You are throwing a party and you need 7 liters of soda for every 12 guests. If you have 90 guests, how many liters of soda do you need?

The result of completing the square for the equation -6x² - 582 = −60x will be (x - 5)² = - 72.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The equation is given below.

-6x² - 582 = −60x

Simplify the equation, then we have

-6x² - 582 = −60x

-6(x² + 97) = - 60x

x² + 97 = 10x

x² - 10x = - 97

x² - 10 + 25 = 25 - 97

(x - 5)² = - 72

The result of completing the square for the equation -6x² - 582 = −60x will be (x - 5)² = - 72.

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If fires occur at points uniformly chosen on (0, A), then [tex]a = \frac{A}{2}[/tex] is the second derivative where should the station be located so as to minimize the expected distance from the fire.

From the question, a fire station is to be located along a road of length A, A < ∞.

If fires occur at points uniformly chosen on (0, A), then we have to find where should the station be located so as to minimize the expected distance from the fire.

E∣X−a∣ = [tex]\int^{A}_{0}|x-a| \frac{1}{A} dx[/tex]

E∣X−a∣ = [tex]\int^{a}_{0}|a-x| \frac{1}{A} dx+\int^{A}_{a}|x-a| \frac{1}{A} dx[/tex]

Now integrating.

E∣X−a∣ = [tex]\frac{1}{A}\left(\frac{a^2}{2}+\frac{A^2}{2}-aA-\left(\frac{a^2}{2}-a^2\right)\right)[/tex]

E∣X−a∣ = [tex]\frac{a^2}{A}-a+\frac{A}{2}[/tex]

If we set the derivative to zero, we get [tex]\frac{2a}{A}-1=0[/tex], where [tex]a = \frac{A}{2}[/tex] is the derivative. One can look at the second derivative, which is always positive, to see if this is the minimizer.

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The complete question is:

A fire station is to be located along a road of length A, A < ∞. If fires occur at points uniformly chosen on (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to minimize E[∣X−a∣] when X is uniformly distributed over (0, A).

Answer: x>17/2

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

7<2x−10

Step 2: Flip the equation.

2x−10>7

Step 3: Add 10 to both sides.

2x−10+10>7+10

2x>17

Step 4: Divide both sides by 2.

2x/2 > 17/2

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Let's solve your inequality step-by-step.

−10+17<2x−10

Step 1: Simplify both sides of the inequality.

7<2x−10

Step 2: Flip the equation.

2x−10>7

Step 3: Add 10 to both sides.

2x−10+10>7+10

2x>17

Step 4: Divide both sides by 2.

[tex]\frac{2x}{2} > \frac{17}{2} \\\\ x > \frac{17}{2}[/tex]

Hope this helped :0

log(x) = 4 can be restated as an exponential statement: 10^4 = x

x = 10000

The value of B in the table will be D. 90

The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.

The ratios between the two variables should be considered in order to determine whether a relationship is proportional. The relationship is proportional if the ratio remains constant. The relationship is not proportional if the ratio changes.

In this case, the relationship between part and whole is 7:10.

Therefore, the value of B will be:

= 10 / 7 × 63

= 10 × 9

= 90

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Two hidden cards out of five numbered cards with 8 as mode and 6 as mean of five numbers is equal to 8 and 1.

Total number of numbered cards is equal to 5

Number of hidden cards are two.

Let us consider two hidden cards be 'a' and 'b'.

Mode of the five numbered cards is 8

Three numbers are 4 , 9 , a, b, 8.

Mode represents the number with higher frequency.

4, 9, 8 only one time as 8 is the mode one of the number should be equal to 8.

let b = 8

Mean of five numbers is 6

Mean = ( Sum of all the numbers ) / total numbers

⇒ 6 = ( 4 + 9 + a + 8 + 8 ) / 5

⇒ 30 = 29 + a

⇒ a = 30 -29

⇒ a = 1

Therefore, two hidden numbers for the given mode and mean is equal to 8 and 1.

The above question is incomplete , the compete question is:

Basil has five numbered cards.

Two of the numbers are hidden. 4 9 ? ? 8

The mode of the five numbers is 8.

The mean of the five numbers is 6

c) Work out the two hidden numbers.

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The rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. To find the rate at which the volume is changing, we need to take the derivative of this equation with respect to time, using the chain rule.

dV/dt = 4/3π(3r²) dr/dt

We know that the radius of the snowball is decreasing at a constant rate, so we can find the value of dr/dt by using the information given in the problem. The radius is decreasing from 34 cm to 18 cm in 30 minutes, which means that:

dr/dt = (34 - 18) cm / 30 minutes = -0.5333 cm/min

Now that we know the rate at which the radius is changing, we can substitute it into the equation for dV/dt and find the rate at which the volume is changing.

We know that the radius is 6 cm at the instant the volume is changing, so we can substitute that into the equation:

dV/dt = 4/3π(3r²) dr/dt = 4/3(π)(3)(6 cm)²(-0.5333 cm/min) = -241.27 cm³/min

So, the rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

Note that the negative sign indicates that the volume is decreasing.

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Answer:

-2x + y = 25

Step-by-step explanation:

just add them together by columns.  X-3x = -2x

3y-2y = y

5+20 =25.

done.

Megan have total 1,071 stamps.

The concept used in this problem is multiplication, specifically using it to find the total number of stamps by multiplying the number of pages by the number of stamps per page. Additionally, it also uses the concept of addition to find the total number of stamps by adding the number of stamps on full pages to the number of stamps on half-full pages.

as given, Megan keeps her stamps in a book that can hold 17 on each page. she has 56 pages full of stamps. So,

Megan has 56 pages * 17 stamps per page = 952 stamps on full pages.

and 14 pages that are only half full. So,

She has 14 pages * (half of 17 stamps per page) = 14 pages * 8.5 stamps per page = 119 stamps on half-full pages.

Therefore, Megan has 952 stamps + 119 stamps = 1,071 stamps in total.

hence, Megan have total 1,071 stamps.

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The exact value of csc A is  (√89) /5

Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.

Since cot ⁡A = 8 /5  and that angle A is in Quadrant I.

tan A = 5/8       (Remember: tan = 1/cot and tan = opposite/adjacent)

opposite = 5 and adjacent = 8

hypotenuse = √(5² + 8²) = √89

sin A = 5/(√89)    (sin = opposite/hypotenuse)

csc A = (√89) /5     (csc = 1/sin)

Thus, the exact value of csc A is  (√89)/5

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Answer:

It is not possible to determine the percentage of samples that pass without additional information.

The shortest possible height of the vase would be 45.650 centimeters.

Rounding to the nearest tenth of a centimeter, the height of a vase is 45.7 centimeters. The vase's height can be as short as possible. Include three digits in your response.

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Henry can claim 15.38% as his percent error.

We know that the formula for the percent error is:

Percent Error = (Absolute Error ÷ Actual Value) × 100

where, Absolute Error = ∣Actual Value - Estimated Value|

In this situation, the actual value is 65 mph and the Estimated value is 55 mph.

So, using above formula for absolute error,

Absolute Error = ∣Actual Value - Estimated Value|

Absolute Error = ∣65 - 55|

Absolute Error = 10

Now we find the percent error using above formula for the percent error.

Percent Error = (10 ÷ 65) × 100

Percent error = 15.38%

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The system of  equations that can be entered is y = 16.9x - 2.3 and y = 3.2x + 18

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

16.9x-2.3=3.2x+18

Express the equation properly

So, we have the following representation

16.9x - 2.3 = 3.2x + 18

Next, we split the equation and introduce the variable y

So, we have

y = 16.9x - 2.3

y = 3.2x + 18

The above is the system of equations

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Answer:

70-14g

Step-by-step explanation:

-20g+70+6g = 70-14g

The probability that at least one person received $20 is 0.3

In math the term called probability is defined as a number that reflects the chance or likelihood that a particular event will occur.

Here we know that two people are picked at random from a group of 50 and given $10 each.

Here we have also know that three people are picked from the same group - one or more people could have been picked both times - and given $10 each.

Then the probability is calculated based on the binomial distribution is written as,

=> P = (50 3) 10³ (1 - 10) ⁵⁻³

When we simplify this one then we get the value of p as 0.3.

Then the following values are calculated through it,

μ = 15

σ = 3.24

σ² = 10.5

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The value of x from the expression 3/4 x +3-2x = -1/4 +1/2x+5 can be simplified as 45/29.

The concept that will be used is simplification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

3/4x +3-2x = -1/4 +1/2x+5

We can simplify by collecting the like terms,

3/4x - 1/2x - 2x = -1/4 + 5 -3

Then we can simplify further as:

-29x/20 = - 9/4

29x = (20*9)/4

29x= 45

x= 45/29

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By resolving the inequality, we discovered that the least possible pair of numbers is (37,39) if the total of two consecutive odd integers is at least 76.

The sum of two consecutive odd integers is at least 76.

First we let the two consecutive odd integers.

The first consecutive odd integer = n

The second consecutive odd integer = n + 2

The sum is at least 76. So the inequality that models the problem is

n + n + 2 ≥ 76

Now we determine the least possible pair of integers by solving the inequality.

2n + 2 ≥ 76

Subtract 2 on both side, we get

2n ≥ 74

Divide by 2 on both side, we get

n ≥ 37

If the least value of x is 37. So

The second odd integer = x + 2 = 37 + 2 = 39

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An inequality which shows the constraint on the amount of flour John has to make pies and cobblers is: B. 3x + 3y ≤ 16

In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:

Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:

3x + 3y ≤ 16

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Answer: no it will not overload it's weight limit

Step-by-step explanation: 190 x 10 = 1900

                                          i'm sorry if i am wrong                                                                                

            then i think i do/ 59 x 10 = 590   so then  1900 + 590 = 2490

The value of given expression 9x=4 equals to 4/9.

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.

Given expression ,

log 9x = log 4

log 9 + log x = log 4

log x = log 4 - log 9

log x = log 4 / 9

x = 4 /9.

Hence, The value of given expression 9x=4 equals to 4/9.

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The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.

The equations are given below.

2y = 180° - 126°

2y = 54°

y = 27°

2x + 1 = 180° - 85°

2x + 1 = 95°

2x = 94°

x = 47°

The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.

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The complete question is attached below.

As number is rounded off to 30,000, the correct option is A i.e, it is closer to 30,000 than 29,000.

We look at the last three digits and round to the closest thousand. If these digits total 500 or more, the thousands digit is rounded up; if they total less than 500, the thousands digit is rounded down while remaining the same.

For example, to solve this question we have to check whether 16796 is closer to 16000 or 17000 in the counting. In this case, 16796 is closer to 16000, hence 17000 is the round figure of 16796.

In this problem, as the number is said to be rounded off to the nearest thousand is 30,000, this means that, the number is closer to 30,000 than 29,000.

The question is incomplete. The picture of number line is missing. It is placed in the attachment below.

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The given statement about Histogram that , " if median of a data set is larger than mean, then the histogram of data will likely have a longer right tail" is FALSE .

A histogram is a graph in which most of data falls to the right of graph's peak and is known as a right-skewed histogram. This type of histogram is  also known as a positively skewed histogram.

The relation between the mean , median and mode in a right-skewed histogram is denoted as : mean > median > mode .

A distribution is called skewed Right if, in histogram , the right tail (smaller values) is much longer than the left tail (larger values).

Therefore , For histogram to have longer right tail , the median should be less than the mean .

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Answer:

3rd one

Step-by-step explanation:

Answer:

3rd one

Step-by-step explanation:

The test hypothesis for the 2010 U. S. Census is H0 = Oregon < Latino.

In math the term called hypothesis is defined as an idea that is suggested as the possible explanation for something but has not yet been found to be true or correct.

Here we know that in 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino.

And here we have also know that random sample of 853 adults in Oregon and 110 of the people surveyed were Hispanic or Latino.

Then the sample proportion is calculated as,

=> sample proportion=113/853=0.1325

And the value of Test statistic is,

=> z = (0.1325-0.117)/√(0.117*(1-0.117)/853)

=> z = 1.41

So, the hypothesis is written as,

=> H0 = Oregon < Latino.

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The value of test statistics z=1.04

First, state the null and alternative hypotheses:

[tex]H_o=u_1=u_2\\H_a=u_1 > u_2[/tex]

Use z-statistics:

[tex]z=\frac{x_1-x_2}{y} ------(1)[/tex]

where x₁ and x₂ are the means and:

[tex]y=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }[/tex]

Calculating the value of test statistics:

[tex]y=\sqrt{\frac{(23.53)^2}{47}+\frac{(71.32)^2}{54} }[/tex]

[tex]y=\sqrt{\frac{533.6609}{47}+\frac{5086.542}{54} }[/tex]

[tex]y=\sqrt{11.780+7.460}[/tex]

[tex]y=\sqrt{19.24}[/tex]

y = 4.386

Now substitute the y value in equation (1)

[tex]z=\frac{75.57-71.32}{4.386}[/tex]

z = 1.04

The test statistics is z = 1.04

The decision rule for rejecting the null hypothesis is:  α≤ test statistics

Using the z-score table, it is possible to determine the p-value, which is:

value = 0.877

Comparing the p-value with the level of significance (α = 0.05):

0.877 > 0.05

Therefore, we fail to reject the null hypothesis.

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The total amount of dish soap added to both amounts will be 786.89 ml.

Describe addition.

In math, addition is the process of adding two or more integers together.

Since you currently have 224.14 mL of dish soap at home, you decide to buy a 562.75 ml container of it.

We will combine the two amounts together to get the total amount of dish soap.

Dish soap is 786.89 ml total (562.75 ml plus 224.14 ml).

Consequently, there is 786.89 ml of dish soap in total.

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Answer: consecutive interior angles and x=66°

Step-by-step explanation:

The angles are consecutive interior angles. The property is consecutive interior angles are supplementary.

2x+24+24=180          [combine like terms]

2x+48=180                 [subtract both sides by 48]

2x=132                       [divide both sides by 2]

x=66

Therefore, the angle is consecutive interior angles and x=66°.

In a recent student government​ election, the number of vote of the winner is 51

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

In a proportion, two ratios are specified to be equal to one another in an equation.

The number of votes of the winner is calculated by writing the ratio

= number of the students who voted / total number of students

let x be the number of students that voted the winner

85 / 100 = x / 60

100x = 60 * 85

x = 5100 / 100

x = 51

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