Help on all parts pls step by step preferably

The total number of options is therefore given by 6 + 15 = 21 options.

The number of options for selecting from two essay subjects and three distinct required lengths are provided by:

[tex]{}^{2}C_1\times{}^{3}C_1=2\times3=6[/tex]

As a result, he has 20 options for the writing task.

For the reading assignment, the number of options from three volumes of essays and five biographies are provided by:

5 x 3 = 15

The total number of options is therefore given by 6 + 15 = 21 options.

Assignment refers to a task or a piece of work assigned to someone, usually by a teacher, professor, or employer. In the academic context, assignments are a way for instructors to evaluate students' understanding of course material and their ability to apply it in a given scenario. Assignments can take different forms, such as essays, research papers, presentations, or group projects.

Assignments can have a significant impact on a student's grade, so it is important for students to take them seriously and submit them on time. They require planning, research, critical thinking, and organization skills to complete successfully. To ensure success, students should carefully read and follow the assignment instructions, use reliable sources, and adhere to the designated formatting and citation styles.

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Step-by-step explanation:

Starting with x^2 + 6x = 9:

1. Move the constant term to the right side: x^2 + 6x - 9 = 0

2. Find the coefficient of x (which is 6) and divide it by 2: 6/2 = 3

3. Square the result from step 2: 3^2 = 9

4. Add the result from step 3 to both sides of the equation to complete the square: x^2 + 6x + 9 = 18

5. Factor the left side of the equation: (x + 3)^2 = 18

6. Take the square root of both sides of the equation: x + 3 = ±√18

7. Simplify the right side of the equation: x + 3 = ±3√2

8. Solve for x by subtracting 3 from both sides of the equation: x = -3 ±3√2

So the solutions are x = -3 + 3√2 and x = -3 - 3√2.

PLS mark my answer brainliest

Solving we get that option (C) that is x equals plus or minus root 18 minus 3 is correct.

Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square.

The steps of the method are as follows:

Isolate the number or variable c to the right side of the equation. Divide all terms by a (the coefficient of x2, unless x2 has no coefficient). Divide coefficient b by two and then square it. Add this value to both sides of the equation.

1). [tex]x^2+6x+\huge \text(\dfrac{6}{2} \huge \text)^2 =9+\huge \text(\dfrac{6}{2} \huge \text)^2[/tex]

2). [tex]\huge \text(x+\dfrac{6}{2} \huge \text)^2=18[/tex]

3). [tex](x+3)^2=18.[/tex]

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Complete Question-

Solve x2 + 6x = 9 for x by completing the square.

A. x = −6

B. x = 0

C. x equals plus or minus square root of 18 minus 3

D. x = x equals plus or minus square root of 18 plus 3

Answer:

shaded area = 372.115 m²

Step-by-step explanation:

the shaded area is calculated as

area of outer Δ - area if inner Δ

area of outer = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

                      = [tex]\frac{1}{2}[/tex] × 35.4 × 32.3

                      = 17.7 × 32.3

                      = 571.71 m²

area of inner = [tex]\frac{1}{2}[/tex] × 20.9 × 19.1

                      = 10.45 × 19.1

                      = 199.595 m²

then

shaded area = 571.71 - 199.595 = 372.115 m²

Answer:

3

Step-by-step explanation:

Hey! Alright so since its equilateral all sides are congruent.

This means you can set these two equations equal to eachother:

5 - 2x = -4x + 9

2x = 4

x = 2

5 - 2(2) = 1

-4(2) + 9 = 1

Have a great day!!

Answer:

PARTE A:

20%

PARTE B:
la probabilidad de que Jeremy saque un 3 o un 5 es 2/5 o 0,4 (40%) como decimal.

Step-by-step explanation:

If we define our population as all the households in the city of Chicago and use the Chicago telephone directory to draw our sample units, we would likely have a survey with sample frame error. Correct option is A.

Sample frame error occurs when the sampling frame, in this case, the Chicago telephone directory, does not accurately represent the population of interest.

In this case, the telephone directory would exclude households without a landline phone or those who choose not to have their phone number listed. This means that the sample would not include all households in the population, leading to biased results.

A representative survey (option B) would be one in which the sample accurately represents the population in terms of relevant characteristics such as age, gender, income, education, and other important demographic factors.

In contrast, a survey containing error (option C) is a general term that includes both sampling error and non-sampling error, such as measurement error or response bias.

Finally, a census (option D) is a study in which data is collected from all individuals or units in a population, not just a sample. Therefore, using a telephone directory to draw a sample from the population does not constitute a census.

In conclusion, using the Chicago telephone directory to draw a sample of households would likely result in a survey with sample frame error, which can lead to biased results and limit the generalizability of the findings to the entire population.

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Martin's total commission is $23.85 + $7.50 = $31.35.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The total cost of the three pairs of shoes is $53.00 * 3 = $159.00

The total cost of the five belts is $15.00 * 5 = $75.00

Martin's commission on the shoes is 15% of $159.00 = $23.85

Martin's commission on the belts is 10% of $75.00 = $7.50

Therefore, Martin's total commission is $23.85 + $7.50 = $31.35.

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The rule for the nth term of the geometric sequence is: [tex]an = 6 * 4^{(n-1)[/tex]

The rule for the nth term of a geometric sequence can be found using the third and fifth terms of the sequence. In this case, the rule is a = 24 and r = 4.

To find the rule for the nth term of a geometric sequence, we use the formula:

an = a1 *[tex]r^{(n-1)[/tex]

where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Given that the third term is 96 and the fifth term is 1,536, we can write two equations:

a * r²  = 96

a *[tex]r^4[/tex]= 1536

Dividing the second equation by the first equation, we get:

r² = 16

Taking the square root of both sides, we get:

r = 4 (since r cannot be negative in a geometric sequence)

Substituting r = 4 into either of the two equations, we get:

a * 16 = 96

a = 6

Therefore, the rule for the nth term of the geometric sequence is:

[tex]an = 6 * 4^{(n-1)[/tex]

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Answer:

384 cm^3

Step-by-step explanation:

the volume formula:

     V = a*b*c,

where a - length, b - width, c - height

so, the volume of the solid is V = 4*8*12 = 384 cm^3

The volume of the solid, if the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters is 384 cm³.

To find the volume of the solid, we need to multiply the length, width, and height together. So, the volume of the solid is:

V = l x w x h
V = 4 cm x 8 cm x 12 cm
V = 384 cm³

Therefore, the volume of the solid is 384 cubic centimeters (cm³).

To find the volume of a solid with given dimensions, you can use the formula for the volume of a rectangular prism, which is Volume = Length × Width × Height. In this case, the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters.

Now, let's plug these values into the formula:

Volume = (4 cm) × (8 cm) × (12 cm)

By multiplying these numbers together, you'll get the volume of the solid:

Volume = 384 cubic centimeters (cm³)

So, the volume of the solid with the given dimensions is 384 cm³.

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Hence, Susan got a 35% discount on the shirt.

The discount equal to the difference between the price paid for and it is par value. Discount is a type of deduction or reduction  in the cost price of a product. It is more used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, although the abbreviations pct., pct, and sometimes pc are also used. A percentage is a dimensionless number; it has no unit of measurement.

To calculate the percentage of  discount Susan got on the  shirt, we need to calculate the  difference between the  original price and the  discounted price and express it as a percentage of the original price:

We know that,

Discount = Original price - Discounted price

According to question,   Original price =  $32.50 and Discounted price = $21.13

Discount = $32.50- $21.13

Discount = $11.37

therefore , discount of Susan got on the  shirt is $11.37.

Now ,we calculate the percentage of discount

Percentage of discount = [tex]\frac{Discount}{Original price}[/tex]x 100%

Percentage of discount = [tex]\frac{11.37}{32.50}[/tex]x 100%

Percentage of discount = 35%

Therefore, Susan got a 35% discount on the shirt.

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Answer:

The Correct answer is 1

2

Falcons had a more effective overall record because of the higher median. Thus, the answer is option B.

The median is usually used for the comparison of two data sets instead of the mean, as it is not affected by outliers.

Compare the total points earned by each team.

The Eagles data set is given below:

3, 7, 10, 10, 13, 14, 17, 21, 24, 24, 27, 27, 37, 40, 55.

As the data set has an odd cardinality, the median is the middle element, therefore it is for:

21.

For the Falcons, we use the same approach and obtain a median about:

24.

Therefore, we can say that the Falcons had a more effective overall record because of the higher median and the best measure of center to compare would be mean.

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Answer:

Step-by-step explanation:

The price per pound of rib eye steak as per the $10.75 paid by Sid for 2.5 pounds of rib ribeye steak  is equal to $4.30.

Amount paid by Sid for rib ribeye steak is equal to $10.75

To find the price per pound of rib eye steak,

we need to divide the total price by the weight in pounds.

Price per pound = Total price / Weight in pounds

In this case, Sid paid $10.75 for 2.5 pounds of rib eye steak, so we have,

Substitute the values we have,

⇒ Price per pound = $10.75 / 2.5 pounds

Simplify the calculation, we get,

⇒ Price per pound = $4.30 per pound (rounded to the nearest cent)

Therefore, the price per pound of rib eye steak is $4.30.

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The value of the expression is,

⇒ [tex]b^{- 4/5}[/tex]

We have to given that;

The expression is,

⇒ [tex]\frac{b^{1/5} }{b}[/tex]

Now, We can simplify the expression as;

⇒ [tex]\frac{b^{1/5} }{b}[/tex]

⇒ [tex]b^{\frac{1}{5}- 1 }[/tex]

⇒ [tex]b^{- 4/5}[/tex]

Thus, The value of the expression is,

⇒ [tex]b^{- 4/5}[/tex]

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Answer:

D, 23

Step-by-step explanation:

In order to find b use sin

Sin (30) = b/46

Sin (30) = b/46b = sin (30) × 46

Sin (30) = b/46b = sin (30) × 46b = 1/2 × 46

Sin (30) = b/46b = sin (30) × 46b = 1/2 × 46b = 23

Answer:

3(8-4x)<6(x-5)

(24-12x)<(6x-30)

collect like terms

24+30<6x+12x

54 <18x

x<54/18

x<3

Therefore x is lesser than 3

Growth Decay

2x, ƒ(x) = (1)²*, 3x, f(x) = (1.3)³x - Growth

f(x) = (0.8)*2, f(x) = (-²)*2 - Decay

(The functions are categorized as either representing growth or decay.)

Growth Decay

2x - Growth (The function 2x represents exponential growth because as x increases, the value of 2x also increases.)

ƒ(x) = (1)²* - Growth (The function ƒ(x) = (1)² represents exponential growth because any number raised to the power of 2 will always be positive.)

f(x) = (7)x-¹ - Decay (The function f(x) = (7)x-¹ represents exponential decay because as x increases, the value of (7)x-¹ decreases.)

3x - Growth (The function 3x represents exponential growth because as x increases, the value of 3x also increases.)

f(x) = (1.3)³x - Growth (The function f(x) = (1.3)³x represents exponential growth because as x increases, the value of (1.3)³x also increases.)

f(x) = (0.8)*2 - Decay (The function f(x) = (0.8)*2 represents exponential decay because any number raised to the power of 2 will always be positive, and multiplying by 0.8 reduces the value.)

f(x) = (-²)*2 - Decay (The function f(x) = (-²)*2 represents exponential decay because any number raised to the power of 2 will always be positive, but the negative sign in front indicates a decay.)

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The weight of Keenan's paperweight is 340 grams using the volume of a pyramid given by V = (1/3)Bh.

To find the weight of Keenan's paperweight, we need to first find its volume. The volume of a pyramid is given by V = (1/3)Bh, where B is the area of the base and h is the height. Substituting the given values, we get:

V = (1/3)(80)(7.5) = 200 cm³

Next, we need to find the mass of the paperweight using the density of the clay. We know that density (p) is defined as mass (m) per unit volume (V), or p = m/V. Rearranging this equation, we get:

m = pV

Substituting the values, we get:

m = (1.7)(200) = 340 grams

Therefore, the weight of Keenan's paperweight is 340 grams.

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Answer:

60g

Step-by-step explanation:

Okay, the first ratio we have is 30:48 (because she uses 30g of coffee beans to make 48 fluid oz).

To find how many coffee beans she uses for 96 fluid oz we need to find the unit rate.

To find the unit rate you divide the number by the greatest common factor of both numbers. The GCF of both numbers is 6 so we divide 30 and 48 by 6. We get the unit ratio of 5:8.

Now we can solve it.

We can solve the equation of   [tex]\frac{x}{96} =\frac{5}{8}[/tex].

To solve this equation we need to multiply 96 by [tex]\frac{5}{8}[/tex]. Doing this gives us our answer of 60.

By dividing the state's total personal income of 268025 million dollars by its population of 5.5935 million, one can estimate the per capita income in 2022 to be around 47,917 dollars per person.

Finding the values of P and t for 2022 is necessary before we can determine the per capita income.

Assuming that t is the number of years since the year 2000, t will equal 22 in 2022.

The state's population in millions in 2022 can be determined using the P equation:

The P equation can be used to calculate the state's population in millions for the year 2022:

P = 0.034 (52) plus 4.909 to equal 5.5935 million

Using the computation for the total amount of personal income earned in the state, we can compute the total personal income in millions of dollars in 2022:

I is equal to 6983(22) + 109359, or 268025 trillion dollars.

To calculate the per capita income, we divide the total personal income by the population:

Total personal income divided by population yields a per-person income of 47,917 dollars (26,8025 / 5.5935).

Consequently, the amount of per capita income predicted for 2022 is almost 47,917 dollars per person.

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Answer: D

Step-by-step explanation: XY+YZ > XZ

Answer: D

Step-by-step explanation:

2 smaller sides added need to bigger than longest

only happens with D

The volume of the pyramid is approximately 105.8 cubic feet.

To calculate the volume of the pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. Since the base of the pyramid is a square, we can use the formula for the area of a square, which is A = s², where s is the length of a side of the square.

Given that the perimeter of the base is 10.7 feet, we can calculate the length of each side of the square by dividing the perimeter by 4: s = 10.7 ft / 4 = 2.675 ft. Therefore, the area of the base is B = s² = 2.675²= 7.16 square feet.

Now we can plug in the values for B and h into the formula for the volume of the pyramid:

Therefore, the volume of the pyramid is approximately 105.8 cubic feet, rounded to the nearest tenth of a cubic foot.

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Answer: .46%

Step-by-step explanation:

=.00456 = .46%  move decimal to right 2 times to convert to percent or x100

1732 + 1273 + 1638 = 4643

this is the answer, hope it helps!

The incorrect solution to the inequality is C ( 2 , 3 )

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

4x - y < 5

On simplifying , we get

Let the point be represented as C ( 2 , 3 )

Substituting the values in the inequality , we get

4 ( 2 ) - 3 < 5

8 - 3 < 5

5 is not less than 5

Hence , the point C ( 2 , 3 ) is not a solution

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If the jar of olives had a circumference of 11. 99 cm, the approximate diameter of the jar is 3.82 cm

The circumference of a circle is given by the formula C = 2πr, where C is the circumference, π is the constant pi (approximately equal to 3.14), and r is the radius. The diameter is twice the radius, so we can also write the formula as C = πd, where d is the diameter.

In this case, the circumference is 11.99 cm, so we can set up the equation

11.99 = πd

To solve for d, we can divide both sides by π

d = 11.99/π

Using a calculator, we get

d ≈ 3.82 cm

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Answer:

A person travels in one complete rotation while riding on a Ferris wheel is 98.596 in terms of pi

Step-by-step explanation:

As we know the formula of circumference of Circle have the value of 2*3.14(pi)*r (radius of the circle), and2r=d (diameter of the circle), so to get the value of r we have to divide 78.5 from 2 to get 15.7 which is radius of circle. so as the person travels in one complete rotation while riding on a Ferris wheel therefore the calculation is done usually considering the above formula, as we apply the formula to the given problem we will get that 2* 3.14* 15.7 = 98.596.

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The approximate number of gallons that are equal to 48,000cm³ is

10.5 Gallons

10.5 Gallons are equal to 48000 cm³ if  1 litre is approximately 1.75 pints, 1 gallon= 8 pints,

1000  cm³    =  1  Litre

48000 cm³  = 48 litre

1 litre is approximately 1.75 pints

=> 48 litre is approximately = 48 * 1.75 pints

= 84 Pints

8 pints  = 1  Gallon

=> 1 pint = 1/8 Gallon

=> 84 Pints = 84/8  Gallons=

= 10.5 Gallons

So, 10.5 Gallons are equal to 48000 cm³

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The bearing of Manchester from Cambridge is 270⁰.

Bearing refers to the direction or angle between two points, usually measured in degrees, that indicates the horizontal angle between a reference point or line and a target point or object.

Bearing is typically expressed as an angle measured clockwise from north, which is known as "true north" or "geographic north".

The bearing of Manchester from Cambridge is the angle made by the plane from Cambridge back to Manchester.

From the diagram the bearing of Manchester from Cambridge is 270⁰.

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