f(x) = x2. What is g(x)?
A. g(x) = -2-3
B. (X) = -x2
C. g(x) = x2-3
D. g(x) = -3/2

Answer:

divide the figure into two parts.

area of square = side²

area of square =12²

area of square =144

area pf trapezium =1/2×(a+b)×h

area of trapezium =1/2×(12+6)×12

area of trapezium =108

area of polygon=144+108=252 unit²

Answer: 3 buses

Step-by-step explanation:

Answer:

Simply multiply 21 until you get a number greater than 47. In this case, 3, even though there is only a little remainder of 5 kids on one bus by themselves.

Step-by-step explanation:

The solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.

a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7

We can solve the system of equations using both inverse matrix (if possible) and reduced row echelon forms.

We begin by converting the above equations into matrix form as follows:

[xy+2x2+2x3=1] [X1-2x2+2x3=-3] [3x1-x2+5x3=7] = [1] [-3] [7]

We represent the coefficient matrix by A and the variable matrix by X.

Then we have AX = B where B = [1] [-3] [7]

To find the inverse of A.

If the inverse of A exists, we can use it to find X = A^(-1)B.

We can find the inverse of A using the formula A^(-1) = adj(A)/|A| where adj(A) is the adjugate of A and |A| is the determinant of A.

We have: det(A) = |[1,2,2;-1,-2,2;3,-1,5]| = 9adj(A) = [11,6,-4;19,9,-5;-7,-4,3]

Therefore, A^(-1) = adj(A)/|A| = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9]

We can use A^(-1) to find X as follows:

X = A^(-1)B = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9][1;-3;7] = [-5/3;1/3;2/3]

Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.

We can also solve the system of equations using the reduced row echelon form of the augmented matrix as follows:[1,2,2,1;-1,-2,2,-3;3,-1,5,7] [R2+R1,R3-3R1] [1,2,2,1;-4,-3,4,-2;0,-7,-1,4] [R2/(-4),R3/(-7)] [1,2,2,1;1/4,1,-1,1/2;0,1,1/7,-4/7] [R1-2R2, R3-(1/7)R2] [1,0,3/2,-1/2;0,1,1/7,-4/7;0,0,0,0]

The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.

The system of equations is consistent, and we can solve for x, y, and z using the first two rows of the above matrix as follows:

x + (3/2)z = (-1/2)y + (1/7)z = (4/7)

Solving for z, we have: z = 2/3

Substituting z into the first equation, we have:

x + (3/2)(2/3) = (-1/2)x = -5/3

Substituting z into the second equation, we have:

y + (1/7)(2/3) = (4/7)y = 1/3

Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0

To solve this system of equations, we begin by converting it into matrix form as follows:[1,2y,2,5;0,-2,2,-4;3,-1,5,2;3,-2,6,-3] [x1;x2;x3;x4] = [0;0;0;0]

We represent the coefficient matrix by A and the variable matrix by X.

Then we have AX = 0. Our task is to find the reduced row echelon form of the augmented matrix [A|0].

We perform the following elementary row operations to the above matrix to obtain the reduced row echelon form:[1,2y,2,5,0;0,-2,2,-4,0;3,-1,5,2,0;3,-2,6,-3,0] [R1-2yR2, R3-3R2, R4-3R2] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,-7,-1,14,0;0,-8,0,9,0] [R3/(-7), R4/(-8)] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,1,1/7,-2/7,0;0,1,0,-9/8,0] [R1+(2y+1)R3] [1,0,0,9/7,0;0,-2,0,-2/7,0;0,1,1/7,-2/7,0;0,0,0,0,0]

The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.

The system of equations is consistent, and we can solve for x1, x2, x3, and x4 using the first three rows of the above matrix as follows:

x1 = -(9/7)x4x2 = (2/7)x4x3 = -(1/7)x4

Therefore, the solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.

