1.47 minutes is how many hours?
(1 hour = 60 minutes)

Using the long division method, it is proved that (x + 2) is a factor of (x³ + 8), because the result of the remainder is 0.

To show that (x + 2) is a factor of (x³ + 8) using long division, we can divide (x³ + 8) by (x + 2) and see if the remainder is 0. If the remainder is 0, then (x + 2) is a factor of (x³ + 8). Here's how the long division would look:

        x² - 2x + 4

x+2 | x³ + 0x² + 0x + 8

      - (x³ + 2x²)

    --------------------

         -2x² + 0x + 8

       - (-2x² - 4x)

         ---------------

              4x + 8

            - (4x + 8)

              --------

                 0

Since the remainder is 0, we can conclude that (x + 2) is a factor of (x³ + 8).

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Answer:

X

=

27

Step-by-step explanation:

Answer: -1.5

Step-by-step explanation:

took the test

The z-score of a bag of almonds weighing 12.2 ounces will be negative 1.5.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

A machine packages bags of almonds.

The weights of the bags are normally distributed with a mean of 14 ounces and a standard deviation of 1.2 ounces.

Then the z-score of a bag of almonds weighing 12.2 ounces will be

z-score = (x - mean) / SD

z-score = (12.2 - 14) / 1.2

z-score = -1.8 / 1.2

z-score = -1.5

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The predicted sales based on the equation were $7,820, but the actual sales deviated from this prediction by $300.

To determine the actual sales for a particular day, we can use the given best fit line equation and the high temperature for the day. The equation, y = 4.1 + 0.12x, represents the relationship between average daily sales (y) in thousands of dollars and the high temperature (x) in Celsius.

Given a high temperature of 31°C and a residual of $300, we can substitute the temperature into the equation and solve for the actual sales.

Explanation:

Substituting x = 31 into the equation y = 4.1 + 0.12x, we have:

y = 4.1 + 0.12 * 31

= 4.1 + 3.72

= 7.82

Therefore, the actual sales for that day, represented by y, is $7.82 thousand or $7,820.

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Answer:

b

Step-by-step explanation:

The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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Answer:

72,072

Step-by-step explanation:

To determine the number of different ways the committee can be formed, we need to calculate the combination of selecting 5 teachers out of 10 and 3 students out of 13.

The number of ways to choose 5 teachers out of 10 is given by the combination formula:

C(10, 5) = 10! / (5! * (10 - 5)!) = 252

Similarly, the number of ways to choose 3 students out of 13 is:

C(13, 3) = 13! / (3! * (13 - 3)!) = 286

To find the total number of ways the committee can be formed, we multiply the number of ways to choose teachers by the number of ways to choose students:

Total number of ways = 252 * 286 = 72,072

Therefore, there are 72,072 different ways the committee can be formed.

Answer:

c; 54

Step-by-step explanation:

to find the answer you can first add all the books together

this can be represented by

3 + 2 + 2.5 + 1.5

this answer is 9

then multiply it by 6

9 * 6 = 54

is is c

Answer:

c. 5

Step-by-step explanation:

1.5m = 1.5*100 cm = 150 cm

Divide 150 cm by 30 cm,

150/30 = 5

Equations

Let's call:

x = time Stanley swam yesterday.

We know he ran for half an hour longer than he swam, thus the time he ran was:

x + 0.5 = time Stanley ran yesterday

We also know he biked for twice the time he ran, thus:

2(x + 0.5) = time Stanley biked yesterday.

The distance covered by Stanley when swimming is

2.5*x

The distance covered by Stanley when running is:

9*(x+0.5)

The distance covered by Stanley while biking is:

16*2*(x + 0.5) = 32(x + 0.5)

The total distance is 64 miles, thus:

2.5*x + 9*(x+0.5) + 32(x + 0.5) = 64

Operating:

2.5x + 9x + 4.5 + 32x + 16 = 64

Simplifying:

43.5x + 20.5 = 64

Subtracting 20.5:

43.5x = 43.5

Thus:

x = 1

Stanley swam for 1 hour, he ran for 1+0.5 = 1.5 hours and biked for 2*1.5=3 hours

Swam: 1 hour, Ran: 1.5 hours, Biked: 3 hours

False, a binary (categorical) predictor should not be used along with nonbinary (numerical) predictors

It is important to note that binary and non-binary predictors can both be utilized.

Categorical variables with two possible outcomes, such as yes/no or true/false, are represented by binary predictors. On the other hand, nonbinary predictors indicate numerical variables that can have a variety of values.

It is feasible to capture the links between several sorts of variables and enhance the predictive ability of a model by using both types of predictors. Utilizing methods like logistic regression and

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Answer:

Step-by-step explanation:

Notice that ∠5 is an internal angle, because it's between the parallels.

∠1  and ∠5 are corresponding angles, becasue they are at the same side of the transveral, and one is internal and the other external. So, ∠1 = 62°.

∠2 and ∠1 are supplementary angles, because they are on a straight angle, so if ∠1 = 62°, then ∠2 = 180° - 62° = 118°.

∠3 and ∠1 are vertical angles, because they have a vertex in common only. So, they are congruent, which means ∠3 = 62°.

Finally, ∠4 and ∠2 are vertical angles, so they are congruent. ∠4 = 118°.

a. hypothesis: µ > previous mean credit card balance b. the previous mean credit card balance and the population standard deviation. c. the null hypothesis and conclude that there is not enough evidence to support the claim that the mean credit card balance has increased.

a. The null hypothesis is that the mean credit card balance for undergraduate students has remained the same or decreased compared to the previous report. The alternative hypothesis is that the mean credit card balance for undergraduate students has increased compared to the previous report.

Null hypothesis: µ ≤ previous mean credit card balance

Alternative hypothesis: µ > previous mean credit card balance

b. The -value cannot be determined without knowing the previous mean credit card balance and the population standard deviation.

c. The conclusion cannot be made without knowing the -value and the level of significance. If the -value is less than the level of significance (usually 0.05), then we reject the null hypothesis and conclude that there is evidence to support the claim that the mean credit card balance for undergraduate students has increased. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean credit card balance has increased.

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Answer: We on da same question i do not know

Step-by-step explanation:

Ben's expected utility of playing the lottery is 120

Ben bought a lottery ticket that could allow him to win $90,000.00 with probability 0.40

ben values money according to the utility function v(m) = m

Ben's utility = m

We need to find Ben's expected utility

expected utility = 0.4 x √m + 0.6 x 0

= 0.4 x √90000 + 0

= 0.4 x 300

= 120

Therefore, if Ben bought a lottery ticket that could allow him to win $90,000.00 with probability 0.40 (and nothing otherwise). ben values money according to the utility function v(m) = m. Ben's expected utility of playing the lottery is $120

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Answer:

f(2) = 3(2) + 1

f(2) = 6 + 1

f(2) = 7

Answer:

f(2) = 7

Step-by-step explanation:

To evaluate f(2) substitute x = 2 into f(x) , that is

f(2) = 3(2) + 1 = 6 + 1 = 7

Answer:

y = (x-7)^2  / 8

Step-by-step explanation:

The focus to vertex distance is (2-(-2))/2 = 2 and the parabola open's upwards.

Thus: a = 1/(4·2) = 8, vertex at (7,0).

This means that:

y = (x-7)2/8

Answer: $ 37.50

Step-by-step explanation:

$50.00 x 25% = 12.50

$50.00 - $12.50 = $37.50

Answer:

y = 18

Step-by-step explanation:

\( \frac{28}{36} = \frac{14}{y} \)

\( \frac{28 \div 4}{36 \div 4} = \frac{14}{y} \)

\( \frac{7}{9} = \frac{14}{y} \)

\( \frac{7}{9} = \frac{14}{y} \)

\(7y = 14 \times 9\)

\(7y = 126\)

\( \frac{7y}{7} = \frac{126}{7} \)

\(y = 18\)

Answer:

Step-by-step explanation:

Apply proportions

y =(36*14)/28 = 18

Answer:

The slope is equal to 2

Hope this helps :)

An equivalent expression is an expression that is equal in value to a given expression. For example, consider the following expression: 4x + 2y

An equivalent expression is an expression that represents the same value as a given expression, regardless of the specific values of any variables that appear in the expression. Equivalent expressions can be obtained by applying the rules of algebra, such as the associative, commutative, and distributive properties.

This expression is equivalent to the following expressions:

2(2x + y)

2y + 4x

(4 + 2)x + 2y

All of these expressions are equivalent because they all represent the same value, regardless of the specific values of x and y. They can all be simplified to the same expression by applying the rules of the algebra.

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The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

C (-13,-2)

Step-by-step explanation:

This is not the question, the correct question is:

A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores.

Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.

Answer:  The numerical limits for grade B is 81 and 92

Step-by-step explanation:

Given that

mean Ж = 79

Standard deviation S = 8.4

B: Scores below the top 6% and above the bottom 59%

To find the numerical value for Grade B

Below the top bottom 6% ( 0.06) is

p ( X < Ж ) = 1 - 0.06

p ( X < Ж ) = 0.94

therefore

P( (X - ц)/S < (X - Ж) / S)) = 0.94

(X - 79) / 8.4 = 1.5548 ( from normal distribution table )

X - 79 = 13.0603

X = 13.0603 + 79

X = 92.06 ≈ 92 ( nearest whole number)

Above bottom 59% ( 0.59) is

p ( X < Ж ) = 0.59

therefore

P( (X - ц)/S < (X - Ж) / S)) = 0.59

(X - 79) / 8.4 = 0.2275 ( from normal distribution table )

X - 79 = 1.9114

X = 1.9114 + 79

X = 80.91 ≈ 81 ( nearest whole number)

So the numerical limits for grade B is 81 and 92

The sum of all angles in a triangle = 180 degree

So :

Angle x + Angle 5x + 72 = 180

x + 5x + 72 = 180

6x = 180 - 72

6x = 108

Divide both side by 6 :

6x/6 = 108/6

x = 18

x = 18

since all the angles are less than 90 degree so the triangle is an acute triangle,

as 5x = 90 thus one angle is of 90 degree

Thus triangle is Acute Right angle triangle

Answer : x = 18, acute right angle triangle

The square of a real number is always non-negative, there are no values of t that satisfy the inequality. Therefore, the soccer ball is never above 15 feet.

The correct answer is none of the given options (A, B, C, or D).

To determine when the soccer ball is above 15 feet, we need to find the values of t that satisfy the inequality h(t) > 15.

Given the quadratic function h(t) = -16t² + 20t + 11, we can set up the inequality:

-16t² + 20t + 11 > 15

Rearranging the inequality:

-16t² + 20t - 4 > 0

Dividing both sides by -4 to simplify:

4t² - 5t + 1 < 0

To solve this quadratic inequality, we can factorize it:

(2t - 1)(2t - 1) < 0

(2t - 1)² < 0

Since the square of a real number is always non-negative, there are no values of t that satisfy the inequality. Therefore, the soccer ball is never above 15 feet.

The correct answer is none of the given options (A, B, C, or D).

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