A drain empties a bathtub at a rate of 0.5 gallons per minute. A
30-gallon tub was full and the shower head was turned off,
how long would it take the tub to empty through the partly
unplugged drain?

Answer:

Step-by-step explanation:

8,2,4

Answer:

TRUE

Step-by-step explanation:

TRUE

Therefore, the given statement "The midsegment of a trapezoid is half the sum of the bases" is True.

A trapezium is a quadrilateral with two parallel sides. It has two non-parallel sides that are called the legs of the trapezium, and the other two sides are called the bases.

The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides of the trapezoid. Since the midsegment connects the midpoints of the two non-parallel sides, it will always have the same length as half the sum of the two bases.

Therefore, the given statement is True.

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To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

The dot plot of the data values is added as an attachment

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

85,88,75,100,90,90,88,72,72,79,88,85

Next, we create a frequency table

So, we have

Values   Frequency

72             2

75             1

79             1

85            2

88            3

90           2

100          1

Total      12

Using the frequency table above, we create the dot plot

See attachment for the dot plot

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According to the given statement, 62 1/2% represents the part of the students who exceeded the minimum standards.

The part of the students who exceeded the minimum standards is 62 1/2%.

To find the part of the students who exceeded the standards, we need to look at the percentage mentioned in the question. The question states that 62 1/2% of the students exceeded the minimum standards. This means that 62 1/2% is the part or proportion of students who exceeded the standards.

Therefore, 62 1/2% represents the part of the students who exceeded the minimum standards.

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Answer:

D

Step-by-step explanation:

the number of students who plays sport are 1/7 of 35 that means that there  are 35/7 students play sport so there is only 5 of 35 students play sport

so number of students thatn dont play sport are 35 - 5 = 30

Answer:

Step-by-step explanation:

oaxy8g7qd c7heuhwciwycowbobwxicx

donvc

True. In determining the partial effect on a dummy variable (d) in a regression model with an interaction variable (xd), the value of the numeric variable (x) needs to be known.

When estimating the partial effect of a dummy variable (d) in a regression model that includes an interaction term (xd), the value of the numeric variable (x) is crucial. The interaction term (xd) is the product of the dummy variable (d) and the numeric variable (x). Therefore, the partial effect of the dummy variable (d) depends on the specific value of the numeric variable (x).

To compute the partial effect, you would need to fix the value of the numeric variable (x) and then calculate the change in the predicted outcome (ŷ) associated with a change in the dummy variable (d). This allows you to isolate the effect of the dummy variable (d) while holding the numeric variable (x) constant.

In summary, knowing the value of the numeric variable (x) is essential when determining the partial effect on a dummy variable (d) in a regression model with an interaction variable (xd). Without knowing the value of the numeric variable, it is not possible to estimate the specific effect of the dummy variable on the outcome accurately.

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v = 8

Given:

-31 = 3v + 9 - 8v

To find:

the value of v

To determine v, we will collect like terms:

subtract 9 from both sides:

Divide price by quantity:

3.00 / 12 = $0.25 per can.

Answer:

Variable terms:

x and y

Constant terms:

7 and -9

Coefficient terms:

-5.6 and 24

(a)The height of the density function f(x) is 0.04

(b) Var(X) = \(\frac{(b-a)^2}{12}=\frac{(17+7)^2}{12}\) = 48

Standard deviation: \(\sqrt{48}\) = 6.93

(c) The value of P(X ≤ −4) is 0.125

We have the information from the question:

A random variable X follows the continuous uniform distribution with a lower bound of −7 and an upper bound of 17.

Now, We assume the X is the random variable .

X ~ Unif(a = -7 , b = 17)

(a) The density function is given by:

\(f(x) =\frac{1}{b-a}\)\(=\frac{1}{17-(-7)}=\frac{1}{24}=0.04\)

The height of the density function f(x) is 0.04

(b) We have to find the mean and the standard deviation for the distribution.

Now, According to the question:

Var(X) = \(\frac{(b-a)^2}{12}=\frac{(17+7)^2}{12}\) = 48

And the standard deviation is given by:

Standard deviation: \(\sqrt{48}\) = 6.93

(c) We have to calculate P(X ≤ −4).

For this case we can use the cumulative distribution function is given by:

F(X) = \(\frac{x-a}{b-a}\)

Plug the values:
F(-4) =   P(X ≤ −4) = \(\frac{-4+7}{17+7}\) = 3/24 = 0.125

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The answer to the question is 'False.'

Raw scores that have been mathematically transformed to have a designated mean and standard deviation are called standardized scores.

Standardized scores are scores that have a mean of 0 and a standard deviation of 1. This means that all standardized scores are expressed in standard deviation units above or below the mean. By using standardized scores, we can compare scores from different tests or distributions that may have different units of measurement or different means and standard deviations. Standard scores are represented by z-scores. Z-scores represent the number of standard deviations from the mean that a particular score falls. Z-scores help in comparing different scores on different scales and determine where a particular score stands in relation to the rest of the scores. A z-score of 0 indicates that the score is at the mean, while a positive z-score indicates that the score is above the mean and a negative z-score indicates that the score is below the mean.

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VY is approximately 16.90.

To find VY, we can use the law of sines in triangle UYV.

The law of sines states that for any triangle with sides a, b, and c, and opposite angles A, B, and C, the following relationship holds:

a/sin(A) = b/sin(B) = c/sin(C)

In our triangle UYV, we have the following information:

UY = 11 (given)

m(UX) = 80.6° (given)

YZ = 17 (given)

We need to find VY.

Let's label the angle at V as angle VYU (m(VYU)).

We know that the sum of the angles in a triangle is 180°, so we can find m(VYU) as follows:

m(VYU) = 180° - m(UX) - m(UYV)

= 180° - 80.6° - 90°

= 9.4°

Now, applying the law of sines:

VY/sin(9.4°) = UY/sin(90°) [Angle UYV is a right angle]

= 11

To find VY, we can rearrange the equation:

VY = sin(9.4°) × 11 / sin(90°)

Using a calculator, we find:

VY ≈ 1.536 × 11 / 1

≈ 16.896

Rounded to the nearest hundredth:

VY ≈ 16.90

Therefore, VY is approximately 16.90.

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A study by a business professor at Arizona State University found that students who missed two classes had grades that were one full letter grade lower than those who attended all classes. This suggests that attending class is essential for academic success.

There are a few reasons why missing class can lead to lower grades. First, students who miss class may miss important information that is covered in lectures. Second, they may miss opportunities to ask questions and get help from the professor. Third, they may fall behind on assignments and readings.

To avoid falling behind, it is important to attend all classes. If you must miss class, be sure to get notes from a classmate and ask the professor for any missed assignments or readings. By attending class and staying on top of your work, you can improve your chances of academic success.

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Complete question:

A study by a business professor at Arizona State University showed that, on average, is students' grades wet down one full grade for every _ classes they missed.

a. one

b. two

c. three

d. four

Answer:i say the answer is the first two and the last two

Step-by-step explanation:

Answer:

HL

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The optimal values of x and y are x = 4 and y = 3.

To find the optimal values of x and y using the graphical solution method, we need to graph the given inequalities and identify the feasible region.

The first inequality, x + y ≥ 7, represents a line with a slope of -1 passing through the point (0, 7). To graph it, we can plot this point and draw the line extending to the right and upwards. The feasible region lies above or on this line.

The second inequality, 5x + 2y ≥ 20, represents a line with a slope of -5/2 passing through the point (0, 10). Again, we can plot this point and draw the line extending to the right and upwards. The feasible region lies above or on this line.

The third condition, x ≥ 0 and y ≥ 0, indicates that x and y must be non-negative. This restricts the feasible region to the positive quadrant of the graph.

The intersection of the feasible regions determined by the two inequalities forms a region bounded by a triangle. We need to find the point within this region that minimizes the objective function x + y.

To find the optimal values, we can evaluate the objective function at the vertices of the feasible region:

Vertex A: (0, 7)

Objective function value: x + y = 0 + 7 = 7

Vertex B: (4, 3)

Objective function value: x + y = 4 + 3 = 7

Vertex C: (4, 5)

Objective function value: x + y = 4 + 5 = 9

The minimum value of the objective function occurs at vertices A and B, where the value is 7. Therefore, the optimal values of x and y are x = 4 and y = 3.

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Answer:

10m

10m

Step-by-step explanation:

Answer:

area of a rectangle can be used to find the basketball court's area

area of rectangle = length* width

area of court = 29m*15m = 435 square metres.

Answer:

300 meters

Step-by-step explanation:

A meter is 3 ft so multiply 3 by 100 and you get 300

Answer:
Then f(x)= e^(x-1)

Step-by-step explanation:

Answer:

Hey stu132057, your the MAD for the data set given is

Step-by-step explanation:

Step 1: Find the mean of the data: (14+13+16+12+17+21+26)/7 = 17

Step 2: Find the difference between each data and mean:Difference between 14 and 17 is 3

Difference between 13 and 17 is 4

Difference between 16 and 17 is 1

Difference between 12 and 17 is 5

Difference between 17 and 17 is 0

Difference between 21 and 17 is 4

Difference between 26 and 17 is 9

Step 3: Add all the differences: 3+4+1+5+0+4+9 = 26

Step 4: Divide it by the number of data:26/7 = 3.7

So, the MAD = 3.7

-------------------------

Have a great day,

Nish

Answer:

1. 31.3%

2. 34.35%

3.62.6%

Step-by-step explanation:

There were 131 acoustic guitars, and 41 of them needed neck repair.

41/131 = 0.3130 = 31.3%

There were 262 total guitars serviced by Emely. 60 of them were acoustic and needed a string repaired, and 30 of them ere acoustic and needed repair, so 90 of them were acoustic and did not need neck repair.

90/262 = 0.3435 = 34.35%

There were 131 electric guitars. 48 of them had a broken string and 34 of them needed body repairs. So 82 of them needed either string or body repairs.

82/131 = 0.6260 = 62.6%

Answer: The answer for this question would be answer choice B "(0, 10) and (1, 15)". (0, 10) represents her starting amount and week saved, and (1, 15) would represent her saving for one week and having $15 total.

Hope this helps!

Answer:273.8455

Step-by-step explanation:

i do what i can

  The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.

The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.

    So, the option c is most suitable option.

Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.

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Answer:

Would the answer be 9?

Step-by-step explanation:

Use PEMDAS.
3/1/3=1
9-1-8
8+1=9

\(9 - 3 \div \frac{1}{3} + 1\)

you can follow the PEDMAS rule where,

P= Parenthesis

E= Exponents

D= Division

M= Multiplication

A= Addition

S= Subtraction

\(3 \div \frac{1}{3} = 1\)

\(9 - 8 = 1\)

\(8 + 1 = 9\)

The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is  0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.

Given that mean μ = 4.2 , standard deviation σ = 1.3

1. P(X >= 5) = P((X - μ)/σ >

                    = (5 - 4.2) /1.3

                    = P(Z ≥ 0.6154)

                    = 1 - P(Z < 0.6154)

                    = 1 - 0.7324

                    = 0.2676

The required probability is 0.2676.

2.Given that n = 8 then  \(\bar x\) = σ/\(\sqrt{(n)\)  = 1.3/√(8) = 0.4596

P(x-bar ≥ 5) = P((\(\bar x\) - μ)/σx-bar ≥ (5 - 4.2)/0.4596)

                        = P(Z ≥ 1.7406)

                        = 1 - P(Z < 1.7406)

                        = 1 - 0.9591

                        = 0.0409

The required probability is 0.0409.

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