Select the graph for the solution of the open sentence
Ix| = -2

Answer:

\(a^{4}\)+9a²+81

Step-by-step explanation:

((a³ - 27) / (a - 3)) (a² - 3a + 9)​

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

Step-by-step explanation:

If both lines are open the rate of filling is:

Since tank is 1/3 full we need to fill the remaining 2/3 of it.

Time required:

The volume of the figure, by splitting it into two cuboids comes to be 3300 ft³.

The volume of a cuboid is the product of its three dimensions i.e. length, breadth, and height.

Let us split the given figure into two cuboids

So, the volume of the figure will be the sum of the volume of both the cuboids.

So, the volume of the cuboid with dimensions 20 ft x 25 ft x 5ft

= 20 x 25 x 5

=2500 ft³.

The volume of the cuboid with dimensions  4 ft x 25ft x 8ft

=4 x 25x 8

=800 ft³.

So, the volume of the figure = 2500 + 800 =3300 ft³.

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Answer:

cronana va de

Step-by-step explanation:

The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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The relation that describes the graph {(-1, 3), (-2, 1), (-3, -3), (-4, -5)}

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The coordinates of given graph:

Hence, the relation is {(-1, 3), (-2, 1), (-3, -3), (-4, 5)}.

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More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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Answer:

\(6p - 2q + 4r - 2p + 3s + 5q\)

group the like terms together:

\( = (6p - 2p) + ( - 2q + 5q) + 4r + 3s\)

simplify:

\( = { \boxed{ \boxed{4p + 3q + 4r + 3s}}}\)

Answer:

The point estimate used was of $69,821.

The error bound is of $101.

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The error bound is half the difference between these two values.

In this question:

90% confidence that the mean household income in the U.S. falls between $69,720 and $69,922.

Point estimate:

(69720+69922)/2 = 69821

The point estimate used was of $69,821.

Error bound:

(69922 - 69720)/2 = 101

The error bound is of $101.

Answer: \(m=\frac{-30}{79},\ y=5.40\)

Step-by-step explanation:

Given

Points are \(\left(6\frac{1}{3},3\right),\ \left(19\frac{1}{2},-2\right)\)

Convert mixed numeral to fraction

\(\left(6\frac{1}{3},3\right)\Rightarrow \left(\dfrac{19}{3},3\right)\\\\\left(19\frac{1}{2},-2\right)\Rightarrow \left(\dfrac{39}{2},-2\right)\)

Slope of the line is

\(\Rightarrow m=\dfrac{3-(-2)}{\dfrac{19}{3}-\dfrac{39}{2}}\\\\\Rightarrow m=\dfrac{5}{\dfrac{38-117}{6}}\\\\\Rightarrow m=\dfrac{-30}{79}\)

Equation of line

\(\Rightarrow \dfrac{y-3}{x-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\text{for y-intercept, put x=0}\\\\\Rightarrow \dfrac{y-3}{0-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\Rightarrow y-3=\dfrac{190}{79}\\\\\Rightarrow y=3+2.40\\\Rightarrow y=5.40\)

Answer:

3

Step-by-step explanation:

3/7/7 which is 3/7 x 7 which is 21/7 which is 3

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Answer:

\( \frac{3}{5} + \frac{2}{7} = \frac{31}{35} = 0.885\)

Answer

B

Step-by-step explanation:

Took quiz

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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we must apply the formula

now we apply the formula to find x,

having already x now we apply the formula to find the vertex at y that intersects at point 12.

According to the double-angle identity:

So, let's solve (a):

(a) Given:

Comparing with the identity:

C = 30°

Then, 2C = 2*30 = 60°

Since

A = 2C, A = 60°

Answer: A = 60°.

(b) Given,

Comparing with the identity:

C = 2x

2C = 2*2x = 4x

Then,

B = 2C = 4x

Answer: B = 4x°.

In summary,

(a) A = 60°.

(b) B = 4x°.

Answer:

A;  62.4 cm

Step-by-step explanation:

Answer:

Step-by-step explanation:express the 15% as a fraction divided by 100.Multiply the result by $9000.

The result is $ 1350

Subtract the result from new price of the car.$9000-$1350

=$7650

Answer:

  1 1/2 miles

Step-by-step explanation:

The problem statement tells us Mara ran 4/5 of 1 7/8 miles.

The procedure usually recommended for multiplying mixed numbers is to convert them to improper fractions first. Doing that, we find the product to be ...

  \(\dfrac{4}{5}\times1\dfrac{7}{8}=\dfrac{4}{5}\times\dfrac{1\times8+7}{8}=\dfrac{4}{5}\times\dfrac{15}{8}\\\\=\dfrac{4\cdot3\cdot5}{5\cdot4\cdot2}=\dfrac{3}{2}=\boxed{1\dfrac{1}{2}}\)

Mara ran 1 1/2 miles.

Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

Answer:

1) 78

2) 28

3) 74

4) 28

5) 74

6) 106

7) 74

8) 74

9) 78

10) 78

Step-by-step explanation:

72km/h = 72,000m/3,600s = 20m/s.

Using Kinematics, we have

v = u + at

= (20m/s) + (-2m/s²)(5s)

= 10m/s.

Hence the velocity will be 10m/s. (or 36km/h)

Answer:

R = (0,-8)

Step-by-step explanation:

Let's look at the difference between S, and the midpoint M.

S(6,0) - M(3,-4) = N(3,4) This will help us find R(x,y)

Next, take M, and subtract N from it.

M(3,-4) - N(3,4) = (0,-8). This is the value of R.

Step-by-step explanation:

Inequality Interval Notation Graph

Sajan Rai

Solve the inequalities below. Write the solution set in interval notation and graph the solution.

8x−12>158x-12>15

Solution:

Interval notation for the solution:

(-∞,5/8) U (5/8, ∞)

To graph the solution, we need to find the points that make the inequality true and shade the region that corresponds to these points. On the number line, we can start by finding x values that make the inequality equal to zero:

8x - 12 = 0

x = 12/8 = 3/2

and

15 - 8x = 0

x = 15/8 = 9/4

Next, we need to test values that are less than 3/2 and greater than 9/4 to determine the direction of the inequality. If the inequality is true for values less than 3/2, then we shade the region to the left of 3/2. If the inequality is true for values greater than 9/4, then we shade the region to the right of 9/4. In this case, since the inequality is "greater than," the shading goes to the right of 9/4 and to the left of 3/2.

a. Category with the greatest frequency is 20 - 24

b. 14 students

c. The percentage is 7%

Frequency is simply described as the number of times an event or observation happened in a given study or experiment that is carried out.

From the information given, we have that;

a. The category with the greatest frequency is the one with most words spelt, we have;

20 - 24

b. The number of students that spelt 35 - 39 words is traceable to

14 students

c. If the total number of students is 200

Then, the percent of students in the 35 - 39 category is;

14/200 × 100/1

Multiply the values

7%

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The warmest recorded temperature than the coldest recorded temperature is 54oF

The given parameters are:

Coldest recorded temperature = 80°F, in Alaska

Warmest recorded temperature = 134°F, in California

Next, we calculate the difference between these temperatures

Difference = Warmest recorded temperature - Coldest recorded temperature

Substitute the known values in the above equation

Difference = 134 - 80

Evaluate

Difference = 54

Hence, the amount of temperature difference is 54oF

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Check the picture below.

Answer:

5

Step-by-step explanation:

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