]

Symmetry = The function is not symmetric

End behavior:

x → ∞, y →∞

x → -∞, y → -∞

Thus, the domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.

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76.62 to 88.66

A manager records the repair cost for 4 randomly selected stereos. A sample mean of $82.64 and standard deviation of $14.32 are subsequently computed.

The 90% confidence interval for the mean repair cost for the stereos is 76.62 to 88.66. The population is assumed to be approximately normal. The given data are: Sample mean, x¯= $82.64 Standard deviation, s = $14.32.

The sample size, n = 4. For a given confidence level, the interval within which the population mean lies is known as the confidence interval.

To find the 90% confidence interval for the mean repair cost for the stereos, we use the formula below: Lower limit= x¯ - z (σ / √n)Upper limit= x¯ + z (σ / √n)Here, z is the z-score associated with a 90% confidence level. We can get this value from the standard normal distribution table.

At a 90% confidence level, the z-score is 1.645. Lower limit= 82.64 - 1.645 (14.32 / √4)= $76.62. Upper limit= 82.64 + 1.645 (14.32 / √4)= $88.66.

Therefore, the 90% confidence interval for the mean repair cost for the stereos is 76.62 to 88.66.

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The given statement "If P = 0.08, the result is statistically significant at the a = 0.05 level" is False.

If P = 0.08, the result is not statistically significant at the a = 0.05 level.

Hence, the given statement "If P = 0.08, the result is statistically significant at the a = 0.05 level" is False.

To determine statistical significance, researchers use the P-value, which is the likelihood of obtaining the observed outcomes if the null hypothesis is true. When P is small, the null hypothesis is refused.

A p-value of 0.05 or less is considered statistically significant in most scientific research.

A p-value of less than 0.05 means that the null hypothesis should be refused since there is less than a 5% probability that the results were due to chance.

When the p-value is greater than 0.05, there is no statistically significant variation between the samples being compared.

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Answer:

it's not in a straigt line so ne

Step-by-step explanation:

Because lines a and b are parallel and lines e and f are parallel, the value of "x" is 82 degrees.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees). Parallel lines are lines in a plane that never intersect, no matter how far they are extended. The distance between the parallel lines is continuous since they never intersect.

Here,

Remember that vertical angles are generated by crossing lines that form two non-adjacent angles. These angles are congruent because they have the same vertex.

Take a look at the attached figure. Because lines "a" and "b" are parallel, the angles 82° and x° are vertical angles. As a result, they are congruent.

The value of "x" is 82 degree as lines a and b are parallel and lines e and f are parallel.

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Answer:

125

Step-by-step explanation: first you do 350 dvide by 1.04 and you will get your answer