You entered a room, there are 34 people. You killed 30. How many people are left in the room?

Answer:

  x = s, y = t, z = -6 -s -t

Step-by-step explanation:

These are dependent equations. For some values s and t, the solution is ...

  x = s, y = t, z = -6 -s -t

Answer:

5%

Step-by-step explanation:

To find the tax, we take the price times the tax rate

2 = 40* rate

Divide each side by 40

2/40 =rate

.05 = rate

Changing to percent form

5% = rate

Answer:

tax rate = 2 / 40  = 1 /20 = 0.05 *100 = 5%

Step-by-step explanation:

The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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Answer:

200 minutes of calls

Step-by-step explanation:

Let x represent the number of minutes of calls

Set up expressions that represent the costs for each plan:

0.14x + 21 can represent the first plan

0.10x + 29 can represent the second plan

Now, set them equal and solve for x to find when they will be equal:

0.14x + 21 = 0.10x + 29

0.04x + 21 = 29

0.04x = 8

x = 200

So, the costs will be equal with 200 minutes of calls

The statement that is not true is (a) A = 74 degrees

From the question, we have the following parameters that can be used in our computation:

The dilation of ABC by a scale factor of 2

This means that

Scale factor = 2

The general rule of dilation is that

using the above as a guide, we have the following:

AC = 2 * 5 = 10

C = 53 degrees

BC = 2 * 3 = 6

A = 37 degrees

Hence, the statement that is not true is (a) A = 74 degrees

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Answer:

10 females, 15 males

Step-by-step explanation:

Let the number of females in the class be x. As the number of males is 5 more than the number of females, which is x, the number of males would be shown as x+5.

The number of females plus the number of males equal 25, so we get this equation:

x + (x+5) = 25

x + x + 5 = 25

2x + 5 = 25

2x = 20

x = 10.

So, there are 10 females, and since there are 5 more males than females, there are 10 + 5 = 15 males.

The required of the sidewalk to the nearest square foot is 13.14 ft².

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area.

We have,

Length = 5 ft, width = 2 ft, Radius of circle = 2 ft

Now,

Area of sidewalk = area of rectangle + area quadrant

Area of sidewalk = (5×2) + π(2)^2/4

Area of sidewalk = 10 + 3.14

Area of sidewalk = 13.14 ft²

Thus, required area of the sidewalk is 13.14 ft².

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The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

Since the calculated t= 7.8120 falls in the critical region ≥ 2.306 we reject H0 and conclude that there is a linear correlation between the two variables.

Step-by-step explanation:

We see that r²= 0.981 and r= 0.995 from the figure .

The P- value is less than 0.05  which indicates that the two variables are linearly correlated.

Set up the hypothesis as

H0: β= 0 i.e the two variables X and Y are not related

Ha: β≠0 i.e the two variables are related

The significance Level is set at ∝=0.05

The test statistic , if H0 is true is

t= b/sb

where sb² = s²yx / ∑( x-x`)² = ∑( y-y`)²/n-2 ∑( x-x`)²

assuming that the distribution of Yi for each Xi is normal with the same mean and the same standard deviation , the statistic t conforms to the Student's t distribution with n-2= 8 degrees of freedom

(X - x`)2                 (X - x`)(Y - y`)                       (Y - y`)2

265.69                   259.17                         15.9²=252.81

7174.09                 6953.87                       -82.1²=6740.41

75.69                       87.87                            -10.1=102.01

2052.09                 1671.57                           36.9²=1361.61

4529.29                 5848.37                        86.9²=7551.61

8335.69                7294.87                          79.9²=6384.01

4998.49                5380.27                        -76.1²=5791.21

1069.29                 1016.97                          -31.1=967.21

1043.29                   1159.57                         35.9²=1288.81

3102.49                    3124.77                        -56.1²=3147.21

SS: 32646.1            SP: 32797.3                        33,586.9

Sum of X = 3877

Sum of Y = 3991

Mean X = 387.7

Mean Y = 399.1

Sum of squares (SSX) = 32646.1

Sum of products (SP) = 32797.3

b = SP/SSX = 32797.3/32646.1 = 1.00463

a = Y` - bX `= 399.1 - (1*387.7) = 9.60437

Syx= √∑(y-y`)²/n-2= 33,586.9/8= 4198.3625

sb= syx/ √∑(x-x`)²=4198.3625/32646.1 =0.12860

Putting the values in the regression equation

ŷ = bX + a

ŷ = 1.00463X + 9.60437

The critical region is t ≥ t (0.025) (8)= 2.306

t= b/ sb= 1.00463/ 0.12860=7.8120

Since the calculated t= 7.8120 falls in the critical region ≥ 2.306 we reject H0 and conclude that there is a linear correlation between the two variables.

Answer:

The required function is:

Please check the attached graph.

Step-by-step explanation:

We need to write a function to match the function machine  multiply the input by -3, then  subtract 2.

Let 'x' be the input.

Therefore, multiply the input by -3, then  subtracting 2 would give us the result:

f(x) = 3x - 2

Therefore, the required function is:

Please check the attached graph.

