Translate the following statements into symbolic form using uppercase letters to represent affirmative English statements. Use the letters given in parentheses to form the translations.
If heroin is legalized, then its use may increase but criminal activity will decline. (L, U, C)

The equation for the given parabola is; x = ¹/₁₂(y - 3)² - 2

From the graph, we see that;

Focus = (1, 3)

Directrix; x = -5

General form of equation of a parabola is;

(y - k)² = 4p(x - h)

where;

focus is (h + p, k)

directrix is x = h - p

Thus;

(1, 3) = (h + p, k)

h + p = 1  -----(1)

k = 3

Similarly;

h - p = -5   -----(2)

Add eq 1 to eq 2 to get;

2h = -4

h = -2

-2 - p = -5

p = 3

Thus, equation of the parabola is;

(y - 3)² = 4(3)(x - (-2))

(y - 3)² = 12(x + 2)

divide both sides by 12 to get;

¹/₁₂(y - 3)² = x + 2

x = ¹/₁₂(y - 3)² - 2

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The cone has a volume of (D) 288in3.

To find the volume:

Given:

Formula:

The Pythagorean theorem is used to calculate height.

The volume of the cone:

Therefore, the volume of the cone is (D) 288in³.

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The complete question is given below:
Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?

A. 32

B. 96

C. 128

D. 288

E. 384

\(\Large\textsf{\textbf{Answer\::}}\)

-1, 260

\(\large\textsf{\textbf{Calculations\;:}}\)

First , take a look at the signs of the numbers we're asked to multiply .

One of them is negative , and the other one is positive .

If we have a negative number times a positive number , the product is a positive number .

Multiply :

(-315) × 4

-1, 260 (Ans)

\(\footnotesize\text{hope\:helpful~}\)

Answer:

1) y-4+1(x-5)

Step-by-step explanation:

With point-slope form, you just have to substitue the information that is given to you into the generic formula.

y-y1= m(x-x1)

so the y1 is the y value of the point that is given to you and x1 is the x value of the point that is given to you

m is the slope (also given)

and x and y just stay the same; x &y

The company whose net change is between Care Kingdom and Rock Palace is B. Piedmont Lighting.

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in elementary mathematics. Every number line point is assumed to correspond to a real number, and every real number to a number line point.

In this situation, Care Kingdom +0.12 while Rock Palace has a value of -0.10. It should be noted that Piedmont Lighting is +0.03.

This will be between the numbers.

In conclusion, the correct option is B.

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Answer:

0

Step-by-step explanation:

0 · |-6|

Absolute value means take the non negative number

0* 6

0

The value of the given absolute value equation 0 · |-6| is 0.

Given that an absolute value equation 0 · |-6|, we need to evaluate this.

To evaluate the expression 0 · |-6|, let's break it down step by step:

First, calculate the absolute value of -6:

|-6| = 6

Now, multiply the result from step 1 by 0:

0 · 6 = 0

When you multiply any number by 0, the result is always 0.

In this case, even though |-6| equals 6, multiplying it by 0 will make the overall result 0.

This is a fundamental property of multiplication with zero.

So, the final answer is 0.

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All rational functions can be expressed as f(x)=p(x)/q(x), where p and q are polynomial functions and q(x) cannot be equal to 0.

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are polynomial functions and q(x) ≠ 0.

Rational function is the ratio of two polynomial functions where the denominator polynomial is not equal to zero. It is usually represented as R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions. In past grades, we learnt the concept of the rational number. It is the quotient or ratio of two integers, where the denominator is not equal to zero. Hence, the name rational is derived from the word ratio

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The angle of BDC is 60 degrees.

The angle sum property of a triangle states that the sum of a triangle's three internal angles is 180 degrees. A triangle is a closed figure made up of three line segments that have both internal and external angles. When the values of the other two angles are known, the measure of an unknown interior angle can be determined using the angle sum property.

The data listed above can be inserted into our diagram. ADB and BDC complement one another, therefore their combined degree measurement is 180. Thus, m∠ADB is equal to 180 – 60, or 120 degrees.

Given,

∠ADC = 59

∠BDC = ?

∠ADB = ∠BCD

∠BCD = 90

∠ADB = 90

∠ADC = 59

∠ADB + ∠BDC = 59

90 + ∠BDC = 59

∠BDC = -31

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Answer:

No solution

Step-by-step explanation:

2>1+2x-2x

the two x's would cancel out.

The answer is no solution

Answer:

I mean, I think it varies by house and by location but a general range would be:

Min: 64 *F

Max: 74 *F

The vertex of the Quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

The vertex of a quadratic function given the y-intercept and x-intercept, we need to determine the axis of symmetry, which is the line that passes through the vertex. The x-coordinate of the vertex will be the midpoint between the x-intercepts, while the y-coordinate will be the same as the y-intercept.

Given that the y-intercept is (5, 0) and the x-intercept is (0, 80), we can determine the x-coordinate of the vertex by finding the midpoint of the x-intercepts. The x-coordinate of the midpoint is simply the average of the x-values:

x-coordinate of vertex = (0 + 0) / 2 = 0 / 2 = 0

Since the y-coordinate of the vertex is the same as the y-intercept, the vertex will have the coordinates (0, 0).

Therefore, the vertex of the quadratic function is (0, 0).

In conclusion, the vertex of the quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

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Answer:

134 adult tickets were sold adt tye school play.

Step-by-step explanation:

total tickets = adult + student tickets

total tickets= (2×adult tickets)+adult tickets

total tickets = 3× adult tickets.

402=3×adult tickets.

402÷3=adult tickets

134=adult tickets

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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If the same condition is described as both acute and chronic and separate subentries exist in the icd-10-cm alphabetic index at the same indentation level is True

What is alphabetical index?

An alphabetical index, often known as an index, is a list of words or phrases that appear frequently in a text and which, if listed alphabetically, may assist readers in finding information more quickly.

What is indentation level ?

The much-despised formatting method of indentation gives readers a sense of continuity.

Reasons:

The Alphabetic Index's sub term entries and the Tabular List's inclusion and exclusion notes can both be used to find combination codes.

Only use the combination code when it accurately describes the diagnostic conditions in question or when the Alphabetic Index instructs you to. When the categorization offers a combination code that unambiguously identifies all of the components listed in the diagnosis, multiple coding shouldn't be employed. An additional code should be utilised as a secondary code when the combination code does not provide the requisite specificity in characterising the symptom or problem.

The statement is True

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Answer:

Step-by-step explanation:

Answer:

2 pounds

Step-by-step explanation:

If 1 gram of medication is given to a dog the weighs 0.2 pounds. You multiply both sides by 10

1(10)grams = 0.2 (10)pounds

10 grams = 2 pounds

Answer:

$10.2

Step-by-step explanation:

Use this formula:

Price of product after discount = Initial  Price * ( 1 - (discount/100) )

Answer:

Muscles Gym: 13.33

Energy Gym: 15.00

Step-by-step explanation:

Muscles Gym: You divide "40.00" by "3", which will then give you the answer of "13.33".

Energy Gym: You divide "93.00" by "6", which will then give you the answer of "15.50".

You then add the zero to show the proper number of cents after the decimal point.

I hope this helps!

Answer:

slope = \(\frac{1}{5}\)

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, 6 ) and (x₂, y₂ ) = (4, 5 )

m = \(\frac{5-6}{4-9}\) = \(\frac{-1}{-5}\) = \(\frac{1}{5}\)

By comparing the given series with (D) and taking the limit of their ratios as n approaches infinity, we can determine the convergence/divergence behavior of the given series.

To determine whether the series ∑ n=1 to ∞ (n^3 + 3n) / (25 + 2^n) converges or diverges using the limit comparison test, we need to compare it with a known series. The limit comparison test states that if the ratio of the terms of two series approaches a finite nonzero value as n approaches infinity, then both series either converge or diverge.

Let's examine the answer choices provided:

(A) ∑ n=1 to ∞ (n^1) / (B)

(B) ∑ n=1 to ∞ (n^2) / 1

(C) ∑ n=1 to ∞ (n^2) / 5

(D) ∑ n=1 to ∞ (n^3) / 1

Out of these choices, we can see that (D) ∑ n=1 to ∞ (n^3) / 1 has the same power of n in the numerator as the given series. Therefore, we can use the limit comparison test with this series to determine whether the given series converges or diverges.

By comparing the given series with (D) and taking the limit of their ratios as n approaches infinity, we can determine the convergence/divergence behavior of the given series.

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The second payment should be approximately $2,402.82 in order to be economically equivalent to the original payment. Rounded to the nearest cent, the second payment would be $2,402.00.

To find the amount of the second payment that would be equivalent to the original obligation, we can use the concept of present value.

The present value of a future payment is the amount that would need to be invested today at a given interest rate to accumulate to that future payment.

In this case, the first payment of $2,000 was due 3.0 years ago, and the second payment of $2,500 is due 6.0 years from now. The debtor has proposed a payment of $1,250 today and a second payment in 4.5 years from now.

To find the second payment amount, we need to determine the present value of the original second payment of $2,500 using the proposed interest rate of 4.20% compounded monthly.

Using the present value formula:

PV = FV / (1 + r/n)^(n*t)

where PV is the present value, FV is the future value, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

Let's calculate the present value of the second payment:

PV = $2,500 / (1 + 0.0420/12)^(12 * 4.5)

PV ≈ $2,402.82

Therefore, the second payment should be approximately $2,402.82 in order to be economically equivalent to the original payment. Rounded to the nearest cent, the second payment would be $2,402.00.

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Answer:

the answer is B. I hope this helps

Answer:

P = -4

Step-by-step explanation:

Assuming that x = 20 and y = 24, you have to plug in these numbers for x and y to get to this equation P = 20 - 24.  You should get -4 when you subtract 24 from 20 giving you a negative answer.

The linear equation that describes the problem is: 2x + y = 300.

A linear equation can be defined in standard form as Ax + By = C, where:

A, B, and C are integers

x and y are variables.

From the information given, we have the following:

number of games = x

rent for a pair of shoes for any number of games = y

total earnings goal for that day = 300

Therefore, the linear equation would be: 2x + y = 300

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\(\frac{x}{8}=\frac{9}{4} \\\\4x=72\\x=18\\\)

hope this helps :)

32 hours do the lifeguard need to work in one week to earn the same amount of money.

To determine the number of hours the lifeguard needs to work in one week to earn the same amount of money, we can set up an equation based on the given information.

Let's denote the number of hours the lifeguard needs to work as "h."

For the lifeguard at the community pool:

Hourly wage = $9.50

Weekly earnings = Hourly wage * Number of hours worked = $9.50 * h = 9.50h

For the lifeguard at the county club:

Hourly wage = $8.25

Weekly earnings = Hourly wage * Number of hours worked + Weekly bonus = $8.25 * h + $40 = 8.25h + 40

We want to find the number of hours (h) that makes the weekly earnings equal for both lifeguards.

So we set up the equation:

9.50h = 8.25h + 40

To solve this equation, we can subtract 8.25h from both sides:

9.50h - 8.25h = 8.25h - 8.25h + 40

1.25h = 40

Dividing both sides by 1.25, we get:

h = 40 / 1.25

h = 32

Therefore, the lifeguard needs to work 32 hours in one week to earn the same amount of money as the lifeguard at the county club with the weekly bonus.

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Answer:

Step-by-step explanation:

6,000-7,500 liters (1,500-2,000 gallons) of blood daily. The average adult body contains about five quarts of blood, which continually circulates throughout the body. Hope this helps!

(a) To find the amount in the account at the end of 1 year, we use the formula:

A = P(1 + r)^n

where A is the amount in the account at the end of the year, P is the principal (the initial amount deposited), r is the interest rate as a decimal, and n is the number of times the interest is compounded in a year. In this case, P = $4500, r = 0.06 (since the interest rate is 6%), and n = 1 (since the interest is compounded once a year). So, we have:

A = $4500(1 + 0.06)^1

= $4500(1.06)

= $4770

Therefore, the amount in the account at the end of 1 year is $4770.

(b) To find the amount in the account at the end of 2 years, we again use the formula:

A = P(1 + r)^n

However, in this case, n = 2 (since the interest is compounded twice in 2 years). So, we have:

A = $4500(1 + 0.06)^2

= $4500(1.1236)

= $5061.20

Therefore, the amount in the account at the end of 2 years is $5061.20.

Answer:

8 houses

Step-by-step explanation:

48-40=8 houses left to be sold