Graph the inequality.
4x + by 2 10

The correct set of hypotheses is: b. H0: μ ≤ 10.0% Ha: μ > 10.0%.

In hypothesis testing, the null hypothesis (H0) represents the statement that is being tested or assumed to be true, while the alternative hypothesis (Ha) represents the statement that contradicts or challenges the null hypothesis. In this case, the null hypothesis states that the average yearly rate of return on the stocks is less than or equal to 10.0%, and the alternative hypothesis states that the average yearly rate of return on the stocks is greater than 10.0%.

By formulating the hypotheses in this way, you are testing whether there is sufficient evidence to support the claim made by your investment executive that the average yearly rate of return on the stocks she recommends is at least 10.0%.

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Answer:

ldk

Step-by-step explanation:

Answer:

It's -7

Step-by-step explanation:

-7 • -4=28 (multiplying 2 negatives gives you a positive)

28 - 20 =8

The initial speed of the ball can be determined using the range equation for projectile motion. The horizontal distance traveled by the ball is given by:

Range = (Initial velocity) * (Time of flight)

In this case, the range is 120 m and the angle of projection is 37 degrees. The time of flight can be calculated using the equation:

Time of flight = (2 * Initial velocity * sin(angle)) / g

where g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the given values, we can solve for the initial velocity:

120 m = (Initial velocity) * [(2 * sin(37)) / 9.8]

Solving this equation will give us the initial velocity of the ball.

The time it takes for the ball to reach the wall can be found using the horizontal component of the velocity. Since air resistance is negligible, the horizontal velocity remains constant throughout the motion. The horizontal distance traveled by the ball is 120 m, and the horizontal velocity is given by:

Horizontal velocity = Initial velocity * cos(angle)

By dividing the horizontal distance by the horizontal velocity, we can find the time it takes for the ball to reach the wall.

To find the velocity components of the ball when it reaches the wall, we can use the equations for projectile motion. The horizontal component of the velocity remains constant and is equal to the initial horizontal velocity. The vertical component of the velocity can be calculated using the equation:

Vertical velocity = Initial velocity * sin(angle) - (g * time)

where time is the time it takes for the ball to reach the wall (found in part.

Using the given values, we can calculate the horizontal and vertical components of the velocity.

The speed of the ball when it reaches the wall can be found by calculating the magnitude of the velocity vector at that point. This can be calculated using the equation:

Speed = sqrt((Horizontal velocity)^2 + (Vertical velocity)^2)

Calculating this will give us the speed of the ball when it reaches the wall.

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A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

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Answer:

we have:

8x³ + mx² - 6x + n

= 8x³ - 8x² + (m + 8)x²- (m + 8)x + (m + 2)x - (m + 2) + m + 2+ n

= 8x²(x - 1) + (m + 8)x(x - 1) + (m + 2)(x - 1) + (m + n + 2)

= (x - 1)[8x² + (m + 8)x + m + 2] + (m + n + 2)

because the remainder if divided by (x-1) is 2

=> m + n + 2 = 2

⇔ m + n = 0 (1)

we also have:

8x³ + mx² - 6x + n

= 8x³ - 12x² + (m + 12)x² - 3/2.x.(m + 12) + ( 12 + 3/2.m)x - (9/4.m +  18) + n +9/4m + 18              

= 4x²(2x - 3) + 1/2.(m + 12)x(2x - 3) + (3/2m + 12).1/2.(2x - 3) + 9/4m + n + 18

= (2x - 3)(4x² + (m + 12)/2.x + 3/4m + 6) + 9/4m + n + 18

 because the remainder if divided by  (2x - 3) is 8

=> 9/4m + n + 18 = 8

⇔ 9/4m + n = -10 (2)

from (1) and (2), we have:

m + n = 0

9/4m + n = -10

=> m = -8

      n = 8

Step-by-step explanation:

The inverse Laplace transform of F(s) = 12s / (\(s^3\) + 6s^2 + 5s) + 3 / (2s^2 + 4) is determined to find the function f(t).

To find f(t), we need to apply the inverse Laplace transform to F(s). Let's break down the expression for F(s) into two separate fractions:

F(s) = 12s / (\(s^3\) + 6s^2 + 5s) + 3 / (2s^2 + 4)

First, let's consider the fraction 12s / (\(s^3\)+ 6s^2 + 5s). We can factor the denominator as follows: s(\(s^2\)+ 6s + 5). By applying partial fraction decomposition, we can express this fraction as A/s + (Bs + C)/(\(s^2\) + 6s + 5).

Next, let's focus on the fraction 3 / (2\(s^2\) + 4). We can factor out 2 from the denominator, giving us: 3 / 2(\(s^2\) + 2). By comparing this with the standard form of the Laplace transform for a second-order differential equation, we can deduce that this fraction corresponds to the Laplace transform of the function cos(\(\sqrt(2)\)t).

Putting everything together, we can express F(s) as A/s + (Bs + C)/(\(s^2\) + 6s + 5) + 3cos\((\sqrt(2)\)t)/2. By applying the inverse Laplace transform to each term, we can determine the corresponding functions. The final expression for f(t) will involve a combination of exponential functions and the cosine function, which can be calculated using the inverse Laplace transform techniques.

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Answer:

45

Step-by-step explanation:

9x5=45,

45 divided by 9 =5

45 divided by 5 =9

(Fact Families)

Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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Answer:

c(12 + 9 + 6)

12(2.25c)

Step-by-step explanation:

12c + 12 (3/4c) + 12 (1/2c)

12(1c) + 12(3/4c) + 12 (1/2c)

12(c + 3/4c + 1/2c)

12(2 1/4c)

12(2.25c)

Or

12c + 12 (3/4c) + 12 (1/2c)

12c + 9c + 6c

c(12 + 9 + 6)

The height of the flagstaff by suing trigonometric ratios is found to be 27 m.

Given,

Height of the ladder, AD = 18 m

The distance to the point below the top of a vertical flagstaff where the ladder reaches, CD = 18m

Angle of elevation of flagstaff from the foot of the ladder, ∠ CAB = 60 °

Δ ACD is isosceles triangle.(Image is attached)

∠ ACB = ∠ CAD = 30 °

In △ ABD, by using the trigonometric ratios, we get that:

Sin 30 ° =  BD / AD

1 / 2 = BD / 18

BD = 9 m

So, the height of the flagstaff will be:

BC = BD + DC =9 + 18 = 27 m

Therefore, we get that, the height of the flagstaff by using trigonometric ratios is found to be 27 m.

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The interval of convergence \(f(x) = 10/ x^2-6x-16\) is (-8, 2)

By expressing the function as a partial fraction, we have;

\(f(x) = 10/[(x - 8)(x + 2)]\)

The next thing is to write f(x) as a sum of two fractions when denominators are  (x - 8) and (x + 2), we have;

\(f(x) = A/(x - 8) + B/(x + 2)\)

Multiplying both sides by (x - 8)(x + 2), we have;

10 = A(x + 2) + B(x - 8)

Given that  x = 8, we have;

10 = A(10),

A = 1

Given that x = -2, we have;

10 = B(-10)

B = -1

Hence, we have  \(f(x) = 1/(x - 8) - 1/(x + 2)\)

Power series for each term.

The power series for 1/(x - 8) is:

\(1/(x - 8) = -1/8 × 1/(1 - x/8) = -1/8 × ∑(x/8)^n, n=0\) to infinity

The power series for -1/(x + 2) is:

\(-1/(x + 2) = -1/2 × 1/(1 + x/2) = -1/2 × ∑(-x/2)^n\), n=0 to infinity

Thus, power series for f(x) is:

\(f(x) = 1/(x - 8) - 1/(x + 2) = -1/8 × ∑(x/8)^n - 1/2 ×∑(-x/2)^n\\= ∑[(-1/8)(x/8)^n + (-1/2)(-x/2)^n]\\= ∑[(-1/8)^{n+1} × x^n + (-1/2)^{n+1} × x^n]\)

We can therefore say that, the power series converges for values of x such that |x/8| < 1 and |-x/2| < 1, or equivalently, for -8 < x < 2.