Answer:

They are both located on the Vertical Line.

Step-by-step explanation:

If you go ahead and head over to demos calculator, proceed to type in those points. When you look at where both of those are located, they are on a Vertical line.

A graph that shows a function must pass the vertical line test

The true statement is (b) No; the graph fails the vertical line test.

For a graph to show a function, the graph must pass the vertical line test

The given graph do not pass the vertical line test;

This is so because, a line drawn from the x-axis would touch the graph at at least two different points

Hence, the true statement is (b) No; the graph fails the vertical line test.

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Answer: I think it is -5, but im not very sure srry

Step-by-step explanation:

Answer: The answer is wrong because you wrote it wrong.

Step-by-step explanation: The range is the list of all possible Y values that can go into a function. The possible Y values start at 0, and go to 5. Therefore, the range would actually be [0,5]

Answer:  The correct answer is y-intercept = -1

Step-by-step explanation:

The table provided:

   x    y

  5     4

  6     5

Find the slope:

Slope (m) = ΔY/ΔX = 1/1 = 1

The slope-intercept form for this line: y = x – 1

The graph is provided below.

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Answer:

x = 25, y = 9

Step-by-step explanation:

Since the triangles are congruent then corresponding angles and sides are congruent, thus

∠ O = ∠ P , substitute values

6y - 14 = 40 ( add 14 to both sides )

6y = 54 ( divide both sides by 6 )

y = 9

and

NG = IT , that is

x - 2y = 7 ( substitute y = 9 into the equation )

x - 2(9) = 7

x - 18 = 7 ( add 18 to both sides )

x = 25

Answer:

1) \((a+ib)(a-ib)\)

2) \(a^2+i^2b\)

Step-by-step explanation:

1) \(a^2+b^2\)

=> \(a^2 - (-1)b^2\)      (We know that -1 = \(i^2\) )

=> \(a^2-i^2b^2\)

=> \((a)^2-(ib)^2\)

Using Formula \(a^2 -b^2 = (a+b)(a-b)\)

=> \((a+ib)(a-ib)\)

2) \(a^2-b\)

=> \(a^2+(-1)b\)      (We know that -1 = \(i^2\) )

=> \(a^2+i^2b\)  (It cannot be simplified further)

Answer:

\(\boxed{(a+ib)(a-ib)}\)

\(\boxed{a^2+i^2b}\)

Step-by-step explanation:

\(a^2 + b^2\)

Rewrite expression.

\(a^2- (-1)b^2\)

Use identity :  \(-1=i^2\)

\(a^2- i^2 b^2\)

Factor out square.

\(a^2-(ib)^2\)

Apply difference of two squares formula : \(a^2-b^2 =(a+b)(a-b)\)

\((a+ib)(a-ib)\)

\(a^2-b\)

Rewrite expression.

\(a^2+(-1)b\)

Use identity :  \(-1=i^2\)

\(a^2+i^2b\)

The company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find the point at which the company starts to turn a profit, we need to find the value of x for which the revenue is greater than the cost of production.

The revenue function is R(x) = 7x, and the cost of production is C(x) = 13x + 132.

So, we need to solve the inequality:

R(x) > C(x)

7x > 13x + 132

Subtracting 13x from both sides, we get:

-6x > 132

Dividing both sides by -6 (and flipping the inequality because we're dividing by a negative number), we get:

x < -22

Therefore, the company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.

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The probability that the sample proportion exceeds 0.12 is given as follows:

0.6103 = 61.03%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

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

The parameters of the binomial distribution are given as follows:

n = 90, p = 0.13.

Hence the mean and the standard error are given as follows:

The probability that the sample proportion exceeds 0.12 is one subtracted by the p-value of Z when X = 0.12, hence:

Z = (0.12 - 0.13)/0.0354

Z = -0.28

Z = -0.28 has a p-value of 0.3897.

Hence:

1 - 0.3897 = 0.6103.

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The range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

Given that the function is f(x)=IxI+5.

We are required to find the range of the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y. The value of x is known as domain of the function and the value of y is known as codomain of the function. Range of a function is a limit of values in which the values of function lies.

Function is f(x)= IxI+5

We know that IxI=x for x>=0 and -x<0.

We have to just put the value of IxI in f(x) to get the range of function.

f(x)=x+5 for x>=0 and -x+5 for x<0.

Hence the range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

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Answer:

x = 74.2

Step-by-step explanation:

Recall: SOH CAH TOA

Reference angle (θ) = 70°

Angle opposite reference angle = x

Adjacent side = 28

Since we have Adjacent side and opposite side, we would apply the trigonometric ratio, TOA:

Tan θ = Opp/Adj

Substitute

Tan 70 = x/27

27*Tan 70 = x

x = 74.2 (nearest tenth)

Step-by-step explanation:

sum=addition

3/10 +1/3

find the LCM of 10 and 3 Which is 30

9+10/30=19/30

I hope it helps ☺️

Answer: x<2 or (−∞,2)

Step-by-step explanation:

Answer:

1001

Step-by-step explanation:

$2200/month&£-£+£+£

Answer:

3÷1/6

Step-by-step explanation:

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