an object moves from location d to location f on a trajectory (dotted line) in the direction indicated; arrows representing the velocities at locations d, e, and f are also indicated.

The value of h for which b in plane spanned by a1 and a2 is 3.

If b is spanned by a1 and a2, then for some constant x and y

b = x*a1 + y*a2

(3, -5, h) = x(1, 3, -1) + y(-5, -8, 2)

So we get equations

x - 5y = 3

3x - 8y = -5

-x + 2y = h

Solving x - 5y = 3 and 3x - 8y = -5

(3x - 8y) - 3(x - 5y) = -5 - 3*3

7y = -14

y = -2

Also x = 3 + 5y = 3 + 5*-2

So x = -7

Now h = -x + 2y

= -(-7) + 2*(-2)

= 7 - 4

= 3

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An object's distance from its beginning point during the course of its motion is displayed as a position-time graph. A line's slope increases with its steepness, and an object's motion changes more quickly as a result.

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Answer:

Addition (+)

Step-by-step explanation:

If we were to take the problem and form an expression, it would look like this:

3 times a number (3 ×?) decreased by 2 (- 2) divided by 6 (÷ 6)

Putting it all together it forms:

The four operations are addition, subtraction, multiplication and division.

We can see the multiplication, subtraction, and division, but not addition.

Therefore, the operation that is missing is Addition.

[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]2\log_5(5x^3)+\cfrac{1}{3}\log_5(x^2+6)\implies \log_5( ~~ (5x^3)^2 ~~ )+\log_5\left( ~~ (x^2+6)^{\frac{1}{3}} ~~ \right) \\\\\\ \log_5( ~~ 25x^6 ~~ )+\log_5\left( ~~ (x^2+6)^{\frac{1}{3}} ~~ \right)\implies \log_5\left( ~~ (25x^6)\sqrt[3]{(x^2+6)} ~~ \right)[/tex]

To add the two rational expressions, we need to find a common denominator:

3x + 2 / x - 1 + 2x - 5 / x - 1 = (3x + 2)(x - 1) / (x - 1)(x - 1) + (2x - 5)(x - 1) / (x - 1)(x - 1)

Now that we have a common denominator, we can add the numerators and simplify:

= (3x^2 - x + 2x - 5) / (x - 1)(x - 1)

= (3x^2 + x - 5) / (x - 1)(x - 1)

This is the simplified sum of the two rational expressions.

Your height and the length of your shadow are related by the formula 1/Tangent (height of the sun). Your shadow would be 5.67 times longer than you if the sun were to be at its lowest point in the sky (10 degrees). At 5 degrees, the proportion is 11.43. (A person of average height (5.8 feet) would therefore cast a shadow that is 66 feet long.)

The length of the shadow is influenced by the Sun's position in the sky. The shadows are long when the Sun is low in the horizon. The shadows are substantially shorter when the Sun is high in the sky.

Because the sun's rays are slanted in the morning and evening but are directly overhead at noon, the shadows are longer in the morning and evening and shorter in the noon. The distance of the object from the light source affects how big the shadow is.

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The probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.

P(C) = P(C∣G)P(G) + P(C∣Gc)P(Gc) = (1)(0.6)+(0.2)(0.4) = 0.68

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.

P(G∣C) = (P(G)P(C∣G))/P(C)

=1(0.6)/0.68

=0.882

So the probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.

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The probability that the inspector in charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.

P(C) = P(C∣G)P(G) + P(C∣Gc)P(Gc) = (1)(0.6)+(0.2)(0.4) = 0.68

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.

P(G∣C) = (P(G)P(C∣G))/P(C)

=1(0.6)/0.68

=0.882

So the probability that the inspector in charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.

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The Area of the circle is  = 3.14 x (6 cm)^2

Area = 113.04 cm^2

The theory used in this question is the formula for the area of a circle, which states that the area of a circle is equal to π multiplied by the square of the radius.

given below

Step 1: Use the formula A = πr^2 to calculate the area of the circle.

Step 2: Identify the radius, r, which is equal to 6 cm.

Step 3: Substitute the values into the formula, A = πr^2.

Step 4: Calculate the area by multiplying 3.14 (π) by the square of 6 cm (6 cm x 6 cm).

Step 5: The area of the circle is 113.04 cm^2.

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The primary reason for the use of random assignment in the research study was to ensure that participants in each group were similar to each other in terms of relevant factors, such as age, gender, or health status.

By randomly assigning participants into two groups, the researchers could ensure that any difference observed between the two groups was due to the intervention and not due to any other factor.

Random assignment eliminates the possibility of bias being introduced into the study, as the two groups are as similar as possible.

This means that any observed difference between the two groups can be attributed directly to the intervention, in this case, the vitamin E supplement.

By randomly assigning participants, the researchers could be sure that the results of the study were valid and could be relied upon.

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There are a few recursive formulas that can be used to calculate the nth term based on the pattern of the given data. For n 2, they are the nth term of the mathematical progression a = a - 1 + d. Geometric Progression nth term a = a - 1 r for n > 2.

Given that each phrase, an, goes back to the term before it, an1, the formula an=2an1+3 is recursive. According to this equation, the term we are looking for is equal to the previous term multiplied by two and then added to three. 4,11,25 make up the first three terms in this chain.

Almost identical to reading one, writing recursive functions:

A recursive sequence, also called a recurrence sequence, is a series of numbers that are indexed by integers and produced by solving a recurrence equation.

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Answer: 3

Step-by-step explanation:

The proportion of the area in each tail is 0.025, or 2.5%. This means that 2.5% of the area of the normal distribution lies in each of the two tails.

The total area of the normal distribution is 1.

The area of the left tail is 0.3413.

The area of the right tail is 0.3413.

Therefore, the proportion of the area in each tail is 0.341.

The normal distribution is a symmetric probability distribution that has a single peak and two tails extending outwards from the peak. The proportion of the area in each tail of the normal distribution is 0.025, or 2.5%. This proportion is the same for both tails and is determined by the fact that the normal distribution is symmetric. This means that 2.5% of the area of the normal distribution lies in each of the two tails. This area can be calculated by multiplying the total area of the normal distribution by 0.025. The total area of the normal distribution is equal to 1, and so the area in each tail is equal to 0.025. This proportion is constant regardless of the mean and standard deviation of the normal distribution. The proportion of the area in each tail of the normal distribution is an important concept in statistics, as it is used to calculate probabilities of certain events occurring.

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The complete question is

What proportion of the area is in each tail of a normal distribution with mean 0 and standard deviation 1? Enter your answer to 3 decimal places.

Here, the 11.5 oz of vinegar ingredient is needed in order to make 46 oz of furniture polish .

So in this problem it says a furniture polish can be made containing or combining vinegar and olive oil and the amount of oil should be three times the amount of vinegar. So I'm gonna make vinegar X. And oil three X. How much of each ingredient is needed in order to make 46 oz of furniture Polish. So I'm gonna go ahead and add these together. Okay. Yes. Which means that four x. equals 46 and divide by four So X. is 11.5. So that means that for vinegar we need 11.5 oz. And then I'm going to multiply that by three to get 34.5 oz for the oil. And if you can find those together just to check you get 46. So this would be the amount of both ingredients.

To make 46 oz of furniture polish, you will need 3 times as much olive oil as vinegar.

So, you need 46 oz / 4 = 11.5 oz of vinegar.

And 11.5 oz * 3 = 34.5 oz of olive oil.

Therefore,the 11.5 oz of vinegar ingredient is needed in order  to make 46 oz of furniture polish .

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The function that best represents the data in the table is y = 2.7x. This is because the circumference of the tree is directly proportional to the number of years it has been alive, which can be represented by a linear equation.

The circumference of a circle is the total length of the edge of the circle. It is calculated using the formula C = 2πr, where r is the radius of the circle. This formula is based on the fact that the circumference of a circle is equal to the length of the perimeter of the circle, which is equal to the product of the circumference and the radius. The circumference is an important measure used in many areas of mathematics and geometry, including area and volume calculations.

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The statement "the law of sines can be used to solve triangles where three sides are known" is false.

A triangle is a three-sided polygon, with each side representing a line segment connecting two vertices. To fully determine a triangle, we need to know at least three pieces of information about it, such as the lengths of its sides, or the measures of its angles.

The law of sines is a mathematical formula that relates the ratios of the lengths of the sides of a triangle to the angles opposite those sides. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.

