Solve systems of equations by substitution for x-2y= -8 and 6x+7y=9

The value of t for a 99% confidence interval depends on the sample size. With larger sample sizes (typically >30), t approaches the value of Z (standard normal distribution critical value).



In statistical inference, the value of t used for constructing a confidence interval depends on the desired confidence level and the sample size. For a 99% confidence interval, the critical value of t can be determined from the t-distribution table or calculated using software.The value of t for a 99% confidence interval is based on the degrees of freedom, which is generally determined by the sample size minus one (n - 1) for an independent sample. The larger the sample size, the closer the t-distribution approaches the standard normal distribution. For large sample sizes (typically n > 30), the critical value of t becomes very close to the value of Z (the standard normal distribution critical value) for a 99% confidence level.

To calculate the specific value of t, you need to know the sample size (n) and the degrees of freedom (df = n - 1). With these values, you can consult a t-distribution table or use statistical software to find the appropriate critical value. For a 99% confidence interval, the value of t will be higher than the corresponding value for a lower confidence level such as 95% or 90%, allowing for a wider interval that captures the true population parameter with higher certainty.

Therefore, The value of t for a 99% confidence interval depends on the sample size. With larger sample sizes (typically >30), t approaches the value of Z (standard normal distribution critical value).

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Answer:

We should invest in 7.74% compounded daily as it yields a higher return.

The total investment after 10 years is $10,841.22.

Step-by-step explanation:

a.) at 7.74% compounded daily

\(final = principal(1 + \frac{i}{m} )^{m \times n} \\ = 5000(1 + \frac{0.0774}{365} )^{365 \times 10} \\ = 10 \: 841.2235\)

I assumed there are 365 days in a year.

b.) at 7.8% compounded quarterly

\(final = principal(1 + \frac{i}{m}) ^{m \times n} \\ = 5000 (1 + \frac{.078}{4} )^{4 \times 10} \\ = 10 \: 762.2505\)

Answer:

incorrect

Step-by-step explanation:

2x8=16

16+2=18

The probability that the average fracture strength of randomly selected pieces of this glass exceeds 14.5 is equals to the 0.62% and the confidence interval that includes, with probability 0.95 is equal to (13.608, 14.392).

We have, information about the fracture strength of tempered glass.

Mean, μ = 14

Standard deviations σ = 2

Sample size, n = 100

We have to determine probability that the average fracture strength selected pieces of this glass exceeds 14.5,

\(P( \bar x > 14.5).\)

As we see sample size n = 100 > 30 According to central limit theorem, the sampling distribution of sample means is normal. Using the Z-Score formula for sample means in sampling distribution of means,\(Z = \frac{ x - \mu}{\frac{\sigma} {\sqrt n }}\)

Now, the required probability is \(P( \bar x > 14.5).\)

\(= P(\frac{ \bar x - \mu}{\frac{\sigma}{\sqrt n }} > \frac{14.5 - 14}{\frac{2}{\sqrt{100}}} )\)

\(= P( z > 0.5 \times 5)\)

= P( z > 2.5 )

Using the Z-distribution table, the value P( z > 2.5) is 0.0062. So, required probability is 0.0062 or 0.62%. Now, the interval that includes, with probability 0.95, that is c = 0.95 and so, z_{\alpha/2} = 1.96 ( Z-table). Thus, the interval is

\(CI = \bar x ± z_{ \frac{ \alpha}{2}} × \frac{ σ}{ \sqrt{n}}\)

=> CI = 14 ± 1.96 × 0.20

=> CI = 13.608 to 14.392

Hence, required interval is (13.608, 14.392).

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Answer:

96π or 301.59 in³

Step-by-step explanation:

V(cone) = 1/3πr²h

= 1/3·π·6²·8

= 96π or 301.59

Answer:

301.58  

Step-by-step explanation:

The function’s average rate of change over the interval from x = 1 to x = 2 is: -2. The correct option b.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

We have the interval from x = 1 to x = 2.

To find the function’s average rate of change over the interval from x = 1 to x = 2 is:

We interpreted the interval in the coordinate form.

The curve from (1, 2) to (2, 0) is a straight line.

And the slope of the line is the average rate of change of the function.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = (0-2) / (2-1)

m = -2/1

m = -2

Therefore, the average rate of change is -2.

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Answer:

2340

Step-by-step explanation:

3 3/4=15/4            3 1/4=13/4    turn the mixed fractions into improper fractions

(15/4)(3)(13/4)=36.5625ft³        this is the volume of the shipping box

(1/4)(1/4)(1/4)=1/64ft³                  this is the volume of the fish food box

36.5625/(1/64)                          divide it to find out how much fish boxes can fit

36.5625×64                             flip the fraction and multiply

2340

There are 8 different ways to choose the leadership of the tribe.

To calculate the number of different ways to choose the leadership of the tribe, we need to consider the hierarchy and the number of positions to be filled.

First, we have one chief position. There is only one chief, so there is only one way to choose the chief.

Next, we have two supporting chief positions (supporting chief a and supporting chief

b). Since each supporting chief position can be filled independently, there are 2 ways to choose the supporting chiefs.

Lastly, for each supporting chief, we have two inferior officer positions. Since each supporting chief position has two inferior officer positions, there are 2 ways to choose the inferior officers for each supporting chief.

Therefore, the total number of different ways to choose the leadership of the tribe is calculated by multiplying the number of choices for each position:

1 (chief) * 2 (supporting chiefs) * 2 (inferior officers for each supporting chief) * 2 (inferior officers for the other supporting chief).

Multiplying these values together, we get: 1 * 2 * 2 * 2 = 8.

So, there are 8 different ways to choose the leadership of the tribe.

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Answer:

36

Step-by-step explanation:

-3(-6)2=36

Answer:

63

Step-by-step explanation:

(s-13) +s = s + 50

2s - 13 = s + 50

add 13 both sides, subtract the s from both sides

s = 63

Answer:

s = 63°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

s + 50 is an exterior angle of the triangle , then

s + 50 = s - 13 + s

s + 50 = 2s - 13 ( subtract s from both sides )

50 = s - 13 ( add 13 to both sides )

63 = s

The equation for the temperature, d, in terms of t (the number of hours since midnight), is:  d = 16 × sin((π/12) × t) + 55

To find an equation for the temperature, we need to determine the amplitude, period, phase shift, and vertical shift of the sinusoidal function.

The amplitude is half the difference between the high and low temperatures, which is (71 - 39) / 2 = 16 degrees. The period is the number of hours in a day, which is 24 hours. Since the temperature is at its highest point at 12:00 PM (midday), there is no phase shift. The vertical shift is the average of the high and low temperatures, which is (71 + 39) / 2 = 55 degrees.

Putting these values together, the equation for the temperature, d, in terms of t can be written as:

d = 16 × sin((2π/24) × t) + 55

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The researcher tested the null hypothesis that there is no difference in average sprinting times between athletes who stretched before an event and those who did not stretch.

To determine if stretching helps sprinters run faster, the researcher formulated a null hypothesis. The null hypothesis states that there is no significant difference in average sprinting times between athletes who stretched before an event and those who did not stretch.

To test this hypothesis, the researcher would conduct an experiment where they divide the sprinters into two groups: one group that stretches before the event and another group that does not stretch. The sprinters in both groups would then compete in the sprinting event, and their times would be recorded.

After collecting the data, the researcher would compare the average sprinting times of the two groups using statistical analysis. If the analysis shows that the difference in average times between the groups is not statistically significant, meaning that it could have occurred by chance, then the null hypothesis would be supported. This would suggest that stretching before a sprinting event does not have a significant impact on sprinting times.

However, if the analysis reveals a statistically significant difference in average times between the groups, it would reject the null hypothesis. This would provide evidence that stretching does affect sprinting performance, and the researcher could conclude that stretching helps sprinters run faster based on the observed data.

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Answer: 35

Step-by-step explanation:

Answer:

7 :D

Step-by-step explanation:

Lets go step by step!

When we do something to one side, we must do it to the other!

2x - 5 < 9

2x - 5 + 5 < 9 + 5

2x < 14

2x/2 < 14/2

x < 7

Your answer is 7 :D

Have an amazing day!

Please rate and mark brainliest!

Answer:

x=7

Step-by-step explanation: Okay so,

2x−5=9

First, you take the 5 and add it to the 9:

2x=9+5=

2x=14

Then you divide 2x by 2 and what you do to one side you do to the other, so you also divide 14 by 2:

2x/2=14/2=

x=7

Hope this helps!

Answer:

(2) The statement is true.

-1 < r < 1

Rounding up to the nearest whole number, we would need a sample size of at least 105 businesses to construct a 99% confidence interval with a 4% margin of error.

To determine the sample size required to construct a 99% confidence interval for the proportion of businesses with a 4% margin of error, we need to use the formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (99% confidence level corresponds to a Z-score of approximately 2.576)

p = estimated proportion (since we don't have an estimate, we can assume p = 0.5 to get a conservative estimate)

E = margin of error (0.04 or 4%)

Plugging in the values, we have:

n = (2.576^2 * 0.5 * (1-0.5)) / 0.04^2

n = (6.638176 * 0.25) / 0.0016

n ≈ 104.364

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The total number of bit strings of length 10 over the alphabet {a,b} that have exactly four a's and start with bb or end with bb is 510.

To solve this problem, we can use the principle of multiplication and addition.

First, we need to find the number of bit strings of length 10 with exactly four a's. We can place the four a's in any of the 10 positions, so we have 10 choose 4 (or 10C4) ways to do this. For each of these arrangements, the remaining six positions must be filled with b's, so there is only one way to do this.

Therefore, there are 10C4 = 210 bit strings of length 10 with exactly four a's. Next, we need to count the number of bit strings that start with bb or end with bb.

For bit strings that start with bb, the remaining eight positions can be filled with any combination of a's and b's, so there are 2^8 = 256 such bit strings.

Similarly, for bit strings that end with bb, the first eight positions can be filled with any combination of a's and b's, so there are also 256 such bit strings.

However, we have counted the bit string bbbbbbbbb and bbbaaaaaaa twice (once for each case). Therefore, we need to subtract 2 from the total count.

Thus, the total number of bit strings of length 10 over the alphabet {a,b} that have exactly four a's and start with bb or end with bb is 256 + 256 - 2 = 510.

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The volume of the solid is cubic units 2966.20.

Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the x-axis. y=e^x,y=0,x=-2, and x=4

The method of disks will be used to obtain the volume of the solid generated by revolving the region about the x-axis.

Volume of the solid generated is given by∫[a,b] π (f(x))² dx, where a = -2, b = 4 and f(x) = e^x.

This formula computes the volume of each disk-shaped slice, which is a disk of radius e^x and thickness dx.

Thus, we use the formula to compute the integral from x = -2 to x = 4.∫[a,b] π (f(x))² dx = ∫[-2, 4] π (e^x)² dx= π ∫[-2, 4] e^(2x) dx

Now integrating, we get:∫[-2, 4] e^(2x) dx = 1/2 (e^8 - e^-4) π

The volume of the solid generated when R is revolved about the x-axis is π(1/2 (e^8 - e^-4)), which is approximately equal to 2966.20 cubic units.

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c = 20 × 5

c = 100

and that's all

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

Solution for f(3)

A regular polygon with interior angles that measure 140 degrees has 9 sides. All interior angles are congruent, meaning they have the same degree measure.

To find the number of sides in a regular polygon with a given interior angle measure, we can use the formula:

n = 360 / (180 - x)

where n is the number of sides and x is the measure of each interior angle in degrees.

This formula is derived from the fact that the sum of the interior angles in a polygon with n sides is given by the formula (n-2) * 180. In a regular polygon, each interior angle measures (Sum of interior angles / n). If we substitute the formula for the sum of interior angles into the formula for the measure of each interior angle, we get:

x = (n-2) * 180 / n

Solving for n:

n = 360 / (180 - x)

So, when we plug in the given interior angle measure of 140 degrees, we get:

n = 360 / (180 - 140)

n = 360 / 40

n = 9

Therefore, a regular polygon with interior angles that measure 140 degrees has 9 sides.

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How many sides does a regular polygon have if each interior angle measures 140?

Answer:

3 hours

Step-by-step explanation:

it is $100 for 1 hour right. Ok so forget about the hourly rates. Then you are left with $300. $300 total÷100 per hour = 3 hours.

Answer:

The total is 3 hours

      Hope this help! good luck :)

Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Answer:  p(θ|x) dθ = 1 − α.

Step-by-step explanation: the critical value is computed based on the given significance level α and the type of probability distribution of the idealized model

7 is a value of k that transforms f into g, where g(x) = f(x) + k. Using the concept of x and y-axis:

A two-dimensional number line, like two perpendicular axes, can be used as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. The origin is the point at which all lines in a coordinate system intersect.

The coordinates that are shown on the x and y axes give rise to their respective names. The vertical y-axis is aligned with the horizontal x-axis. They are referred to as axes because they are perpendicular to one another.

From the graph it is observe that,

Graph of Function f(x) cut at y axis in the point 3

graph of function g(x)  cut y axis in the point 4

So, the difference between the cut of y axis is k

Thus, {g(x)-f(x)=k}

Hence, k = [4 - (-3)] = 7

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The reliability of the machine can be estimated to be 0.9833, calculated as (1000 - 1) / 1000 + (600 - 5) / 600.  we can take the average of the two reliability estimates, giving us a reliability of 0.9833.

The reliability of a machine can be estimated by taking the ratio of machines that did not fail to the total number of machines operated in a given period. In this case, the reliability of the machine from Factory A can be estimated to be 0.99 (1000 - 1 / 1000). The reliability of the machine from Factory B can be estimated to be 0.9833 (600 - 5 / 600). To estimate the reliability of the machine based on both factories, we can take the average of the two reliability estimates, giving us a reliability of 0.9833.

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Landlords might employ security deposits as a financial safety net to cover any damages that a tenant might cause throughout the period of the lease. The landlord can fully refund the security deposit if the renter vacates the property in good condition.