Question 9 of 10
What is cos 30°?
60°
2
90°
30
√3
OA. √3
B.
O C. 1
O.D. √3
2
O E.
F.
1/2

Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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The smallest rational number among -5/16, -13/24, -3/4, and -7/12 is -3/4.

We have,

To determine the smallest rational number among -5/16, -13/24, -3/4, and -7/12, we need to compare their values.

Let's convert all the given rational numbers to have a common denominator of 48:

-5/16 = -15/48

-13/24 = -26/48

-3/4 = -36/48

-7/12 = -28/48

Now, the values of these rational numbers, when expressed with a common denominator, are:

-15/48, -26/48, -36/48, -28/48

Among these values, the smallest one is -36/48, which is equivalent to -3/4.

Therefore,

The smallest rational number among -5/16, -13/24, -3/4, and -7/12 is -3/4.

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Answer:

11:55 is closest time time to mid night

Option D is correct, 12:03AM is the closet time to midnight.

Midnight is typically defined as the beginning of a new day, precisely at 12:00 AM.

In a 12-hour clock format, AM (ante meridiem) is used to represent the time before noon (from midnight to 11:59 AM), while PM (post meridiem) is used to represent the time after noon (from 12:00 PM to 11:59 PM).

12.06am is 6 minutes past midnight.

11.50am is 10 minutes from midday, or, if you prefer, 11 hours and 55 minutes past midnight.

12.03am is 3 minutes past midnight.

Hence,  the closet time to midnight is 12:03 AM.

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Answer:

same thing for the rest, you just change the value of the radius according to the question

Step-by-step explanation:

area = pi * radius²

1)

a = pi * 10²

a = ~3.14 * 100

a = 314 mi²

It will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

To solve the problem using graphical approximation techniques, we can plot the two investment functions on a graphing calculator and find the point of intersection where the value of the $2,900 investment surpasses the value of the $3,100 investment.

Let's use the formula \(A = P(1 + i)^n\),

where A is the amount at the end of n periods, P is the principal value, i is the interest rate per period, and n is the number of compounding periods.

For the $2,900 investment at 15% compounded quarterly:

P = $2,900

i = 15% = 0.15/4

= 0.0375 (interest rate per quarter)

For the $3,100 investment at 9% compounded quarterly:

P = $3,100

i = 9% = 0.09/4

= 0.0225 (interest rate per quarter)

Now, plot the two investment functions on a graphing calculator or software using the respective formulas:

Function 1:\(A = 2900(1 + 0.0375)^n\)

Function 2:\(A = 3100(1 + 0.0225)^n\)

Graphically, we are looking for the point of intersection where Function 1 surpasses Function 2.

By observing the graph or using the "intersect" function on the calculator, we can find the approximate value of n (number of quarters) when Function 1 is greater than Function 2.

Let's assume the graph shows the intersection point at n = 15.6 quarters. Since the number of quarters cannot be fractional, we round up to the nearest integer.

Therefore, it will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

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Answer:

\(a_{73}=367\)

Step-by-step explanation:

\(a_n=a_1+(n-1)d\\a_{73}=7+(73-1)(5)\\a_{73}=7+(72)(5)\\a_{73}=7+360\\a_{73}=367\)

Answer:

x = 55°

Step-by-step explanation:

x = 180° - 85° - 40° = 55°

Answer:

It's answer is....abkt

Step-by-step explanation:

It's simple add all and there will be your answer

Answer:

\(m = \frac{14 - 7}{2 - 0} = \frac{7}{2} \)

\(14 = \frac{7}{2} (2) + b\)

\(14 = 7 + b\)

\(b = 7\)

\(y = \frac{7}{2} x + 7\)

Answer:

b=43.16

Step-by-step explanation:

You can use the Pythagorean Theorem so a^2+b^2=c^2

b^2+21^2=48^2

b^2 + 441 =2304

b^2 = 1863

b^2 = square root of 1863

b=43.1625

b=43.16

Answer:

481

Step-by-step explanation:

Lets say width = x

Length = x+24

Perimeter is 100 so

100=x+24+x+24+x+x

100=4x+48

100-48=4x

52=4x

x=13

So width = 13

Length = 37

37x13=481

The cubic equation cannot have more than one solution whenever α > 0.

Rolle's theorem states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one point c in the open interval (a, b) such that the derivative f'(c) = 0.
Now, let's consider the cubic equation x^3 + αx^2 + β = 0. To apply Rolle's theorem, we need to show that this equation satisfies the conditions mentioned above.
Since the cubic equation is a polynomial, it is continuous and differentiable for all real numbers. Now, let's differentiate the equation with respect to x:
f'(x) = 3x^2 + 2αx
For Rolle's theorem to hold, we need f'(x) = 0. Solving this equation for x:
3x^2 + 2αx = 0
x(3x + 2α) = 0
This equation has two solutions: x = 0 and x = -2α/3. Since α > 0, x = -2α/3 is a distinct real number different from 0. Thus, we have two distinct points where the derivative is zero.
However, Rolle's theorem states that there can only be one such point if there's only one solution to the cubic equation. Since we found two points where the derivative is zero, it implies that the cubic equation cannot have more than one solution whenever α > 0.

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The probability P(A and B)  that both events will occur is 8/13

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

Event A = 6 and 6

Event B = 20 and 6

Event A and B = 6

Total = 6 + 6 + 20 + 6 - 6 + 20 = 52

Using the above as a guide, we have the following:

P(A) = 12/52

P(B) = 26/52

P(A and B) = 6/52

The probability that both events will occur is represented as

P(A and B) = P(A) + P(B) - P(A and B)

And this is calculated as

P(A and B) = P(A) + P(B) - P(A and B)

Substitute the known values in the above equation, so, we have the following representation

P(A and B) = 12/52 + 26/52 - 6/52

Evaluate

P(A and B) = 32/52

Simplify

P(A and B) = 8/13

Hence, the probability that both events will occur is 8/13

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Close ties between the members of the group typically are formed during the norming stage of group development.

The norming stage of group development is the third stage, where the group begins to establish a sense of cohesion and unity. During this stage, members start to accept each other's ideas and opinions, develop relationships with one another, and establish patterns of communication and interaction. As a result of these positive developments, close ties between the members of the group often begin to form.

In the norming stage, group members also start to identify common goals and work together to achieve them. This shared sense of purpose can further strengthen the bonds between group members and contribute to the formation of close ties.

Overall, the norming stage is an important period of transition for groups as they move from the early stages of forming and storming to a more cohesive and productive group dynamic. The close ties formed during this stage can help to foster a supportive and collaborative environment that benefits the group as a whole.

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The distance between the two towers is 30 meters, and the height of the second tower (Tower B) is 90 meters.

We have two towers. Let's call the first tower Tower A, and the second tower Tower B. The height of Tower A is given as 30 meters. The angle of elevation of the top of Tower A from the foot of Tower B is 60 degrees. The angle of elevation of the top of Tower B from the foot of Tower A is 30 degrees. Our goal is to find the distance between the two towers and the height of Tower B.

In triangle ABC, where A is the foot of Tower A, B is the top of Tower B, and C is the top of Tower A:

tan(30 degrees) = AB / BC

Since tan(30 degrees) = 1 / √3, we can rewrite the equation as:

1 / √3 = AB / BC

Cross-multiplying, we get:

BC = AB * √3

In triangle ABC:

tan(60 degrees) = AC / BC

Since tan(60 degrees) = √3, we can rewrite the equation as:

√3 = AC / BC

Substituting the value of BC from Step 3:

√3 = AC / (AB * √3)

Cross-multiplying, we get:

AC = AB * 3

We have two equations:

BC = AB * √3

AC = AB * 3

Dividing equation 2 by equation 1:

AC / BC = 3 / √3

Simplifying, we get:

√3 = 3 / √3

Cross-multiplying, we get:

3 = 3

Since 3 = 3 is a true statement, we can conclude that the two towers are at the same distance as their heights. Therefore, the distance between the two towers is 30 meters.

Using the value of the distance between the towers (30 meters), we can substitute this value into one of the previous equations to find the height of Tower B. Let's use equation 2:

AC = AB * 3

Substituting AB with the distance (30 meters):

AC = 30 * 3

Simplifying, we find:

AC = 90 meters

Therefore, the height of Tower B is 90 meters.

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Answer:(a=5,b=3)

7a-3b = 26--------(1)

a + 2b =11---------(2)

on mutlplying by7 in eq 2

= 7a+14b=77-------(3)

from eq(1) and (3) (on substracting)

7a+14b=77

7a-3b=26

________

=-17b=51

b=51/17

b=3

on putting value of b in eq 1

7a-3b = 26

=7a-9=26

7a=35

a=5

Step-by-step explanation:

hope it helps

mark me brainliest

Answer:

1408

Step-by-step explanation:

Answer:

y=x-1

Step-by-step explanation:

Answer:

y=x1

Step-by-step explanation:

The compound interest formula is:

Where

P is principal

r is rate of interest

n is number of compounding

t is number of years

Putting the given information, we have:

Interest amount is:

15,439.60 - 13,500 = $1939.60 (in a year/12 months)

In 10 months:

Justin would owe $1616.33 after 10 months.

The ordered pairs that are solutions to the inequality are:

(-3, 3), (0, -1), and (2, 4).

Option A, B, and C are the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

3x - 2y ≤ 6

We will check for the following options.

(-3, 3) = (x, y)

3 x (-3) - 2 x 3 ≤ 6

-9 - 6 ≤ 6

-15 ≤ 6

This is true.

(0, -1) = (x, y)

3 x 0 - 2 x (-1) ≤ 6

0 + 2 ≤ 6

2 ≤ 6

This is true.

(2, 4) = (x, y)

3 x 2 - 2 x 4 ≤ 6

6 - 8 ≤ 6

-2 ≤ 6

This is true.

(3, 0) - (x, y)

3 x 3 - 2 x 0 ≤ 6

9 - 0 ≤ 6

9 ≤ 6

This is not true.

Thus,

The ordered pairs that are solutions to the inequality are:

(-3, 3), (0, -1), and (2, 4).

Option A, B, and C are the correct answer.

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Area of ceiling: 6 x 5 = 30 square meters:

Area of 4 walls = 107 - 30 = 77 square meters

2 walls = 6 + 6 = 12 meters long

2 walls = 5 + 5 = 10 meters long

12 + 10 = 22

77 square meters / 22 meters = 3.5 meters

The walls are 3.5 meters high.

The most appropriate choice for profit and loss will be given by

Uncle Ben will feed his cows 2 pounds of grain supplement.

What is profit and loss?

If the selling price is more than the cost price, then the difference between the selling price and the cost price will give the profit.

If the selling price is less than the cost price, then the difference between the selling price and the cost price will give the loss.

Here,

For 1 pound

Cost price of grain supplement  = \(0.70 \times 1\)

                                                      = $\($0.70\)

Selling price of milk = \(0.20 \times 5\)

                                 = $\(1\)

Profit = $(\(1 - 0.70\))

         = $0.30

For 2 pounds

Cost price of grain supplement  = \(0.70 \times 2\)

                                                      = $\($1.40\)

Selling price of milk = \(0.20 \times 9\)

                                 = $\(1.80\)

Profit = $(\(1.80 - 1.40\))

         = $0.40

For 3 pounds

Cost price of grain supplement  = \(0.70 \times 3\)

                                                      = $\($2.10\)

Selling price of milk = \(0.20 \times 12.3\)

                                 = $2.46

Profit = $(\(2.46 - 2.10\))

         = $0.36

For 4 pounds

Cost price of grain supplement  = \(0.70 \times 4\)

                                                      = $\($2.80\)

Selling price of milk = \(0.20 \times 15.5\)

                                 = $3.1

Profit = $(\(3.1 - 2.80\))

         = $0.30

For 5 pounds

Cost price of grain supplement  = \(0.70 \times 5\)

                                                      = $\($3.50\)

Selling price of milk = \(0.20 \times 18\)

                                 = $3.60

Profit = $(\(3.60 - 3.50\))

         = $0.10

For 6 pounds

Cost price of grain supplement  = \(0.70 \times 6\)

                                                      = $\($4.20\)

Selling price of milk = \(0.20 \times 20\)

                                 = $4

Loss = $(\(4.20 - 4\))

         = $0.20

For 7 pounds

Cost price of grain supplement  = \(0.70 \times 7\)

                                                      = $\(4.90\)

Selling price of milk = \(0.20 \times 21.5\)

                                 = $\(4.30\)

Loss = $(\(4.90 - 4.30\))

         = $0.60

For 8 pound

Cost price of grain supplement  = \(0.70 \times 8\)

                                                      = $\($5.60\)

Selling price of milk = \(0.20 \times 22.5\)

                                 = $\(4.50\)

Loss = $(\(5.60 - 4.50\))

         = $1.10

For 9 pounds

Cost price of grain supplement  = \(0.70 * 9\)

                                                      = $\(6.30\)

Selling price of milk = \(0.20 * 23\)

                                 = $\(4.60\)

Loss = $(\(6.30 - 4.60\))

         = $1.70

Since profit from 2 pounds of grain supplement is the most, Uncle Ben will feed his cows 2 pounds of grain supplement.

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Complete Question

Farmer Ben knows that feeding a grain supplement to his cows will produce more milkaccording to the following schedule:

ignoring all other issues, how many pounds of grain supplement should farmer ben feed his cows if the price of milk is $0.20 per pound and the price of grain supplement is $0.70 per pound?

The table has been attached here

The square root of 10 will be greater than 3.

The square root of a number is the value which when multiplied by itself results into the number. Mathematically -

n = x²

then -

x = \(\sqrt{n}\)

Given are two numbers as -

\(\sqrt{10}\) and 3.

Now, the square root of 10 will be 3.16 (approx.)

On comparing the square root of 10 with 3, we can clearly see that the square root of 10 will be greater than 3. Mathematically -

\(\sqrt{10}\) > 3.

Therefore, we can conclude that the square root of 10 will be greater than 3.

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Answer:

y=21

Step-by-step explanation:

y=7 and x=4 when x=12 thats 3 times 4 so multiply 7 by 3 and you get 21

The volume of the medication required, we subtract it from the nebulizer output to find the amount of saline needed.

To determine the amount of saline needed to make the medication last the full hour, we need to calculate the total volume of medication required and subtract it from the volume delivered by the nebulizer.

Given:

- Albuterol dose: 15 mg

- Atrovent dose: 0.5 mg

- Nebulizer output: 10 mL per hour

- Nebulizer flow rate: 4 LPM (liters per minute)

First, we need to convert the nebulizer flow rate to mL per hour:

4 LPM * 60 min = 240 mL per hour

Next, we calculate the total volume of medication required by adding the doses of albuterol and Atrovent:

Total medication volume = 15 mg + 0.5 mg

Now, we need to convert the total medication volume from milligrams to milliliters. To do this, we need to know the concentration of the medication (mg/mL) or the volume of the medication that corresponds to the given dose. Without this information, we cannot convert the dose to volume accurately.

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Answer:

Step-by-step explanation:

Selling price of two irons is Rs.1050 each.

Loss on one iron = Rs.300

Profit on second iron = Rs.450

We know that ,

Cost price = Selling price + loss ,when loss is given

and cost price = Selling price - profit ,when profit is given.

therefore, cost price of first iron = 1050 + 300 =1350 rupees

cost price of second iron = 1050 - 450 = 600 rupees

total cost price = 1350 + 600 = 1950 rupees

total selling price = 1050 + 1050 = 2100 rupees

since total cost price < selling price

so, there is a profit of 2100 - 1950 = 150 rupees.

Answer:

m<BCD=60

Step-by-step explanation:

4x+6=7x-12

3x=18

x=6

4(6)+6

24+6

30

30+30=60

======================================================

Reason:

Use the HL (hypotenuse leg) theorem to prove that triangle BCF is congruent to triangle DCF.

It then leads to the fact that angle BCF is congruent to angle DCF.

Set those angle expressions equal to one another. Solve for x.

angle BCF = angle DCF

4x+6 = 7x-12

4x-7x = -12-6

-3x = -18

x = -18/(-3)

x = 6

Then,

Both angles are the same measure to confirm the correct x value.

Lastly, add up those angles to get angle BCD.

30+30 = 60 degrees is the final answer.

Answer:

A. (2,4)

Step-by-step explanation: