Select the correct answer from each drop-down menu.
Consider the equation below.
-2(57 + 8) = 14 + 6x
The equation was solved using the following steps.
Step 1:
-101 - 16 = 14 + 6
Step 2:
-16. - 16 = 14
Step 3:
-16.5 = 30
Step 4:
30
=
-16
15
Step 5:
Complete the statements below with the process used to achieve steps 1-4.
-2 to 5x and 8.
6x.
Step 1:
Step 2:
Step 3:
Step 4:
16.
V
-16.

There is a 38.29% likelihood that at most five goblets must be chosen to find four that are not seconds.

a. Among six randomly selected goblets, the likelihood that only one is a second is calculated as follows:[tex]P(only one is a second) = P(X = 1) = (6C1 x 0.1 x 0.9⁵) = 0.47 or 47%[/tex]Therefore, Among six randomly selected goblets,

The likelihood that at least two are seconds is calculated as follows[tex]:P(at least 2 seconds) = 1 - P(0 second or 1 second)P(0 second or 1 second) = P(X = 0) + P(X = 1) = (6C0 x 0.1⁰ x 0.9⁶) + (6C1 x 0.1 x 0.9⁵) = 0.531P(at least 2 seconds) = 1 - P(0 second or 1 second) = 1 - 0.531 = 0.469 or 46.9%[/tex]Therefore, it is 46.9% likely that at least two of the six selected goblets are seconds.c. If goblets are examined one by one, the probability that at most five must be selected to find four that are not seconds is calculated as follows:

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Answer:

see below

Step-by-step explanation:

<2 and <3 are same side interior angles

Since p and q are parallel, <2 and <3 add to 180 ( or are supplementary)

Answer:

They are consecutive interior angles

Step-by-step explanation:

Answer:

adding

Step-by-step explanation:

adding because you can use your fingers

Answer:

It is 18

Step-by-step explanation:

A^2+31^2=36^2

After that you simplify then solve and you'll get 18

9514 1404 393

Answer:

  18.3 m

Step-by-step explanation:

The Pythagorean theorem is helpful here. It tells you the sum of the squares of the sides of the triangle is equal to the square of the hypotenuse.

  h^2 + 31^2 = 36^2

  h^2 = 36^2 -31^2 = 1296 -961 = 335

  h = √335 ≈ 18.303

Rounded to the nearest tenth, the height of the building is 18.3 m.

The median speed at which Dave drove to work is 62 mph.

To find the median speed at which Dave drove to work, we need to arrange the average speeds in ascending order and determine the middle value.

Arranging the average speeds in ascending order:

44, 45, 54, 59, 62, 63, 66, 67, 70

Since we have nine values, the middle value is the 5th value, which is 62.

Therefore, Dave's average speed on the way to work was 62 mph.

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Answer:

The slope is 1.

Step-by-step explanation:

An isoquant is a curve that represents all the various combinations of two factors of production that can produce a particular level of output. The formula for the given production function is

F(k,l)=.75L+K, where Q=1. Now, we will draw the isoquant for the given function.

The graph of the isoquant will be plotted with the help of two axes, K and L, where K represents capital, and L represents labor.

Steps to draw the Isoquant for the given production function F(k,l)=.75L+K:

Here's the graph of the Isoquant for the given production function:

F(k,l)=.75L+K where Q=1:

f(k, l) = 0.75L + Kf(k, l) = 0.75L + KQ = 1

Isoquant1 = 1; K = 1 - 0.75L0.75(4) + 1 = 1 + 0.75(0)1 + 0 = 0.75(3) + 1= 1 + 2.25

Isoquant0.75(1) + 1 = 1 + 0.75(2)0.75 + 1 = 1 + 1.5= 1 + 0.75(1)

Isoquant0.75(0) + 1 = 1 + 0.75(4)1 + 0 = 3

isoquant's graph indicates the various combinations of two factors of production, labor, and capital, that can produce a particular level of output, Q = 1.

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Answer:

x=1/49, x=1

Step-by-step explanation:

part a:

so if (7^2)=49, you are left with 49x=1. we have to use inverse operations to isolate the variable x. this means we have to divide by 49 on both sides since 49 is multiplied with x. so, you are left with 1/49. x=1/49.

part b:

so according to the zero property, if you raise any number to the power of 0, you get 1. therefore, we are left with 1x=1. we can simplify this to x=1, which is the answer!

i think this is what you're asking for, if i misunderstood please comment under my response!

Answer:

x=1/49, x=1

hope this helped

Answer:

x < 15

Step-by-step explanation:

Step 1: Write inequality

-x/3 + 10 > 5

Step 2: Solve for x

Answer:

x = -2

y = 8

Step-by-step explanation:

8x + 5y = 24

y = -4x

Substitute y;

8x + 5(-4x) = 24

Distribute;

8x - 20x = 24

-12x = 24

Divide both sides by -12

x = -2

Substitute x;

y = -4(-2)

y = 8

The solution to the system of equations is x = -2 and y = 8.

To solve the system of equations:

8x + 5y = 24

y = -4x

We can use the second equation (y = -4x) to substitute for 'y' in the first equation. This process is known as substitution. Replace 'y' in the first equation with (-4x):

8x + 5(-4x) = 24

Now, simplify and solve for 'x':

8x - 20x = 24

Combine the x terms:

-12x = 24

Next, isolate 'x' by dividing both sides by -12:

x = 24 / -12

x = -2

Now that we have the value of 'x', we can find 'y' by substituting '-2' back into the second equation:

y = -4(-2)

y = 8

The solution to the system of equations is x = -2 and y = 8.

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Answer:

okay so to figure out a perfect square a number has to be outlined by itself. 8 is not. 4 is because 2 times itself is 4. 81 is because 9 time itself is 81. 44 is not. 49 is because 7 times itself is 49. 125 is not. 150 is not. 144 is because 12 times itself is 144.

Troy should include $1,200 in gross income related to his gambling activities.

Nicci claimed the standard deduction, she can exclude the $720 refund from her gross income.

For Troy, the amount he should include in gross income related to his gambling activities is the net winnings, which is calculated by subtracting his losses from his winnings.

Net Winnings = Winnings - Losses

Net Winnings = $2,500 - $1,300

Net Winnings = $1,200

Therefore, Troy should include $1,200 in gross income related to his gambling activities.

For Nicci, if she claimed the standard deduction on her 2021 tax return, she does not need to include the state refund in her gross income. State tax refunds are generally not taxable if the taxpayer did not itemize deductions in the year for which the refund is received. Since Nicci claimed the standard deduction, she can exclude the $720 refund from her gross income.

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Answer:

127.75

Step-by-step explanation:

64+32+16+8+4+2+1+.5+.25=127.75

Answer:

127.75

Step-by-step explanation:

Answer:

gradient = 3

Step-by-step explanation:

Calculate the gradient ( slope) using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (4, 9)

m = [tex]\frac{9-3}{4-2}[/tex] = [tex]\frac{6}{2}[/tex] = 3

9.5 To find matrix P and diagonal matrix D such that [tex]P^{-1}AP = D[/tex], the given matrix A needs to be diagonalized.

9.5 [tex]A^{23}[/tex] can be calculated by multiplying A to itself 23 times.

9.6 The system of differential equations can be solved using the diagonalized form of A obtained in question 9.4.

9.4 To find matrix P and diagonal matrix D, we need to diagonalize the given matrix A. Diagonalization involves finding the eigenvalues and eigenvectors of A. By calculating the eigenvalues and eigenvectors, we can construct matrix P using the eigenvectors as its columns. The diagonal matrix D is formed by placing the eigenvalues on the diagonal. The obtained matrices P and D satisfy the equation [tex]P^{-1}AP = D[/tex].

9.5 To find [tex]A^{23}[/tex], we can multiply the matrix A to itself 23 times. The resulting matrix will have the values of A raised to the power of 23.

