Which statement is true about the sum of two rational numbers?
OIt can always be written as a fraction.
OIt can never be written as a fraction.
It can always be written as a repeating decimal.
OIt can never be written a terminating decimal.

Answer:

B (the second one)

Step-by-step explanation:

The thin yellow line in A only goes from 14-30. However, the correct numbers listed range from 12-30. Line B matches up with this data

Answer:

A = 104 ft²

Step-by-step explanation:

We're given that the width of the rectangle is 8 so that's the value of w. All we have to do is just plug in 8 into the equation:

A=w²+5w

A=(8)²+5(8)

A=64+40

A = 104 ft²

Answer:

banks change people fees to make a profit off of them other wise they would be giving away free money.

Step-by-step explanation:

hope this helps and what you were asking for.

The whole number closest to √22 is 5.

The square root of 22 is:

= √22

= 4.69

The whole number that it is closest to will depend on the first decimal point.

If it is 5 or above then it will be closest to 5.

If it is 4 and below, then it is closest to 4.

The first decimal point is 6 so √22 is closer to 5.

In conclusion, the square root of 22 is closer to 5.

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The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

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The number that satisfies all the given conditions is 8000. It is a 5-digit number, a perfect cube, and a perfect square.

To find the 5-digit number that satisfies the given conditions, let's analyze the requirements step by step:

1. The number is a perfect cube and a perfect square: This means the number must have an even exponent for each prime factor. The smallest 5-digit perfect cube is 1000 \((10^3)\), and the smallest 5-digit perfect square is 10000 \((10^4)\). So the number must be between 1000 and 10000.

2. When the number is divided by 4, the result is a perfect square but not a perfect cube: Dividing a number by 4 means it must be divisible by 2 twice. Therefore, the number must have at least two 2's in its prime factorization. The number 8000\((20^3)\) satisfies this condition.

3. When the number is divided by 27, the result is a perfect cube but not a perfect square: Dividing a number by 27 means it must be divisible by 3 three times. Therefore, the number must have at least three 3's in its prime factorization. The number 729\((9^3)\)satisfies this condition.

By considering these conditions, the only number that satisfies all the given requirements is 8000. It is a 5-digit number, a perfect cube\((20^3)\), a perfect square\((40^2)\), and when divided by 4, it results in 2000 \((40^2)\) which is a perfect square but not a perfect cube. When divided by 27, it results in 296.3 \((7^3)\) which is a perfect cube but not a perfect square.

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Answer:

let the two numbers = x and y

according to the statement : x-y=4

x+y=22

by elimination method: 2x=26

x=13

so... y = 13-4=9

Answer:

The two numbers (x and y) are 13 and 9 respectively. 13 minus 9 is 4 and 13 plus 9 is 22.

Step-by-step explanation:

Let the two numbers be x and y.

The difference between x and y (x - y) = 4. (eqn 1)

Their sum (x + y) = 22. (eqn 2)

From eqn 1, we can get that x = 4 + y

Substituting x as (4 + y) in eqn 2 gives the following:

(4+y) + y = 22

4 + 2y = 22

and 2y = 22 - 4

2y = 18

dividing both sides by 2 gives y = 9.

Substituting y as 9 in eqn 1 gives

x - 9 = 4

x = 4 + 9

x = 13

Sometimes the triangle's circumcenter is outside of it. In actuality, it may lie outside the triangle, as in the case of an acute triangle, or it may land at the midway of the hypotenuse of a right triangle.

the location that is equally spaced from each of a triangle's three vertices and where the three perpendicular bisectors of its sides meet.

The circumcenter of a triangle is found at the junction of all sides' perpendicular bisectors, or lines that are at right angles to each side's midpoint. The triangle's perpendicular bisectors are shown to be contemporaneous by this (i.e. meeting at one point).

Sometimes the triangle's circumcenter is outside of it. In actuality, it may lie outside the triangle, as in the case of an acute triangle, or it may land at the midway of the hypotenuse of a right triangle.

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Assume that Alex's age is x

Since Johnny's age is three times Alex's age, so Johnny's age is 3 x

Since the sum of their ages is 72, add their ages and equate the sum by 72

Divide both sides by 4 to find x

So Alex's age is 18 years

The equation that represents the situation in which case the percent of successful free throws is 75% during the game is; ( 8 + x ) = 0.75 ( 15 + x ).

It follows from the task content that the equation which represents the situation in which case the percent of successful free throws rises to 75% is to be determined.

As evident in the task content; Initially, Shaq made 8 out of 15 free throws he attempted.

Therefore, let the number of consecutive free throws he has to make to raise the success rate to 75% be; x.

Therefore, it follows from percent proportion that;

( 8 + x ) / ( 15 + x ) = 75 / 100

The simplified equation which represents the required situation is therefore;

( 8 + x ) = 0.75 ( 15 + x ).

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The problem is saying there are two distinct zeros, and both are strictly lie between 0 and 1. The least positive integer value of "a" is 5 for which such a polynomial exists.

Let f(x) = ax² - bx + c , be our polynomial.

where a,b are integers coefficient and c constant. It has two distinct real roots lying between 0 and 1. f(x) can be written as, f(x) = a(x−α)(x−β)

where α and β are the roots of the equation.

we can be observed that f(0)f(1) > 0

As a,b and c are integers f(0)f(1) > 1

f(0) = aαβ , f(1)=a(1−α)(1−β)

=> a²(α)(1−α)(β)(1−β) > 0 -------(1)

Using A.M ≥ G.M, we get

(α+1−α+β+1−β)/4 > (αβ(1−α)(1−β))¹/⁴

Arithmetic Mean and Geometric Mean cannot be equal because the equation has distinct roots.

a²/16 > a²(αβ(1−α)(1−β)).

=> a²/16 > 1

=> a > 4

Therefore, the minimum value of 'a' is 5

The discriminant of the equation,

Δ = b²−4ac ≥ 0

=> b² >20c

consider the minimum value of c = 1,

we get b² >20

=> Minimum Value of b = 5.

Hence, the least positive integer of 'a' is 5.

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Explanation:

Point slope form in general is

y-y1 = m(x-x1)

Where m is the slope and (x1,y1) is the given point. From here you plug in the slope m = -3/4 and the point (x1,y1) = (4,2). There's not much to do from here.

Side note: parallel lines have equal slopes, but different y intercepts.

The correct statement is c. The Adjusted R-squared is a measure used in multiple regression analysis that is between 0 and 1. It is different from the R-squared value in simple linear regression.

The Adjusted R-squared can decrease if the addition of another X regressor does not sufficiently lower the sum of squared residuals (SSR) relative to the impact of increasing the number of predictors (k). It measures the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size, rather than the ratio of the sum of squared residuals to the total sum of squares. It provides a measure of how well the regression model fits the data, and it ranges between 0 and 1. A value closer to 1 indicates that a higher proportion of the variance in the dependent variable is explained by the predictors.

Adding another X regressor to the multiple regression model can impact the Adjusted R-squared. If the additional regressor does not significantly contribute to reducing the sum of squared residuals (SSR) relative to the increase in the number of predictors (k), the Adjusted R-squared can decrease. This means that the added regressor does not improve the model's ability to explain the variance in the dependent variable adequately.

However, the Adjusted R-squared does not directly measure the ratio of the sum of squared residuals to the total sum of squares. Instead, it represents the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size. It penalizes models with a large number of predictors that may overfit the data, thereby providing a more reliable measure of the model's goodness of fit.

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More plainly, the sequence is defined recursively by

\(a_{n+1} = \begin{cases} 3a_n - 9 & \text{if } a_n \text{ is odd} \\ 2a_n - 7 & \text{if } a_n \text{ is even} \end{cases}\)

and some starting value \(a_1\).

We're given that the sequence alternates between two constants, \(a\) and \(b\), so that \(a_1 = a\).

• If \(a\) is even, then the second term \(b\) must be odd, since

\(a_2 = 2a_1 - 7\)

by the given rule, and 2×(even) - (odd) = (odd). So

\(a_2 = 2a-7 = b\)

In turn, the third term is even, since we jump back to \(a\). From the given rule,

\(a_3 = 3a_2 - 9\)

and so

\(3b-9 = 3(2a-7)-9 = a \implies 6a-30=a \implies 5a=30 \implies a=6\)

\(3b-9 = 6 \implies 3b = 15 \implies b = 5\)

Then the sum of the two integers is \(a+b=\boxed{11}\)

• You end up with the same answer in the case of odd \(a\), so I'll omit this part of the solution. (It's almost identical as the even case.)

On solving the provided question we can say that by null hypothesis There is insufficient proof to conclude that student attendance has changed.

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

This is a z-test for a proportion.

