Find the distance between (−7, 1) and (0, −6). Round your answer to the nearest tenth.

If negative sixteen plus the quotient of a number and 2 is 35, the number is 102.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = x

Negative sixteen plus the quotient of a number and 2 is 35.

This can be written as,

Quotient of a number and 2.

x ÷ 2 = M (quotient)

So,

-16 + M = 35

Now,

Solve for M.

M = 35 + 16

M = 51

Now,

x ÷ 2 = 51

x/2 = 51

x = 51 x 2

x = 102

Now,

We can cross-check.

-16 + 51 = 35

35 = 35

Thus,

The number is 102.

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Answer:

3(14 + 19)

Step-by-step explanation:

From the given information:

We are being told that Nate spent 42 + 57 at a store.

To find another expression that shows how much Nate spent at the store.

Then, we need to factorize 42 + 57

i.e.

We will look for the lowest factor that is divisible by both 42 and 57.

So, the lowest factor divisible by both 42 and 57 is 3

42 + 57 = 3(14 + 19)

Thus, another expression that shows how much Nate spent at the store is  3(14 + 19)

Scientists found an animal skull during an excavation and tested the amount of carbon -14 left in it. They found that 55 percent of the carbon-14 in the skull remained.

55% of the Carbon is left in the skull.

If A₀ was the original amount of Carbon, the amount of Carbon that is remaining will be 55% of A₀  which equals 0.55A₀

Using the given equation:

\(A = A_{o}e^{-0.000124t}\\\\ 0.55A_{o} = A_{o}e^{-0.000124t}\\ \\0.55 = e^{-0.000124t}\\\\In(0.55) = In(e^{-0.000124t})\\\\In(0.55) = -0.000124t*In(e)\\\\In(0.55) = -0.000124t\\\\\)

\(t = \frac{In(0.55)}{-0.000124} \\\\t = 4821\)

Rounding of to nearest year, we can conclude that the animal was buried 4821 years ago.

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When given a displacement function, its derivative is the velocity function. Vice versa, when given a velocity function, its integral is the displacement function.

So, we need to integrate the given function to find the displacement function.

To solve for C, we need to have a known displacement. We know that when t = 0, the object has not moved yet. Therefore, it is safe to assume that d must be 0.

So now we know that the displacemnet function is:

We can now solve for the total displacement when t = 5.

Therefore, the total displacement is 677.083 feet.

Because the particle is moving along a straight line, then the distance is equal to the displacement.

The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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In interpreting effect size, the meaning of effect size at 0.3 is small effect size. So, the correct answer is A).

In interpreting effect size, an effect size of 0.3 is typically considered to be a small effect size. This means that there is a small but still measurable difference or relationship between two variables.

The interpretation of effect size can vary depending on the context and the discipline in which it is being used, but as a general rule, effect sizes of 0.2 or smaller are considered small, effect sizes of 0.5 are considered medium, and effect sizes of 0.8 or larger are considered large. Therefore, an effect size of 0.3 falls in the small effect size range. So, the correct option is A).

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Answer:

3x² - 4x²  - 22x + 21

Step-by-step explanation:

⤵ Distribute:

(x - 3 ) (3x ² + 5x - 7 )

3x³ + 5x ²- 7x - 3 (3x² + 5x - 7)

3x ³ + 5x² - 7x - 9x ² - 15x + 21

⤵ Add similar terms:

3x ³ - 4x² - 7x-15x + 21

3x³ - 4x² - 22 + 21

Hence,  (x - 3 ) (3x ² + 5x - 7 ) standard form is 3x³ - 4x² - 22 + 21.

RevyBreeze

We evaluate the integral using the Fundamental theorem of Calculus, by using and antiderivative of the funtion in the integrand;

An antiderivative of x^3 - 2 x is = 1/4 x^4 - x^2

So we evaluate this antiderivative at the two limits of integration:

At x = 1 the antiderivative becomes: 1/4 (1) - 1 = - 3/4

At x = - 1/2 the antiderivative becomes: 1/4 (-1/2)^4 - (-1/2)^2 = - 15/64

Now we subtract the evaluation at the upper limit minus the evaluation at the lower limit:

- 3/4 - (-15/64) = - 33/64

Allow me to show you the actual area we have calculated in a graph for the integration:

The curve in blue is the original function you provided : f(x) = x^3 - 2x

You can see that there is an area above the x axis that has been integrated and that gives as a result a positive number.

The area below the x axis is the part of the integral that provides the negative part which as you see is dominant in this calculation, therefore resulting in a negative final result.

Please, make sure you type -33/64 in the box provided.

the area enclosed by the curves x = -2, x = 3, y = 3x² - 28, and y = 4x + 11 is -1014/27 square units.

To find the area enclosed by the curves x = -2, x = 3, y = 3x² - 28, and y = 4x + 11, we can integrate the difference between the upper and lower curves with respect to x.

First, let's find the points of intersection between the curves to determine the limits of integration.

Setting the two y-equations equal to each other:

3x² - 28 = 4x + 11

Rearranging the equation:

3x² - 4x - 39 = 0

We can solve this quadratic equation to find the x-values of the points of intersection. Factoring or using the quadratic formula, we find:

(x - 3)(3x + 13) = 0

This gives two solutions: x = 3 and x = -13/3.

Therefore, the limits of integration for the x-coordinate are -13/3 to 3.

To calculate the area, we integrate the difference between the upper curve (3x² - 28) and the lower curve (4x + 11) with respect to x:

A = ∫[-13/3, 3] [(3x² - 28) - (4x + 11)] dx

Simplifying:

A = ∫[-13/3, 3] (3x² - 4x - 39) dx

Integrating term by term:

A = [(x³ - 2x² - 39x)]|_[-13/3 to 3]

Evaluating the definite integral:

A = [(3³ - 2(3)² - 39(3)) - ((-13/3)³ - 2(-13/3)² - 39(-13/3))]

A = [(27 - 18 - 117) - ((-2197/27) - 2(169/9) + 507/3)]

A = [-108 - (-2197/27 + 338/9 + 507/3)]

A = [-108 - (-1902/27)]

A = [-108 + 1902/27]

A = (1902/27) - (2916/27)

A = -1014/27

Therefore, the area enclosed by the curves x = -2, x = 3, y = 3x² - 28, and y = 4x + 11 is -1014/27 square units.

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The amount of sales tax to be paid for the package at the resort is $26.39.

Sales tax refers to the amount to be paid to the governing body for a certain product or service.

Sales tax = cost of the service or product * \(\frac{Sales Tax Rate}{100}\)

Given:

The amount of sales tax to be paid =  \(754 * \frac{3.5}{100} = 26.39\)

Thus the amount to be paid at the resort for the package will be

= 754 + 26.39

= $ 780.39.

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Answer:

80

Step-by-step explanation:

120/3=40

40x2=80

Answer:

The right option is option e.T-shaped.

Step-by-step explanation:

The molecular geometry or shape of clf3 is T-shaped. It acquires such shape because of presence of two lone pairs which take equatorial position and there are greater repulsions. The hybridisation is sp3d and it has 2 lone pairs

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Option e) T-shaped

The shape or molecular geometry  of ClF₃ is T-shaped. It acquires such a shape due to the presence of two lone pairs in the equatorial position and has greater repulsion. The hybrid is sp³d and it has 2 lone pairs.

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Angle 1 is 112

Angle 2 is 68

Angle 3 is 90

Angle 4 is 90

Angle 5 is 22

Angle 6 is 158

The equivalent to √-80 is 4√5

What is square root of imaginary ?

The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. In mathematics the symbol for √(−1) is i for imaginary.

The given expression is √-80

The factors of 80 is

⇒√-(2 * 2* 2 * 2 * 5)

Take 4 out of the root

⇒ 4√-5

Since value inside the root is not to be negative. If it is then it means it is imaginary root or i.

So, the answer will be

⇒ 4√5

Hence, the equivalent to √-80 is 4√5

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The odds against Bucks not winning the race are 2:3, so the probability of Bucks not winning is 0.4 or 40%. This means that for every 10 races, Bucks not is expected to win 4 times, while losing 6 times.

In the given scenario, the odds against the horse Bucks not winning the race are 2:3. To calculate the probability that Bucks not will win the race, we can use the following formula: Probability of an event happening = Number of ways an event can happen / Total number of possible outcomes. In this formula, we can consider the total number of outcomes to be 2 + 3, since these are the only possible outcomes in this situation (either the horse wins or it doesn't). Therefore, the total number of possible outcomes is 5. We can also infer from the given information that the number of ways Bucks not can win is 2. Therefore, the probability of Bucks not winning the race is: Probability of Bucks not winning = Number of ways Bucks not can win / Total number of possible outcomes= 2 / 5= 0.4 or 40%Therefore, the probability that Bucks not will win the race is 0.4 or 40%. This means that for every 10 races, Bucks not is expected to win 4 times, while losing 6 times.

