Solve the following system of equations using substitution.
3m + 4n = - 12
n = - m - 2
A.m = -4, n = 2 O B.m = 4, n= -6
C. m = -8, n = 6 O D.m = 3, n = 1

Answer: the value of k is 3

Step-by-step explanation:

You have to find out what times 14 equals 42.

You divide 42 by 14 and then you get 3.

Hope this helps :)

a) Standard deviation of the sample mean = 1.27. b) the sample size must be at least 16 in order to halve the standard deviation of the sample mean.

a) To find the standard deviation of the sample mean, we can use the formula: Standard deviation of the sample mean = Standard deviation of the population / √(sample size)

Given that the variance of the population is 100, the standard deviation of the population is the square root of the variance, which is 10.

Plugging in the values, we have: Standard deviation of the sample mean = 10 / √62

Using a calculator, we can evaluate this expression to be approximately 1.27 (rounded to two decimal places).

Therefore, the standard deviation of the sample mean is approximately 1.27.

(b) To halve the standard deviation of the sample mean, we need to find the sample size that will make the denominator in the formula √(sample size) equal to half of its current value, which is √62.

Let's denote the desired sample size as N. We want: √N = (√62) / 2

Squaring both sides of the equation, we have:

N = (62 / 4)

N = 15.5

Since the sample size must be a whole number, we round up the value to the next integer.Therefore, the sample size must be at least 16 in order to halve the standard deviation of the sample mean.

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The correct decision rule for a test hypothesis with a significance level of 0.02, with two tails, is given as follows:

C. Reject H0 if Zstat< -2.33 or Zstat > +2.33.

The decision regarding the null hypothesis depends on if the p-value is less or more than the significance level:

For a two-tailed test with a significance level of 0.02, the critical value is given as follows:

z = 2.33.

Hence the decision rule is given as follows:

Hence option C is the correct option for this problem.

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Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

Key distinction between parametric tests and nonparametric tests in terms of scales of measurement is that  parametric tests are used for interval and ratio data and non parametric tests are used for ordinal and nominal data.

i.e., the last given option.

For interval and ratio data, parametric tests are employed, while non-parametric tests are used for ordinal and nominal data

Data containing discrepancies or intervals are displayed in interval data.

The ratio data, which may be added to, subtracted from, multiplied by, or split, is the one in which statistical conclusions are used.

Ordinal data are measurements of quantitative data that are in order, such height and weight.

Nominal data are those that we measure quantitatively but do not require order or sequence, such as hair color or eye color.

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Answer:

{2.86, 2.57}

Step-by-step explanation:

To solve a system of equations, you would want to use the eliminaton or the substitution method. These methods are sujective, so use the one you like the most. I will show you both methods to get a better understanding.

Elimination:

To do the elimination method, you will need to find common terms (x or y) and have an opposite each (-5 or 5). Look at the first equation. Now look at the second equation. Which equation do you think would need to be changed in order to receive a -5 and 5? The second equation. Multiply the second equation by -5. This would give you -5x-10y=-40. Now you are ready to add the two equations together. Notice how the x's cancel out. this leaves you with -14y=-36. To get the y by itself, you will need to divide each side by -14. You will soon get y=2.57. YOU ARE NOT FINISHED. You will need to get the x value. Take one of the equations and add substitute the y into it. Looking at both equations, the second one will be easier to substitue. By adding y into the mix, you will get x+5.14=8. Subtract 5.14 by both sides and you will get x=2.86. You solution should by {2.86, 2.57}.

Substitution:

to do the substitution method, you will look for a variable that is isolated from a coefficient. As seen in the second equation, x is isolated. Use the second equation to isolate x on one side of the equal sign. You would end up with x=8-2y. Substitute the x into the first equation. This would look somethign like this: 5(8-2y)-4y=4. Multiply what is needed. You should end up wiht 40-10y-4y=4. Combine the like terms of the y: 40-14y=4. Subtract 40 from both sides. You should end up with -14y=-36. DOESN'T THIS LOOK FAMILIAR!!! To get the y by itself, you will need to divide each side by -14. You will soon get y=2.57. You will need to get the x value. Take one of the equations and add substitute the y into it. Looking at both equations, the second one will be easier to substitue. By adding y into the mix, you will get x+5.14=8. Subtract 5.14 by both sides and you will get x=2.86. You solution should by {2.86, 2.57}.

Answer:

Jamie has a  foot plank that he needs to cut into 1/9 pieces.

15 ÷ 1/9 = 135  

135 x 1/9 = 15

Step-by-step explanation:

The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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Answer:

\(2c - 3\)

Step-by-step explanation:

\(3c - \frac{1}{3} = \frac{c}{2} = 2c - \frac{1}{3} (2) = 2c - \frac{2}{6} = 2c - 3\)

The sοlutiοn οf the given prοblem οf interest cοmes οut tο be Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.

Tο calculate the simple interest rate, divide the amοunt by the cοst οf financing, the amοunt οf time left, and οther variables. The simple return strategy in marketing is principal student lοans hrs. This methοd is the mοst basic methοd fοr figuring οut invοlvement. The mοst typical methοd fοr calculating incοme is as a share οf the principal amοunt. Tο put this intο perspective, if he wants tο bοrrοw $100 frοm a single οf these friends .

Here,

a. The fοllοwing methοd can be used tο determine the mοnthly payment fοr a lοan:

=> The mοnthly payοut =  (P*r) / (1 - (1+r)(-n)).

We must first determine the entire lοan amοunt, including interest, that Reh must pay back. After 4.5 years οf interest accrual, the lοan sum is:

=>  \(9900 \times (1 + 0.0429/12)^{(12 \times 4.5)\) = 12,723.97

The οverall debt balance is $12,723.97.

The numbers can then be entered intο the fοrmula as fοllοws:

=>  (12723.97*(0.0429/12)) / (1 - (1+(0.0429/12))(-12*10))

is the fοrmula fοr the mοnthly payοut.

Payment due each mοnth: $131.19 (rοunded tο the nearest dοllar)

Reh's mοnthly payment is therefοre $131, rοunded tο the clοsest dοllar.

b. The fοllοwing fοrmula can be used tο determine the tοtal interest charged οver the lοan's term:

=> tοtal interest = (mοnthly payment X n) - P .

There have been a tοtal οf:

=> 120 is equal tο ten years times οne year.

The entire interest paid is thus:

=> ($3,943.80) (tοtal mοnthly installments * n) - P

=> (131.19 * 120) - 9900 (rοunded tο the nearest dοllar)

Sο, rοunded tο the clοsest dοllar, Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.

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Answer:

A)let x be the length of one side , 6 × x= peri.

B)6 × 11 = 66

As you consider the various factors involved in starting a group, the most important factor you have to judge is the group's purpose or goal.

Step 1: Identify the group's purpose or goal - This is crucial because it will guide all other decisions, including membership criteria, communication methods, and meeting schedules.

Step 2: Assess the needs and resources of potential members - This will help you understand their motivations and ensure the group can support their needs while accomplishing its goal.

Step 3: Establish clear membership criteria and expectations - This will ensure that everyone in the group is on the same page and committed to the same goals.

Step 4: Choose an appropriate communication method - This will facilitate smooth and efficient communication among group members.

Step 5: Develop a meeting schedule that works for all members - Regular meetings help keep the group on track and provide opportunities for collaboration and feedback.

By focusing on the group's purpose or goal, you can create a solid foundation for a successful and productive group.

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Answer:

The maximum value of the function is 4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The total cost of the ordered packages for the school picnic  based on the price of items in the list is $113.

Price list

Cost based on number of each items purchased :

The total cost of purchases:

$(80.00 + $32.00 + $1.00) = $113.00

Therefore  the total cost of the ordered packages is $113.00

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To calculate \(\frac{{f(x+h) - f(x)}}{h}\) for the function \(f(x) = ax^3\), we need to substitute the expressions into the formula and simplify.

\(f(x+h) = a(x+h)^3\\\\f(x) = ax^3\)

Now we can calculate the difference:

\(f(x+h) - f(x) = a(x+h)^3 - ax^3\)

Expanding \((x+h)^3\):

\(f(x+h) - f(x) = a(x^3 + 3x^2h + 3xh^2 + h^3) - ax^3\)

Simplifying:

\(f(x+h) - f(x) = ax^3 + 3ax^2h + 3axh^2 + ah^3 - ax^3\)

The terms \(ax^3\) cancel out:

\(f(x+h) - f(x) = 3ax^2h + 3axh^2 + ah^3\)

Now we can divide by h:

\(\frac{{f(x+h) - f(x)}}{h} = \frac{{3ax^2h + 3axh^2 + ah^3}}{h}\)

Canceling out the common factor of h:

\(\frac{{f(x+h) - f(x)}}{h} = 3ax^2 + 3axh + ah^2\)

Now, we evaluate this expression again by setting h = 0:

\(\frac{{f(x+h) - f(x)}}{h} = 3ax^2 + 3ax(0) + a(0)^2\)

\(= 3ax^2\)

Therefore, when we evaluate the expression by setting h = 0, we get \(3ax^2\).

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The following is one of the requirements for using a one-way, between-subjects Anova is the data must be measured on a continuous scale.

One of the requirements for using a one-way, between-subjects ANOVA is that the data must be measured on a continuous scale. This means that the variable being measured (such as time, weight, or temperature) should be able to take on any value within a certain range.

Another requirement for using a one-way, between-subjects ANOVA is that the data must be independent. This means that the observations for each group should not be related to one another in any way. For example, if the groups being compared are different treatment groups in a medical study, it would not be appropriate to use a one-way, between-subjects ANOVA if the patients in each group were related to one another (such as siblings or close friends).

The third requirement is that the data should be approximately normally distributed in each group. A normal distribution is a probability distribution that has a bell shape, which means that the data is symmetric and the mean, median, and mode are equal. The ANOVA assumes that the data is normally distributed and if the data is not normally distributed, the results may be unreliable. This requirement can be checked by using normality test such as Shapiro-Wilk test.

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Answer:

96 liters

Step-by-step explanation:

Two liters are in each bottle, so that means they sold 12 bottles of oil each day. Multiply that with 8 days to get the answer:

12 × 8 = 96

Ninety-six liters.

Answer:

59

Step-by-step explanation:

The equation is

944 - 5x = 1180 - 9x

Notice what is being said. You start with 944 gallons and take off 5 per week

You also start with 1180 gallons and take on 9 per week.

You want to know when the two are equal. The second tank is larger, but it leaks more. That's what's going to bring about equality.

Add 9x to both sides

944 - 5x + 9x = 1180

944 + 4x = 1180                

Subtract 944 from both sides.

4x = 1180 - 944

4x = 236      

Divide by 4

x = 236/4

x = 59 weeks

Answer:

m<-1 and 13/15

Step-by-step explanation:

To find f'(-1), we need to take the derivative of f(x) and then evaluate it at x = -1. Using the chain rule, we get: f'(x) = 8x + 8 / (4x^2 + 8x + 5), f'(-1) = 8(-1) + 8 / (4(-1)^2 + 8(-1) + 5), f'(-1) = -8 + 8 / 1, f'(-1) = 0. So, f'(-1) = 0. We don't need to round to 3 decimal places in this case since the answer is an integer.

To find f'(-1) for f(x) = ln(4x^2 + 8x + 5), we first need to find the derivative of the function with respect to x, and then evaluate it at x = -1. Here's the step-by-step process:

1. Identify the function: f(x) = ln(4x^2 + 8x + 5)
2. Differentiate using the chain rule: f'(x) = (1 / (4x^2 + 8x + 5)) * (d(4x^2 + 8x + 5) / dx)
3. Find the derivative of the inner function: d(4x^2 + 8x + 5) / dx = 8x + 8
4. Substitute the derivative of the inner function back into f'(x): f'(x) = (1 / (4x^2 + 8x + 5)) * (8x + 8)
5. Evaluate f'(-1): f'(-1) = (1 / (4(-1)^2 + 8(-1) + 5)) * (8(-1) + 8)
6. Simplify the expression: f'(-1) = (1 / (4 - 8 + 5)) * (-8 + 8)
7. Continue simplifying: f'(-1) = (1 / 1) * 0
8. Final answer: f'(-1) = 0

Since f'(-1) is an integer, there is no need to round to any decimal places f'(-1) = 0.

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Answer: \(\frac{y}{7} \geq 18\)

Step-by-step explanation:

Key things to remember:

- quotient signals dividing

- at least means greater than or equal to, so we use the greater than or equal to sign

Applying this to the problem, we can translate into a simpler sentence:

y divided by 7 is greater than or equal to 18 --> which leads us to the inequality above

The probability of of a random student having blue eyes and dark hair

 is 35% .

let consider the total students in the school be (U) = 100%

out of them ,

students having blue eyes (A) = 60%

students having  dark hair (B) = 55%

students with neither blue eyes nor dark hair (A∪B)' = 20%

let the students with blue eyes and dark hair be (A∩B) = x %

Then according to the set theorem

U = n(A∪B) + n(A∪B)'

U = n(A) + n(B) - n(A∩B) + n(A∪B)'

100 = 60 + 55 - x +20

∴ x = 60 + 55 +20 - 100

x = 35 %

So the probability of random student having blue eyes and dark hair is 35% .

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The required linear model is y = 3968.75x + 63,500 that represents the amount of fuel on the plane (as y), in gallons, as a function of the flight time(as x), in hours.

A linear function is defined as an equation in which the highest exponent of the variable is always one.

The graph is given in the question, as shown

Let y be represents the amount of fuel on the plane, in gallons,

And x represents the function of the flight time, in hours.

As per the given graph, we take two points (0, 63,500) and (16, 0)

y - 63,500 = [(0-63,500)/(16-0)](x-0)

y - 63,500 = (63,500/16)x

y - 63,500 = 3968.75x

y = 3968.75x + 63,500

Thus, the required linear model is y = 3968.75x + 63,500.

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Answer:

The answe is b

Step-by-step explanation:

Because when u calculat,you’ll only get 1 answer.

pls mark BRAINLIEST

Answer:

C

Step-by-step explanation:

A line segment has two points; it does not go on forever.

A line has rays on either end, so it would go forever in both directions, not one direction.

a) The function gof is gof(x) = 3x + 3.

b) The function gof: RR is well-defined.

a. The value of function gof(x) = 3x + 3.

To find the composition gof, we substitute the expression for g into f:

gof(x) = f(g(x))

= f(x + 1)

= 3(x + 1)

= 3x + 3

b. To prove that gof is both one-to-one and onto, we need to show the following:

(i) One-to-one: For any two different inputs x1 and x2, if gof(x1) = gof(x2), then x1 = x2.

(ii) Onto: For every y in the range of gof, there exists an x such that gof(x) = y.

Proof of one-to-one:

Let x1 and x2 be two different inputs. Assume that gof(x1) = gof(x2).

Then, 3x1 + 3 = 3x2 + 3.

Subtracting 3 from both sides, we have 3x1 = 3x2.

Dividing both sides by 3, we obtain x1 = x2.

Therefore, gof is one-to-one.

Proof of onto:

Let y be any real number in the range of gof, which is the set of all real numbers.

We need to find an x such that gof(x) = y.

Consider the equation 3x + 3 = y.

Subtracting 3 from both sides, we have 3x = y - 3.

Dividing both sides by 3, we obtain x = (y - 3)/3.

Thus, for any y in the range of gof, we can find an x such that gof(x) = y.

Therefore, gof is onto.

Since gof is both one-to-one and onto, it is a bijection.

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Answer:

-2x+19

Step-by-step explanation:

We open the parentheses, so

-12x+15+10x+4

Simplify

-2x+19