How many lines of rotational symmetry does this shape have?

Based on the analysis, the east edge of the basketball court could be located on the line given by either −y − 5x = 100, y + 5x = 100, or −5x − y = 50, as these lines do not intersect with the west edge.

To determine on which line the east edge of the basketball court could be located, we need to find a line that does not intersect with the west edge represented by the equation y = 5x + 2.

The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

Comparing the equation y = 5x + 2 with the given options, we can observe that the slope of the west edge is 5.

Now let's analyze the options:

Option 1: −y − 5x = 100

By rearranging the equation to slope-intercept form, we get y = -5x - 100. The slope of this line is -5, which is not equal to the slope of the west edge (5).

Therefore, this line could be the east edge of the basketball court since it does not intersect with the west edge.

Option 2: y + 5x = 100

Rearranging the equation to slope-intercept form, we get y = -5x + 100. The slope of this line is -5, which is not equal to the slope of the west edge (5).

Thus, this line could be the east edge of the basketball court since it does not intersect with the west edge.

Option 3: −5x − y = 50

Rearranging the equation to slope-intercept form, we get y = -5x - 50. The slope of this line is -5, which is not equal to the slope of the west edge (5).

Hence, this line could be the east edge of the basketball court since it does not intersect with the west edge.

Option 4: 5x − y = 50

By rearranging the equation to slope-intercept form, we get y = 5x - 50. The slope of this line is 5, which is equal to the slope of the west edge (5).

Therefore, this line cannot be the east edge of the basketball court as it intersects with the west edge.

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Explanation:

The number 39 rounds to 40

Then 1/4 of this is 10

We estimate there are 10 students who are under the age of five.

Therefore, we estimate there are 39-10 = 29 students who are five or older.

Answer:

3g

Step-by-step explanation:

We know that

20g = 8g + 4 * r

where r is the weight of a single red circle.

20g = 8g + 4 * r

12g = 4 * r

3g = r

Answer:

12x9

Step-by-step explanation:

12x9 equals ____ square units

A collegiate basketball player hits 80% of his free throw attempts. Assuming free throw attempts are independent, he will try 100 free throws this season the answers are as follows:

a) The mean of X is 80.

b) The standard deviation of X is 4.

c) The probability that the basketball player makes at least 90 of these attempts is approximately is 0.0062.

d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is 0.0064.

As per the question given,  

a) The mean of X is given by the formula: mean = n * p, where n is the number of trials and p is the probability of success on each trial. In this case, the player attempts 100 free throws with a probability of success of 0.8, so the mean is:

mean = 100 * 0.8 = 80

Therefore, the correct answer is 80.

b) The standard deviation of X is given by the formula: standard deviation = sqrt(n * p * (1 - p)). Substituting the values, we get:

standard deviation = sqrt(100 * 0.8 * 0.2) = 4

Therefore, the correct answer is 4.

c) To find the probability that the player makes at least 90 free throws, we can use the normal approximation to the binomial distribution. The mean is 80 and the standard deviation is 4, so we can standardize the value of X as follows:

z = (90 - 80) / 4 = 2.5

Using a standard normal distribution table, we can find the probability that Z is greater than 2.5, which is approximately 0.0062.

Therefore, the correct answer is 0.0062.

d) If the player attempts only 10 free throws, the number of successful attempts X follows a binomial distribution with n=10 and p=0.8. The probability that he makes at most 4 of these attempts is:

P(X <= 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Using the binomial distribution formula, we can calculate each of these probabilities and sum them up. Alternatively, we can use a binomial probability table or a calculator to find the cumulative probability.

Using a binomial probability calculator, we get:

P(X <= 4) = 0.0064 (rounded to four decimal places)

Therefore, the correct answer is 0.0064.

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Answer: Mark up percent = 20%

Step-by-step explanation:

Given: Cost price of each T-shirt = $5.00

Amount required = $450

Total students = 75

Market price for each T-shirt to raise the required amount = (Amount required ) ÷ 75

= $450 ÷ 75

= $ 6

Mark up percent = \(\dfrac{\text{Market price - Cost price}}{\text{Cost price}}\times100\)

\(=\dfrac{6-5}{5}\times100\\\\=20\%\)

Hence, Mark up percent = 20%

The required probability is 0.3491.

Let X denote the number of components that has failed. Since there are thirty components and each individual component has a probability of 0.15 that it will fail, we can conclude that the components are operating independently of each other.  

The probability of failure of a component is P(F) = 0.15.

Now we need to find the probability of at least one of the components failing.

The probability of at least one of the components failing is equal to the probability of one or more components failing. We will use the complement rule to find the probability of no components failing and then subtract it from 1.

P(at least one component has failed) = 1 − P(no component fails) P(no component fails)

                                                              = P(F1 does not fail, F2 does not fail, F3 does not fail, . . . , F30 does not fail)

                                                              = P(F1) × P(F2) × P(F3) × · · · × P(F30)

                                                              = 0.15 × 0.15 × 0.15 × · · · × 0.15

                                                              = (0.15)30

                                                              = 0.0000101379.  

Therefore, P(at least one component has failed) = 1 - 0.0000101379

                                                                                = 0.9999898621.

We are asked to find the probability that at least three of the components has failed, given that at least one of the components has failed.

Let A denote the event that at least three of the components have failed. We need to find P(A|B), where B is the event that at least one of the components has failed. We can use Bayes’ theorem to solve this problem.

P(A|B) = P(A and B)/P(B)The event A and B means that at least three components have failed and at least one component has failed. The probability of A and B is equal to the probability of A given that B has occurred times the probability of B.

Therefore, we need to find two probabilities: P(A|B) and P(B).

We will begin with finding P(B). We already have P(B) from above.

We found P(B) = 0.9999898621.

P(A|B) = P(at least three have failed given that at least one has failed)

          = P(at least three have failed and at least one has failed)/P(at least one has failed)

We can write P(at least three have failed and at least one has failed) as P(A ∩ B).

P(A ∩ B) can be found by the following method:P(at least three have failed and at least one has failed) =

P(A) = P(A|B)P(B) + P(A|Bc)P(Bc)

Since we already know P(B), we just need to find P(A|Bc) and P(Bc) to solve for P(A).

We have P(B) and P(Bc) = 1 − P(B)

                                       = 1 − 0.9999898621

                                       = 0.0000101379.

We now need to find P(A|Bc).

P(at least three have failed and at least one has failed) = P(at least three have failed and no component has failed) + P(at least three have failed and exactly one component has failed) + P(at least three have failed and exactly two components have failed)

P(at least three have failed and no component has failed) = 0 (since at least one component has failed).

P(at least three have failed and exactly one component has failed) = 0 (since at least one component has failed).

P(at least three have failed and exactly two components have failed) = (30 C 2)(0.15)2(0.85)28

                                                                                                                   ≈ 0.3462,

where (30 C 2) = 435 is the number of ways to choose 2 out of 30 components.

Therefore, P(A|Bc) = 0 + 0 + 0.3462

                              ≈ 0.3462.

P(A|B) = P(A ∩ B)/P(B)

          = (P(A|Bc)P(Bc))/P(B) + P(A|B)

          = (0.3462)(0.0000101379)/(0.9999898621) + P(A|B)

          ≈ 0.3491,

where we used the fact that P(A ∩ Bc) = 0, since A cannot occur if Bc has occurred.

Therefore, P(A|B) ≈ 0.3491.

probability is 0.3491.

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To find the volume of the solid enclosed by the paraboloid z = 2 x^2 (y − 2)^2 and the planes z = 1, x = −3, x = 3, y = 0, and y = 4, we need to set up a triple integral over the given region and evaluate it.

The region is bounded by the planes z = 1, x = −3, x = 3, y = 0, and y = 4. Therefore, we need to integrate the given function over the region R = [−3, 3] × [0, 4] × [0, 1].

The volume of the solid is given by the triple integral V = ∫∫∫_R 2x^2(y-2)^2 dz dxdy.

Using the limits of integration, we have:

V = ∫_0^1 ∫_0^4 ∫_{-3}^3 2x^2(y-2)^2 dz dxdy

Evaluating the integral with respect to z, we obtain

V = ∫_0^1 ∫_0^4 2x^2(y-2)^2 (3-(-3)) dxdy

Simplifying and evaluating the integral with respect to x, we obtain:

V = ∫_0^1 ∫_0^4 12x^2(y-2)^ dy

Next, we need to evaluate the integral with respect to y:

V = 16/5 [(4/3)^3 - (2/3)^3]

Thus, the volume of the solid enclosed by the paraboloid z = 2 x^2 (y − 2)^2 and the planes z = 1, x = −3, x = 3, y = 0, and y = 4 is 16/5 [(4/3)^3 - (2/3)^3].

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Answer:

−x+9y−16

Step-by-step explanation:

3y−10−2x−6+6y+x

= 3y+−10+−2x+−6+6y+x

now, we must combine like terms

= 3y+−10+−2x+−6+6y+x

= (−2x+x)+(3y+6y)+(−10+−6)

= −x+9y+−16

The volume of the solid the region defined by the given curves must be rotated about the x-axis is V = \(\frac{384\pi }{5}\).

Given that,

The region defined by the given curves must be rotated about the x-axis to determine the solid's volume, which is y =6 -x², y =2.

We know that,

Take the equation of the curves about the x- axis

y =6 -x², y =2.

Substitute y = 2 in equation y = 6 - x²

2 = 6 - x²

-x² = 2-6

x² = 4

Taking square root on both sides

x = ±2

Now, volume formula is define by using washer method

V =  \(\pi \int\limits^a_b {[f(x)]^2 - [g(x)]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {[6-x^2]^2 - [2]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {(36 + x^4 - 12x^2 - 4}) \, dx\)

V = \(\pi \int\limits^2_{-2} {(x^4 - 12x^2 - 32)} \, dx\)

V = \(\pi( [\frac{x^5}{5}] - 12\times\frac{x^3}{3} -32x)^2_{-2}\)

V = \(\pi[( [\frac{2^5}{5}] - 12\times\frac{2^3}{3} -32(2))-([\frac{-2^5}{5}] - 12\times\frac{-2^3}{3} -32(-2))]\)

V = \(\pi[( [\frac{32}{5}] - 4 \times 8 -64)-( [\frac{-32}{5}] - 4\times(-8) +64)]\)

V = \(\pi[( [\frac{32}{5}] - 32 -64)-( [\frac{-32}{5}] +32 +64)]\)

V = \(\pi( [\frac{384}{5}] )\)

V = \(\frac{384\pi }{5}\)

Therefore, The volume of the solid is V = \(\frac{384\pi }{5}\)

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Answer: 6.4236

Step-by-step explanation:

Answer:

-6.5y - 1.1x

Step-by-step explanation:

Rearrange the problem to where like terms are closer together:

11.7y+5.2y + 1.2x + x - 3.3x

Simplify by adding the like terms and your final answer will be -6.5y -1.1x

Answer: False

Step-by-step explanation:

Because The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try!

Answer:

see explanation

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 9, 31) and (x₂, y₂ ) = (15, - 41) ← 2 ordered pairs from the table

m = \(\frac{-41-31}{15-(-9)}\) = \(\frac{-72}{15+9}\) = \(\frac{-72}{24}\) = - 3

the y- intercept is the value of g(x) when x = 0 , then from the table

y- intercept = 4

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then equation is

y = - 3x + 4

The point p(x, y) lies on the terminal side of an angle theta = startfraction 3 pi over 4 endfraction in standard position. Then x values are negative and the y values are positive.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. When the two rays are creating an exact 180-degree angle, an angle is considered to be straight. It gets its name from the fact that two lines at an angle of 180 degrees resemble one single straight line. Angles, whose measure is always non-negative, have some standard language.

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To find the slope of a line, we need to take two point of the graph where the line crosses the corners of the grid.

We can take the following two points:

We will use the definition of the slope:

And we draw a a triangle between the points to find the change in x and the change in y:

We substitute the changes in the slope formula:

Answer: 3/2

Answer:

Your answer will be (-5,7).

Step-by-step explanation:

Answer:

(-7,5)

Step-by-step explanation:

Answer:

1 pizza

Step-by-step explanation:

divide 3 from 5
how many times does 3 go into 5? 1 time.
Therefore, only 1 pizza can be made.

The firm's cash coverage ratio can be calculated using the formula:

Cash Coverage Ratio = (Operating Income + Depreciation) / Interest Expense.  Therefore, the firm's cash coverage ratio is approximately 6.93.

The cash coverage ratio is a financial metric used to assess a company's ability to cover its interest expenses with its operating income. It provides insight into the company's ability to generate enough cash flow to meet its interest obligations.

In this case, we first calculated the operating income by subtracting the cost of goods sold (COGS) and selling, general, and administrative expenses (SG&A) from the sales revenue. The resulting operating income was $143,106.

Since the question didn't provide information about the depreciation expenses, we assumed it to be zero. If depreciation expenses were given, we would have added them to the operating income.

The interest expense was given as $20,650, which we used to calculate the cash coverage ratio.

By dividing the operating income by the interest expense, we found the cash coverage ratio to be approximately 6.93. This means that the company's operating income is about 6.93 times higher than its interest expenses, indicating a favorable position in terms of covering its interest obligations.

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Answer:

∠x = 39.6°

Step-by-step explanation:

tan x = 19/23 = 0.8261

x = 39.6°

Answer:

\( \boxed{x = p(m - n)} \)

Step-by-step explanation:

\( = > m = n + \frac{x}{p} \\ \\ = > m = (n \times \frac{p}{p} ) + \frac{x}{p} \\ \\ = > m = \frac{pn}{p} + \frac{x}{p} \\ \\ = > m = \frac{pn + x}{p} \\ \\ = > mp = pn + x \\ \\ = > x + pn = pm \\ \\ = > x = pm - pn \\ \\ = > x = p(m - n)\)

Answer:

x = -3/4

Step-by-step explanation:

8x = -6

Divide each side by 8

8x/8 = -6/8

x = -3/4

Answer:

-3/4

Step-by-step explanation:

8x = -6

x = -6/8 = -3/4

x = -3/4

1. The equation to slope-intercept form is y = -2/3(x) + 490. The slope is -2/3 and the y-intercept is 490.

2. You should start at the y-intercept (0, 490) and move right by 3 units and downward by 2 units, and then connect the points.

3. The equation in function notation is f(x) = -2/3(x) + 490. The graph of the function is the rate of change with respect to the number of sandwich lunch sold.

4. A graph of the function with intercepts is shown below.

5. The graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, a linear equation that models Sal's Sandwich Shop's profit is given by;

2x + 3y = 1,470

By subtracting 2x from both sides of the equation and dividing by 3, we have:

2x + 3y - 2x = 1,470 - 2x

y = -2/3(x) + 490

Therefore, the slope is -2/3 and the y-intercept is 490.

Part 2.

In order to graph the equation by using the slope-intercept method, you would start at the y-intercept (0, 490) and move right by 3 units and down by 2 units, and then connect the points.

Part 3.

Next, we would write the equation in function notation as follows;

f(x) = -2/3(x) + 490

where:

The graph represents the rate of change of the function with respect to the number of sandwich lunch sold.

Part 4.

In this context, we would use an online graphing calculator to plot the linear function as shown in the image attached below.

Part 5.

Assuming Sal's total profit on lunch specials for the next month is $1,593 and the profit amounts remain the same, a system of equations to model this situation is given by:

2x + 3y = 1593; y = -2/3(x) + 531.

2x + 3y = 1,470; y = -2/3(x) + 490.

In conclusion, we can logically deduce that the graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.

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Complete Question:

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.

Answer:

to get x look at that triangle that it is in I know the angles in a triangle add up to 180° so it will be 180 - 63 degrees plus 36 degrees then to get z it will be 36 + 63 because interior angles add up to one exterior angle then to get y addz + 13 degrees then subtract it from 180°

Given, Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph.Both Jada and Elena start walking along a walking trail at the same time.

Let us determine the distance covered by both of them.Distance travelled by Jada in 3 hours is:Distance = Speed × Time= 3 mph × 3 hours= 9 miles Distance travelled by Elena in 3 hours is:Distance = Speed × Time= 2.8 mph × 3 hours= 8.4 miles Thus, Jada will walk 0.6 miles farther than Elena after 3 hours.

To determine how far Jada will walk after 3 hours, we need to calculate the distance traveled based on her speed.

Jada walks at a speed of 3 miles per hour (mph), so we can calculate her distance using the formula:

Distance = Speed × Time

Plugging in the values, we have:

Distance = 3 mph × 3 hours

Distance = 9 miles

Therefore, Jada will walk a distance of 9 miles after 3 hours.

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The given information is as follows:

Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph. If they both begin walking along a walking trail at the same time.

Therefore, Jada will walk 9 miles after 3 hours.

The distance covered by Jada after 3 hours can be calculated as follows:

Distance = Speed x Time

Since Jada walks at a speed of 3 mph, the distance covered by her in 3 hours can be calculated as:

Distance covered by Jada = 3 mph x 3 hours

= 9 miles.

Therefore, Jada will walk 9 miles after 3 hours.

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Step-by-step explanation:

a) 2x+7= -3

2x = -10

x = -5.

b) 7x-3= 9x+5

7x - 9x = 5 + 3

-2x = 8

x = -4

h) (2x-1)3= -125

6x - 3 = -125

6 x = -128

x = 21.33

c) 6x+7-2x = -x-8

6x -2x -x = -8 -7

3x = -15

x = -5

i) 2 (x+7)2= 242

2x + 14 * 2 = 242

2x + 28 = 242

2x = 242 + 28

2x = 270

x = 135.

d) -9+6x= 15+2x

6x -2x = 15 + 9

4x = 24

x = 6.

j) 1 + √2x + 3 = 6

√2x + 4 = 6

√2x = 6+4

√2x = 10

x = 7.1

e) 4x-8= -4 (2x-3)+4

4x - 8 = -8x +12 + 4

4x -8 = -8x + 16

4x - 8x = 16 - 8

-4x = 8

x = -2.

k) √3x + 22 = 4

√3x = 4 + 22

√3x = 26

x = 15

f) 2x+17 = 5 (x+1)

2x + 17 = 5x + 5

2x - 5x = 5 -17

-3x = -12

x = 4.

g) 7x-5= -3 (-x-9)

7x - 5 = 3x + 27

7x - 3x = 27 + 5

4x = 32

x = 8.

Answer:

(1/3)(9*9*10)=270cm^3 pyramid volume

270/(4*4*4)=4.22cubes

round

5 wax cubes

Answer:

y will be 8??

Step-by-step explanation:

y = 8 x= 16

Answer:

I am going to assume that "y" varies directly as "x."

y = kx

4 = k(2)

2 = k

y = kx

y = 2(16)

y = 32

Step-by-step explanation:

There ya go. :)

Answer:

Slope = -2/3

Step-by-step explanation:

Slope = change in y / change in x OR the rise/run

Slope = (5 - 1)/(-3 -3)

Slope = 4/-6

Slope = -2/3

Hope this helped!

Solution :

As we know that,

We have :

Substituting the values :

\( \longmapsto \: \sf{Slope \: (m) \: = \: \dfrac{1 \: - \: 5 }{3 \: - \: ( - 3)} } \\ \\ \longmapsto \: \sf{Slope \: (m) \: = \: \dfrac{1 \: - \: 5 }{3 \: + \: 3} } \\ \\ \longmapsto \: \sf{Slope \: (m) \: = \: \dfrac{ - 4}{6} } \\ \\ \longmapsto \: \sf{Slope \: (m) \: = \: \cancel\dfrac{ - 4}{6} } \\ \\ \longmapsto \: \bf{ \orange{Slope \: (m) \: = \: \dfrac{ - 2}{3} }}\)

Yes, you can still cover the remaining squares with dominoes. The necessary and sufficient condition for this to work is that the chessboard originally had an even number of squares.


A standard chessboard has 64 squares. If one corner square is missing, we are left with 63 squares. Each domino covers exactly 2 squares, so we need 31.5 dominoes to cover the remaining squares. Since we cannot use half a domino, this means we need a whole number of dominoes. Therefore, the number of squares must be even.

Conversely, if the chessboard originally had an even number of squares, then we can remove any one square and still have an odd number of squares left. Since each domino covers 2 squares, it is easy to see that we can always cover an odd number of squares with dominoes, by placing one domino vertically in the middle of the board. Therefore, in this case we can also cover the remaining squares with dominoes.

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