16. Describe, step-by-step how to find the slope of a line through two points.

Answer:

Step-by-step explanation:

As a rule, worth remembering, the fractions with denominators of multiples of 2, 5 or combination of the two, result in terminating decimals and all the rest- non-terminating.

Considering this we can state:

Step-by-step explanation:

\(\sf 16-2t=t+9+4t \\ \: \: \: \: \: \: \: \: \: \: \: \:16 = 9 + 5t + 2t \\16 - 9=7t \\ 7t = 7 \\ t = \frac{7}{7} \\ t = 1\)

t=1

Answer:

solution given:

16-2t=t+9+4t

keeping like terms on one side.

16-9=t+4t+2t

7=7t

dividing both side by 7,we get

7/7=7t/7

we get t=1

Step-by-step explanation:

Answer:

  Does Not Exist (DNE)

Step-by-step explanation:

You want the limit of f(x) = 1/(x-3) as x approaches 3.

The limit at a point exists if and only if the left limit at that point is equal to the right limit at that point.

F(x) = 1/(x -3) changes sign at x = 3, so the left limit and right limit have opposite signs. The limit at x = 3 does not exist.

Answer:

Step-by-step explanation:

Answer:

(2, 1)

Step-by-step explanation:

The solution is the point where the two lines intersect. In this case, that is (2, 1)

The required Solutions of the given quadratic equation are 9 or -1.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

x²−8x−9=0

To solve it by completing the square.

x² − 8x + 16 − 16 −9=0

(x - 4)²  = 25

x - 4 = ± 5

So,

x - 4 = 5     or    x - 4 = -5

x = 9          or     x = -1

Thus required Solution of equation are 9 or -1.

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The proportion of the variability in calories is explained by the relation between fat content and calories is 89.1% .

Here, we have,

Given that,

Correlation coefficient = 0.944

Correlation determination r² = 0.891136

To determine the proportion of variability in calories explained by the relation between fat content and calories, we need to calculate the coefficient of determination, which is the square of the linear correlation coefficient (r).

Given that the linear correlation coefficient is 0.944, we can calculate the coefficient of determination as follows:

Coefficient of Determination (r²) = (0.944)²

Calculating this, we find:

Coefficient of Determination (r²) = 0.891536

Therefore, approximately 89.1% of the variability in calories is explained by the relation between fat content and calories.

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3,058.08 cubic yards

radius = 9 yd

π = 3.14

Volume of a sphere = 4/3 πr³

Volume of sphere = 4/3 × 3.14 × 9³

Volume of sphere = 3052.08

To the nearest hundredth, the volume 3,058.08 cubic yards

The 95% confidence interval for the given population proportion is between 0.1716 to 0.2884.

The confidence interval for a population proportion is calculated by the formula,

\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)

Where \(\bar{p}\) is the sample proportion and α is the level of significance.

It is given that,

The statistics reported on CNBC projects, a surprising number of motor vehicles are not covered by insurance. The sample results are

The sample size n = 200;

The number of successes = 46

So, the sample proportion \(\bar{p}\) = 46/200 = 0.23

For a 95% confidence interval, the level of significance is

α = 1 - 95/100 = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Then, the z-score for the value 0.025 is

\(z_{\alpha/2}\) = 1.96 (from the table)

Thus, the confidence interval is

\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)

⇒ C.I = 0.23 ± (1.96) × \(\sqrt{\frac{0.23(1-0.23)}{200} }\)

⇒ C.I = 0.23 ± 1.96 × 0.0298

⇒ C.I = 0.23 ± 0.0584

So, the upper limit is 0.23 + 0.0584 = 0.2884 and the lower limit is 0.23 - 0.0584 = 0.1716.

Therefore, the 95% confidence interval for the given population proportion lies between 0.1716 to 0.2884.

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Answer:

28

Step-by-step explanation:

Determine which integer in the solution set will make the equation true. t − 42 = −14 {−56, −28, 3, 28}

replace 28 for t:

t − 42 = −14

28 − 42 = −14

−14 = −14

Answer:

  28

Step-by-step explanation:

You want the value of t that satisfies t − 42 = −14.

The solution to this 1-step linear equation is to add the opposite of the unwanted constant (-42).

Adding 42 to both sides of the equation gives ...

  t -42 +42 = -14 +42

  t = 28

The integer that makes the equation true is 28.

