Which of the values in the set {1, 2, 3, 4} is a solution to the equation 3x + 3 = 15? (4 points) Group of answer choices 1 3 4 2

Answer:

-6,3

Step-by-step explanation:

Answer:

If it is M x N then it is 161.

If it is 63 x M x N then it is 10,143.

The determinant of the matrix D obtained by adding 4 times the third row to the second row of the 5x5 matrix A is 24.

Waht is the matrix?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. In mathematics, matrices are used to represent and manipulate linear transformations, such as rotations, scalings, and shears, in a vector space.

The determinant of a matrix is a scalar value that represents the magnitude of the matrix and the change it induces in a vector space. The determinant of a matrix is a linear function of the rows or columns of the matrix, meaning that adding a multiple of one row (or column) to another row (or column) will multiply the determinant by the same scalar.

In this case, if we add 4 times the third row to the second row of the 5x5 matrix A, the determinant of the resulting matrix D will be multiplied by the scalar 4:

det(D) = 4 * det(A) = 4 * 6 = 24

Hence, the determinant of the matrix D obtained by adding 4 times the third row to the second row of the 5x5 matrix A is 24.

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Answer:

These are confusing Beth , b/c you have to remember that they will add to 100%

Step-by-step explanation:

so

green = 3*  yellow

100% = green + yellow + 35% + 25%

100% = 3* yellow + yellow +60%

40% = 4* yellow

10% = yellow

30% = green

there are 14 purples in the bag , which is 35% of total

14/.35 = 40

there are a total of 40 pins

so

4    are yellow  (10% of 40  or 40* 0.1)

12 are green    (30% of 40  or 40*0.3)

14  are purple  (35% of 40 or 40*0.35)

10  are grey  (25% of 40  or 40*0.25 )

see?  : |

Answer:

Step-by-step explanation:

(a+2,b)=(4,5)

Since the points are equal we can equate them to find a

Comparing a + 2 to 4

We have

a + 2 = 4

Send 2 to the right side of the equation

a = 4 - 2

We have the final answer as

Hope this helps you

Step-by-step explanation:

Here,

according to the question,

(a+2, b)=(4,5)

since, they are equal, equating with their corresponding elements we get,

(a+2)=4

or, a= 4-2

Therefore, the value of a is 2.

Also you can find value of b in same way,

b=5.

Therefore, the value of a abd b are 2 and 5 respectively.

Hope it helps...

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Stanton uses the phrase "high carnival" (line 15) mainly to emphasize what she sees as: utter domination of women by men (option A).

In a comprehension passage, some questions are given that follow the passage. The questions are to be answered by using the data given in the passage, even if it differs from real-life facts.

Now,

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The measure of angle BCA is 81 degrees.                                            

The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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Answer: 72 degrees

Step-by-step explanation:

ok, so the interior angles of a pentagon are 108 degrees, and the line that the two angles are on is equal to 180 degrees, so 180-108 is 72 degrees

The correct answer is the minimal cover of F is:F = {AB→C, AB→S, AB→E, ES→S}

Given, relation schema R(ABC,DE) with functional dependencies F:AB→SCDE→ABAB→SEES→C.

The candidate key of a relation R is a minimal set of attributes that can uniquely identify each tuple in R. To find the candidate key, we can compute the closure of each subset of attributes in R. Let's begin by finding the closure of AB, the subset of R. We can use the functional dependency AB→SC to compute the closure of AB as follows: AB+ = ABSC (by AB→SC)

Next, let's compute the closure of DE, the other subset of R. We can use the functional dependency DE→AB to compute the closure of DE as follows: DE+ = DEABSE (by DE→AB and AB→SE)

Now we have two potential candidate keys, AB and DEABSE. However, we need to check if they are minimal. To do this, we check if any subset of these candidate keys can also function as a candidate key. We can see that neither AB nor DEABSE has any proper subset that can function as a candidate key.

Therefore, both AB and DEABSE are candidate keys for the relation R. Next, let's compute the minimal cover of F. The minimal cover of a set of functional dependencies F is a minimal set of functional dependencies that is equivalent to F.

To find the minimal cover of F, we can use the following steps:

Step 1: Eliminate redundant dependencies. We can eliminate the dependency AB→SC since it is implied by AB→C.

Step 2: Decompose dependencies. We can decompose the dependency AB→SE into two dependencies, AB→S and AB→E, since S and E are not a subset of any other attribute set in F.

Step 3: Eliminate extraneous attributes. We can eliminate the attribute C from the dependency ES→C since C is already determined by AB→C.

Therefore, the minimal cover of F is:F = {AB→C, AB→S, AB→E, ES→S}

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The solution of the systems of linear equations is x = 13.81 and y = 73.381. The average salaries were equal in the year 1999. The average salary that year was about $73381.

What is the system of linear equation?

A collection of two or more linear equations is a system of linear equations. The graph of a system of two equations is a pair of lines in the plane for two variables (x and y).

The intersection point of the lines is ( 13.81, 73.381).

The average salaries were equal after 14 years since 1985.

The average salaries were equal (1985 + 14) = 1999.

The average salary that year was about $73381.

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Step-by-step explanation:

angles in a triangle add up to 180°

90° + 60° + a = 180°

a = 180° - 90° - 60°

a = 30°

so the unknown angle in the triangle is 30°

90/32 = 30/x

90 × x = 30 × 32

90x = 960

90x/90 = 960/90

x = 10.7

60/y = 90/32

90 × y = 60 × 32

90y = 1920

90y/90 = 1920/90

y = 21.3

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-8}-\underset{x_1}{(-4)}}}\implies \cfrac{-10}{-8+4}\implies \cfrac{-10}{-4}\implies \cfrac{5}{2}\)

Answer:

x = -17

Step-by-step explanation:

7(2x + 3) = 12x - 13

Distribute

7*2x +7*3 = 12x-13

14x +21 = 12x-13

Subtract 12x from each side

14x-12x+21 = 12x-12x-13

2x+21 = -13

Subtract 21 from each side

2x+21-21 = -13-21

2x = -34

Divide by 2

2x/2 = -34/2

x = -17

Answer:

Step-by-step explanation:

The missing reasons are Cofunction identity, Cosine difference identity, Cofunction identity, Cosine function is even and sine function is odd respectively.

Given:

The given expression is \(\sin (x-y)\).

To find:

The justification for each step.

Explanation:

Cofunction identities:

\(\sin\left(\dfrac{\pi}{2}-x\right)=\cos x\)

\(\cos\left(\dfrac{\pi}{2}-x\right)=\sin x\)

Cosine difference identity:

\(\cos(x-y)=\cos x\cos y+\sin x\sin y\)

Cosine function is even, so \(\cos(-x)=\cos x\).

Sine function is odd, so \(\sin(-x)=-\sin x\).

We have,

\(\sin (x-y)\)

\(=\cos\left|\dfrac{\pi}{2}-(x-y)\right|\)                                             Step 1: Cofunction identity

\(=\cos\left|\dfrac{\pi}{2}-x+y\right|\)                                                 Step 2: Distributive property

\(=\cos\left|\left(\dfrac{\pi}{2}-x\right)+y\right|\)                                            Step 3: Associative property

\(=\cos\left|\left(\dfrac{\pi}{2}-x\right)-(-y)\right|\)                                        Step 4: Factoring out   

\(=\cos\left(\dfrac{\pi}{2}-x\right)\cos(-y)+\sin\left(\dfrac{\pi}{2}-x\right)\sin(-y)\)       Step 5: Cosine difference identity

\(=\sin(x)\cos(-y)+\cos(x)\sin(-y)\)                           Step 6: Cofunction identity

\(=\sin(x)\cos(y)-\cos(x)\sin(y)\)                                Step 7: Cosine function is even, sine function is odd

Therefore, the missing reasons are Cofunction identity, Cosine difference identity, Cofunction identity, Cosine function is even, sine function is odd respectively.

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The number of hours in a week a student played basketball is \(11\frac{3}{8}\).

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.

Also given that 1/4 of the exercise of a student came from playing basketball.

Therefore, Time playing basketball is one-fourth of the total time exercised which is,

= (3 + 1/4)×(1/4).

= (13/4)×(1/4).

= (13/8).

Therefore, In a week the student played (13/8)×7.

= 91/8.

= \(11\frac{3}{8}\).

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The simplified form of the expression 2√6 - 4√24 + √96 is -2√6. The square roots have been simplified, and the terms involving √6 have been combined to give the final result of -2√6.

To simplify the expression 2√6 - 4√24 + √96, we need to simplify the square roots and combine like terms.

First, let's simplify the square roots:

√6 cannot be simplified further because it does not have any perfect square factors.

√24 can be simplified as multiplying √(4 × 6), which equals 2√6.

√96 can be simplified as √(16 × 6), which equals 4√6.

Now, let's substitute these simplified square roots back into the expression:

2√6 - 4√24 + √96 becomes:

2√6 - 4(2√6) + 4√6

We can combine the like terms:

2√6 - 8√6 + 4√6 equals (-8 + 2 + 4)√6 which simplifies to -2√6.

The simplified form of the expression 2√6 - 4√24 + √96 is -2√6. The square roots have been simplified, and the terms involving √6 have been combined to give the final result of -2√6.

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A slope is defined as the unit rate of change of variable "y" with respect to x. The unit rate of change of variable "y" with respect to x is 8

A slope is defined as the unit rate of change of variable "y" with respect to x. It is also known as the gradient.

The formula for calculating the slope of a line is expressed as:

Slope = y2-1/x2-x1

Using the coordinate points (1, 8) and (2,16)

Slope = 16-8/2-1
Slope = 8/11
Slope = 8

Hence the unit rate of change of variable "y" with respect to x is 8

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Answer:

the equation

Step-by-step explanation:

see pictures

We find that it takes approximately 47 months to recover the initial investment.

To calculate the time it takes to recover the initial investment on a monthly basis, we need to consider the savings in fuel costs and the cost of funds over time.

First, let's calculate the monthly savings in fuel costs by subtracting the average natural gas cost from the fuel oil cost:

Savings in fuel costs = Fuel oil cost - Natural gas cost

= $145 - $60

= $85

Next, let's calculate the present value of the savings in fuel costs over the recovery period. Since the savings occur monthly, we can use the formula for the present value of an annuity:

Present value of savings = Savings in fuel costs * (1 - (1 + interest rate)^(-n)) / interest rate

Where:

Savings in fuel costs is $85 per month

Interest rate is 9% per year, which is 0.75% per month

n is the number of months it takes to recover the initial investment

Now, let's calculate the present value of the savings using the given values:

Present value of savings = $85 * (1 - (1 + 0.0075)^(-n)) / 0.0075

Next, let's calculate the present value of the initial investment using the formula for present value:

Present value of initial investment = Initial investment / (1 + interest rate)^n

Where:

Initial investment is $2500

Interest rate is 9% per year, which is 0.75% per month

n is the number of months it takes to recover the initial investment

Now, let's calculate the present value of the initial investment using the given values:

Present value of initial investment = $2500 / (1 + 0.0075)^n

To recover the initial investment, the present value of savings must equal the present value of the initial investment:

$85 * (1 - (1 + 0.0075)^(-n)) / 0.0075 = $2500 / (1 + 0.0075)^n

To solve for n, we can rearrange the equation and solve for n using trial and error or by using numerical methods.

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Answer: b

Step-by-step explanation:

Because he establish and strong government in 322 bce and  He was followed by his son Bindusara in 298 BCE so this is the answer nd i already did this question and got it right

She needs to deposit of amount  $92,421.48 today to do this.

We need to find out the present value of $1,000 per month for the next 10 years by considering the interest rate and compounding period given. We are given,Anita wants to withdraw $1,000 per month for the next 10 years.The bank pays interest at 6% compounded monthly.We can calculate the present value of $1,000 per month for the next 10 years by using the formula for Present Value of Annuity. The formula for Present Value of Annuity is given by:PVA= A((1- (1+r)^-n)/r), wherePVA = Present Value of AnnuityA = Amountn = Number of Periodsr = Interest Rate per PeriodFirst, we calculate the interest rate per period as follows:r = 6% per annum/ 12 monthsr = 0.5% per monthNumber of periods (n) = 10 years x 12 months per year = 120 months Amount of Annuity (A) = $1,000Using the above values, we can calculate the present value of the annuity as follows:PVA = 1000 * ((1- (1+0.5%)^-120)/(0.5%))PVA = $92,421.48Therefore, she needs to deposit $92,421.48 today to do this. Therefore, the correct option is $92,421.48.

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Equation of a line:

9x - 7y = -63

To find the x-intercept we have to substitute y = 0 into the equation, as follows:

9x - 7*0 = -63

9x = -63

Dividing by 9 at both sides of the equation:

9x/9 = -63/9

x = -7

To find the y-intercept we have to substitute x = 0 into the equation, as follows:

9*0 - 7y = -63

-7y = -63

Dividing by -7 at both sides of the equation:

-7y/(-7) = -63/(-7)

y = 9

Answer

x-intercept: −7; y-intercept: 9

Answer:

=2x-2

Step-by-step explanation:

Writing linear equations given two points can be a useful skill when graphing linear equations.

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Answer:

13

Step-by-step explanation:

Replace X with 2

Evaluate the function. g(x) = 3x^2 – 2x + 5 Find f(2)​

g(x) = 3(2)^2 – 2(2) + 5

Next conduct PEMDAS

Exponents are first so solve 2^2 which is 2 x 2 = 4

g(x) = 3(4) – 2(2) + 5

Next step is multiplication multiply 3 x 4 and 2x2

g(x) = 12 – 4 + 5

conduct adding and subtracting left from right

g(x) = 13

Answer:

1

Step-by-step explanation:

-10n+8n=10

-2n=10

n=-5

So, one solution

Answer:

There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).

Step-by-step explanation: