a rectangular pool measures 4 yd by 5yd a concrete deck of uniform width is constructed around the pool. the deck anf pool togeyher cover and area of 90 yd. how wide is the deck?

we have

[tex] y = -6x^{2} + 3x + 2 [/tex]

we know that

the vertex form of the vertical parabola equation is equal to

[tex] y=a(x-h)^{2} +k [/tex]

where

(h,k) is the vertex of the parabola

To find the equation rewritten in vertex form let's factor the equation

Factor the leading coefficient

[tex] y = -6(x^{2} - 0.5x) + 2 [/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex] y = -6(x^{2} - 0.5x+0.0625-0.0625) + 2 [/tex]

[tex] y = -6(x^{2} - 0.5x+0.0625) + 2 +0.375 [/tex]

[tex] y = -6(x^{2} - 0.5x+0.0625) + 2.375 [/tex]

Rewrite as perfect squares

[tex] y = -6(x-0.25)^{2} + 2.375 [/tex]

therefore

the answer is

[tex] y = -6(x-0.25)^{2} + 2.375 [/tex]

Answer:

coincides with

Step-by-step explanation:

just got it right on edg

Vertical asymptotes at   x = {-2π, -π, 0, π, 2π}

Given:  [tex]y=csc(x)[/tex]

To find : For what values of x , it has vertical asymptotes.

Explanation:

A given function will have vertical asymptotes when its denominator becomes equal to zero.

We know that,    [tex]csc(x)=\frac{1}{sin x}[/tex]

So,  [tex]Sin(x)=0[/tex]  will give vertical asymptotes

       x = {-2π, -π, 0, π, 2π}

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Answer:

Option A is correct.

Step-by-step explanation:

In this figure we have to find the measurement of angle C.

As it clear from the picture the angle c is an acute angle which is less than 90° angle. We always measure the angles from the given point A. Therefore this is 50° angle.

So the answer would be option A. 50°.

The degree of the function is one. Then function y = x will be a linear function.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

If the degree of the equation is one. Then the function will be a linear function.

The function is given below.

y = 1x

y = x

The power of the variables 'x' and 'y' will be one. Then the function is a linear equation.

The degree of the function is one. Then function y = x will be a linear function.

More about the function link is given below.

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The angle between the minute and hour hands of a clock at 4 PM decreases at a speed of 330 degrees per hour. However, the rate at which the distance between the tips of the hands changes depends on the specific time and must be calculated using trigonometric differentiation.

To solve this problem, we first need to understand the rate at which an hour hand and a minute hand of a clock cover the distance. The hour hand takes 12 hours to complete a 360 degree rotation, i.e., it moves at a rate of 30 degrees per hour. The minute hand covers a 360 degree rotation in 60 minutes (or 1 hour), i.e., it moves at a rate of 360 degrees per hour.

At 4 PM, the hour hand will be at 120 degrees (4 hours * 30 degrees/hour) and the minute hand will be at the top of the clock, or at 0 degrees. Therefore, the minute and hour hands are 120 degrees apart. However, this angle decreases over time since the minute hand moves faster than the hour hand. To determine how fast this angle is decreasing, we calculate the relative angular velocity of the minute hand with respect to the hour hand, which is the difference of their velocities, 360 degrees - 30 degrees = 330 degrees per hour. This is the speed at which the angle between the two hands is changing.

Trigonometry is used to calculate the distance between the tips of the hands, however, the variation of this distance with respect to time is complex and depends on the specific time. So at any given time, the rate of change in the distance between the tips of the hands should be calculated using principles of trigonometric differentiation.

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The rate at which the distance between the tips of the hands of a clock is changing at 4 PM can be calculated using the rates at which the minute and hour hands are moving. At 4 PM, the rate is approximately -30 degrees per hour. Using the formula for the distance between two points on a circle, the rate of change of the distance can be calculated to be approximately 8*sqrt(3) inches per hour.

To find the rate at which the distance between the tips of the hands is changing, we need to consider the speeds at which each hand is moving. The minute hand moves at a constant speed of 1 revolution per hour, or 360 degrees per hour. The hour hand moves at a speed of 1/12 revolution per hour, or 30 degrees per hour.

At 4 PM, the minute hand is pointing at the 12 and the hour hand is pointing at the 4. The angle between the minute hand and the hour hand is 120 degrees. To find the rate at which this angle is changing, we take the derivative of the angle with respect to time, which gives us -30 degrees per hour.

Since the lengths of the hands are given in inches, the rate at which the distance between the tips of the hands is changing will be in inches per hour. Using the formula for the distance between two points on a circle, which is given by 2r*sin(theta/2), where r is the radius of the circle (in this case, the length of the minute hand) and theta is the angle between the two points (in this case, the angle between the minute hand and the hour hand), we can calculate the rate of change of the distance. Plugging in the values, we have 2*4*sin(120/2) = 2*4*sin(60) = 2*4*sqrt(3)/2 = 8*sqrt(3) inches per hour.

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Esmeralda deleted 10 minutes of music from her 40-minute playlist. With the remaining 30 minutes of music, she has enough for a 30-minute workout.

To determine if Esmeralda has enough music on her playlist for a 30 minute workout, we need to calculate how much music she has remaining after deleting 25%.

Let's start by finding 25% of the original music duration. To do this, we multiply the original duration (40 minutes) by 0.25:

25% of 40 minutes = 40 minutes * 0.25 = 10 minutes

Therefore, Esmeralda deleted 10 minutes of music.

To find out how much music she has left, we subtract the deleted music from the original duration:

Remaining music = Original duration - Deleted music = 40 minutes - 10 minutes = 30 minutes

Since the remaining music duration is exactly 30 minutes, Esmeralda has enough music on her playlist to last for a 30-minute workout.

Calculating S'(5) and S'(25) involves estimating the slope of the tangent to the temperature-speed graph of Coho salmon at those temperatures. The provided data is insufficient for an exact calculation and more information or a graph is needed.

The influence of temperature on the maximum sustainable swimming speed (S) of Coho salmon can be analyzed using calculus to find the rate of change of speed with respect to temperature, commonly represented as S'(T). To estimate the values of S'(5) and S'(25), one would typically use a graph of S versus T and look for the slope of the tangent to the curve at T=5 and T=25.

However, the given data is insubstantial for such an analysis. More context or a graph is needed to provide a specific estimate. Generally, one might use the values given for S at temperatures nearby T=5 and T=25 to calculate the approximate rates of change at these points through the use of difference quotients or other numerical methods if a graph or formula is not available.

To solve for t in the equation rt-2n=y, add 2n to both sides to get rt=y+2n, and then divide by r to find t=(y+2n)/r.

To solve the equation rt-2n=y for t, we need to isolate t on one side of the equation. Here's a step-by-step solution:

Thus, the value of t in terms of y, n, and r is t = (y + 2n) / r.

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The probability that a lot containing exactly two defective electronic baseball games manufactured by Tempco will still be shipped is approximately 0.821 or 82.1%. This problem is solved using the concept of hypergeometric distribution in probability theory.

This problem is a case of hypergeometric distribution in probability theory. In the given situation, the total number of games in the lot is 36, of which 34 are okay and two are defective. The inspector selects eight games out of these 36. We must calculate the probability that neither of the two defective games is in the selected 8.

This can be calculated as follows: The probability of selecting a good game first is 34/36. After we choose a good one, we now have 33 good games left in a set of 35 games, so the probability of choosing another good one is 33/35. We continue this way until we have selected all eight games. Thus, the probability that all eight games selected will be good, and therefore the lot will be shipped, is (34/36) * (33/35) * (32/34) * (31/33) * (30/32) * (29/31) * (28/30) * (27/29) = 0.821. So, the probability that a lot containing exactly two defective electronic baseball games manufactured by Tempco will still be shipped is approximately 0.821, or 82.1%, when expressed as a percentage.

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The maximum error in the area of a circle with an estimated radius of 14 inches and a measurement error of "+/-0.08 inches" can be calculated using differentials as approximately 7.03 inches².

To estimate the maximum error in calculating the area of a circle with a radius of approximately 14 inches (with a measurement error of "+/-0.08 inches"), we can use differentials. The formula for the area of a circle is A =
^(2), where π is a constant (approximately 3.14159). The differential dA, which represents the change in area, is given by dA = 2πr * dr, where dr is the change in radius.

With an error in radius measurement of"+/-0.08 inches", we have dr = 0.08 inches. Therefore, the error in the area, referenced as dA, can be calculated as:

dA = 2 * π * 14 inches * 0.08 inches

This gives dA ≈ 2 * 3.14159 * 14 * 0.08 inches², which can be calculated to determine the maximum error in the area.

After performing the calculation, we find that the maximum error in the area of the circle is about 7.03 inches².

The solution is, the practical domain is all real numbers from 5 to 7, inclusive. and the practical range is all real numbers from 58 to 81.2.

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Here, we have,

Clarence works more than 5 hours and less than 7 so the practical domain is all real numbers from 5 to 7, inclusive.

Function: f(t) = 11.6 t

Restrictions: 5 ≤ t ≤ 7

Domain: possible values of t: all real values between 5 and 7 inclusive

Range: possible values of f(t): from 11.6 * 5 to 11.6 *7 = from 58 to 81.2, inclusive.

Using this domain, the practical range is:

From f(5) = 11.6(5) = 58

To f(7) = 11.6(7) = 81.2

inclusive.

Answer:

the practical domain is all real numbers from 5 to 7, inclusive. and the practical range is all real numbers from 58 to 81.2

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The statement "If x > 0 and a > 1, then (ln x/ln a) = ln (x/a)" is false.

This can be shown by using the properties of logarithms.

The correct relationship is given by the change of base formula, which states that for any positive x, a, and b, where a and b are not equal to 1.

The following holds:

[tex][ \frac{\ln x}{\ln a} = \log_a x ][/tex]

Therefore, the correct relationship is:

[tex][ \frac{\ln x}{\ln a} = \log_a x ][/tex]

This shows that the original statement is false.

Answer:

3 • h = 18

Step-by-step explanation:

Yes because

15/15 equals 1 whole

While 9/15 is not equal to one

Meaning 1 whole is bigger than 9 out of 15 of something

A single six-sided die has specific outcomes for events: at most 2 consists of {1, 2}, rolling a 3 consists of {3}, and rolling an even number includes {2, 4, 6}.

When a single die is rolled, the possible outcomes for different events are as follows:

The event where the die comes up at most 2 includes the outcomes {1, 2}.

The event where the die comes up 3 includes the single outcome {3}.

The event where the die comes up even includes the outcomes {2, 4, 6}.

It is important to list all possible outcomes clearly to understand the probabilities for each event. For instance, the probability of each of these events can be calculated by counting the favorable outcomes and dividing by the total number of possible outcomes, which is 6 in the case of a single six-sided die roll.

Answer:

its C and E

Step-by-step explanation:

Data sets b, c, and d have outliers, identified by calculating the Interquartile Range (IQR) and checking for values more than 1.5 times the IQR above the third quartile or below the first quartile. The approach to outliers depends on context, and alternative methods such as the standard deviation may yield different results.

To determine which data sets have outliers, we can use an appropriate numerical test involving the Interquartile Range (IQR) to identify outliers. The IQR is the range between the first quartile (Q1) and the third quartile (Q3) of the data set, and an outlier is typically defined as a value that is more than 1.5 times the IQR above the third quartile or below the first quartile.

Let's calculate the IQR for each data set:

After calculating the IQR for each set and checking for outlier definition, we find:

When a data value is identified as an outlier, it’s important to consider the context before deciding what action to take. In some cases, it may be appropriate to investigate further to understand why this value is so different from the others. In other cases, the outlier may be removed or handled statistically if it unduly influences results.

Depending on the data's distribution, using a criterion such as any data values farther than two standard deviations from the mean might yield different results for identifying outliers. This approach is most appropriate for data that is mound-shaped and symmetric.

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72.6 is 82.5 percent of 88. To find what percent 72.6 is of 88, divide 72.6 by 88 and then multiply by 100%. This gives you 82.5%, which means 72.6 is 82.5 percent of 88.

To find what percent 72.6 is of 88, you can use the formula:

Percentage = (Part / Whole) × 100%

In this case, the 'Part' is 72.6 and the 'Whole' is 88. Plugging these numbers into the formula:

Percentage = (72.6 / 88) × 100%

Percentage = 0.825 × 100%

Percentage = 82.5%

So, 72.6 is 82.5 percent of 88.

The polynomial with rational coefficients and roots -5 and 3i will be [tex]p(x)=x^3+5x^2+9x+45=0[/tex].

Polynomial p(x)=0 has the roots: -5 and 3i

It is required to write a polynomial with rational coefficient and the given roots.

The polynomial has a complex root 0+3i. So, there will be one more root of the polynomial which is 0-3i.

Now, the roots of the polynomial are

[tex]\alpha =-5\\\beta=0+3i\\\gamma=0-3i[/tex]

So, the required polynomial can be written as,

[tex](x-\alpha)(x-\beta)(x-\gamma)=(x-(-5))(x-(0+3i))(x-(0-3i))\\=(x+5)(x-3i)(x+3i)\\=(x+5)(x^2-(3i)^2)\\=(x+5)(x^2+9)\\=x(x^2+9)+5(x^2+9)\\=x^3+5x^2+9x+45[/tex]

Therefore, the polynomial with rational coefficients and roots -5 and 3i will be [tex]p(x)=x^3+5x^2+9x+45=0[/tex].

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As per linear equation, the half of 9(1/2) inches is 4(3/4) inches or 4.75 inches.

A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.

The given measurement is 9(1/2) inches.

Therefore, the half of the given measurement is

= [9(1/2) ÷ 2] inches

= [19/2 ÷ 2] inches

= 19/4 inches

= 4(3/4) inches

= 4.75 inches

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Answer:

The correct option is 4. The average rate of change from x = −1 to x = −3 is -1.

Step-by-step explanation:

It is given that the graph of parabola going through (-1,7) and (-3,9).

It means the value of at x=-1 is 7.

[tex]f(-1)=7[/tex]

The value of at x=-3 is 9.

[tex]f(-3)=9[/tex]

The slope of a function f(x) for the interval [a,b] is

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

We have to find the average rate of change from x = −1 to x = −3. Here a=-1 and b=-3. So the average rate of change from x = −1 to x = −3 is

[tex]m=\frac{f(-3)-f(-1)}{-3-(-1)}[/tex]

[tex]m=\frac{9-7}{-3+1}[/tex]

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

[tex]m=-1[/tex]

The average rate of change from x = −1 to x = −3 is -1. Therefore the correct option is 4.

Answer:

BC≅AC

Step-by-step explanation:

From the given figure, triangle ABC is such that ∠CAB=∠CBA=70°, therefore the sides of the triangle that are AC and BC will be congruent to each other as if two angles of the same triangle are equal then the sides opposite to those angles are also equal  to each other, therefore

BC is congruent to AC that is BC≅AC.