-7=5x-24 divided by -3

The expression that represents the amount of money the friends still need to collect to meet their goal is

To find the amount of money the friends still need to collect to meet their goal, we need to subtract the total amount they have collected from the total contribution goal:

Total contribution goal: 7x^2 - 4xy + 8

Total amount collected: (5xy + 16) + x^2 + (4x^2 - 7)

= 5xy + x^2 + 4x^2 + 16 - 7

= 5xy + 5x^2 + 9

Subtracting the total amount collected from the contribution goal:

7x^2 - 4xy + 8 - (5xy + 5x^2 + 9)

= 2x^2 - 9xy - 1

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The minimal size for a pool and deck constructed as in the application, with the deck extending an additional 10 meters is 1400 meter square.

Given that,

We have to find the minimal size for a pool and deck constructed as in the application, with the deck extending an additional 10 meters on each side of the pool and a further 5 meters along the corresponding sides of the pool. The pool's area is 1800 square meters.

We know that,

Area of the Total space = (l+10)(b+20)

Here,

b=1800/l

l= 30

So,

b=60

Area of the total space is (30+10)(60+20) = 40×80 = 3200 m²

The minimum area of deck = 3200-1800 = 1400 m²

Therefore, The minimal size for a pool and deck constructed as in the application, with the deck extending an additional 10 meters is 1400 meter square.

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The value of x in the right triangle is 10.43 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in the triangle is 180 degrees. Therefore, let's find the value of x in the right triangle.

tan 41 = opposite / adjacent

opposite side = x

adjacent side = 12

Therefore,

tan 41° = x / 12

cross multiply

x = 12 tan 41°

x = 12 × 0.86928673781

x = 10.4314408538

Therefore,

x = 10.43 units

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The gradient of the line joining the points (1,-1) and (4,9) is 10/3, while the gradient of the line joining (5,1) and (2,-2) is 1. The x-intercept of the equation 3y = 2x - 2 is 1, and the y-intercept is -2/3. These calculations follow the formula for gradient and the methods for finding intercepts in linear equations.

1) To find the gradient of a line joining two points, you can use the formula: gradient = (change in y)/(change in x).
Given the points (1,-1) and (4,9), the change in y is 9 - (-1) = 10 and the change in x is 4 - 1 = 3.
Therefore, the gradient of the line joining these points is 10/3.
2) Similarly, to find the gradient of a line joining two points (5,1) and (2,-2), we can use the same formula. The change in y is -2 - 1 = -3 and the change in x is 2 - 5 = -3.
Therefore, the gradient of the line joining these points is -3/-3 = 1.
3) To find the x-intercept, we set y to 0 and solve for x.
Given the equation 3y = 2x - 2, if we substitute y with 0, we have 3(0) = 2x - 2, which simplifies to 0 = 2x - 2.
To solve for x, we can add 2 to both sides: 0 + 2 = 2x - 2 + 2, which gives us 2 = 2x.
Dividing both sides by 2, we get x = 1.
Therefore, the x-intercept of the equation 3y = 2x - 2 is 1.
To find the y-intercept, we set x to 0 and solve for y.
Using the same equation, if we substitute x with 0, we have 3y = 2(0) - 2, which simplifies to 3y = -2.
To solve for y, we can divide both sides by 3: (3y)/3 = (-2)/3, which gives us y = -2/3.
Therefore, the y-intercept of the equation 3y = 2x - 2 is -2/3.
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Answer:

Step-by-step explanation:

To solve for f, we can cross-multiply the equation:

f/40 = 10/f

Multiplying both sides by 40f gives:

f^2 = 400

Taking the square root of both sides yields:

f = ±20

Therefore, the solutions for f are f = 20 and f = -20. However, since f represents a physical quantity (presumably a frequency), we take only the positive value:

f = 20

The system of equations that could be used to determine the number of small cars rented and the number of large cars rented is;

x + y = 10

x + y = 105x + 7y = 66

Let

Number of small cars rented = x

Number of large cars rented = y

x + y = 10

x + y = 105x + 7y = 66

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Answer:

y = -8

x = -4

okay i hope you got it

Answer:

A sample size of 28.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question:

We need to find n for which s = 0.09, with p = 0.66. So

\(s = \sqrt{\frac{p(1-p)}{n}}\)

\(0.09 = \sqrt{\frac{0.66*0.34}{n}}\)

\(0.09\sqrt{n} = \sqrt{0.66*0.34}\)

\(\sqrt{n} = \frac{\sqrt{0.66*0.34}}{0.09}\)

\((\sqrt{n})^{2} = (\frac{\sqrt{0.66*0.34}}{0.09})^{2}\)

\(n = 27.7\)

Rounding to the nearest whole number

A sample size of 28.

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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The width cannot be negative, the width of the walkway is 6 feet. The total area of the garden and the walkway is given as 648 square feet. We know the area of the garden is length multiplied by width, which in this case is 12 feet by 15 feet, so the garden area is\(12 \times 15 = 180\) square feet.

To find the area of the walkway, we subtract the garden area from the total area. Therefore, the area of the walkway is 648 - 180 = 468 square feet.

The walkway surrounds the garden on all sides, so its length and width will be greater than the corresponding dimensions of the garden.

To calculate the width of the walkway, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 + 2x (twice the width of the walkway) and the width is 15 + 2x.

So, we have the equation\((12 + 2x) \times (15 + 2x) = 468\).

Expanding and rearranging the equation, we get\(4x^2 + 54x - 228 = 0.\)

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that x = 6 or x = -9/2.

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Answer:

a. 0.45 customers

b. 0.0145 hours

c. 1.05 customers

Step-by-step explanation:

Missing word "A vending machine dispenses hot chocolate or coffee. service time is 30 seconds per cup and is constant. customers arrive at a mean rate of 72 per hour, and this rate is Poisson-distributed."

λ = 72 customers per hours

μ = 120 customers per hours

a. Lq = λ²/ 2μ(μ-λ)

Lq = 72² / 2(120)(120-72)

Lq = 9/20

Lq = 0.45 customers

b. Ws = Wq + 1/μ = Lq/λ + 1/μ

Ws = 9/20 customers/72 customers + 1/120 customers

Ws = 0.0145 hours

c. Ls = Lq + r

Ls = 9/20 + 72/120

Ls = 1.05 customers

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

We can solve this problem by:-

Here,

X=38°(Being vertically opposite angle)

So, X=38°

Vertical angles are congruent

The value of x = 38 degrees.

Given :

We are given with two lines that intersects .

we need to find out the vertical angle for the given angle.

When two lines intersects then the opposite angles are equal .

Opposite angles we call it as vertical angles .

Vertical angles are equal when two line intersects.

From the given diagram , vertical angles x  and 38  are congruent .

so \(x=38\)

The value of x is 38 degrees.

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Answer: no

Step-by-step explanation: 2 is not less than 1

Answer:

No because if you plug in f with 2 it is saying 2 is less than 1 which is not true so it would be

No

The profit for 24 sales is $64.

The profit for 24 sales, we first need to calculate the revenue and then determine the profit based on the given information.

The revenue function is given as f(x) = 5x, where x represents the number of hamburgers sold.

To find the revenue for 24 sales, we substitute x = 24 into the revenue function:

Revenue = f(24)

= 5 × 24

= 120 dollars

Now, let's calculate the profit.

The profit is $20 less than 70% of the revenue.

We can express this mathematically as:

Profit = 0.7 × Revenue - $20

Substituting the value of Revenue we calculated earlier:

Profit = 0.7 × 120 - $20

= 84 - $20

= $64

We must first compute the revenue for 24 sales before calculating the profit based on the available data.

The revenue function is denoted by the formula f(x) = 5x, where x is the quantity of hamburgers sold.

We add x = 24 to the revenue function to get the revenue for 24 sales:

f(24) = 5 x 24 = 120 dollars is the revenue.

Let's now determine the profit.

The profit is $20 below the revenue's 70%.

This may be written mathematically as:

Revenue - $20 x Profit = 0.7

Substituting the earlier determined figure of Revenue:

Earnings = 0.7 x 120 - $20 = 84 - $20 = $64

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Answer: 118

Step-by-step explanation:

Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.

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This is an example of a survey or sampling technique called systematic sampling. The students are selecting every 10th student from the population (in this case, the population is the entire student body) to survey.

This technique can be useful when the population is too large to survey everyone or when a random sample is difficult to obtain. By using systematic sampling, the students can obtain a representative sample of the student body without having to survey every single student.

However, it's important to note that systematic sampling can introduce bias if there is a pattern or structure in the population that is related to the sampling interval. For example, if every 10th student is in a particular grade level or section of the school, this could skew the results of the survey. To mitigate this potential bias, researchers should ensure that the sampling interval is random and that they are not selecting every nth person based on any identifiable characteristics.

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Answer:

The unit rate is 20.

Step-by-step explanation:

Divide 100 (words) by 5 (minutes) to get 20 words every minute.

Answer:

3log(z)/2−2log(x)−5log(y)

Step-by-step explanation:

The cost of the 1 ounces of canned beets is,

⇒ 3.23 / 17

⇒ 0.19

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ 17 ounces of canned beets for 3.23.

Hence, We get;

The cost of the 1 ounces of canned beets is,

⇒ 3.23 ÷ 17

⇒ 3.23 / 17

⇒ 0.19

Therefore, The cost of the 1 ounces of canned beets is,

⇒ 0.19

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Answer:

Step-by-step explanation:

\(\tt 5ab-b, \: when\: a=4\: and \:b=9\)

\(\tt 5(4)(9)-(9)\)

\(\tt \:5\times 4\times 9-9\)

\(\tt 180-9\)

\(\tt 171\)

Hope it helps! :)

Answer:

it could be 32 if im correct

Step-by-step explanation:

Answer:

32 is correct........

Answer:

-8/7 is your simplified answer :)

Step-by-step explanation:

Have a nice day <3

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

0.6

Step-by-step explanation:

The third side of the triangle ABC is AB. Using the Pythagorean Theorem, its length is 12. \(12^{2} +16^2=20^2\)

∠F is congruent to ∠C and so the sin(∠F) = sin(∠C)

The sin(∠C) = opposite/hypotenuse

= |AB| / |AC|

= 12/20

= 3/5

= 0.6

so the answer is 0.6

Answer:

h = 9 m

Step-by-step explanation:

\(V_{cone}=340\: m^3\)

diameter (d) = 12 m

\(\implies radius\:(r)= \frac{12}{2}=6\:m\)

\( \because \: V_{cone}= \frac{1}{3} \pi {r}^{2} h \\ \\ \implies \: h = \frac{3V_{cone}}{\pi {r}^{2} } \\ \\ \implies \: h = \frac{3(340)}{3.14 {(6)}^{2} } \\ \\ \implies \: h = \frac{1020}{113.04} \\ \\ \implies \: h = 9.02335456 \\ \\ \implies \: h \approx 9 \: m\)

Answer:

\((5xy + 7)(5xy-7) = 25x^2 y^2 - 49\)

Step-by-step explanation:

\((a - b)(a +b ) = a^2 - b^2 \\\\From \ given \ expression \ a = 5xy \ , \ b = 7\\\\Therefore , (5xy + 7 )(5xy - 7 ) = ( 5xy)^2 - ( 7)^2 \\\)

                                             \(= 25x^2 y^2 - 49\)

Answer:

25x²y² - 49

Step-by-step explanation:

We can do this by using the a+b formula:

(a+b)(a-b)= a² - b²

So,

(5xy+7)(5xy-7)

=(5xy)² - 7²

= 25x²y² - 49

Another way we can do this by expanding the algebraic expression:

(5xy+7)(5xy-7)

= 5xy(5xy-7) + 7(5xy-7)

= 25x²y² - 35xy + 35xy - 49

= 25x²y²- 49

Answer:

\(x=-1\)

Step-by-step explanation:

\(4=6+2x\)

Flip the equation:

\(2x+6=4\)

Subtract 6 from both sides:

\(3x+6-6=4-6\)

\(2x=-2\)

Divide both sides by 2:

\(2x/2=-2/2\)

\(x=-1\)

Answer:

x= -1

Step-by-step explanation:

firstly group the like terms

4-6=2x

-2=2x

divide both sides by 2

-2/2=2x/2

-1=x

therefore x is -1