Solve the system by substitution.
3x + y = 19
-6x – 5 = y

Answer:

15h + 4

Step-by-step explanation:

5(3h + 2) - 6

Distribute

5 x 3h = 15h

5 x 2 = 10

rewrite equation

15h + 10 - 6

Subract

10 - 6 = 4

Hope This Helps!! :)

We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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Answer:

v=3√3in

Step-by-step explanation:

Answer:

3√3in c:

Step-by-step explanation:

The probability that the machine produces fewer than 5 defective widgets in a production run of 100 items is 0.10

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 5 widgets.

It has a 0.07 defective rate.

Defective rate fewer than 5

Total Probability = P of 4 defective + P for 3 defective + P for 2 defective + P for  1 defective.

Total Probability = 4/100 + 3/99 + 2/98 + 1/97

Total Probability ≈ 0.10

Therefore, the required probability for fewer than 5 defective rate is 0.10

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The percentage occupied by fresh water on Earth is 47%. The pH of the solution with H+ concentration 0.08606951774271 M is 1.1.

To calculate the percentage of fresh water on Earth, we can subtract the percentage of water in the oceans (53%) from 100%. This gives us 47%, which represents the percentage occupied by fresh water.

The pH of a solution is a measure of its acidity or alkalinity. It is determined by the concentration of hydrogen ions (H+) in the solution. In this case, the H+ concentration is given as 0.08606951774271 M. The pH scale ranges from 0 to 14, with values below 7 indicating acidity and values above 7 indicating alkalinity. By calculating the negative logarithm (base 10) of the H+ concentration, we find that the pH of the solution is approximately 1.1.

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Answer:

10

Step-by-step explanation:

The ordered pair which makes both inequalities true is: D. (3, 0).

In Mathematics, an inequality can be used to show the relationship between two (2) or more integers and variables in an equation.

In order to determine ordered pair which makes both inequalities true, we would substitute the points into the inequalities as follows:

At (0, 0), we have:

y > -2x + 3  

0 > -2(0) + 3

0 > 3 (false).

y < x – 2

0 < 0 - 2

0 < -2 (false)

At (0, -1), we have:

y > -2x + 3  

-1 > -2(0) + 3

-1 > 3 (false).

y < x – 2

-1 < 0 - 2

-1 < -2 (false)

At (1, 1), we have:

y > -2x + 3  

1 > -2(1) + 3

1 > -1 (true).

y < x – 2

1 < 1 - 2

1 < -1 (false)

At (3, 0), we have:

y > -2x + 3  

0 > -2(3) + 3

0 > -3 (true).

y < x – 2

0 < 3 - 2

0 < 1 (true).

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Answer:

The length of the rectangle is 17 yards and the width of the rectangle is 14 yards.

Explanation:

To find the perimeter of the rectangle, you had to add twice the length of the rectangle to twice the width of the rectangle since the shape of a rectangle is made up of two legs (each representing the rectangle's length) and two legs (each representing the rectangle's width.

The perimeter can be mathematically seen as p = 2l+2w, where p is the amount corresponding to the perimeter of the rectangle, l is the amount representing the length of the rectangle, and w is the quantity reflecting the width of the rectangle. This equation can be modified using the equation l = w+3, since it is given that the length is 3 yards longer than the width.

Therefore, the p = 2l+2w equation can be modified to solve for w using the given conditions and the equation defining l.

p = 2l+2w  

p = 2(w+3)+2w               [Substituting l = w+3]

p = 2w+6+2w

p = 4w+6

p-6 = 4w+6-6

p-6 = 4w

(p-6)/4 = 4w/4

w = (p-6)/4

w = (62-6)/4                  

w = 56/4

w = 14

Now the length of the rectangle can be determined using the equation l = w+3.

l = 14+3 = 17

Hope this helps Also Plz mark brainliest:)

Answer:

A

Step-by-step explanation:

By adding both the x and y coordinates individually and dividing them by two u get the mid point

Answer:

this question makes no sense

Step-by-step explanation:

This question doesn’t make sense, fix it

the solution of the given system of IVP isx(t) = \(7 [1] [2] [-2] e^(-t) + 10 [0] [0] [1] e^(2t) + 6 [0] [-1] [1] e^(2t)\)

Let's find out the eigenvalues of \(A|A - λI| = 0\)

Where, λ is the eigenvalue of the matrix A.I = Identity matrix of order 3|A - λI| = |3 -1 0| |1 2 -2| |0 0 1| - λ|1 0 0| |0 1 0| |0 -1 1| |0 0 1| |0 0 0| |0 0 0| |0 0 0|

Then, |A - λI| = [3 -1 0] [1 2 -2] [0 0 1] - λ[1 0 0] [0 1 0] [0 -1 1] [0 0 1] [0 0 0] [0 0 0] [0 0 0]= |3 -1 0| [2 2 -2] [0 0 1] - λ[0 0 0] [0 0 0] [0 -1 1] [0 0 1] [0 0 0] [0 0 0] [0 0 0]= [3 -1 0] [0 0 0] [0 0 0] - λ[0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0]= (3 - λ)(λ - 2)(λ - 2)

On solving, we get λ1 = -1, λ2 = 2, and λ3 = 2

Now, let's find the eigenvectors of A corresponding to the above eigenvalues.\((A - λ1I)x1\)= 0For λ1 = -1, we get (A + I)x1 = 0(A + I)x1 = [4 -1 0] [1 3 -2] [0 0 2] [1 0 0] [0 1 0] [0 0 1] [0 0 0] [0 0 0] [0 0 0]On solving,

we get the eigenvector corresponding to λ1 as x1 = [1] [2] [-2](A - λ2I)x2 = 0For λ2 = 2, we get (A - 2I)x2 = 0(A - 2I)x2 = [1 -1 0] [4 -6 2] [0 0 0] [1 0 0] [0 1 0] [0 0 1] [0 0 0] [0 0 0] [0 0 0]On solving,

we get the eigenvector corresponding to λ2 as x2 = [0] [0] [1](A - λ3I)x3 = 0For λ3 = 2, we get (A - 2I)x3 = 0(A - 2I)x3 = [1 -1 0] [4 -6 2] [0 0 0] [1 0 0] [0 1 0] [0 0 1] [0 0 0] [0 0 0] [0 0 0]

On solving, we get the eigenvector corresponding to λ3 as x3 = [0] [-1] [1]Thus, \(x = c1 x1 e^(-t) + c2 x2 e^(2t) + c3 x3\) \(e^(2t)\)where c1, c2, and c3 are constants.

Initial condition: x(0) = [7] [4 -2 0] [10] [4 -4 2] [2]x(0) = c1 [1] [2] [-2] + c2 [0] [0] [1] + c3 [0] [-1] [1]c1 = 7, c2 = 10, c3 = 6

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Answer:

If I entered it in correctly it would look something like this,,

Answer:

Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.

Step-by-step explanation:

Katarina's equation

4x - 2/3y = 8

In order to convert Katrina's linear equation into standard form,

She should find the least common denominator

4x - 2/3y = 8

{4x(3) - 2y(1)} / 3 = 8

(12x - 2y) / 3 = 8

Multiply both sides by 3

(12x - 2y) / 3 × 3 = 8 × 3

12x - 2y = 24

Divide both sides by 2

(12x - 2y) / 2 = 24 / 2

6x - y = 12

The advice sofiya gave Katrina is to Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.

Answer:

B) Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.

Step-by-step explanation:

edg2020

Answer:

its b i think

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

They can't add 5 into it because they are not like terms if it was 5h instead then yes you could but it is just 5.

D) y = 2x + 8

Parallel lines are coplanar lines that never intersect.

Parallel Slopes

All parallel lines have the same relationship between their slopes. For 2 lines to be parallel, their slopes must be equal. The question tells us that the slope of the first line is 2. This means that only answer choices B and D are viable.

The slopes of answer choices A and C are perpendicular to the line given.

Testing the Answers

Both B and D could be parallel to the line given; however, we are also told that the line must pass through (-2, 4). To see which answer is correct, we can plug in the x and y-values and solve. If a line passes through a point, then the equation will be true when the values are plugged in.

Let's start with answer B.

Since this statement is not true, we know that y = 2x + 4 does not pass through the point (-2, 4).

Next, we need to test answer choice D.

This is true, so y = 2x + 8 must pass through the point (-2, 4). Since answer choice D has a parallel slope and passes through (-2, 4), it must be the correct answer.

There is no graph in your question

To show the formation of a sulfide ion from a neutral sulfur atom, we need to add two electrons to the sulfur atom, as sulfide ion has a charge of -2. Therefore, the equation for this process is: S + 2e- → S2-

In this equation, S represents the neutral sulfur atom, while S2- represents the sulfide ion that is formed after the addition of two electrons. This reaction is a reduction reaction, as sulfur is gaining two electrons to form a negatively charged ion.
In summary, the equation S + 2e- → S2- shows the formation of the sulfide ion from a neutral sulfur atom by adding two electrons to it. This equation highlights the importance of electron transfer in chemical reactions and how it can lead to the formation of new compounds.

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Answer:

AB = 17, x = 6

Step-by-step explanation:

3x - 1 = 34 / 2

3x - 1 = 17

3x = 18

x = 6

AB = 17

x = 6

Answer:

this is the same quiestion i was doing if u get answer plz send me

Answer:

$100

Step-by-step explanation:

Given data

Principal = 500

Interest= 5%

Time = 4years

Applying the simple interest expression

SI= PRT/100

substitute

SI= 500*5*4/100

SI= 10000/100

SI= 100

Hence the interest after 4 years is $100

Answer:

7° F

Step-by-step explanation:

Originally the temperature was -5°.

It rose 12 degrees after that.

This means we have to add 12 degrees to the original temperature.

-5 + 12 = 7

So, on Tuesday, the temperature was 7° F.

Hope this helps! :)

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity is equal to the number of total observations (N) minus the number of groups (k). So, it can be represented as (N - k).

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity depend on the sample size and the number of groups being compared.

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Answer:

17/50 or 34/100

Step-by-step explanation:

12%(utilities)+22%(food)=34%=34/100

34/100=17/50

Answer:     162.1875%. Based on the given conditions, formulate: 103.8 / 64 Convert decimal to fraction:dfrac 1038/10 64Div

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

\(4 \times (4 - .4) -. 4\)

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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At the end of the eighth week, there will be 51,200 ants in the colony.

To determine the number of ants in the colony at the end of the eighth week, we need to consider that the number of ants doubles each week. Starting with 400 ants, we can calculate the number of ants at the end of each week using exponential growth.

Week 1: 400 ants

Week 2: 400 * 2 = 800 ants

Week 3: 800 * 2 = 1600 ants

Week 4: 1600 * 2 = 3200 ants

Week 5: 3200 * 2 = 6400 ants

Week 6: 6400 * 2 = 12800 ants

Week 7: 12800 * 2 = 25600 ants

Week 8: 25600 * 2 = 51200 ants

It's important to note that this calculation assumes ideal conditions of exponential growth and does not account for any factors that could limit or affect the ant population in real-life situations. Additionally, the actual growth of an ant colony may be influenced by various factors, such as resource availability, competition, and external threats.

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The possibility are 1,716 possible ways to cast the roles of Larry, Curly, and Moe from a group of 13 actors.

There are 13 actors auditioning for the roles of Larry, Curly, and Moe, there are 13 choices for who can be cast in the first role, 12 choices left for who can be cast in the second role, and 11 choices left for who can be cast in the third role (assuming that no actor can play more than one role).

To determine the number of ways the roles of Larry, Curly, and Moe could be cast with 13 different actors auditioning, we can use the concept of permutations.

In this case, we have 13 actors and 3 roles to fill, so we calculate it as follows:

Permutations = 13 * 12 * 11 Permutations

= 1,716

So, there are 1,716 different ways the roles of Larry, Curly, and Moe could be cast from the 13 actors auditioning.

Therefore, the number of ways the roles can be cast is:

13 x 12 x 11 = 1,716

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