Use the diagram to find the length. PB is the perpendicular bisector of AC. QC is the perpendicular bisector of BD. AB = BC = CD.
 Given BD = 16 and PC = 10, find PB.
PB =

The region common to both the inequality graphs represents the possible solutions for the given set of inequality.

Given is that Mayerlin has {x} dimes and {y} nickels. She has no more than 20 coins worth no less than $1.30 combined

We can write the inequalities as -

x + y < 20                         .... (1)

x/10 + y/20 > 1.30             .... (2)

Refer to the graph of the inequalities attached. The region common to both the inequality graphs represents the possible solutions for the given set of inequality.

Therefore, the region common to both the inequality graphs represents the possible solutions for the given set of inequality.

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The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486

First, we need to calculate the z-score for the sample mean:

z = (x - μ) / (σ / √n)

z = (168.58 - 169) / (2.2 / √10)

z = -0.67

Next, we need to find the probability that a randomly selected bundle of steel rods will have a mean length greater than 168.58 cm. This is equivalent to finding the area under the standard normal distribution curve to the right of z = -0.67.

Using a standard normal distribution table or calculator, we find that the probability is 0.7486.

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Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Using translation concepts, the function f(x) was evaluated by comparing to the graph of a base function g(x) = x².

A translation is signified by a change with in function graph, based on operations in its definition including such multiplication or sum/subtraction.

Thus, the resultant function is obtained as (X)=4(X+9)²

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The slope of the curve  y⁴ = y² - x² is 1 and repeat the process for the second point.

Find the slopes of the curve y⁴ = y² - x² at the given points, we need to differentiate the equation implicitly with respect to x.
Differentiating both sides of the equation with respect to x, we get:
4y³ * (dy/dx) = 2y * (dy/dx) - 2x
Next, we can solve for (dy/dx) by isolating it on one side of the equation:
4y³ * (dy/dx) - 2y * (dy/dx) = -2x
(2y - 4y³) * (dy/dx) = -2x
(dy/dx) = -2x / (2y - 4y³)
Now, substitute the x and y values for each point into the equation to find the slopes at those points.
For example, if one point is (1, 1), we substitute x = 1 and y = 1 into the equation:
(dy/dx) = -2(1) / (2(1) - 4(1)³)
(dy/dx) = -2 / (2 - 4)
(dy/dx) = -2 / -2
(dy/dx) = 1
Repeat the process for the second point, and you will have the slopes of the curve at both points.

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Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

Answer:

A. G(x) = \(x^2+7\)

Step-by-step explanation:

→For the function to shift upwards 7 units, 7 must be added to the function, like so:

G(x) = \(x^2+7\)

→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.

This means the correct answer is A.

Heuristic is 0 for every city Heuristic is 1 for every city Selecting an inadmissible heuristic has a -50% penalty.

To find the shortest path to a destination city from a start city using roads (e.g., traveling from Arad to Bucharest) using A* search, the following heuristics are admissible:

Manhattan distance ("go first east/west and then north/south") between a city and start city.

Euclidean distance ("as the crow flies") between a city and destination city.

Euclidean distance ("as the crow flies") between a city and start city.

Manhattan distance ("go first east/west and then north/south") between a city and destination city.

The following heuristics are inadmissible:

Twice the Euclidean distance ("as the crow flies") between a city and destination city.

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Answer:

127

Step-by-step explanation:

PR is straight line with the measure of 180 degrees

to find PQT we need to subtract 53 from 180

180 - 53 = 127

Anlges on the same side of the transversal add up to 180 degrees.

What is Transversal?

A transversal is a line in geometry that connects two lines in the same plane at two separate places. Transversals help determine if two or more lines in the Euclidean plane are parallel.

Solution:

Using the property of Lineaar Pair Angle the Interior Angles on the same side of the Transversal add up to 180 degrees.

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5x + 2y = 57 These are the equations

x + y = 18

5x + 2y = 57

-5x - 5y = -90 This is the procedure to find x and y

-3y = -33

y = -33/-3

y = 11

x + 11 = 18

x = 18 - 11

x = 7

The numbers are 7 and 11

Answer:

8 hours

Step-by-step explanation:

We can use a ratio to solve

12 hours    x hours

----------   = ------------

93 dollars    62 dollars

Using cross products

12 * 62 = 93x

Divide each side by 93

12*62/93 = 93x/93

8 = x

8 hours

Answer:

-0.089

Step-by-step explanation:

Given that:

Males - Group 2:

Total number of males, n = 874

Number that said yes, = 396

P1 = 396 / 874 = 0.453

Females - Group 1 :

Total number of Females, n = 902

Number that said yes, = 489

P2 = 489 / 902 = 0.542

Point estimate of the difference in sample proportion:

P1 - P2

0.453 - 0.542

= −0.089

Answer:

3.51%

Step-by-step explanation:

From the given information:

For the first stream, the present value can be computed as:

\(= 100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}}\)

Present value for the second stream is:

\(=\dfrac{600}{(1+i)^{10}}\)

Relating the above two equations together;

\(100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}} =\dfrac{600}{(1+i)^{10}}\)

consider \(v = \dfrac{1}{1+i}\), Then:

\(\implies 100+200v^n + 300v^{2n} = 600 v^{10}\)

where:

\(v^n = 0.75941\)

Now;

\(\implies 100+200(0.75941) + 300(0.75941))^2 = 600 (v)^{10}\)

\((v)^{10} = \dfrac{100+200(0.75941) + 300(0.75941))^2 }{600}\)

\((v)^{10} = 0.7082\)

\((v) = \sqrt[10]{0.7082}\)

v = 0.9661

Recall that:

\(v = \dfrac{1}{1+i}\)

We can say that:

\(\dfrac{1}{1+i} = 0.9661\)

\(1 = 0.9661(1+i) \\ \\ 0.9661 + 0.9661 i = 1 \\ \\ 0.9661 i = 1 - 0.9661 \\ \\ 0.9661 i = 0.0339 \\ \\ i = \dfrac{0.0339}{0.9661} \\ \\ i = 0.0351 \\ \\ \mathbf{i = 3.51\%}\)

Answer:$54 for 3 hours of work

Step-by-step explanation:

Multiply 18 times 3

and you get 54

The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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Using the amount of Jim's money donated, we found that the percentage of a person's savings a company donate is 14%.

What is meant by percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Frequently, it is indicated with the percent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to  parts per hundred. Per 100 is what the word per cent means. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

Given, the money saved by Jim = $1250

Money donated by the company in Jim's name = $175

We are asked to find the percentage of a person's savings a company donate.

For this, we have to find what percentage of $1250 is $175.

Percentage = (Money donated / Total savings) * 100

                  = ( 175 / 1250) * 100 = 14%

Therefore the percentage of a person's savings a company donate is 14%.

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The inverse of matrix A, if it exists, is:

A^(-1) = [7/43, 2/43; 10/43, 9/43]

To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.

Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:

det(A) = (9 * 7) - (-2 * -10)

= 63 - 20

= 43

Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.

The formula to calculate the inverse of a 2x2 matrix is:

A^(-1) = (1/det(A)) * [d, -b; -c, a]

Plugging in the values from matrix A and the determinant, we have:

A^(-1) = (1/43) * [7, 2; 10, 9]

Simplifying further, we get:

A^(-1) = [7/43, 2/43; 10/43, 9/43].

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Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

A total of 8 workers are required for a building time of 15 days.

In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:

n ∝ 1 / t

n = k / t

Where k is the proportionality ratio, which can be eliminated by building the following formula:

n₁ · t₁ = n₂ · t₂

If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:

n₂ = n₁ · (t₁ / t₂)

n₂ = 10 · (12 / 15)

n₂ = 10 · (4 / 5)

n₂ = 8

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Answer:

D. Place the point of the compass on the midpoint of AB and mark

the points directly above and below the midpoint.

Step-by-step explanation:

Below are the simple steps to follow to draw a perpendicular bisector of line AB.

First step

Set the compass at the end of one line segment and move the compass so that it would be slightly longer than half of the line AB.

Second step

Set the compass at point A and make some arcs just above line AB.

Third step

Draw an arc from point B with the same compass width.

Fourth step

Carefully set a ruler at the intersection of the arcs and draw the line segment.

Answer:place the point of the compass on point a and draw an arc across ab.

Step-by-step explanation:

Answer:

\(-54\)

Step-by-step explanation:

If the number being halved is x, we can write the expression

\(7-0.5x=34\)

Now, bring like terms and solve!

\(-0.5x=27\)

Multiple both sides by -2 and you get

\(x=-54\)

Wanna check the answer? Well...

\(7-(-54*0.5)=7+27=34\)

Answer:

The permeter will be 26 units

Step-by-step explanation:

First to find this you need to know what the value of x is to do this I will use the equation 3x - 7 = x + 2

1. add seven to both sides leaving 3x = x + 9

2. Then subtract the 1x from both sides leaving 2x = 9

3. Then divide 9 by 2 which will be 4.5, x = 4.5

Then just plug 4.5 into each x value 4.5 + 2 and 3(4.5) - 7

1. 4.5 + 2 = 6.5

2. 3(4.5) - 7              13.5 - 7 = 6.5

The perimeter of the rectangle below in simplest form will be 4(x - 3).

Length of the rectangle = 3x - 7

Width of the rectangle = x+2

The perimeter of a rectangle is given as 2(length + width). The perimeter of the rectangle given will then be:

= 2(length + width)

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

= 6x - 14 + 2x + 4

= 4x - 12 = 4(x - 3)

Therefore, the perimeter of the rectangle in simplest form will be 4(x - 3).

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I am going to do this problem with more of an algebraic approach weather or not its the way your teacher wants you to do it like this.

The way to do things algebraically is to just set variables for what you want to find and set up equations to represent each sentence.

As seen there are hamburgers and chickens in this problem. So let's set the numbers of hamburgers to x, and the numbers of chickens to y.

Now write out each sentence using variables.

1.) Tia sold 78 hamburgers and chicken tenders.

x+y=78

2.) If she sold 24 more hamburgers than chicken tenders.

x=y+24

Now that we have the 2 equations, its time to solve.

Since we have x=y+24, we can replace the x in the first equation with the second equation

y+24+y=78

2y+24=78

Now we can subtract 24 from both sides.

2y=54

Simplify

y=27

Solve for x

x=27+24=51

Done!

it's probably 17424 feet

Answer: 4/13

Step-by-step explanation:

Number of cards in a deck = 52

Number of spades = 13

Number of aces = 4

Number of ace of spade = 1

Probability of either a spade or an ace :

P(spade or ace) = P(spade U ace)

P(spade U ace) = p(spade) + p(ace) - p(spade n ace)

Probability = required outcome / Total possible outcomes

P(spade) = 13 / 52

P(ace) = 4 / 52

P(spade n ace) = 1 / 52

P(spade U ace) = p(spade) + p(ace) - p(spade n ace)

= 13/52 + 4/52 - 1/52

= 16 / 52 = 4 /13

(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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The number of vehicle administered by department A only = 18

The number of vehicle administered by department B only = 8

The number of vehicle administered by department C only = 1

Given data

50 vehicles belong to an enterprise that has three departments, A, B and C

6 vehicles are available for the use of all three departments

2 vehicles give service to neither of the departments

24 vehicles are administrated by department B

16 of the 24 used by B are also used by the others departments

There are twice as many vehicles in department A as there are in department C.

equal numbers of vehicles are allocated when used by any two departments

number of vehicles on department A = 2 * number of vehicles in department C.

say A = 2C

B = 24

let x represent the number of vehicles used by any two departments

16 of the 24 used by B are also used by the others departments and equal numbers of vehicles are allocated when used by any two departments hence

16 = 2x + 6

2x = 16 - 6

2x = 10

x = 5

B only = 24 - 2x - 6 = 18 - 2x = 18 - 10 = 8

A only = A - 2x - 6 = 2C - 10 - 6 = 2C - 16

C only = C - 2x - 6 = C - 10 - 6 = C - 16

adding up all the vehicles as allocated to get to the sum of 50

24 - 2x - 6 + A - 2x - 6 + C - 2x - 6 + x + x + x + 6 + 2 = 50

24 - 6 - 6 - 6 + 6 + 2 - 2x - 2x - 2x + x + x + x + A + C = 50

24 - 10 - 6x + 3x + 2C + C = 50

14 - 3x + 3C = 50

3C - 3X = 50 - 14

3C - 3(5) = 36

3C - 15 = 36

3C = 36 + 15 = 51

C = 17

C only

C only = C - 16

C only = 17 - 16

C only = 1

A only
A only = 2C - 16

A only = 2 * 17 - 16 = 34 - 16 = 18

The number of vehicle administered by department A only = 18

The number of vehicle administered by department B only = 8

The number of vehicle administered by department C only = 1

The number of vehicle administered by department A = 2C = 34

The number of vehicle administered by department B = 24

The number of vehicle administered by department C = 17

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Answer:

12 feet

Step-by-step explanation:

1 inch= 8 feet

1/2 inch= 4 feet

1/4 inch= 2 feet

(2x2)/2= 2  (one triangle)

2x4=8 (rectangle)

2+2=4 +8=12

^2 was added 2 times cause there are 2 triangles

(you did not need a 3rd measurement cause the triangle measurements were equal)