9.6 The system of differential equations can be solved using the diagonalized form of matrix A obtained in question 9.4. Since A = [tex]PDP^{-1}[/tex], we can rewrite the system of differential equations in terms of P and D. Then, by performing a change of variables using [tex]P^{-1}[/tex], the system can be transformed into a diagonal system. This diagonal system can be solved by solving each diagonal equation separately. The solutions can then be transformed back to the original variables using P.

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Answer:

a) perimeter = 8π + 6 + 8 + 10

= (8π + 24) ft

= about 49.13 ft

8(3.14) + 24 = about 49.12 ft

b) area = π(4^2) + 10(8) + (1/2)(6)(8)

= (16π + 104) ft²

= about 154.27 ft²

16(3.14) + 104 = about 154.24 ft²

Approximately, the value of the series is -7,619,287 to within an error of at most [tex]10^-5.[/tex]

The series is

[tex](-1)^(n+1) * n^6 n=1.[/tex]

We have to approximate the value of the series to within an error of at most 10^-5.

To obtain an approximation for the series, let us evaluate the sum S6.

Hence, the series S is given as:

[tex]S = (-1)^(1+1)*1^6 + (-1)^(2+1)*2^6 + (-1)^(3+1)*3^6 + ... + (-1)^(n+1)*n^6[/tex]

To obtain an approximation to this series, we will use the Alternating Series Estimation Theorem, which is given by:

|SN - S| <= |Rn|, where Rn is the remainder when SN is used to approximate the sum S.

Therefore, we have to determine the sum S6, the alternating series SN6, and the remainder R6.

|S6 - SN6| = R6

= |-7,605,967|

≈[tex]7.61 x 10^6.[/tex]

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=========================================================

Explanation:

Point C is located at (-2, -3).

When we apply an x axis reflection, the x coordinate stays the same and the y coordinate flips from negative to positive.

The x axis reflection rule is [tex](x,y) \to (x,-y)[/tex]

So that's how we go from (-2,-3) to (-2,3)

Answer:

-2,3

Step-by-step explanation:

Reflection in the x -axis:

A reflection of a point over the x -axis is shown. The rule for a reflection over the x -axis is. (x,y)→(x,−y) .

Answer:

D

Step-by-step explanation:

Answer:

45 minutes

Step-by-step explanation:

Let, after time [tex]t[/tex] minutes, they meet again at the same point.

In time [tex]t[/tex] minutes, let Sony completes x lap while Iogan completes y laps. Note that x and y must be the counting numbers.

As Sonny took 15 minutes to drive 1 lap, so,

[tex]t=15x\cdots(i)[/tex]

While Iogan Sonny took 9 minutes to drive 1 lap, so,

[tex]t=9y[/tex]

[tex]\Rightarrow 15x=9y[/tex] [from equation (i)]

[tex]\Rightarrow \frac {x}{y}=\frac{9}{15}[/tex]

[tex]\Rightarrow \frac {x}{y}=\frac{3}{5}[/tex]

As x,y must be counting number, so

(x,y)=(3,5),(6,10),...,(3n,5n) where n is a positive integer.

So, the minimum number of laps required are

x=3 and y=5  (when they meet for the first time)

Now, from equation (i),

The time required to meet them for the first time, t=15x3=45 minutes.

Mr Morake's Municipal bill showed R201,27 for water Usage at the end of August 2018 and he stated that the basic charge was not included on the water bill, then he is incorrect.

Mr Morake's municipal bill showed R201,27 for water usage at the end of August 2018. He stated that the basic charge was not included on the water bill. Verify if this statement is correct.

A basic charge is a fixed fee that appears on a water bill regardless of the volume of water used. It covers the cost of the water distribution system, maintenance of the infrastructure, and customer support. It's not linked to your actual water usage and is included in every monthly bill, according to most municipal billing systems.

What is a basic charge?

A basic charge is a fixed fee that is charged for water usage. The fee is fixed and does not change from month to month. It is a fee that is typically charged by municipalities. It is used to help cover the costs of maintaining the water infrastructure.

The basic charge includes the following costs:

Water infrastructure management Pumping stations Reservoirs Pipeline maintenance meter maintenance Customer service This charge ensures that the water system is maintained and that customers receive excellent service, even if their water usage is low.

So, if Mr Morake's municipal bill showed R201,27 for water usage at the end of August 2018 and he stated that the basic charge was not included on the water bill, then he is incorrect. As previously stated, the basic charge is included on every monthly bill, according to most municipal billing systems.

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The equation has a slope of -2 and the value of 5 is the y-intercept.

When ever you need to find the y-intercept, you need to look at the number without x.

Answer:

x=5

Step-by-step explanation:

-1+x=4

+1   +1

x=5

hope this helps :)

Square 3, multiply -2 and subtract -4 from the result. Therefore, option C is the correct answer.

The given function is f(x) = -2x²-4.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Substitute x=3 in f(x) = -2x²-4, we get

f(3) = -2(3)²-4

Square 3, multiply -2 and subtract -4 from the result. that is

f(3) = -2×9-4

= -22

Square 3, multiply -2 and subtract -4 from the result. Therefore, option C is the correct answer.

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Answer:

6. b

7. d

8. a

9. c

10.around 40

Step-by-step explanation:

no idea but i think i did my best

Answer:

X2+8X+6=0

We add all the numbers together, and all the variables

X^2+8X+6=0

a = 1; b = 8; c = +6;

Δ = b2-4ac

Δ = 82-4·1·6

Δ = 40

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

X1=−b−Δ√2aX2=−b+Δ√2a

The end solution:

Δ−−√=40−−√=4∗10−−−−−√=4√∗10−−√=210−−√

X1=−b−Δ√2a=−(8)−210√2∗1=−8−210√2

X2=−b+Δ√2a=−(8)+210√2∗1=−8+210√2

Step-by-step explanation:

Answer:

Option (D)

Step-by-step explanation:

Rate of emptying the fuel tank = 7.5 liters per minute

Fuel emptied in x minute = 7.5x liters

Volume of the fuel in the fuel tank initially = 175 liters

Therefore, amount of fuel left in the tank after x minutes = (175 - 7.5x) liters

Function representing the emptying of the fuel tank will be,

f(x) = 175 - 7.5x

Option (D) will be the answer.

The angle ZB can be computed using the dot product of vectors ZB and ZC, and the area of the triangle can be found using the cross product of vectors ZB and ZC.

To find the angle ZB, we first calculate the vectors ZB and ZC:

[tex]\(ZB = B - Z = (-1, 4, 1) - (4, 10, 7) = (-5, -6, -6)\)[/tex]

[tex]\(ZC = C - Z = (3, 7, 2) - (4, 10, 7) = (-1, -3, -5)\)[/tex]

Then, we calculate the dot product of ZB and ZC:

[tex]\(ZB \cdot ZC = (-5, -6, -6) \cdot (-1, -3, -5) = 43\)[/tex]

Using the dot product formula, we can find the angle between the two vectors:

[tex]\(\cos(ZB) = \frac{{ZB \cdot ZC}}{{\|ZB\| \cdot \|ZC\|}} = \frac{{43}}{{\sqrt{77} \cdot \sqrt{35}}}\)[/tex]

Finally, we can calculate the angle ZB using the inverse cosine function:

[tex]\(ZB = \cos^{-1}\left(\frac{{43}}{{\sqrt{77} \cdot \sqrt{35}}}\right)\)[/tex]

To find the area of the triangle formed by the three points, we calculate the cross product of vectors ZB and ZC:

[tex]\(ZB \times ZC = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -5 & -6 & -6 \\ -1 & -3 & -5 \end{vmatrix}\)[/tex]

By expanding the determinant, we obtain the resulting vector:

[tex]\(ZB \times ZC = (12, -1, -9)\)[/tex]

The magnitude of this vector represents the area of the triangle:

[tex]\(\text{Area} = \left\|ZB \times ZC\right\|\)[/tex]

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