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The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.Therefore, the algorithm has a total runtime of O(|V|+|E|).

a) Algorithm to determine if a graph has a cycle:The algorithm is implemented using DFS (Depth First Search) traversal, which starts from every vertex in the graph. During the DFS traversal, we maintain a set of vertices on the current path. We continue DFS traversal of each unvisited neighbor vertex, and if a neighbor is already on the path set, then we have found a cycle.

The algorithm to determine if a graph has a cycle is given below -Graph G(V, E)Start DFS from each vertex v in VIf DFS utility detects a cycle, then return true.

Else, return false.Let's take a look at the DFS algorithm below -DFS(vertex u)

1. Mark u as visited.

2. For every unvisited neighbor v of u, doDFS(v)

3. If v is already on the current path, return true to denote the existence of a cycle.

4. If there is no cycle, return false to denote that the graph does not contain a cycle.

The overall runtime of the algorithm is O(|V|+|E|).

The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.

b) Justification of the correctness and runtime of the algorithm:The algorithm provided uses a DFS traversal.

Therefore, the algorithm can detect a cycle in an undirected connected graph. If there is a cycle, then the algorithm will correctly detect it.

Since the algorithm starts DFS from each vertex, it will detect the cycle even if it starts from a vertex other than the one containing the cycle.

Therefore, it's correct.The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.

Therefore, the algorithm has a total runtime of O(|V|+|E|).

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Answer:

12/13

Step-by-step explanation:

side² = 13² - 5² = 169 - 25 = 144

side = √144 = 12

sin ∅ = 12/13

Answer:

x=1/2

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer :  The lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.

Explanation:

Given that the mean lifetime of light bulbs is 850 hours with a standard deviation of 44 hours and it is normally distributed. We need to test the hypothesis that 850 hours against the alternative.

Therefore, we need to use a hypothesis test for mean. Let us assume a null hypothesis and an alternative hypothesis for the given data.

Null Hypothesis : The null hypothesis H0 states that there is no significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours.                                                                                                               Mathematically, it is expressed asH0: μ = 850    

Alternative Hypothesis : The alternative hypothesis Ha states that there is a significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours.                                                                                      Mathematically, it is expressed asHa: μ ≠ 850Here, μ represents the population mean and is equal to 850.                                                We know that Z-score is given as, Z = (x - μ)/σwhere x = Sample Mean, μ = Population Mean, σ = Standard Deviation

Now, we need to find the Z-score for the given data. Z = (x - μ)/σZ = (15 - 850)/44Z = -18.75As we know that the area under the curve at 5% level of significance on each tail is 0.025 and the Z-score corresponding to this is ±1.96. The rejection region is in the left tail of the curve and the right tail of the curve.

Hence the critical value of Z at 5% level of significance for a two-tailed test is ±1.96. Z critical value = ±1.96Since the calculated value of Z is less than the critical value of Z, we fail to reject the null hypothesis. Hence, we can conclude that the lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.

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Answer: x = -5

New Equation (after substituting) 4x = 3x - 5

Subtract 3x from both sides

x = -5

Answer: Justin earns a base salary of $1500 per month at

the jewelry shop. He also earns a 3% commission

on all sales. If Just sold $82,975 worth of jewelry

last month, how much would he make for the

month including his base salary and commission?

Step-by-step explanation: $1500 + 3% + $82,975 = 84475. 03 or 84475

Answer:

(-2, 4)

Step-by-step explanation:

Hopes this helps!

Answer:

C. 333.14

Step-by-step explanation:

Both the basketball and baseball has got the shape of a sphere. So that;

volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

where r is the radius

i. Volume of the baseball = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

                           =  [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.25)^{3}[/tex]

                           = 3315.5655

volume of the baseball = 3316.57 cube inches

ii. Volume of the basketball =  [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

                            = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.55)^{3}[/tex]

                            = 3649.8372

Volume of the basketball = 3649.84 cube inches

The required difference = volume of basketball - volume of baseball

                                  = 3649.84 - 3316.57

                                  = 333.27 cube inches

The difference of the volumes of the basketball and baseball is 333.27 cube inches.

