6) You are shooting the puck along the path
seen in the picture of the air hockey table.
Find the mZxº and the mzmº.

There are no values of k that make the linear system consistent.

To determine the values of k for which the linear system is consistent, we need to check if the system of equations has a unique solution, infinitely many solutions, or no solution.

The given system of equations is:

8x1 - 7x2 = 2

12x1 + kx2 = -1

We can solve this system using various methods, such as substitution or elimination. Let's use the elimination method to simplify the system.

To eliminate x2, we can multiply equation 1 by k:

8kx1 - 7kx2 = 2k

Now, we can subtract equation 2 from equation 3:

(8k - 12)x1 + (-7k - k)x2 = (2k + 1)

Simplifying equation 4, we have:

(8k - 12)x1 - 8kx2 = 2k + 1

Now, for the system to be consistent, the coefficient of x1 and the coefficient of x2 in the resulting equation should be the same.

Comparing the coefficients, we get:

8k - 12 = 0 (coefficient of x1)

-8k = -1 (coefficient of x2)

Solving the first equation:

8k - 12 = 0

8k = 12

k = 12/8

k = 3/2

Now, substitute the value of k in the second equation to check if it is satisfied:

-8k = -1

-8(3/2) = -1

-12 = -1

The equation -12 = -1 is false. Therefore, there are no values of k for which the linear system is consistent.

In conclusion, there are no values of k that make the given linear system consistent.

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The domain and range of the inverse of the function f(x) = 0.5x need to be determined. The domain and range of the inverse function g(x) = 2x are both all real numbers.

To find the domain and range of the inverse of a function, we can swap the roles of x and y in the original function and then solve for y.

The original function is f(x) = 0.5x. Swapping x and y, we get x = 0.5y. Solving this equation for y, we multiply both sides by 2, giving us y = 2x.

The domain of the inverse function, denoted as g(x), is the set of all possible x-values. In this case, the domain of g(x) is the same as the range of the original function f(x). The range of f(x) is all real numbers, so the domain of g(x) is also all real numbers.

Similarly, the range of the inverse function is the set of all possible y-values. In this case, the range of g(x) is the same as the domain of the original function f(x). The domain of f(x) is all real numbers, so the range of g(x) is also all real numbers.

Therefore, the domain and range of the inverse function g(x) = 2x are both all real numbers.

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Answer:

(- 2, - 10 )

Step-by-step explanation:

Given the 2 equations

y = x - 8 → (1)

y = 5x → (2)

Substitute y = 5x into (1)

5x = x - 8 ( subtract x from both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

Substitute x = - 2 into either of the 2 equations for y

Substituting into (1)

y = - 2 - 8 = - 10

solution is (- 2, - 10 )

Answer: A and B

Step-by-step explanation:

The shape is moving from right to left and down

The correct option is A) 9∕8, evaluating the exponent expression with a = -2 and b = 3, we find that the value is -8.

We are given the expression a^b, where a = -2 and b = 3. Substituting these values into the expression, we have (-2)^3.

To evaluate this expression, we raise -2 to the power of 3. When we raise a negative number to an odd power, the result will be a negative number.

So, (-2)^3 will yield a negative value.

Calculating (-2)^3, we multiply -2 by itself three times: (-2) × (-2) × (-2). This equals -8.

Therefore, the correct option is A) 9∕8 and the value of the exponent expression (-2)^3 is -8.

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The answer tο the questiοn "Which cοnfidence level was chοsen?" is that it cannοt be determined based οn the given infοrmatiοn.

Statistical inference refers tο the prοcess οf drawing cοnclusiοns οr making predictiοns abοut a pοpulatiοn based οn sample data. It invοlves using statistical methοds and techniques tο analyze the data and make inferences abοut the underlying pοpulatiοn parameters. Statistical inference allοws researchers tο generalize their findings frοm a sample tο the entire pοpulatiοn and make infοrmed decisiοns οr predictiοns.

Twenty-five wοοden beams were οrdered fοr a cοnstructiοn prοject. The sample means and the sample standard deviatiοn was measured:[tex]\bar{x} = 260 \, \text{cm}$, $s = 2 \, \text{cm}$.[/tex] The calculated confidence interval for the mean is [tex][259.32; 260.68]$.[/tex]

To determine the confidence level chosen, we need to consider the properties of a confidence interval. In this case, the confidence interval is given as[tex]$[259.32; 260.68]$[/tex], which represents an interval estimate for the population mean.

A confidence interval is typically written as [tex]\bar{x} \pm E$,[/tex]where [tex]$\bar{x}$[/tex] is the sample mean and E is the margin οf errοr. The margin οf errοr depends οn the sample size, standard deviatiοn, and the desired level οf cοnfidence.

In the given infοrmatiοn, the sample mean [tex]$\bar{x}$[/tex] is 260 cm, and the sample standard deviatiοn s is 2 cm. Hοwever, the level οf cοnfidence is nοt directly prοvided.

Tο determine the cοnfidence level chοsen, we need additiοnal infοrmatiοn abοut the calculatiοn οr the specific cοnfidence level used. Withοut this infοrmatiοn, we cannοt determine the exact cοnfidence level that cοrrespοnds tο the given cοnfidence interval.

Therefοre, the answer tο the questiοn "Which cοnfidence level was chοsen?" is that it cannοt be determined based οn the given infοrmatiοn.

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a. The estimated proportion of driveshafts that would fail prior to reaching 1200 operating hours is approximately 0.246, or 24.6%.

b. The 95% confidence interval for the true mean lifespan is approximately (1244.79, 1303.21) hours.

(a) First, we need to standardize the value 1200 using the sample mean and standard deviation. We calculate the z-score as follows:

z = (x - μ) / σ,

z = (1200 - 1274) / 108

≈ -0.685

Using a standard normal distribution table or calculator, we find that the proportion is approximately 0.246.

(b) The formula for the confidence interval is:

CI = x ± z * (σ / √n),

CI = 1274 ± 1.96 * (108 / √50)

CI = 1274 ± 1.96 * (108 / √50)

CI ≈ 1274 ± 1.96 * 15.297

The 95% confidence interval for the true mean lifespan is approximately (1244.79, 1303.21) hours.

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Answer:

1=4

5=8

2=5

Step-by-step explanation:

Answer:

1, 5, 2 is the x values.

Step-by-step explanation:

you just subtract 3 from the y's

The probability that it will not be windy is 88% or 0.88.

No, tomorrow be not a good day to fly a kite.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means

The weather reporter says that there is a 12% chance that it will be moderately windy tomorrow.

Now, the probability that it will not be windy

= 100 - 12

= 88%

= 0.88

No, the lite totally depends on the wind but the next day the probability of no wind is 88%.

This probability is high probability.

So, there is huge probability that the kite will not fly.

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Answer:

Each litters can be represented as; x and y respectively to the 7% and the 28%

x + y =1

7x + 28y =19.6

This a simultaneous equation and can either be solved by using elimination or substitution method

Using the substitution method

eqn1, x=1-y

putting into eqn2

7(1-y)+28y =19.6

7-7y+28y=19.6

21y=12.6

y=3/5

but x=1-y

so

x=1-3/5

x=2/5

The 90% confidence interval for the mean score for all students is [79.35, 86.75].

A 90% confidence interval was calculated to estimate the mean score for all students based on a sample of six students' scores. The sample mean was found to be 82.83, and the standard deviation was 3.67.

Using a t-distribution with five degrees of freedom (n-1), the critical value for a 90% confidence level was determined to be 2.571. By applying the formula for confidence intervals, the lower bound of the interval was calculated as 82.83 - (2.571 * (3.67/√6)) = 79.35, and the upper bound was calculated as 82.83 + (2.571 * (3.67/√6)) = 86.75.

This means that we can be 90% confident that the mean score for all students falls within the range of 79.35 to 86.75.

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Answer:

26 degrees

Step-by-step explanation:

180 - 48 = 132 - 106 = 26

this one should work

Answer: x = 106°

Step-by-step explanation:

106° + 48° + x° = 180°

154 + x = 180

x = 106°

The system in the requested form, using prime notation for derivatives and ï notation for variables, is ï' = e^2tï - 8tï' + 7sin(t) and ï'' = 2tan(t)ï' + 7ï - 2cos(t).

The system can be written in the form:

x' = e^2tx - 8ty + 7sin(t)

y' = 2tan(t)y + 7x - 2cos(t)

Using prime notation for derivatives, the system becomes:

x' = e^2tx - 8ty + 7sin(t)

y' = 2tan(t)y + 7x - 2cos(t)

Furthermore, we can write x and y using ï' notation as:

x = ï

y = ï'

Substituting these expressions into the system, we have:

ï' = e^2tï - 8tï' + 7sin(t)

ï'' = 2tan(t)ï' + 7ï - 2cos(t)

In summary, the system in the requested form is:

ï' = e^2tï - 8tï' + 7sin(t)

ï'' = 2tan(t)ï' + 7ï - 2cos(t)

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Answer:

The amount of olive oil and balsamic vinegar to use are;

You use 22 tablespoons of olive oil and 12 tablespoons of balsamic vinegar

Step-by-step explanation:

From the question, we have;

The number of tablespoons of olive oil added for every 3/2 tablespoon of balsamic vinegar = 11/4 tablespoons

Therefore, in the mixture, the ratio of olive oil to balsamic vinegar = 11/4:3/2

Let 'x', and 'y' represent the the number of tablespoons of olive oil and balsamic vinegar, in the mixture 34 tablespoons of bread dip, we can write;

x + y = 34 tablespoons

x/y = (11/4)/(3/2) = 11/6

∴ x = 11/6 × y

∴ x + y = 11/6 × y + y = 34

11/6 × y + y = 17·y/6 = 34

17·y = 34 × 6 = 204

y = 204/17 = 12

The number of tablespoons of balsamic vinegar in the bead dip, y = 12 tablespoons of balsamic vinegar

x = 11/6 × y = 11/6 × 12 = 22

The number of tablespoons of olive oil in the bead dip, x = 22 tablespoons of olive oil.

Answer:

650.3

Step-by-step explanation:

Answer:

the total payment will be 91.43 and the total interest pay will be 13.43.

Step-by-step explanation:

Tbh I dont get what you mean that much, but I think you mean 48 months of payment times the monthly payment, soooo.

13.43x 48= 644.64

644.64 after four years. I really really hope this helps you. Have a good day

Answer:

Total distance = 30m

Total displacement = 0m

Step-by-step explanation:

a) Distance is a scalar quantity that does not specify direction

Hence if a trail runner zig-zags 15m to the west and then 15m to the east, the total distance will be the sum of the distance travelled both to the west and east.

total distance =  distance through west + distance through east

total distance = 15m + 15m

total distance = 30m

Hence the runner's total distance is 30m

b) Displacement is a vector quantity and it specifies direction. Hence we will take into consideration the direction taken

Since East direction is positive, the displacement through east is +15m

Since West direction is negative, the displacement through west is -15m

Total displacement  = +15 - 15

Total displacement = 0m

Hence the runner's total displacement is 0m

Answer:

(2x+1)(x-1) = 2x^2 - x - 1

Step-by-step explanation:

Answer:

2x^2 - x - 1

Step-by-step explanation:

Lets rewrite it to the area formula

(2x+1)(x-1)

Simplify-(distributive property of multiplication)

(2x*x) + (2x*-1) + (1*x) + (1*-1) =

Simplify

2x^2 + (-2x) + x + (-1)

Simplify

2x^2 - x - 1

The answer is 2x^2 - x - 1

If my answer is wrong, pls correct me

If you like my answer and my explanation, mark me as brainliest!

-Chetan K

Answer:

m<C = 110

Step-by-step explanation:

<a = <b

<b = 35 so,

<a = 35

<c = x

<a + <b + <c = 180

35 + 35 + x = 180

70 + x = 180

x = 180 - 70

x = 110

Answer:

a. The price per ticket is 4 bucks, and b. you get 1/4 of a ticket for a dollar.

1. the penguin walks 75 feet in 45 seconds, and 2. it takes 27 seconds to walk 45 feet.

Step-by-step explanation:

Tickets:

16 dollars divided by 4 tickets is 4 dollars, so 4 dollars = 1 ticket. therefore, 1 dollar gives you 1/4 of a ticket.

Penguins

formula: X = feet, Y = seconds

X*0.6=Y

10 feet*0.6=6 seconds

(?) feet*0.6= 45 seconds

75 feet*0.6=45 seconds

same thing, but backwards this time

45 feet*0.6=(?) seconds

45 feet*0.6= 27 seconds

Hey can I have brainly please I am really close to leveling up

thx

Answer:

Step-by-step explanation:

Answer:

1. (x,y)=

2. (3, 480°), (3,-240°), (-3, -60°)

3. (-17, -1.08)

4. on the second circle from the center and 153° clockwise from the horizontal axis

Step-by-step explanation:

took quiz...100%

Answer:

midpoint = -4.5, 1.5

Step-by-step explanation:

x1 = -9, y1 = 7, x2=0 , y2=-4

midpoint = (x1 +x2)/2 , (y1 + y2)/2

= (-9 + 0)/2 , (7 + -4)/2

=-9/2 , 3/2

midpoint = -4.5, 1.5

As per the confidence interval Lower Bound is 94.874 and the Upper Bound is 105.126

Sample Mean = 100

Sample Standard Deviation = 8

Sample Size = 20

Calculating the confidence interval -

Confidence Interval = Sample Mean ± (Critical Value) x (Standard Deviation / √(Sample Size))

Substituting the values

= 100 ± (2.860) x (8 / √20)

= 100 ± 2.860 x (8 / 4.472)

= 100 ± 2.860 x 1.789

= 100 ± 5.126

Calculating the lower bound -

Lower Bound

= 100 - 5.126

= 94.874

Calculating the upper bound -

Upper Bound

= 100 + 5.126

= 105.126

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Answer:

Equation = 298.56=6(0.07m+23.90+0.10(23.90))

Minutes = 335

Step-by-step explanation:

Okay, so first simplify to get 298.56=0.52m+172.08

Next subtract to get 0.52m=126.48

Then divide 0.52 to get 335

I hope this helps ! :)

Answer:

[tex]\boxed {\boxed {\sf b= \sqrt{192}}}[/tex]

Step-by-step explanation:

Since this is a right triangle, we can use Pythagorean Theorem to find the sides.

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse.

In this triangle, 8 and x are the legs because they form the right angle. 16 is the hypotenuse because it is opposite the right angle.

[tex]a=8 \\c=16[/tex]

Substitute the values into the formula.  

[tex]8^2+b^2=16^2[/tex]

Solve the exponents.

[tex]64+b^2=256[/tex]

Subtract 64 from both sides to isolate the variable.

[tex]64-64+b^2= 256-64 \\b^2=192[/tex]

Take the square root of both sides.

[tex]\sqrt {b^2}=\sqrt{192}\\ b=\sqrt{192}[/tex]

The missing side is equal to √192

The rate of change of the function is -1/6

From the question, we have the following parameters that can be used in our computation:

(3,-1) and (-3,0)

The rate of change of the function is calculated as

Rate = Change in y/Change in x

Using the above as a guide, we have the following:

Rate = (0 + 1)/(-3 - 3)

Evaluate

Rate = -1/6

Hence, the rate of change of the function is -1/6

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Answer:

Hello There!!

Step-by-step explanation:

Firstly,select three ordered pairs from the table. Secondly,substitute the first pair of values in to the form of the quadratic equation: f(x) = ax^2 + bx + c and then solve for a.

hope this helps,have a great day!!

~Pinky~

Answer:

Proportional and h.200=g

Step-by-step explanation: