what is the solution to the system of equations? 3x-2y=19 y=x-7
A) (6,-1)
B) (33,26)
C) (1,-6)
D) (5,-2)

Answer:

9) m^2 - 81 = 0

solution,

here,

m^2 - 81 = 0

or, m^2 = 81

or, m^2 = 9^2

or, m = 9 ( removing or cutting both square)

Therefore; m =9

Answer:

Quadratic Equation | Factoring

Solve each quadratic equation using factoring.

1) v² + 5v + 6 = 0

doing middle term factorisation

v²+(3+2)v+6=0

v²+3v+2v+6=0

v(v+3)+2(v+3)=0

(v+3)(v+2)=0

either

v=-3

or

v=-2

2) g² - 3g = 4

keeping all terms in one side

g²-3g-4=0

doing middle term factorisation

g²-(4-1)g-4=0

g²-4g+g-4=0

g(g-4)+1(g-4)=0

(g-4)(g+1)=0

either

g=4

or

g=-1

3)w² + 4w = 0

w(w+4)=0

either

w=0

or

w=-4

4) s² - 8s + 12 = 0

doing middle term factorisation

s²-(6+2)+12=0

s²-6s-2s+12=0

s(s-6)-2(s-6)=0

(s-6)(s-2)=0

either

s=6

or

s=2

5) x ²+ 2x - 35 = 0

doing middle term factorisation

x²+(7-5)x-35=0

x²+7x-5x-35=0

x(x+7)-5(x+7)=0

(x+7)(x-5)=0

either

x=-7

or

x=5

6) r(r + 2) = 99

opening bracket

r²+2r=99

keeping all terms in one side

r²+2r-99=0

r²+(11-9)r-99=0

r²+11r-9r-99=0

r(r+11)-9(r+11)=0

(r+11)(r-9)=0

either

r=-11

or

r=9

7)k(k-4)=-3

opening bracket

k²-4k=-3

keeping all terms in one side

k²-4k+3=0

k²-(3+1)k+3=0

k²-3k-k+3=0

k(k-3)-1(k-3)=0

(k-3)(k-1)=0

either

k=3

or

k=1

8)t²+ 3t + 2 = 0

doing middle term factorisation

t²+(2+1)t+2=0

t²+2t+t+2=0

t(t+2)+1(t+2)=0

(t+2)(t+1)=0

either

t=-2

or

t=-1

9)m ^ 2 - 81 = 0

m²=81

doing square root in both side

\(\sqrt{m²}=\sqrt{9²}\)

m=±9

either

m=9

or

m=-9

10) h²- 17h + 70 = 0

doing middle term factorisation

h²-(10+7)h+70=0

h²-10h-7h+70=0

h(h-10)-7(h-10)=0

(h-10)(h-7)=0

either

h=10

or

h=7

Answer:

A quotient is the number we get when we divide one number by another.

for example

8 ÷ 4 = 2. In this case, the number 2 will be the quotient since it is the result we got when we divided 8 and 4.

I'm going to assume that "1,457 . 47 =" was meant to have a division sign, if that is the case then the answer is B 31.

Answer:

\(\frac{5}{2}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{2}{5}\) x + 3 ← is in slope- intercept form

with slope m = - \(\frac{2}{5}\)

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{2}{5} }\) = \(\frac{5}{2}\)

The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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The proof that shows that ΔPRS ≅ ΔQSR by HL congruence theorem is explained below.

The HL congruence theorem can be used to prove that two triangles are congruent to each other if we can show that the two triangles are right triangles that have a pair of corresponding congruent legs, and a pair of congruent hypotenuse.

The proof for stating that triangles PRS and QSR are congruent is given below.

Statement                                          Reasons                                                  

1. QS ≅ PR, PS ⊥ RS, QR ⊥ RS          1. Given

2. <RSP and <SRQ are right angles  2. Definition of perpendicular

3. SR ≅ RS                                          3. Reflexive property of congruency

4. ΔPRS ≅ ΔQSR                                4. HL

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i) Null hypothesis: Proportion of Americans who believe that nuclear capabilities of other countries seriously threaten world peace is equal to 2/3.

Alternative hypothesis: Proportion of Americans who believe that nuclear capabilities of other countries seriously threaten world peace is different from 2/3.

ii) Null hypothesis: Proportion of gaming headsets with manufacturing flaws that make game-play impossible is less than or equal to 9%. Alternative hypothesis: Proportion of gaming headsets with manufacturing flaws that make game-play impossible is greater than 9%.

iii) Null hypothesis: Mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe is less than or equal to 106°F. Alternative hypothesis: Mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe is greater than 106°F.

In hypothesis testing, the null hypothesis is the default assumption, while the alternative hypothesis is what the researcher wants to prove.

The next step is to conduct a hypothesis test, where a test statistic is calculated, and its probability of occurrence is determined assuming that the null hypothesis is true.

If this probability is very small (usually less than 5%), then the null hypothesis is rejected in favor of the alternative hypothesis.

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Complete Question

1. For the following scenarios, state the null hypothesis and the alternative hypothesis to be used when a hypothesis test is performed.

Scenario i) After the Cold War, it was claimed that two of three Americans say that the chances of world peace are seriously threatened by the nuclear capabilities of other countries. Is there evidence that this proportion is actually different? To investigate this, a random sample of 400 Americans was taken, and it was found that only 248 hold this view.

Scenario ii) JP wants to test whether at least 9% of gaming headsets have manufacturing flaws that make game-play impossible. A sample of 150 headsets revealed that 12 contained a defect.

Scenario iii) The mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe should be no more than 106°F. Past experience has indicated that the standard deviation of temperature is 2°F. The water temperature is measured on nine randomly chosen days, and the average temperature is found to be 99°F

Answer:

x = -1

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define equation

5x - (x + 4) + 1 = 3 - 2(x + 6)

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

Answer:

ANSWER, A

Step-by-step explanation:

\(\frac{x^{2} }{20} +\frac{y^{2} }{36} =1\)

The conclusion of the hypotheses is that: We will reject the Null hypothesis and conclude that the median number of part-time employees has increased

Let the significance level be: α = 0.5

Since we want to find out whether the median number of part-time employees has increased, then:

Number of restaurants that have more than 18 part-time employees = 7 (+ve )

Number of restaurants that have less than 18 part-time employees = 1 (-ve)

Number of restaurants with exactly 18 part-time employees = 1

Let us first define the hypotheses:

Null hypothesis : H₀ : median ≤ 18

Alternate hypothesis : Hₐ : median ≥ 18

Sample size: = 7 + 1 = 8

The actual hypothesis that should be tested is:

H₀ : p = 0.5

Hₐ : p ≠ 0.5

Applying the binomial distribution to get the number of +ve signs:

nP = 8(0.5)

= 4 +ve signs ( Thus, it is a right tailed test which is the upper tail of the binomial distribution )

P ( ≥ 7 )+ve signs  = p(7) +ve signs  + p(8) +ve signs

P ( ≥ 7 )+ve signs = 0.0313 + 0.0039 = 0.0352

P-value = 0.0352 < 0.05  

Thus, we will reject the Null hypothesis and conclude that the median number of part-time employees has increased

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Complete question is:

The median number of part-time employees at fast-food restaurants in a particular city was known to be 18 last year. City officials think the use of part-time employees may be increasing. A sample of nine fast-food restaurants showed that seven restaurants were employing more than 18 part-time employees, one restaurant was employing exactly 18 part-time employees, and one restaurant was employing fewer than 18 part-time employees. Can it be concluded that the median number of part-time employees has increased

Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures in the context of a problem are found using basic arithmetic operations such as multiplication and division.

One application of proportions is for ratio problems, as fractions are built from the ratios to find the equivalent amounts.

Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza, hence the fraction of Pepperoni pizzas out of the total is given by:

Pepperoni = 7/(10 + 7 + 5 + 8) = 7/30 of the total.

If 35 pepperoni pizzas were ordered, the total number is found as follows:

7x/30 = 35

7x = 30 x 35

x = 30 x 5

x = 150 pizzas.

2 out of every 25 pizzas were burned, hence the number of burned pizzas is given by:

2/25 x 150 = 2 x 6 = 12 pizzas.

The cheese fraction is given by:

10/30.

Hence, out of 360 pizzas, the number is given by:

10/30 x 360 = 10 x 12 = 120 cheese pizzas

The mushroom fraction is given by:

8/30.

Hence, out of 360 pizzas, the number is given by:

8/30 x 360 = 8 x 12 = 96 mushroom pizzas

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Answer:

What does the "+8" mean in the expression 2x + 8?

The +8 is the 8 more advertisement orders received on Friday.

It's 8 more than x.

How many more advertisements were ordered on Friday than Thursday

8

The number of days

2

The number of advertisement ordered on Friday

x + 8

The total number of advertisement on both days

2x + 8

Answer:

A

Step-by-step explanation:

I took the test

Answer:

x=0

This can be solved by reasoning.

And confirmed by substituting 0 into the expression.

Answer:

The sample means for three samples of 20 are shown in the table.

A 3-column table with 3 rows. Column 1 is labeled Sample with entries Sample 1, Sample 2, Sample 3. Column 2 is labeled Sample Mean with entries 12, 8, 16. Column 3 is labeled Actual mean with entries 10.5, 10.5, 10.5.

Compute the variation of each predicted population mean from the sample means in the tabl

Step-by-step explanation:

Answer:

3x + 5y ≤ 480

Step-by-step explanation:

Let x = number of 15-inch laptops.

Let y = number of 17-inch laptops.

3x + 5y ≤ 480

Answer:

1

Step-by-step explanation:

Yes the answer is just 1

Since the power of 2 in the inside will be multiplied by the power of the 4 in the outside will be 8 (The number 11 doesn't change)

A power divided by a power that is equivalent to it is 1

The maximum amount of new loans this bank can make is $8,000.

To determine the maximum amount of new loans a bank can make, we need to consider the bank's required reserves and the money multiplier. Required reserves refer to the portion of deposits that banks are legally required to hold as reserves and not loan out. The money multiplier represents the potential expansion of the money supply through the lending process.

In this case, the bank has a required reserve ratio of 20% and a new deposit of $510,000. The required reserves can be calculated by multiplying the new deposit by the required reserve ratio: $510,000 * 20% = $102,000.

Now, let's calculate the maximum amount of new loans the bank can make. It can lend out the excess reserves, which is the difference between the total reserves and the required reserves. The total reserves are equal to the bank's existing reserves plus the new deposit: $100,000 + $510,000 = $610,000. Therefore, the excess reserves are $610,000 - $102,000 = $508,000.

Since the bank can lend out a portion of its excess reserves, we multiply the excess reserves by the money multiplier. In this case, the money multiplier is 5. Therefore, the maximum amount of new loans the bank can make is $508,000 * 5 = $2,540,000.

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Answer:3(b+6)

Step-by-step explanation:

The factorization of the expression is 3(b+6).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is 3b + 18​. The factorization of the expression will be done as,

E = 3b + 18

Take 4 as common from the above expression.

E = 3b + 18

E = 3(b+6).

Therefore, the factorization of the expression is  3(b+6).

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Answer: 4π cm or 12.56 cm

Step-by-step explanation: To find the circumference of this circle, start with the formula for the circumference of a circle which is C = 2πr.

Since the radius is 2 centimeters, we can

plug in 2 centimeters for r in the formula.

So we have (2)(π)(2 cm) which is equal to 4π cm.

So the circumference of this circle is 4π cm.

Remember that π is approximately equal to 22/7 or 3.14 so we can estimate the value of the circumference by plugging in 3.14 for π.

So we have (4)(3.14) which is equal to 12.56.

So the circumference of the circle is

approximately equal to 12.56 cm.

a) To find the moment generating function (MGF) for x, we use the formula:

M(t) = E(e^(tx))

where E denotes expected value. Since x has a probability density function (PDF), we integrate the expression e^(tx) times the PDF over all possible values of x to find the expected value:

M(t) = ∫ e^(tx) f(x) dx

where f(x) is the given PDF for x. Substituting the given PDF, we get:

M(t) = ∫ e^(tx) (2/3) x^2 dx    (from x = 0 to x = 1)

Evaluating the integral, we get:

M(t) = (2/3) ∫ e^(tx) x^2 dx

We can use integration by parts twice to evaluate this integral, or we can look it up in a table of integrals to find:

M(t) = (2/3) (2/(t^3)) (e^t - 1 - t)

Therefore, the moment generating function for x is:

M(t) = (4/(3t^3)) (e^t - 1 - t)

b) To compute the first moment, we differentiate the MGF once with respect to t and evaluate at t = 0:

E(x) = M'(0) = (4/(3t^4)) (te^t - 3e^t + 3)

Evaluating at t = 0, we get:

E(x) = 1

Therefore, the first moment of x is 1.

To compute the second moment, we differentiate the MGF twice with respect to t and evaluate at t = 0:

E(x^2) = M''(0) = (4/(3t^5)) ((t^2 + 2t) e^t - 4te^t + 6e^t)

Evaluating at t = 0, we get:

E(x^2) = 2

Therefore, the second moment of x is 2.

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Answer:

the change in Jason's position relative to the leader per minute is [-] ft/minute.

Step-by-step explanation:

First, we need to convert 1 3/4 minutes to fractional minutes. We can do this by expressing 1 3/4 as 7/4 minutes.

Next, we need to find the change in Jason's position relative to the leader in fractional minutes. We can do this by dividing Jason's position relative to the leader by the time in fractional minutes: -11 1/5 feet / (7/4 minutes) = -33/5 feet / (7/4 minutes).

Finally, we need to convert this result to feet per minute. We can do this by multiplying the numerator by the reciprocal of the denominator: -33/5 feet / (7/4 minutes) = -(33/5 feet) * (4/7 minutes/feet) = -24/7 feet/minute.

The change in Jason's position relative to the leader per minute is -24/7 feet/minute. The negative sign indicates that Jason's position relative to the leader decreased over time.

In simplified form, the change in Jason's position relative to the leader per minute is [-] ft/minute.

The rank of the controllability matrix is 2, which is equal to the order of the system, the system is controllable.

Given, \({A}=\[\begin{bmatrix}-1 & 0 \\ 0 & -2\end{bmatrix}\] \\\\\)

\({B}=\[\begin{bmatrix}1 \\ 1\end{bmatrix}\)

The continuous-time system can be represented as below;

\(\[\dot{\vec{x}}={A}\vec{x}+{B}u(t)\]\)

Where \(\[\vec{x}\]\) is the state vector, and u(t) is the input to the system.

To check if the system is controllable or not, we need to calculate the controllability matrix.

\(\[{\mathcal{C}}=\begin{bmatrix}{B} & {A}{B}\end{bmatrix}=\begin{bmatrix}1 & -1 \\ 1 & -2\end{bmatrix}\]\)

The system is said to be controllable if the controllability matrix has full rank. Here, rank \(\[\begin{Bmatrix} {\mathcal{C}}\end{Bmatrix}=2\]\)

Therefore, the rank of the controllability matrix is 2, which is equal to the order of the system, the system is controllable.

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The complete question is;

Consider the continuous-time system for which \({A}=\left[\begin{array}{rr}-1 & 0 \\ 0 & -2\end{array}\right], {B}=\left[\begin{array}{l}1 \\ 1\end{array}\right]\) find the rank of controllability matrix.

We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752.

The correct practical interpretation is: "We are 95% confident that the proportion of all central Florida reefers who use led lighting falls between .648 and .752."

This means that if we were to take multiple random samples of 700 experienced central Florida reefers, 95% of the intervals created would contain the true population proportion of reefers who use LED lighting.

So, based on this sample, we can say with 95% confidence that the true proportion of all central Florida reefers who use LED lighting is somewhere between .648 and .752.

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We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752 from mean.

The correct practical interpretation is: "We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752." This means that based on the sample of 700 experienced reefers, we can estimate with 95% confidence that the true proportion of all reefers in central Florida who use LED lighting is likely to be between .648 and .752.

This confidence interval was constructed using sampling techniques, and in repeated sampling, 95% of the intervals created would contain the population mean.
We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752.

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Answer:

1% of 37.25=0.3725

If we write the first integer as the variable n, all numbers that come after it can be written as n+1, n+2, etc.

so the sum of four consecutive integers is:

sum = n + (n+1) + (n+2) + (n+3)

if we simplify:

sum = 4n +6

and if we want to know what the first integer is, we can re-write the equation as:

\(\frac{sum-6}{4}\) = n

and that is your answer.

Answer:

I am just answering so that potato can get brainliest

Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

Answer:

x = \(\frac{17}{5}\)

Step-by-step explanation:

(8x - 12) = (3x + 5) ← remove parenthesis

8x - 12 = 3x + 5 ( subtract 3x from both sides )

5x - 12 = 5 ( add 12 to both sides )

5x = 17 ( divide both sides by 5 )

x = \(\frac{17}{5}\)

or x = 3.4 ( in decimal form )

When we carry out a chi-square goodness-of-fit test for a normal distribution, the null hypothesis states that the population does have a normal distribution.

The null hypothesis states that the population has a normal distribution The chi-square goodness-of-fit test is not specifically used for testing the normal distribution. It is typically used to test whether observed data follows an expected theoretical distribution In the case of a chi-square goodness-of-fit test for a normal distribution, the null hypothesis would state that the observed data follows a normal distribution.

The chi-square goodness-of-fit test is a statistical test used to determine if there is a significant difference between the observed frequencies in a sample and the expected frequencies based on a theoretical distribution or model The null hypothesis in a chi-square goodness-of-fit test states that the observed data follows the expected distribution or model. The alternative hypothesis suggests that there is a significant difference between the observed and expected frequencies.

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Answer:

above sea level

Step-by-step explanation: