How should the coefficients a, b, and c be chosen so that the system ax+by - 32-3 - 2x - by+cz= -1 ax + 3y -cz-3 has the solution x = 1, y = - 1 and 2 = 2? о 0 30 o 001 0 - 200 Боо 이 Solve for x 18. 1 0-3 2 x -6 |1 3х-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:

(- 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:

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

Answer:

Joe's been riding 4 hours because if you divide 48 by 12 it gives you 4 and it's by hours so it would be 4 hours. point blank period.

Step-by-step explanation:

Answer:

$130.06

Step-by-step explanation:

Interest is calculated as shown;

I = A - P

A is the amount

P is the principal

Given

Principal = $316

Rate R = 9% = 0.09

Time t = 4yrs

Substiutte and get Amount A

A  =P(1+r)^n

A = 316 (1+0.09)^4

A = 316(1.09)^4

A = 316(1.4116)

A = 446.06

Interest = 446.06 - 316

Interest = 130.06

Hence the interest is $130.06

Step-by-step explanation:

its83

(a+b)^2=a^2+2ab+b^2

x^2+(-9)2x-2=0

b^2=81

83+(-2)=81

The area under the standard normal distribution curve between z=0 and z=0.25 is 0.0987.

First cumulative probability = z = 0 and

Second cumulative probability = z = 0.25

The Standard Normal Distribution Table, often known as the Z-table, may be used to determine the area under the standard normal distribution curve between z=0 and z=0.25. The table shows the total likelihood (area) up to a specified z-value. The cumulative probability, which can be found by looking up the z-value of 0 in the table, is 0.5000. The cumulative probability is 0.5987 when we look up the z-value of 0.25.

Calculating the area -

Area = First cumulative probability - Second cumulative probability

= 0.5987 - 0.5000

= 0.0987

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To find out on which interval are both functions f(x) = x^2 + 2x and g(x) = log (2x + 1) negative, we need to analyze the intervals of negative values of both functions.

We can plot their graphs to have a better understanding:

Graphs of f(x) = x² + 2x and g(x) = log(2x + 1)

Now, we need to observe the intervals where both functions lie below the x-axis: The function f(x) = x^2 + 2x is below the x-axis on the interval (-∞, -2).

The function g(x) = log(2x + 1) is below the x-axis on the interval (-1/2, 0).

Therefore, the interval on which both functions are negative is (-2, 0).Thus, the correct option is (–2, 0).

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Answer:

to present another's viewpoint

Answer:-

D, to analyze specific data i guess

The variable that could theoretically be measured on a continuous scale is task completion time.

Task completion time is the duration between the initiation and completion of a specific task. It is continuous as it can take a large range of values on a continuous scale without any gap. It is frequently calculated in various businesses and researches to determine the efficiency and productivity of a particular task or process.

The other variables, such as method of contraception used, length of time of residence in a state, intelligence, authoritarianism, alienation, and county of residence, are all discrete variables. These variables take non-numerical values and are separate from each other by a gap.

These variables can be classified and counted into different categories, such as the number of individuals using a particular method of contraception, number of years of residence in a particular state, number of individuals belonging to a particular county, or number of individuals showing authoritarianism.

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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:

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

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:

v = -1/6

Step-by-step explanation:

Combine all like terms, getting 18v = -3. Then, divide both sides by 18 to get -3/18, or v = -1/6

Hopefully this helps- let me know if you have any questions!

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: A and B

Step-by-step explanation:

The shape is moving from right to left and down

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:

they are subtracting 6 from each number

Confidence interval are 5.9 < μ < 8.5 for the population mean.

Given:

Let x = 6,9,3,9, 6, 6, 8, 8, 7, 10,5,9

N = 12, ∑x = 86 x = 86/12 = 7.16

[tex]s=\sqrt{\frac{(x-\bar x)^2}{N-1} } = \sqrt{\frac{(6-7.16)^2+.....+(9-7.16)}{12-1} }[/tex]

[tex]\sqrt{\frac{45.66}{11} } =2.03[/tex]

At 98% confidence interval.

[tex]z=1-\frac{95}{100} =0.05\\[/tex]

[tex]t=2.201[/tex]

Confidence interval.

[tex]\bar x \pm t\frac{s}{\sqrt{n} } = 7.16\pm 2.201(\frac{2.03}{\sqrt{12} } )[/tex]

[tex]5.9 < \mu < 8.5[/tex]

Therefore, 95% confidence interval are 5.9 < μ < 8.5

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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

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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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:

Step-by-step explanation:

5- There are 2 right-angled triangles and 1 equilateral triangle or you can just say triangles

6- area for a triangle is a=bh(1/2)

so 4×3=12(1/2)=6

and 4×3=12(1/2)=6

In both triangles, they're a=6

7- 4×6=24(1/2)=12

the top flag is a=12

8-12+6+6=24

9- the rectangular flag has an area of 24 since a=bh and the added areas of the triangles are 24. I conclude that these are two ways of finding the area of this rectangular flag.

hope this helps : )

Answer:

A. Reduction

B. 2

Step-by-step explanation:

A: A reduction is when the image is getting smaller. The apostrophes show the new, or second, image. It is called "prime." Because the prime is smaller than the original, it is a reduction.

B: Scale factor is when you divide, which number changes it. In other words, the image moved from 4 to 2, from 2 to 1, etc, which means we are DIVIDING by 2.

Answer:

72

Step-by-step explanation:

32pi×360/2pi(8)=72

central angle= arc length 360/2pi×r

The measure of the arc is 72 degree

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

The measure of the arc, we use the formula:

⇒ Arc length = (angle measure / 360°) x 2πr

where r is the radius of the circle.

Now, We know that;

The radius is 8 inches, and that the arc length is 3.2π inches.

So, we can plug in those values and solve for the angle measure:

3.2π = (angle measure / 360°) x 2π(8)

3.2π = (angle measure / 360°) x 16π

Divide both sides by 16π:

0.2 = angle measure / 360°

Multiply both sides by 360°:

Angle measure = 72°

Thus, The measure of the arc is 72 degree

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