However, the law of sines cannot be used to solve a triangle if all three sides are known. To solve a triangle, we need to have additional information, such as the angles or some side-angle pairs. The law of sines can only be used to find missing side lengths or angle measures if we have at least one side length and one angle measure, or two side lengths and an angle not contained between them.

In conclusion, the statement "the law of sines can be used to solve triangles where three sides are known" is false. To solve a triangle, we need additional information in the form of angles or side-angle pairs.

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We are unable to establish causation or cause-and-effect correlations using observational data. Observational studies are fantastic for describing a particular group, contrasting groups, or looking at the patterns or relationships between variables.

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The 12 in 12x+13

Reason:

A coefficient is the number to the left of a variable. The 12x has a coefficient of 12 and variable of x. We multiply the two items together.

12x = 12 times x = 12*x

3% of children are likely to be ill in two days.

Let's call the fraction of children who are ill today x.

The fraction of children who are healthy today is (1 - x).

The fraction of children who were healthy today and will be healthy tomorrow is (1 - x) * 0.95.

The fraction of children who were ill today and will still be ill tomorrow is x * 0.55.

The fraction of children who will be ill in two days is x * 0.55 + (1 - x) * 0.05 = 0.55x + 0.05 - 0.95x = -0.4x + 0.05.

So, if 20% of children are ill today, then x = 0.2, and the fraction of children who are likely to be ill in two days is -0.4 * 0.2 + 0.05 = 0.03.

Therefore, 3% of children are likely to be ill in two days.

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3% of children are likely to be ill in two days.

Let's call the fraction of children who are ill today x.

The fraction of children who are healthy today is (1 - x).

The fraction of children who were healthy today and will be healthy tomorrow is (1 - x) * 0.95.

The fraction of children who were ill today and will still be ill tomorrow is x * 0.55.

The fraction of children who will be ill in two days is x * 0.55 + (1 - x) * 0.05 = 0.55x + 0.05 - 0.95x = -0.4x + 0.05.

So, if 20% of children are ill today, then x = 0.2, and the fraction of children who are likely to be ill in two days is -0.4 * 0.2 + 0.05 = 0.03.

Therefore, 3% of children are likely to be ill in two days.

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The congruent angles of an isosceles right triangle measure is 45° each.

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The ratio of x/y is then 2/3, which is a positive number.

In quadrant I, both the x and y coordinates are positive. Therefore, a ratio of x/y will be positive. To illustrate this, let's say that the point (x, y) is located at (2, 3). This means that x=2 and y=3. The ratio of x/y is then 2/3, which is a positive number.

To calculate the ratio, we divide the x coordinate by the y coordinate: x/y = 2/3. This will give us the ratio of the point (x, y) in the indicated quadrant. If the result is a positive number, then the ratio is positive. If the result is a negative number, then the ratio is negative. In this example, the result is a positive number, so the ratio is positive.

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It is often useful to find the constant term of a polynomial in order to find its roots.

Roots of polynomials are the solutions for any given polynomial for which we need to find the value of the unknown variable. If we know the roots, we can evaluate the value of polynomial to zero.

The polynomials are the expression written in the form of:

[tex]$$a_n x^n+a_{n-1} x^{n-1}+\ldots . .+a_1 x+a_0$$[/tex]

The formula for the root of linear polynomial such as ax+b is x=-b / a

The general form of a quadratic polynomial is[tex]$a x^2+b x+c$[/tex] and if we equate this expression to zero, we get a quadratic equation, i.e. [tex]$a x^2+b x+c=0$[/tex]

The formulas for higher degree polynomials are a bit complicated.

Hence, it is often useful to find the constant term of a polynomial in order to find its roots.

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Step-by-step explanation:

Use the Pythagorean theorem: a^2 + b^2 = c^2. In this case, sides a and b are each 7sqrt(3), and c is the diagonal of the square.

a^2 + b^2 = c^2

(7sqrt3)^2 + (7sqrt3)^2 = c^2

294 = c^2

c = sqrt(294) = 7sqrt(6)

The square root of 7 belongs to the set of irrational numbers and the set of real numbers. Option B is correct.

In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.

The square root of 7 is an irrational number because it cannot be expressed as a finite decimal or a fraction. Irrational numbers are a subset of real numbers, which is a set that includes all the real numbers, including both rational and irrational numbers.

Option B) "irrational and real numbers" is the correct answer.

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100 grams to convert the cups is 1/2 cup.

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In this case, the standard deviation is 3.7, so the variance is 3.7², or 13.69. This means that the data points in the data set are, on average, 13.69 units away from the mean.

The variance of a data set is a measure of how the data points are distributed around the mean. It is calculated by squaring the standard deviation, which is the average distance of the data points from the mean.

Variance is a useful measure for quantifying the spread and variability of the data points in a data set. By knowing the variance, it is possible to make predictions about how likely it is that a given data point will fall within a certain range from the mean.

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Analytical techniques or a graphing tool can be used to locate the function's vertical asymptotes.

On a function graph, a vertical asymptote is a line that the graph approaches but never crosses. It can be discovered by examining the function's equation and how it behaves as it gets closer to infinity. By resolving the equation and determining the values of x that cause the denominator to equal 0, one can use analytical techniques to determine the vertical asymptotes of the function. For instance, the function will have a vertical asymptote at x = 5 if the equation is f(x) = (x-3)/(x-5), as the denominator of the equation equals 0 at this point. Vertical asymptotes can also be found using graphing tools. One can observe the behavior of the equation by charting its graph.

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For finding median in continuous series, all of the four factors are important.

The median is a central value in a data set that separates the upper and lower halves of the data.

In a continuous series, it is important to find the median because it gives us a good indication of the typical value in the series.

To find the median in a continuous series, four factors are important:

a. Particular frequency of the median class: This refers to the number of observations that fall into the median class.

b. Lower limit of the median class: The lower limit of the median class defines the start of the interval in which the median falls.

c. Upper limit of the median class: The upper limit of the median class defines the end of the interval in which the median falls.

d. Cumulative frequency preceding the median class: This refers to the total number of observations that fall into classes before the median class.

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The average value for X is 9/18. Hence, the answer is D. 9.

The exponential distribution probability is given as P(X ≤ 9 ) = 1 − E−9/18. The average value for X is calculated as follows.

The expected value (mean) of an exponential distribution of a random variable X with rate parameter λ is given by E[X] = 1/λ.

In the given problem, λ = 18. Thus, the expectation of the random variable X is 1/18.

The calculation for the expected value of X can be represented as:

E[X] = 1/λ = 1/18

Thus, the average value for X can be represented as:

Average Value of X = E[X] = 1/18 = 9/18

Therefore, the average value for X is 9/18. Hence, the answer is D. 9.

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There are other equations that have the same number of solutions as Priya's equation, y = -1/2x - 7. For instance:

y = -1/2x - 7 + k (where k would be any constant value)

or

y equals mx plus b, where m is -1/2 and b is -7.

The slope and y-intercept of the equations are the same as Priya's equation. This means that the equations will meet Priya's equation at exactly one point, giving them the same solution.  However, it is important to note that the constant value (k) or the y-intercept (b) can be changed to make the equation different from Priya's equation, but as long as the slope (m) remains the same, the two lines will intersect at exactly one point.

I determined that because both equations have the same slope (-1/2) and the same y-intercept (-7). This means that they will intersect at exactly one point on the coordinate plane, resulting in one solution in common.

The slope of a line is represented by the coefficient of x in the equation, and the y-intercept is represented by the constant term. In both equations, the slope is -1/2 and the y-intercept is -7, so they are the same line, and therefore will have exactly one solution in common.

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The equation would become y = -3.99(23)2 + 37.2(23) - 102 which can then be simplified to y = -2213.71 + 755.6 and further simplified to y = -1458.11. This rearrangement and simplification can be completed to find the estimated y value when x is 23, which is y = 227.8.

A) y = -3.99x2 + 37.2x - 102

B) y = -3.99(23)2 + 37.2(23) - 102 = 227.8

y = -3.99(23)2 + 37.2(23) - 102

y = -3.99(529) + 857.6 - 102

y = -2213.71 + 755.6

y = -1458.11

y = 227.8

Using the given data set of x and y values, a quadratic regression equation can be written in Desmos as y = -3.99x2 + 37.2x - 102. To estimate the y value if x is 23, the equation can be rearranged and all values plugged in. The equation would become y = -3.99(23)2 + 37.2(23) - 102 which can then be simplified to y = -2213.71 + 755.6 and further simplified to y = -1458.11. This rearrangement and simplification can be completed to find the estimated y value when x is 23, which is y = 227.8.

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