\(H0:p=.34 H1:p not=.34\\\alpha=0.01 ... this is a\\2-tailed test\\critical values are +2.58, -2.58\\p=.34 (given) q=1-p=.66\\p^=.33\\z=(p^-p)/sqrt(pq/n)\\z=(.33-.34)/sqrt(.34*.66/8302)\\z=-.01/.0051961\\z=-1.92\)

1.96 does not fall in the reject region

There is insufficient proof to conclude that student attendance has changed.

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The total cost of the triangular felt of the 24 square feet is 47.76 Dollars. Then the correct option is C.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Mr. Brooks is buying felt to cover a triangular putting green of his miniature golf course.

The base of the green is 4 feet wide, and the height is 12 feet.

The area of the triangle will be

\(\rm Area = \dfrac{1}{2}*base *height\\\\Area = \dfrac{1}{2}*4*12\\\\Area = 24\)

The area of the triangle is 24 square feet.

The felt costs $1. 99 per square foot. Then the cost of 24 square feet will be

\(\rm Total\ cost = 1.99*24\\\\Total\ cost =\$ \ 47.76\)

The total cost of the 24 square feet is 47.76 Dollars. Then the correct option is C.

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Answer:

6 weeks=6*7 days=42days

7/42 =1/6 =0.16667

OR

7 days=1 week

therefore 1/6=0.16667

Note that both must be in the same unit.

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Skewness of the normal distribution. When it comes to normal distribution, the skewness is equal to zero.

Skewness is a measure of the distribution's symmetry. When a distribution is symmetric, the mean, median, and mode will all be the same. When a distribution is skewed, the mean will typically be larger or lesser than the median depending on whether the distribution is right-skewed or left-skewed. It is not appropriate to discuss mean or median in the case of normal distribution since it is a symmetric distribution.

Therefore, the answer is None of the above.

In normal distribution, the skewness is equal to zero, and it is not appropriate to discuss mean or median in the case of normal distribution since it is a symmetric distribution.

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Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

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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The probability of flipping "heads" in a fair coin is 1/2. Fraction: 1/2, Decimal: 0.5, Percent: 50%

Probability is a measure of the possibility of an event occurring. It is a way to quantify how probable or likely it is that a particular outcome will happen. Probability is typically expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.

Now,

As in flipping a coin

Total outcomes=2  i.e. Heads and Tails

Favorable outcomes=1  i.e. Heads

Then,

The probability of flipping "heads" in a fair coin is 1/2, which can also be expressed as 0.5 in decimal form or 50% in percentage form.

Fraction: 1/2

Decimal: 0.5

Percent: 50%

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Answer:

11 feet (Option C)

Step-by-step explanation:

Let the longer side be l and the shorter side be b.

We know that,

→ Perimeter of rectangle = 2 ( longer side + shorter side )

Here,

→ 32 = 2 (l + b)

→ 32 = 2l + 2(5)

→ 32 = 2l + 10

→ 32 - 10 = 2l

→ 22 = 2l

→ \( \sf \dfrac{22}{2} \) = l

→ 11 = l

→ 11 feet = longer side

\( \therefore \) Length of the longer side is 11 feet.

Answer: For all three functions, the direction of fastest increase at the point (1, 1, 1) is the direction of the gradient vector of the function at that point.

For function (a), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[2/x³, 2y, 22] = [2, 2, 22].

The direction of this gradient vector is given by the direction in which each of its components is increasing the most rapidly. In this case, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

For function (b), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[4y + 4z, 4x + 4z, 4x + 4y] = [4, 4, 4].

Again, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

For function (c), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[2x, 2y, 2z] = [2, 2, 2].

As before, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

Therefore, for all three functions, the direction of fastest increase at (1, 1, 1) is the direction of the positive x, y, and z axes.

Step-by-step explanation:

Answer:

-3/2

Step-by-step explanation:

Given the funtion

(2x+3)² - 6x+9 = 0

(2x+3)² = 6x + 9

Expand

4x²+12x+9 = 6x + 9

4x²+12x - 6x = 0

4x²+6x = 0

4x² = -6x

4x = -6

x = -6/4

x = -3/2

Hence the value of x is -3/2

Answer:

25 Celsius es igual a 77 F, 77 es mas grande que 40 F

Step-by-step explanation:

Espero que la info. ayude

El símbolo de grado no se usa para informar la temperatura usando la escala Kelvin, sino que se indican como Kelvin. El agua hierve a 100 grados Celsius o 212 grados Fahrenheit, o 373,15 Kelvins. El agua se congela a 0 grados Celsius o 32 grados Fahrenheit, o 273,15 Kelvins. El cero absoluto es 0 Kelvin.