i need help. this is algebra 2 and im currently going “bootcamp for it*

Answer:

-7√2 + 7√2 i.

Step-by-step explanation:

To convert a complex number from polar form to rectangular form, we use the following formula:

a + bi = r(cos θ + i sin θ)

where a and b are the rectangular coordinates, r is the modulus or magnitude, and θ is the argument or angle.

In this case, we have:

r = 14

θ = 135°

So, we can plug these values into the formula and simplify:

a + bi = 14(cos 135° + i sin 135°)

a + bi = 14(-√2/2 + i * (-√2/2))

a + bi = -7√2 + 7√2 i

Therefore, the complex number in rectangular form is -7√2 + 7√2 i.

The volume of the shaded portion of the cone is V = 621.667 inches³

Given data ,

Let the volume of the shaded region be V

Now , the volume of the larger cone be A

Let the volume of the smaller cone be B

Volume of Cone = ( 1/3 ) πr²h

V = A - B

And , A = ( 1/3 ) ( 9 )² ( 25 )

On simplifying , we get

A = ( 1/3 ) ( 81 ) ( 25 )

A = 675 inches³

And , B = ( 1/3 ) ( 4 )² ( 10 )

B = ( 160/3 ) inches³

So , Volume of shaded region V = A - B

V = 675 inches³ - ( 160/3 ) inches³

V = ( 1,865/3 ) inches³

V = 621.667 inches³

Hence , the volume of cone is 621.667 inches³

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The perimeter of the figure is 8x+16

Perimeter is a math concept that measures the total length around the outside of a shape. We can calculated perimeter is a shape by adding all the sides together.

The perimeter of circle is 2πr, where r is the radius, perimeter of a square is 4l and a parallelogram is 2(l+b)

Perimeter of a rectangle is expressed as;

P = 2(l+b)

P= 2(3x+6+x+2)

P= 2(4x+8)

P= 8x+16

Therefore the perimeter of the figure is 8x+16

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Since the coordinates of the translated triangle are (3,5), (5, 6), and (2, 9), the translation vector is (x, y)   → (x + 2, y + 1).

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

By translating the pre-image of this triangle vertically upward by 1 unit and horizontally right by 2 units, the coordinates of the image include the following:

(x, y)                               →                  (x + 2, y + 1)

(1, 4)                        →                  (1 + 2, 4 + 1) = (3, 5).

(3, 5)                        →                  (3 + 2, 5 + 1) = (5, 6).

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yes, the answer is actually 180

Statement           Reason

We are given that M is the midpoint of CD and that MD = 3. To prove that CM = 3, we need to show that CM is equal to the difference between CD and MD, and that CD is equal to twice MD because M is the midpoint of CD.

Using the segment addition postulate, we can express CM as CD - MD. From the definition of midpoint, we know that CD is twice MD, so we can substitute 2MD for CD in the expression for CM.

Simplifying the expression for CD, we get CD = 6. Substituting CD = 6 and MD = 3 into the expression for CM, we get CM = 6 - 3 = 3. Therefore, we have proven that CM is equal to 3.

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The sum of the lengths of the longest and shortest bulb = 16 1/3 inches

The correct answer is an option (c)

Here, the line plot represents the Length of Hyacinth Bulbs inches.

We need to find the sum of the lengths of the longest and shortest bulb.

We knnow that a Line plot displays data as check marks above a number line that represents the frequency of each value.

From the attached line plot, we can observe that the length of the longest bulbs = 10 in. and the length of the shortest bulbs = 6 1/3

So,  the sum of the lengths of the longest and shortest bulb would be,

10 + 6 1/3 = 16 1/3

Therefore, the correct answer is an option (c)

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The monthly payment on the loan is $442.88 and the total interest on the loan is  $1,405.68.

we need to calculate the monthly interest rate. Since the annual interest rate is 5%, we can divide by 12 to get the monthly interest rate:

r = 0.05 / 12 = 0.00417

Next, we need to calculate the total number of payments over the three-year period.

Since there are 12 months in a year, the total number of payments is:

n = 3× 12 = 36

Now we can plug in the values into the loan payment formula:

P = (15000 × 0.00417×(1 + 0.00417)³⁶) / ((1 + 0.00417)³⁶ - 1)

= $442.88

To calculate the total interest on the loan

we can multiply the monthly payment by the total number of payments and subtract the principal amount:

Total interest = (monthly payment × total number of payments) - principal amount

Total interest = ($442.88 × 36) - $15,000

= $1,405.68

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The radius of the circle P is 20 centimetres.

P is in the shape of a circle. Q is in the shape of a quarter circle of radius 20 cm.

The area of Q is 4 times the area of P. Therefore, the radius of circle P can be found as follows:

area of circle Q = πr² / 4

area of circle Q = 3.14 × 20² ÷ 4

area of circle Q = 3.14 × 400 / 4

area of circle Q = 314 cm²

Therefore,

Hence,

area of circle p = πr²

4(314) = 3.14 × r²

r² = 1256 / 3.14

r = √400

r = 20 cm

Therefore, the radius of the circle P is 20 cm.

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The required graph of the given equation y=x+2, y=-x+2, and y=|x|+2 has been shown.

The first equation, y = x + 2, represents a straight line with slope 1 and y-intercept 2. The graph passes through the point (0, 2) and has a positive slope, which means it slants upwards from left to right.

The second equation, y = -x + 2, also represents a straight line, but with slope -1 and y-intercept 2. The graph passes through the point (0, 2) and has a negative slope, which means it slants downwards from left to right.

The third equation, y = |x| + 2, represents the absolute value function of x translated up 2 units. The graph of y = |x| is a V-shape with its vertex at the origin, and when we add 2 to every y-coordinate, the graph is shifted upwards by 2 units. The resulting graph has a V-shape with its vertex at (0, 2).

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Answer:

 5/6 - 4 1/2 = 10/3 = 3 1/3

Step-by-step explanation:

their was 10/3 punch left its also equivalent to 3 1/3

The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

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Answer: The probability that Chang gets dressed with a white shirt and tan pants is 25%.

Step-by-step explanation:Given that Chang has 2 shirts, a white one and a black one, and he also has 2 pairs of pants, one blue and one tan, to determine what is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants the following calculation must be performed:

Each shirt = 50% chance Each pants = 50% chance 0.50 x 0.50 = X0.25 = X Therefore, the probability that Chang gets dressed with a white shirt and tan pants is 25%.

The length of ST is 5.6 units.

Similar triangles are a set of given triangles which have some common relations when their corresponding properties are compared. Though they are similar, but not congruent.

Considering the given information, we have on comparison;

TU/ SU = OU/ CU

4/ SU = 5/ 12

5SU = 4 x 12

       = 48

SU = 48/5

     = 9.6

So that;

SU = ST + TU

9.6 = ST + 4

ST = 5.6

The length of ST is 5.6 units.

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The values of μ, μ² and σ² of the random variable X in the probability density function are μ = -1/2, μ² = -3/10 and σ² = -11/20

Given that

g(x) = 6x(1 - x)

The expected value, μ is calculated as

[tex]\mu = \int\limits^a_b {x \cdot f(x)} \, dx[/tex]

So, we have

[tex]\mu = \int\limits^1_0 {x \cdot 6x(x - 1)} \, dx[/tex]

Integrate

μ = 1.5x⁴ - 2x³

So, we have

μ = 1.5(1)⁴ - 2(1)³ + 1.5(0)⁴ - 2(0)³

Evaluate

E(x) = μ = -1/2

The variable, μ² is calculated as

[tex]\mu^2 = \int\limits^a_b {x^2 \cdot f(x)} \, dx[/tex]

So, we have

[tex]\mu^2 = \int\limits^1_0 {x^2 \cdot 6x(x - 1)} \, dx[/tex]

Integrate

μ² = 3x⁴(4x - 5)/10

So, we have

μ² = 3(1)⁴(4(1) - 5)/10 - 3(0)⁴(4(0) - 5)/10

Evaluate

E(x²) = μ² = -3/10

Calculating the variance σ², we have

σ² = E(x²) - E(x)²

This gives

σ² = (-3/10) - (-1/2)²

Evaluate

σ² = -11/20

Hence, the variance is -11/20

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The value of ratio is,

⇒ 1 : 9

We have to given that;

Volume of cones are,

⇒ V₁ = 27 in³

⇒ V₂ = 343 in³

Hence, The value of ratio is,

⇒ V₁ : V₂

⇒ 27 : 243

⇒ 27 / 243

⇒ 9/81

⇒ 1 / 9

Thus, The value of ratio is,

⇒ 1 : 9

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The exact values of x for x² - 8x - 5 = 0 are x = 4 + √21 or x = 4 - √21

To solve for x in the equation x² - 8x - 5 = 0, we can use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

Using this formula, we can identify the values of a, b, and c in the equation x² - 8x - 5 = 0.

Here, a = 1, b = -8, and c = -5.

Substituting these values into the formula, we get:

x = (-(-8) ± √((-8)² - 4(1)(-5))) / 2(1)

Simplifying this expression, we get:

x = (8 ± √(64 + 20)) / 2

x = (8 ± √84) / 2

Now, we can simplify the square root of 84 as 2√21:

x = (8 ± 2√21) / 2

We can further simplify this expression by factoring out 2 from the numerator:

x = 2(4 ± √21) / 2

Canceling out the 2s, we get:

x = 4 ± √21

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An attractive tax credit or deduction that can be considered is a reward for those who expend in renewable energy sources, such as solar power systems, wind turbines, or geothermal technology.

This payment can take the form of a tax credit, awarding taxpayers with a dollar-for-dollar payoff to lessen their tax debt for the year they initiated the investment.

These investments in green energy assets facilitate diminishing greenhouse gases emissions, providing ecological welfares by dropping one's carbon footprint. Moreover, this spending can lower an individual’s obligation on traditional energy options, economizing them long term on utility costs. In turn, supplying these incentives encourages people to invest in recyclable energy resources, ultimately leading to a decrease in global climate change elements alongside propelling the globe into a more sustainable future.

Overall, any brand new regulation on taxation allowance needs to bear mindful inspection by assembly members, carefully examining financial and revenue implications.

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The range of weights that one crate could weigh is between 127.6 and 154.8 pounds.

Harriet has 6 crates of watermelons.

Each crate alone weighs 17.8 pounds and contains between 32 and 36 watermelons.

The weight of each watermelon is between 3.9 and 4.3 pounds.

One crate of watermelons could weigh between 127.6 pounds

(6 crates x 32 watermelons x 3.9 pounds per watermelon + 17.8 pounds crate weight) and

154.8 pounds (6 crates x 36 watermelons x 4.3 pounds per watermelon + 17.8 pounds crate weight).

Therefore, the range of weights that one crate could weigh is between 127.6 and 154.8 pounds.

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Answer:

The equation Y=970(0.51)^x represents the percentage of change over time. As x increases, Y decreases due to the exponentiation of 0.51. This means that the percentage of change is decreasing over time.

For example, if we plug in x=1, the equation outputs Y=495.7, which represents a 49.43% decrease from the initial value of 970. As x continues to increase, the percentage of change decreases, approaching 0% but never quite reaching it.

Overall, this equation can be used to model a variety of situations where there is a gradual decrease in the percentage of change over time.

Answer:

2 1/5 or 35/14

Step-by-step explanation:

The arithmetic mean is adding all the numbers up and dividing by how many # there are.

Add:

0+2+4+3+1+1+5+0+4+3+2+5+3+2 = 35

Divide:

35/14 = 2 1/5

Answer:

2.5

Step-by-step explanation:

mean=sum of all numbers/total number

=35/14

=2.5

The median income from the given income distribution would be Rs. 34, 000.

The lowest income of the highest 10 % would be Rs. 40, 000.

Find the total number of earners sampled :

= 5 + 25 + 60 + 100 + 125 + 140 + 150 + 156

= 761 people

This means that the median income would be at :

= ( 761 + 1 ) / 2

= 381 position

The income at the 381 st position is Rs. 34, 000 so this must be the median.

The lowest of the highest 10 % would be the 90th percentile which would have the position of:

= 90 % x 761

= 685 position

The income at the 685 th position is Rs. 40, 000.

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The solution to the problem is that the number is 46.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The equation that can be used to solve the problem is q - 22 = 24.

To solve this equation, we need to isolate q on one side of the equation.

q - 22 = 24

Adding 22 to both sides, we get:

q - 22 + 22 = 24 + 22

Simplifying, we get:

q = 46

Therefore, the solution to the problem is that the number is 46.

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Answer:

y = 28

Step-by-step explanation:

(20 + 5y + 4)/2 = 3y - 2

5y + 24 = 6y - 4

y = 28

The probability that a gorilla in this particular zoo will live between 14.3 and 19.4 years is 86% (or 0.86)

From the Empirical Rule, for a Normal Distribution, approximately:

68% of the data falls within one standard deviation of the mean

95% of the data falls within two standard deviations of the mean

99.7% of the data falls within three standard deviations of the mean

To estimate the probability of a gorilla living between 14.3 and 19.4 years, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:

For 14.3 years: (14.3 - 16) / 1.7 = -1.18

For 19.4 years: (19.4 - 16) / 1.7 = 2

Now we can use a standard normal distribution table to find the probabilities associated with these z-scores:

The probability of a gorilla living less than 14.3 years is approximately the same as the probability of a standard normal variable being less than -1.18, which is about 0.12.

The probability of a gorilla living less than 19.4 years is approximately the same as the probability of a standard normal variable being less than 2, which is about 0.98.

Therefore, the probability of a gorilla living between 14.3 and 19.4 years is approximately the difference between these two probabilities: 0.98 - 0.12 = 0.86.

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The value of tan( 5π/6) is -1/√3

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The values of function of angles depends on the quadrant they fall on.

First quadrant ( 0-90°) = all functions are positive

Second quadrant ( 91°-180°) = only sine is positive

Third quadrant ( 181°- 270°) = only tan is positive

Fourth quadrant ( 271° -360°) = only cos is positive

Pi is a measurement of angle in radians and it is equivalent to 180°

therefore;

5π/6 = 5×180/6

= 150°

the equivalent of 150° is

180° -150 = 30°

since 150 falls on the second quadrant, tan of 150 will be negative.

Tan 150 = -tan 30

= -1/√3

therefore the value of tan 150 = -1/√3

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The length of BE in given figure of ABCD rectangle is 7.2 units.

Given that the length of the rectangle ABCD is = 12 units

Breadth of the rectangle ABCD is = 9 units

Area of the rectangle ABCD = Length*Breadth = 12*9 = 108 square units.

In another way, In triangle ABC, BE is the height on the side AC which is diagonal of the rectangle.

So diagonal AC = square root of (12² + 9²) = square root of 225 = 15 units.

So the area of triangle ABC = (1/2)*BE*AC = (1/2)*BE*15 = 15BE/2 square units.

Since diagonal of a rectangle divides the rectangle into two similar triangles.

So the area of ABCD = 2*area of triangle ABC = 2*(15BE/2) = 15BE square units.

According to condition now,

15BE = 108

BE = 108/15 = 7.2 units

Hence, the length of BE is 7.2 units.

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