Hence, the interval of convergence for the power series is (-8, 2).

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Answer:

47°

Step-by-step explanation:

vertical angles are congruent

Answer:

f(x)=X^2+4

f(x)=42

42=X^2+4

X^2+4=42

X^2=42-4

X^2=38

X=sqrt(38)=6.16

\( \sqrt{?} \)

The newspaper's assertion is unjustified. It can be shown that the interval does not contain 0.5 based on the 99% confidence interval of (0.322, 0.511). (which is half).

This indicates that the population parameter (mean, percentage, and standard deviation) is between a and b with x% confidence.

This indicates that at least half of students prefer using a computer to take their notes. Since the interval's lower limit (0.322) is higher than 0.5, there is a 99% likelihood that the actual percentage of students who prefer taking notes on computers is higher than 0.5.

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Step-by-step explanation:

hope you can understand

Answer:

\(-\frac{15}{7}\)

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

it should be -\(\frac{15}{7}\)

Step-by-step explanation:

Venn diagram:

The percentage of students that studied mathematics = 25%
The percentage of students that studied electronics = 20%
The percentage of students that studied Communications = 55%
The percentage of students that studied both electronics and Communications subjects = 10%

P(studied Communications or electronics or both subjects)
= P(studied Communications) + P(studied electronics) - P(studied both electronics and Communications subjects)
= 55% + 20% - 10%
= 65%

Therefore, the probability that a student studied Communications or electronics or both subjects is 65%.

P(studied mathematics and Communications subjects)
= P(studied mathematics) × P(studied Communications)
= 25% × 55%
= 13.75%

Therefore, the probability that a student studied mathematics and Communications subjects is 13.75%.

Drawing a Venn diagram, we have 25% studying Mathematics (M), 20% studying Electronics (E), and 55% studying Communications (C).10% studied both Electronics and Communications.

Therefore, the percentages become as follows: M = 25% - 10% = 15% E = 20% - 10% = 10% C = 55%.

Part 2 - To obtain the probability that a student studied Communications or Electronics or both subjects

P(Communication or Electronics) = P(Communication) + P(Electronics) - P(Communication and Electronics) = 55% + 20% - 10% = 65%.

The probability that a student studied Communications or Electronics or both subjects is 65%.

Part 3 -To obtain the probability that a student studied Mathematics and Communications subjects,

P(Mathematics and Communications) = P(Mathematics) * P(Communications) = 25% * 55% = 13.75%.

The probability that a student studied Mathematics and Communications subjects is 13.75%.

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The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Therefore, we can say: limit sin(x) as x approaches pi/2 does not exist lim sin(x) as x approaches 0 = 0.

Although the function (sin x)/x is not defined at zero, it approaches 1 arbitrarily close as x approaches zero. In other words, when x gets closer to zero, the limit of (sin x)/x = 1.

We can put g(x) equal to -1/x and h(x) equal to 1/x because sin(x) is always between -1 and 1. As x approaches either positive or negative infinity, we know that the limit of both -1/x and 1/x is zero, and as a result, the limit of sin(x)/x is also zero.

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One of the reasons for difficulty in developing probability without measuring theory is that the measure theory provides a rigorous mathematical framework for defining probabilities. Measure theory is used to formalize the concepts such as probability spaces, events, random variables etc.

Measure theory is used to give a systematic approach for defining measures, which are mathematical functions that assign a numerical value of sets. Measures are used to define probabilities of events in context to probability theory. Measures ensures that probabilities satisfy non-negativity, additivity, and normalization.

By utilizing measure theory, mathematicians and statisticians were able to establish a very solid and highly accepted foundation for probability theory. Measure-theoretic probability provides a comprehensive framework that enables the study of probability in a mathematically sound manner.

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The complete question is: Determine one reason for difficulty distinguished philosophers must have faced while trying to develop probability without measure theory.

The missing number in the median set is 6.

We are given that;

Median set=18

Now,

To find the missing number, you need to know the number of elements in the set and their order. The median is the middle value of a set when it is arranged in ascending or descending order. If the set has an odd number of elements, the median is the exact middle value. If the set has an even number of elements, the median is the average of the middle two values.

For example, if the set is {2, 4, 6, 8, 10}, the median is 6 because it is the middle value. If the set is {3, 5, 7, 9}, the median is (5 + 7) / 2 = 6 because it is the average of the middle two values.

Therefore, by median the answer will be 6.

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Answer:

the answer is $36.04

Step-by-step explanation:

34 dived into 100= 0.34 times 6 equals 2.04 34+2.04=36.04

Answer:

15,000 m²= 1.5 hectares

2.5 hectares= 25, 000 m²

Step-by-step explanation:

Sana makatulong

Answer:

=2g+9

Step-by-step explanation:

5g+14−3g−5

=5g+14+−3g+−5  

=5g+14+−3g+−5

=(5g+−3g)+(14+−5)

=2g+9

Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.

Let's denote the number of additional free throws that Michelle needs to make as "x." Since she has made 14 out of her 20 free throws this season, her current shooting percentage is:

Current shooting percentage = (Number of made free throws / Total number of attempted free throws) * 100

                        = (14 / 20) * 100

                        = 70%

To find the number of additional free throws she needs to shoot to achieve a shooting percentage of 90%, we set up the following equation:

(14 + x) / (20 + x) = 90/100

We can now solve this equation to find the value of x:

(14 + x) / (20 + x) = 0.9

Cross-multiplying gives:

0.9 * (20 + x) = 14 + x

18 + 0.9x = 14 + x

0.9x - x = 14 - 18

-0.1x = -4

Dividing both sides by -0.1 gives:

x = 40

Therefore, Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.

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Answer:

8

Step-by-step explanation:

4+4

8

You can rewrite it as

2+2+2+2

8

Sherry's commitment and love for reading allowed her to embark on a literary adventure that spanned two days. From the initial taste of 1/3 to the final bite of the remaining line 2/3, she had read the entire book, savoring every word and getting lost in the magic of storytelling.

Sherry's reading adventure began with her diving into a book, eager to explore its contents. She managed to devour a portion of the book, specifically 1/3 of it, before feeling the sweet embrace of sleep and deciding to call it a night.

The following day arrived, and Sherry's desire to unravel the remaining mysteries of the book was still burning bright within her. Determined to quench her thirst for knowledge, she dedicated herself to reading the rest of the book. With focused determination, she turned page after page, immersing herself in the story's captivating world.

As the hours ticked by, Sherry felt the satisfaction of progress. With each passing chapter, she could sense herself inching closer to the climax and resolution of the story. The characters became like old friends, and the plot twists kept her on the edge of her seat.

Finally, as the sun dipped below the horizon, Sherry turned the last page and completed the final chapter. She had done it. She had finished reading the entire book. The sense of accomplishment washed over her, accompanied by a bittersweet feeling that the journey had come to an end.

Reflecting on her reading experience, Sherry realized that she had initially read 1/3 of the book before retiring for the night. That meant there were still 2/3 of the book left for her to discover on the subsequent day. And indeed, she did just that. She dedicated her time and energy to devouring the remaining 2/3 of the book, leaving no page unturned.

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The ratio used to find the measurement of angle x is given as follows:

cos(x) = 40/68.

The three trigonometric ratios are defined as follows:

For angle x, we have that:

Hence the ratio is given as follows:

cos(x) = 40/68.

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