If x^2 -7x=30 and x>0, what is the value of x-5

Answer:

8.048 liters

Step-by-step explanation:

Convert 8542 ml to liters:  (8542 ml)(1 liter/1000 ml) = 8.542 liters

Now subtract 0.458 liters to find the amount that a fish tank can hold:

 8.542 liters

-0.458  liters

8.048 liters is the fish tank capacity

Answer:

In bold below.

Step-by-step explanation:

Find derivative which gives the velocity:

V = h' = -32t + 28

At maxm height V = 0 so

-32t + 28 = 0

Time to reach maxm height t = -28/-32 = 0.875 seconds.

So maxm height

= -16(0.875)^2 + 28*0.875 + 8

= 20.25 ft.

Answer

30 months if she uses 4 pounds a month for 120 pounds

The rate of growth for this situation is 30 months.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Sally ordered her groceries online and she accidentally ordered 120 pounds of flour.

Sally only uses 4 pounds of flour every month.

∴ The rate of growth for Sally is (120/4) = 30 months.

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Answer:

32 is it

Step-by-step explanation:

We want to simplify:

For doing so, we use the distributive property, and we get:

And we break the parenthesis to obtain:

Lastly, we simplify the similar terms and we get:

This means that the expression simplified is 4x+4.

Answer:

7. uses like or as to compare two things

8. personification - in this case, the tropical storm is being given the human quality of sleeping

Hope this helps!

Answer:

(3, 2)

2 = 5 x 3 - 9

  = 15 - 9

  = 6

2 is not = 6

y = 5x - 9

y - 5x = -9

y - 5x = 4

Use elimination

-15

ANSWER: So there are no solutions

Answer:

-8/9

Step-by-step explanation:

-1 1/8

=> - 9/8

=> Multiplicative inverse of 9/8 is:

=> - 8/9 [Sign does not change only the numerator goes to the denominator and denominator to the numerator]

=> -8/9 is the multiplicative inverse of -1 1/8

if you add 288cm and multiply by 216 then you shall get 433 and so if you

The answer to the given problem is that the drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S = 10/7x² - 280/7x + 2940/7 mg.

What is the given problem?

The drug manufacturer has developed a time-release capsule. The number of milligrams of the drug in the bloodstream is given by S = 20x/17 - 280x/10 + 980x/3 + 3/7 mg.

In order to simplify the given problem, we will first find the LCM of 17, 10, and 3, which is 510.

Therefore, we can simplify S as:

S = 300x/170 - 1190x/510 + 1700x/170 + 1020/510 mg

Simplifying the above expression:

S = 10/17x - 280/51x + 10x + 2 mgS = 10/7x² - 280/7x + 2940/7 mg

Therefore, the drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S = 10/7x² - 280/7x + 2940/7 mg.

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The drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by `\(S=20x-280x^{(3/7)}+980x^{(10/7)\)`.

What is a time-release capsule?

A time-release capsule is a medication that is released gradually over a certain amount of time. The medication is released into your bloodstream in small, consistent doses rather than all at once.

How to find the number of milligrams of the drug in the bloodstream?

In order to determine the number of milligrams of the drug in the bloodstream,

we need to substitute the value of x in the formula \(`S=20x-280x^{(3/7)}+980x^{(10/7)`\) and simplify it.

For instance, let's take x = 17/7,

then: S = 20(17/7) - 280(17/7\()^{(3/7)\) + 980(17/7\()^{(10/7)\)

= 10.81 mg

Similarly, we can find the value of the number of milligrams of the drug in the bloodstream for other values of x.

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Solving single variable equations involves isolating the unknown variable on one side of the equals sign.

When solving a single variable equation, the goal is to isolate the variable on one side of the equation. This is typically done by performing inverse operations to eliminate any constants or coefficients attached to the variable.

The steps involve simplifying both sides of the equation, combining like terms, and applying inverse operations such as addition, subtraction, multiplication, or division to move the variable to one side. The process continues until the variable is isolated, and the solution is obtained.

It's important to perform the same operation on both sides of the equation to maintain equality. By following these steps, the unknown variable can be determined, solving the single variable equation.

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The area of the figure is 13 cm².

We have,

From the figure,

We can make two rectangles.

Now,

Length = 5 cm

Width =  1 cm

Area of one rectangle.