Answer:

it is b or 20,000 or it is the base salary, you can put all 3 to be safe since they are all technichaly the same.

Step-by-step explanation:

so y=mx+B is the equation right here m the slope which is rise over run or y/x=.1 and B is the y inercept and 20,000 it is the starting point on the graph. where it overlaps with the y axis, in this case 20,000 which as it says earlier is his base salary

Answer:

Option C, 15.14 units²

Step-by-step explanation:

area of the triangle,

6.82×5.04×sin(61.73)/2

= 15.1365001284..

= 15.14 units² (rounded to the nearest tenth)

The required area of the irregular triangle is 15.14 unit². Option C is correct.

Given that,
A figure of the triangle is shown,
Side AB = a =6.82
Side BC = b = 5.04
Angles, ∠A = 45.03°, ∠B = 61.73°.

The triangle is a geometric shape which includes 3 sides and the sum of the interior angle should not be greater than 180°.

Altitude is perpendicular bisector to the side of the triangle from the opposite vertex of the triangle.

The area of the given triangle can be given as,
Area = 1/2 * a * b sinB
       =  1/2 * 6.82 * 5.04 * sin61.73°
       =  1/2 * 6.82 * 5.04 * 0.88
       =  15.14 unit²

Thus, the required area of the irregular triangle is 15.14 units². Option c is correct.

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The velocity of the ball that Katie serves to Liam is 4.52 meters per second south.

Speed is the time rate at which an object is moving along a path,

To find the velocity of the ball that Katie serves to Liam, we need to divide the displacement (9.5 meters south) by the time taken (2.1 seconds).

Velocity = displacement / time

Velocity = 9.5 m / 2.1 s

Velocity ≈ 4.52 m/s south

Therefore, the velocity of the ball that Katie serves to Liam is 4.52 meters per second south.

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The solution of the equation 2x+y=4 and 3x-2y=-1 is the value of x = 1, while the value of y = 2

We have, the sets of equations as:

2x+y=4 and 3x-2y=-1?

As here, let 2x+y = 4 ----(i) and 3x-2y = -1 ----(ii)

As here to solve the value of x and y we will first equalise the co-efficient of x.

Here, the co-efficient of x in the first equation is 2, while in the second equation it is 3

So, for equalising, we will first multiply the first equation by 3 and the second by 2,

Thus, we will get it as:

6x+3y=12 ----(iii)

6x-4y=-2----(iv)

Now subtracting (iv) from (iii)

We will get,

7y = 14

=>y=2

Putting the value of y in (i),

2x=4-y = 4-2 =2

=>x = (2/2)=1

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The complete question may be like:

What is the solution of the equations 2x+y=4 and 3x-2y=-1?​

The probability that the PolyU team wins the relay race can be determined by calculating the cumulative probability that their combined time is less than or equal to the "time to beat" of 120 minutes.

Let's denote the time taken by George as X and the time taken by Jean as Y. Both X and Y are normally distributed with means and standard deviations given as follows:

George: X ~ N(70, 15^2)

Jean: Y ~ N(65, 10^2)

Since the times taken by George and Jean are independent, we can use the properties of normal distributions to calculate the probability of their combined time being less than or equal to 120 minutes.

To find the probability that X + Y ≤ 120, we need to find the joint distribution of X and Y and then calculate the probability of the combined time being less than or equal to 120. Since X and Y are normally distributed, their sum X + Y will also follow a normal distribution.

The mean of the sum X + Y is given by the sum of the individual means:

Mean(X + Y) = Mean(X) + Mean(Y) = 70 + 65 = 135 minutes.

The variance of the sum X + Y is given by the sum of the individual variances:

Var(X + Y) = Var(X) + Var(Y) = 15^2 + 10^2 = 325 minutes^2.

The standard deviation of the sum X + Y is the square root of the variance:

SD(X + Y) = √(Var(X + Y)) = √325 ≈ 18.03 minutes.

Now, we can use the properties of the normal distribution to calculate the probability P(X + Y ≤ 120) by standardizing the value:

Z = (120 - 135) / 18.03 ≈ -0.8313

Using a standard normal distribution table or a calculator, we can find the cumulative probability for Z = -0.8313, which represents the probability of the combined time being less than or equal to 120 minutes. Let's assume this probability is P(Z ≤ -0.8313) = p.

Therefore, the probability that the PolyU team wins the relay race can be given as 1 - p, as the team wins when their combined time is less than or equal to 120 minutes.

In summary, to find the probability of the PolyU team winning the relay race, we need to calculate the cumulative probability P(Z ≤ -0.8313) and subtract it from 1.

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Answer:

4

Step-by-step explanation:

x>4

it would be that symbol before the 36 but I don't have it

Answer:

C. 4

Step-by-step explanation:

If he makes 2 for every five then he will make 4 for every 10 he shoots

The significance level, account for multiple testing, and recognize the limitations and context when interpreting p-values.

The p-value is a crucial concept in statistical hypothesis testing. It refers to the probability of observing a test statistic as extreme as or more extreme than the one observed, given that the null hypothesis is true.

In other words, it is the probability of obtaining the observed result by chance, assuming that there is no true effect.
There are several key guidelines that researchers need to keep in mind when interpreting p-values.

This threshold should not be taken as a hard-and-fast rule and other factors such as the study design sample size and effect size should also be considered.
Secondly, the p-value alone cannot determine the validity or importance of a research finding.

It is just one piece of evidence that needs to be considered along with other factors, such as the magnitude of the effect, the precision of the estimates, the plausibility of alternative explanations, and the practical implications of the findings.
Thirdly, the p-value can be influenced by various factors, such as the choice of statistical test, the assumptions made about the data, and the presence of outliers or influential observations.

Therefore,

Researchers should always report the assumptions and limitations of their analyses and consider conducting sensitivity analyses to test the robustness of their results.
In summary,

The key guidelines for interpreting p-values include understanding their meaning and limitations, considering other factors in addition to p-values, and being aware of the factors that can influence their interpretation.

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Therefore, the directional derivative of f at P=(1,-1,-2) in the direction of A=3i+2j-6k is -2.

To find the directional derivative of f(x,y,z) at P=(1,-1,-2) in the direction of A=3i+2j-6k, we first need to find the gradient of f at P, which is given by:

grad(f) = ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Here, f(x,y,z) = xy + yz + zx, so we have:

∂f/∂x = y + z

∂f/∂y = x + z

∂f/∂z = x + y

Thus, at P=(1,-1,-2), we have:

∇f(P) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

= (y+z)i + (x+z)j + (x+y)k

= (0+(-2))i + (1+(-2))j + (1+0)k

= -2i - 1j + 1k

Next, we need to find the unit vector in the direction of A:

|A| = sqrt(3^2 + 2^2 + (-6)^2) = 7

u = A/|A| = (3/7)i + (2/7)j - (6/7)k

Finally, we can compute the directional derivative of f at P in the direction of A as:

(DAf) | 1(1,-1,-2) = ∇f(P) · u

= (-2i - 1j + 1k) · (3/7)i + (2/7)j - (6/7)k

= -6/7 - 2/7 - 6/7

= -2

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The equation of the parabola is y = 2(x - 2)^2 + 4

The given parameters are:

A parabola is represented as:

y = a(x - h)^2 + k

Substitute (h,k) = (2,4)

y = a(x - 2)^2 + 4

Substitute (x,y) = (3,6)

6 = a(3 - 2)^2 + 4

Evaluate the difference

6 = a(1)^2 + 4

This gives

6 = a + 4

Subtract 4 from both sides

a = 2

Substitute a = 2 in y = a(x - 2)^2 + 4

y = 2(x - 2)^2 + 4

Hence, the equation of the parabola is y = 2(x - 2)^2 + 4

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Maximizing the power of an experiment increases the probability of rejecting H0 when H0 is true, so the answer is C.

The power of an experiment is the probability of correctly rejecting the null hypothesis (H0) when the alternative hypothesis (Ha) is true. In other words, it is the probability of avoiding a Type II error (failing to reject a false null hypothesis).By maximizing the power of an experiment, we increase the likelihood of detecting a true effect if it exists, which reduces the chances of making a Type II error (accepting a false null hypothesis).

Alpha (Type I error rate) and beta (Type II error rate) are related to the significance level and the power of an experiment, but maximizing the power of an experiment does not minimize alpha or beta directly.

Alpha (Type I error rate) and beta (Type II error rate) are related to the significance level and the power of an experiment, but maximizing the power of an experiment does not minimize alpha or beta directly.

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In general, observational studies are more problematic than randomized controlled trials because they can produce spurious relationships.

Observational studies rely on the natural variation in exposures and outcomes that occur in the population, without any intervention or manipulation by the researcher.

This can lead to confounding variables, which are factors that are associated with both the exposure and the outcome and can produce a false association between them.

Randomized controlled trials, on the other hand, assign participants to different exposure groups at random, which reduces the risk of confounding and allows for a more accurate assessment of causality.

Therefore, researchers must be cautious when interpreting observational studies and consider the potential for spurious relationships.

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The triangle with 358 dots on each side will have a total of 128,164 dots.

Let's analyze the pattern to determine the relationship between the number of dots on each side of the triangle and the total number of dots.

If we examine a few examples, we can observe the following:

- A triangle with 1 dot on each side will have a total of 1 dot.

- A triangle with 2 dots on each side will have a total of 1 + 2 + 1 = 4 dots.

- A triangle with 3 dots on each side will have a total of 1 + 2 + 3 + 2 + 1 = 9 dots.

From these examples, we can see that the total number of dots in a triangle is the sum of consecutive odd numbers. The sum of the first n odd numbers is given by the formula n^2.

To determine the number of dots in the triangle with 358 dots on each side, we need to calculate the sum of the first 358 odd numbers. Applying the formula, we get:

Y = 128,164

Therefore, the triangle with 358 dots on each side will have a total of Y dots, which is equal to 128,164.

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Answer:

$6.75

Step-by-step explanation:

Divide 33.75 by 5, they are $6.75 each

a) EDCB is a trapezoid because it has one pair of parallel sides.

b) Whether EDCB is isosceles or not cannot be determined without additional information.

a) A trapezoid is a quadrilateral with one pair of parallel sides. Looking at the given shape EDCB, if we can establish that one pair of its sides is parallel, then it can be classified as a trapezoid. However, the information provided does not specify the relationships between the sides of EDCB. Without additional details, we cannot definitively confirm if EDCB is a trapezoid or not.

b) The question of whether EDCB is isosceles cannot be answered based on the given information alone. Isosceles trapezoids have two pairs of congruent sides, with the base angles opposite the parallel sides being congruent. The information provided does not mention the lengths of the sides or angles of EDCB, so we cannot determine if it is isosceles or not.

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Answer:

it's not b and c

Step-by-step explanation:

it's a and c

brainliest please

The probability that the opening price of the stock is less than 40 is approximately 0.5588 or 55.88%.

The opening price of the stock is modeled as a continuous random variable that is uniformly distributed on the interval [35 3/4, 44 1/4].

The probability that the opening price is less than 40 can be found by calculating the area under the probability density function of the uniform distribution between 35 3/4 and 40.

The probability density function of a uniform distribution on the interval [a, b] is given by:

f(x) = 1/(b-a) for a <= x <= b

f(x) = 0 otherwise

In this case, a = 35 3/4 and b = 44 1/4. Therefore, the probability density function of the opening price is:

f(x) = 1/(44 1/4 - 35 3/4) = 1/8.5 = 0.1176 for 35 3/4 <= x <= 44 1/4

f(x) = 0 otherwise

To find the probability that the opening price is less than 40, we need to integrate the probability density function from 35 3/4 to 40:

P(X < 40) = ∫[35 3/4, 40] f(x) dx = ∫[35 3/4, 40] (1/8.5) dx

= [(1/8.5) * x] from 35 3/4 to 40

= (1/8.5) * (40 - 35 3/4)

= 0.5588

Therefore, the probability that the opening price of the stock is less than 40 is approximately 0.5588 or 55.88%.

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Answer:

64°

Step-by-step explanation:

Given:

A complete angle is 360 degrees

A complete angle is 360 degreesOne right angle (90 degrees)

A complete angle is 360 degreesOne right angle (90 degrees)An angle of 154 degrees

A complete angle is 360 degreesOne right angle (90 degrees)An angle of 154 degreesTwo cross angles that are equal

Find: ∠b - ?

.

First, let's find the size of the smaller cross angles:

180° - 154° = 26°

Since there's two of them, we have to multiply this number by 2:

26° × 2 = 52°

Now, we can find ∠b:

∠b = 360° - 90° - 154° - 52° = 64°