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Answer:

\({ \boxed{ \tt{4x + 4x \: → \: 8x}}} \\ \\ { \boxed{ \tt{3x + 5x + 8 \:→ \: 8x + 8 }}} \\ \\ { \boxed{ \tt{ - 7x + 4 + 3x \: → \: - 4x + 4}}} \\ \\ { \boxed{ \tt{4x + 4x + 4x + 4x \: → \: 16x}}}\)

Answer:

4x + 4x → 8x

3x + 5x + 8 → 8x + 8

-7x + 4 + 3x → -4x + 4

4x + 4x + 4x + 4x → 16x

Step-by-step explanation:

The left side consists of a series of expressions and the right side is the list of choices to match to. This is simple math if you already know how to combine like terms. Combining like terms is combining numbers that represent the same value. Take a look at 4x + 4x for example, 4x and 4x are two numbers with the same value. Not that they both have the number 4, but that they have the same special variable. If there are two or more numbers with the same variable like x for example, combine the two, meaning you add the numbers. Just don't add the variables because clearly, the variable is an unknown number so you can't add variables. Instead, you can apply the same variable to the sum of two or more numbers. So 4x + 4x equals 8x. Do the same process again to the other 3 expressions. Also, you can't add a number with a variable to a number alone. They don't represent the same value.

3x and 5x are the same value so combine them. Now you only have 8x + 8 left as the simplified version of the expression.

-7x and 3x are the same value so combine them. Don't forget that the 7 is negative. Use a calculator if needed. Now you only have -4x + 4 as the simplified version of the expression.

Similar to 4x + 4x in the first expression, just add all of the numbers up. There isn't a number alone in this expression. 16x should be your final answer.

I hope this helps! Let me know if I am wrong. :D

Answer:

Step-by-step explanation:

To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.

The midpoint of the interval is the average of the lower and upper bounds:

Midpoint = (0.039 + 0.479) / 2 = 0.259

The width of the interval is the difference between the upper and lower bounds:

Width = 0.479 - 0.039 = 0.44

Half of the width is obtained by dividing the width by 2:

Half Width = 0.44 / 2 = 0.22

Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:

p ± E = 0.259 ± 0.22

So, the correct option is:

D. 0.259 ± 0.22

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A standard normal random variable (Z) has a mean of 0 and a standard deviation of 1. The probability of Z being greater than 0 is equal to the area under the normal curve to the right of 0, which is exactly half of the total area under the curve (since the curve is symmetric around the mean of 0). Therefore, P(Z>0) is equal to 0.5.

A standard normal random variable, like Z in your question, follows a standard normal distribution, which is a special type of normal distribution with a mean of 0 and a standard deviation of 1. Now, you're asked to find the probability P(Z > 0).

Since the standard normal distribution is symmetrical around the mean (0), the probability of Z being greater than 0 is equal to the probability of Z being less than 0. In other words, half of the distribution is on the right side of the mean, and the other half is on the left side.

Therefore, P(Z > 0) = 0.5, which is your answer.

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On solving the provided question, we can say that Probability 8 drive to work\(= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123 = > 1 - 0.1236 = 0.8764\)

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

x = number that drive to work alone

Likelihood that exactly eight people drive alone to work is equal to the probability that no more than seven people drive alone.

\(P(x < = 7) = 1 - P(x > 7) = 1- P(x = 8)\)

That probability

Probability 8 drive to work

\(= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123\\=1 - 0.1236 = 0.8764\)

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Answer:

c = 4,9

d = 4,6

Answer:

ex :  8/5

you divided the numerator by the denominator and it because a decimal

so ur answer for 8/5 would be 1.6

not really sure if this is what ur looking for but thats how u convert a fraction to a decimal  

Good luck <3

Using the Euclidean distance between pairwise observations, the pairwise observation is most dissimilar is Observations 1 & 3. The correct answer is A.

In order to determine the most dissimilar pairwise observation using the Euclidean distance, we need to calculate the distance between each pair of observations. The Euclidean distance between two observations is the square root of the sum of the squared differences between their corresponding values in each variable.

For example, for observations 1 and 2:

d(1,2) = √((2-5)² + (22-21)²) = √(9 + 1) = √(10)

We can calculate the distances between all pairs of observations and then identify the pair with the largest distance as the most dissimilar.

d(1,2) = √(10)

d(1,3) = √((2-12)² + (22-1)²) = √(1400)

d(2,3) =√((5-12)² + (53-1)²) = √(1865)

Therefore, the most dissimilar pairwise observation is between observations 1 and 3 with a distance of √(1400). The correct answer is A.

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In this context, the dependent variable is t (amount of tax due) and the independent variable is c (cost of the order).In this scenario, the variables are t (the amount of tax due) and c (the cost of the order).

To determine which variable is independent and which is dependent, we need to understand their relationship.In this case, the amount of tax due, t, is calculated based on the cost of the customer's order, c. The tax amount is dependent on the cost of the order because it is directly influenced by the value of c. As the cost of the order changes, the amount of tax due will also change accordingly.

On the other hand, the cost of the order, c, is independent. It is not influenced or determined by the amount of tax due. The customer can choose the cost of their order, and the tax will be calculated based on that chosen amount.

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Answer:1250

Step-by-step explanation:

The distance 'x' between the base of the building and the base of the ladder is approximately 5.54 feet.

Using trigonometry, we know that the tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the tangent of 70° is equal to the height of the building (17 feet) divided by the distance 'x' between the base of the building and the base of the ladder:

tan(70°) = 17 / x

To solve for 'x', we can rearrange the equation:

x = 17 / tan(70°)

Calculating this using a calculator:

x ≈ 5.54 feet

Therefore, the distance 'x' between the base of the building and the base of the ladder is approximately 5.54 feet.

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Answer:

he would only have 5 gallons left after 4 hours

Answer:

Substitute using the average rate of change formula.

((−(5)^6−3+2)−(−(5)^4−3+2)) / ((6)−(4))

Simplify the expression.

−7500

Step-by-step explanation:

Answer:

Step-by-step explanation:

The function is:

Find values of f(4) and f(6);

Average rate of change in the given interval is:

To use the divergence theorem, we need to find the divergence of the vector field F =\((2x, 2y, z^2)\\\). The divergence of F is given by:

div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 2 + 2 + 2z

= 2z + 4

Next, we need to find the outward normal vector n for the surface S, which is defined by the equation \(x^2 y^2 z^2\\\) = 1. We can write this equation as:

f(x, y, z) = \(x^2 y^2 z^2\\\) - 1 = 0

Then, the gradient of f is given by:

∇f \(= (2xy^2z^2, 2x^2yz^2, 2x^2y^2z)\\\)

At any point on the surface S, the gradient ∇f is perpendicular to the tangent plane of S. Therefore, the outward normal vector n is equal to ∇f/|∇f|. We have:

|∇f|^2 = \((2xy^2z^2)^2 + (2x^2yz^2)^2 + (2x^2y^2z)^2\\\)

= \(4x^2y^4z^4 + 4x^4y^2z^4 + 4x^4y^4z^2\\\)

= \(4x^2y^2z^2(x^2y^2 + x^2z^2 + y^2z^2)\\\)

= \(4x^2y^2z^2\)

So, the outward normal vector is:

n = ∇f/|∇f| =\((2xy^2z^2, 2x^2yz^2, 2x^2y^2z) / (2xyz)\)

Now, we can use the divergence theorem to find the surface integral of F over S:

∫∫S F · dS = ∭V div F dV

where V is the solid enclosed by S. We can express V as:

\(x^2 y^2 z^2 ≤ 1 → -1 ≤ x ≤ 1, -1 ≤ y ≤ 1, -1 ≤ z ≤ 1\)

Therefore, the integral becomes:

∫∫S F · dS = ∭V (2z + 4) dV

= ∫-1^1 ∫-1^1 ∫-1^1 (2z + 4) dx dy dz

We can integrate over z first:

∫-1^1 (2z + 4) dz = [z^2 + 4z]_-1^1 = 6

Then, we can integrate over y:

∫-1^1 6 dy = 12

Finally, we can integrate over x:

∫-1^1 12 dx = 24

Therefore, the surface integral of F over S is 24.

Using the divergence theorem, the value of the surface integral ∫∫∫ (2x)(2y)(z^2) ds over the surface S defined by x^2 + y^2 + z^2 = 1 can be evaluated.

The divergence theorem, also known as Gauss's theorem, relates the surface integral of a vector field over a closed surface to the triple integral of the divergence of the vector field over the region enclosed by the surface. In this case, we need to evaluate the surface integral of the vector field F = (2xy, 2xy, 2xz^2) over the surface S defined by x^2 + y^2 + z^2 = 1.

Applying the divergence theorem, we have:

∬∬ F · dS = ∭ div(F) dV

where dS represents the outwardly oriented differential surface area vector and dV represents the differential volume element.

First, let's find the divergence of the vector field F. The divergence of F, div(F), is given by:

div(F) = ∂(2xy)/∂x + ∂(2xy)/∂y + ∂(2xz^2)/∂z

Simplifying the partial derivatives, we get:

div(F) = 2y + 2x + 4xz

Now, we can rewrite the triple integral in terms of the divergence:

∭ div(F) dV = ∭ (2y + 2x + 4xz) dV

The region enclosed by the surface S is a unit sphere centered at the origin. Therefore, we can rewrite the triple integral in spherical coordinates:

∭ (2y + 2x + 4xz) dV = ∫∫∫ (2ρsinφcosθ)(2ρsinφsinθ)ρ^2sinφ dρ dθ dφ

Integrating over the appropriate ranges, we find the value of the triple integral. The resulting value will be the answer to the original surface integral ∫∫∫ (2x)(2y)(z^2) ds.

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In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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