= 5 x 1

= 5 cm²

Length = 4 cm

Width = 2 cm

Area of another rectangle.

= 4 x 2

= 8 cm²

Now,

Area of the figure,

= 5 + 8

=  13 cm²

Thus,

The area of the figure is 13 cm².

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Answer:

13) x = 30

14) x = 22.5

15) x = 36

Step-by-step explanation:

13) 4x+2x = 180

6x = 180

x = 30

14) 3x+5x = 180

8x = 180

x = 22.5

15) 2x+3x+2x+3x = 360

10x = 360

x = 36

Answer:

x=36

Step-by-step explanation:

The correct decision rule for a test hypothesis with a significance level of 0.02, with two tails, is given as follows:

C. Reject H0 if Zstat< -2.33 or Zstat > +2.33.

The decision regarding the null hypothesis depends on if the p-value is less or more than the significance level:

For a two-tailed test with a significance level of 0.02, the critical value is given as follows:

z = 2.33.

Hence the decision rule is given as follows:

Hence option C is the correct option for this problem.

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P-value is0.1558 and the z- value is 1.012 when a random sample of 40 drivers was questioned to determine whether the commute time differs in the winter.

Given that,

The Census Bureau informs us that Cleveland, Ohio residents commute on average for 33 minutes. A random sample of 40 drivers was questioned to determine whether the commute time differs in the winter.

The standard deviation of the population is estimated to be 7.5 minutes, and the average commute time for the month of January was calculated to be 34.2 minutes.

Let = μ average commute time in winter.

So, Null Hypothesis, H₀ : μ = 33 minutes      {means that the commuting times are same in the winter}

Alternate Hypothesis, H₁ : μ≠  33 minutes      {means that the commuting times are different in the winter}

The test results that would be utilised in this z test statistics for one sample given our understanding of population standard deviation;

T.S. = ((X bar-mean)/ standard deviation)/root n   ~ N(0,1)

Here, X bar = sample mean commute time for the month of January = 34.2

Standard deviation = population standard deviation = 7.5 minutes

n = sample of drivers = 40

The value of z test statistics is 1.012.

Also,

P-value of the test statistics is given by;

P-value = P(Z > 1.012) = 1 - P(Z  1.012)

= 1 - 0.84423

= 0.1558

Therefore, P-value is0.1558 and the z- value is 1.012 when a random sample of 40 drivers was questioned to determine whether the commute time differs in the winter.

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Answer:

Step-by-step explanation:

sin 75°

sin(30°+45°)

sin30°*cos45°+cos30°sin45°

1/2*1/\(\sqrt{2}\) + \(\sqrt{3}\)/2*1\(\sqrt{2\)

1/2\(\sqrt{2}\)+\(\sqrt{3}\)/2\(\sqrt{2}\)

1+3/2\(\sqrt{2}\)

cos(-75°)

-cos(180°-105°)

-cos(-105°)

cos 105°

cos(45°+60°)

cos45°cos60°-sin45°sin60°

1/\(\sqrt{2}\) *1/2-1/\(\sqrt{2}\) *\(\sqrt{3}\) /2

1/2\(\sqrt{2\)-\(\sqrt{3\)/2\(\sqrt{2}\)

1-\(\sqrt{3}\)/2\(\sqrt{2}\)

sin(75)

=0.96

cos(-75)

=0.25

The probability of one of three students being accepted to a program while the other two are not accepted is 3.2%, or 1.5:1, which is equivalent to a 66.7% chance.

The probability of one of three students being accepted to a program while the other two are not accepted can be calculated by dividing the total number of favorable outcomes by the total number of possible outcomes.

To calculate this, we need to know the probability of each individual student being accepted. For example, if the probability of each student being accepted is 0.2, the probability of one student being accepted while the other two are not would be (0.2)x(1-0.2)x(1-0.2), or 0.032. This would be written as a 3.2% chance.

The probability of one student being accepted while the other two are not can also be calculated using a permutation formula. The formula for this is

P(n,r) = n!/(n-r)!,

where n is the total number of students and r is the number of students accepted.

In this case, n = 3 and r = 1. So, P(3,1) = 3!/2! = 3/2 = 1.5.

This means that there is a 1.5:1 ratio of one student being accepted while the other two are not. This is equal to a 66.7% chance.

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The surface area of the regular pyramid, as determined from the net, is approximately 178.3 square millimeters.

To find the surface area of the regular pyramid using the net, we need to calculate the areas of its individual components and sum them up.

The net includes four equilateral triangles. One triangle is shaded and serves as the base, while the other three triangles are unshaded and share a side with the shaded triangle.

Let's start by calculating the area of the base, which is the shaded equilateral triangle. We are given that the side length of the shaded triangle is 10 millimeters. The formula for the area of an equilateral triangle is:

Area of an equilateral triangle = (side length^2 × √3) / 4

Plugging in the values, we have:

Area of the base = (10^2 × √3) / 4 ≈ 43.3 square millimeters

Now, let's calculate the area of each unshaded triangle. We are given that the height of each unshaded triangle is 9 millimeters. The formula for the area of any triangle is:

Area of a triangle = (base × height) / 2

Since the base of each unshaded triangle is the same as the side length of the shaded triangle (10 millimeters), we have:

Area of each unshaded triangle = (10 × 9) / 2 = 45 square millimeters

Since there are three unshaded triangles, the total area of the unshaded triangles is:

Total area of unshaded triangles = 3 × (Area of each unshaded triangle) = 3 × 45 = 135 square millimeters

Finally, we can find the surface area of the regular pyramid by summing the area of the base and the total area of the unshaded triangles:

Surface area of the regular pyramid = Area of the base + Total area of unshaded triangles = 43.3 + 135 = 178.3 square millimeters

Therefore, the surface area of the regular pyramid, as determined from the net, is approximately 178.3 square millimeters.

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An example of geometric series is  2 + 6 + 18 + 54.

When a set of numbers follow a particular order, they are said to be in sequence.

A set of numbers are said to be in geometric sequence if the ratio between second and first term is same as the ratio between third and second term and so on. The geometric sequence is presented as

Sum of n terms = a, ar, ar², ar³,  ......, arⁿ⁻¹, arⁿ.

where,

The first term is a.

Every two consecutive terms, r is the common ratio.

The number of terms is n.

When the numbers in geometric sequence are added together, it is called a geometric series. The geometric series is presented as

Sum of n terms = a + ar + ar² + ar³ + ...... + arⁿ⁻¹ + arⁿ.

where,

The first term is a.

Every two consecutive terms, r is the common ratio.

The number of terms is n.

Let us take an example.

The numbers 2, 6, 18, 54 are in geometric sequence because 6:2 = 18:6 = 54:18 and when we will write it as 2 + 6 + 18 + 54, it will become a geometric series.

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Answer:

\(\huge\boxed{x^3-y^3=508}\)

Step-by-step explanation:

\(\underline{+\left\{\begin{array}{ccc}x+y=10\\x-y=6\end{array}\right}\qquad|\text{add the sides of the equations}\\.\qquad2x=16\qquad|\text{divide both sides by 2}\\.\qquad\boxed{x=8}\\\\\text{Substitute it to the first equation}\\8+y=10\qquad|\text{subtract 8 from both sides}\\\boxed{y=2}\\\\x^3-y^3=8^3-2^3=512-8=504\)

a) There are 22,100 possible combinations of 3 cards that can be drawn from a standard deck of 52 cards.

b) There are only 4 possible combinations of 3 aces that can be drawn from a standard deck of 52 cards.

a) The number of different combinations of 3 cards from a deck of 52 cards is given by the combination formula:

C(52, 3) = 52! / (3! * (52-3)!) = 22,100

Therefore, there are 22,100 possible combinations of 3 cards from a deck of 52 cards.

b) Since there are 4 aces in a standard deck of 52 cards, the number of different combinations of 3 aces is given by the combination formula:

C(4, 3) = 4! / (3! * (4-3)!) = 4

Therefore, there are only 4 possible combinations of 3 aces from a deck of 52 cards.

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Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

Answer: 518

Step-by-step explanation: Just try it

Answer:

518

Step-by-step explanation:

take the amount of money Justin has (487) and subtract it from the cost of the computer (1,005) to find the difference.

Answer:

f(-3) = -3(-3) + 7

= 9 + 7

= 16

Answer:

a. 10%

b. 80%

c. 20%

Step-by-step explanation:

Hope this helps!