Answer:

-21 Feet

Step-by-step explanation:

-336/16

The balloon's elevation during the second minute will be 21 feet.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A sight-seeing balloon pilot starts to land her inflatable. In the main moment the inflatable rise - 336 feet. In the subsequent moment, the inflatable's height changes by 1/16 of that sum.

Then the balloon's elevation during the second minute is given as,

⇒ - 336 x (1/16)

⇒ - 336 / 16

⇒ - 21 feet

The balloon's elevation during the second minute will be 21 feet.

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Answer:

a. 80.83 ft b. 40.42 ft

Step-by-step explanation:

Let h = height of pole = 70 ft, L = length of cable and x = distance of cable on ground to pole and Ф = angle between cable and ground.

a) How long is the cable?

Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and L being the hypotenuse side, by trigonometric ratios,

sinФ = h/L

L = h/sinФ

L = 70 ft/sin60°

L = 70 ft/0.8660

L = 80.83 ft

b) How far from the pole should the cable be attached to the ground?

Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and x being the adjacent side, by trigonometric ratios,

tanФ = h/x

x = h/tanФ

x = 70 ft/tan60°

x = 70 ft/1.7321

x = 40.42 ft

The length of the cable is 80.83 ft and the distance from the pole should the cable be attached to the ground is 40.42 ft and this can be determined by using the trigonometric function.

Given :

a) The trigonometric function can be used in order to determine the length of the cable.

[tex]\rm sin\theta=\dfrac{h }{L}[/tex]

where h is the height of the pole, L is the length of the pole, and [tex]\theta[/tex] is the angle from the ground.

Substitute the known terms in the above expression.

[tex]\rm L=\dfrac{h }{sin\theta}[/tex]

[tex]\rm L = \dfrac{70}{sin60}[/tex]

L = 80.83 ft.

b) The trigonometric function can be used in order to determine the distance from the pole should the cable be attached to the ground.

[tex]\rm tan \alpha =\dfrac{h}{x}[/tex]

where x is the distance between pole and cable.

Substitute the known terms in the above expression.

[tex]\rm x = \dfrac{70}{tan 60 }[/tex]

x = 40.42 ft.

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Answer: -g - 10h

Step-by-step explanation:

(5g - 3h) - (6g + 7h)

= 5g - 3h - 6g - 7h

= 5g - 6g - 3h - 7h

= -g - 10h

Answer:

37.8

Step-by-step explanation:

1000 - 300 = 700

I = Prt

I = (700)(1.8%)(3)

I = 37.8

To find the probability a randomly selected z-score is between -1 and 1.2, we need to use the standard normal distribution table.

A standard normal distribution table shows the area to the left of the z-score. To find the area between two z-scores, we need to find the area to the left of the larger z-score and subtract the area to the left of the smaller z-score. So, the probability that a randomly selected z-score is between -1 and 1.2 is given by: P(-1 ≤ z ≤ 1.2) = P(z ≤ 1.2) - P(z ≤ -1)

Using the standard normal distribution table, we get: P(-1 ≤ z ≤ 1.2) = 0.8849 - 0.1587 = 0.7262. Therefore, the probability that a randomly selected z-score is between -1 and 1.2 is approximately 0.7263, which is the closest option to our answer. The correct option is option D.

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Answer:

Step-by-step explanation:

The alternative hypothesis in the one-way ANOVA F test states that the population means are not all equal.

In the one-way ANOVA F test, we are comparing the means of several groups or categories. The null hypothesis assumes that all population means are equal, while the alternative hypothesis suggests that there is a difference between at least two of the population means.

The alternative hypothesis can be stated as "the population means are not all equal," indicating that there is variability or disparity among the different groups being compared.

By rejecting the null hypothesis and accepting the alternative hypothesis in the one-way ANOVA F test, we conclude that there is evidence to suggest that the means of the different groups are not equal, indicating some form of group differentiation or distinction in the underlying populations.

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Answer:

see in the picture mark brainliest if correct

The system of linear equations admits an unique solution.

The system of linear equations given by:

-x + 3y = 7   ------------------------(1)

2x + y = 4   ------------------------(2)

We can find whether the system of linear equations admits a unique solution or not by using any one of the methods such as elimination, substitution or matrices.

For this question, we can solve the given system of equations using the substitution method:

From Eq. (2), we get:

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

Substituting Eq. (3) into Eq. (1), we get:

-x + 3(4 - 2x) = 7

=> -x + 12 - 6x = 7  

=> -7x = -5  

=> x = 5/7

Substituting the value of x in Eq. (3), we get:

y = 4 - 2(5/7)

=> y = 18/7

Therefore, the unique solution of the given system of linear equations is:x = 5/7 and y = 18/7.

Thus, the given system of linear equations admits a unique solution.

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Answer:

The correct anser is B. (i think. sorry if wrong) have a wonderfull day. dont let them bring you down. your amazing just the way you are.

Step-by-step explanation:

Step-by-step explanation:

\blue{\large \rightarrow }\: \boxed{ \sf{ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} }}

Answer: The estimate is not valid based on the given sample.

Explanation:

The given information can be used to determine if the estimate is valid or not. It is estimated that at a certain college, at most 25% of the students ride bicycles to class, and a random sample of 90 college students is taken. The number of students who ride bicycles to class in the sample is 28.                                                                                            Therefore, to determine if the estimate is valid, the proportion of students who ride bicycles to class in the sample must be calculated.                                                                                                                                                                   The proportion of students who ride bicycles to class in the sample is 28/90 = 0.31 ≈ 31%.The proportion of students who ride bicycles to class in the sample is greater than the estimated proportion of students who ride bicycles to class, which is 25%.

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To find the distance from point Q=(-28, 41) to the line represented by the equation (x, y) = (2, 1) + t(4, 3), we can use the formula for the distance between a point and a line in the coordinate plane. Therefore, the distance from point Q to the line is 233/5.

The distance between a point (x0, y0) and a line Ax + By + C = 0 is given by the formula:

d = |Ax0 + By0 + C| / √(A^2 + B^2)

In this case, we have the line represented parametrically as (x, y) = (2, 1) + t(4, 3), where t is a parameter. To use the formula, we need to convert this parametric representation to the standard form Ax + By + C = 0.

Expanding the parametric equation, we have:

x = 2 + 4t

y = 1 + 3t

From these equations, we can rearrange them to isolate t:

t = (x - 2) / 4

t = (y - 1) / 3

Setting the two expressions for t equal to each other, we get:

(x - 2) / 4 = (y - 1) / 3

Simplifying, we have:

3x - 6 = 4y - 4

4y - 3x = 2

Now we have the equation of the line in standard form. The coefficients A, B, and C are 4, -3, and 2, respectively.

To find the distance between point Q=(-28, 41) and the line, we can substitute the values into the distance formula:

d = |4(-28) + (-3)(41) + 2| / √(4^2 + (-3)^2)

Calculating the numerator and the denominator, we have:

d = |-112 - 123 + 2| / √(16 + 9)

d = |-233| / √25

d = 233 / 5

Therefore, the distance from point Q to the line is 233/5.

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Answer:

The answer u put in the thing is correct!

Step-by-step explanation:

Answer:

whats the definition?

Step-by-step explanation:

Answer:

what’d she say? xD

Step-by-step explanation:

The solution is, She said that he was a fun gi, the girl mushroom say about the boy mushroom after their first date.

A mushroom is the reproductive structure produced by some fungi. It is somewhat like the fruit of a plant, except that the "seeds" it produces are in fact millions of microscopic spores that form in the gills or pores underneath the mushroom's cap.

here, we have,

She said that he was a fun gi.

This is a pun because fungi is a mushroom and here it is a play on words because of "fun guy" sounding the same as "fun gi".

Since they are both mushrooms, the joke stands and these types of puns are very common among people because of their simplicity.

The solution is, She said that he was a fun gi, the girl mushroom say about the boy mushroom after their first date.

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Answer: y-9=-1/2 x (x+4)

Step-by-step explanation: