Otis is packing two gift boxes in a shipping carton. The rest of the space in the carton will be filled with packing pellets. What is the volume of the space that needs to be filled with packing pellets?

The sequence's eighth partial total, then, is zero.

A series is a collection of things that is in order in mathematics. (or events). Similar to a group, it has individuals. (also called elements, or terms). The total length of the series is the number in ordered components (possibly endless).

The sequence is: 24, -24, 24, -24, ...

To find the 8th partial sum, we need to add the first 8 terms of the sequence.

S8 = 24 + (-24) + 24 + (-24) + 24 + (-24) + 24 + (-24)

Simplifying this expression, we see that every pair of adjacent terms cancels each other out, leaving us with:

S8 = 0 + 0 + 0 + 0

Therefore, the 8th partial sum of the sequence is 0.

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Answer:

Oxygen; 34.01°C

Step-by-step explanation:

The oxygen freezes first as it has a higher (warmer) freezing point. For both to freeze, the temperature must drop a further 34.01°C as:

-218.79 - (-252.8)

= 252.8 - 218.79

= 34.01

The volume of the canister is 339.1 cubic inches.

The volume of a cylinder is calculated by using the formula V=πr²h, where r is the radius of the cylinder and h is the height of the cylinder.

The radius of the cylinder is half of the diameter, so the radius of the canister is 3 inches.

Using the formula, we can calculate the volume of the canister as follows:

V = π×3²×12

V = 108×3.14

V = 339.1 cubic inches

Therefore, the volume of the canister is 339.1 cubic inches.

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Answer:

Step-by-step explanation:

This is a trick question,  about the red marks again.   those marks are important b/c they tell you that the lengths are the same, so that the angles MUST also be the same.  That is  ,  D and E are equal

so set up your equations with that info

180 = 84 +2p

now use your algebra skillz to solve

180-84 / 2 = p

96/2 = p

48 = p

see??

Answer:

x = 0 , x = 3

Step-by-step explanation:

Equate the 2 expressions and solve for x

3x² - 2x + 1 = 7x + 1 ( subtract 7x + 1 from both sides )

3x² - 9x = 0 ← factor out 3x from each term

3x(x - 3) = 0

Equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 3 = 0 ⇒ x = 3

The cat population in Catonsville in 2007 was 200. The answer is option B.

Population refers to the total number of people, animals, or objects in a particular group or area. It is the entire group or collection of individuals, things, or events that we are interested in studying or describing.

We can use the given equation to find the cat population at any given time in years since the beginning of 2010. However, to find the population in 2007, we need to make a conversion from years since the beginning of 2010 to years since the beginning of 2007.

From the beginning of 2007 to the beginning of 2010, there are 3 years, so if we subtract 3 from the number of years since the beginning of 2010, we will get the number of years since the beginning of 2007. Therefore, we need to substitute t = -3 into the given equation and solve for p:

\(p = 1600(2)^t\\p = 1600(2)^(-3)\\p = 1600(1/8)\\p = 200\)

Therefore, the cat population in Catonsville in 2007 was 200. The answer is option B.

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Answer:

y=15

Step-by-step explanation:

Answer:

Y=15

Step-by-step explanation:

4-1=3

18-3=15

15+3=18

So, 15+4-1=18

In this question, the z-score associated with the 97.5 percent confidence interval is option e) 1.960.

In statistics, the z-score is used to determine the number of standard deviations a particular value is away from the mean in a normal distribution. The z-score is commonly used in confidence interval calculations, where it corresponds to a certain level of confidence.

The 97.5 percent confidence interval corresponds to a two-tailed test, meaning we need to find the z-score that captures 97.5 percent of the area under the normal distribution curve, with 2.5 percent of the area in each tail.

Looking up the z-score in a standard normal distribution table or using statistical software, we find that the z-score associated with the 97.5 percent confidence interval is approximately 1.960.

Therefore, the correct answer is e) 1.960. This z-score is used when constructing a 97.5 percent confidence interval, which means there is a 97.5 percent probability that the true population parameter lies within the interval calculated using this z-score.

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The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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Thus we only take the positive root:x = 27/8 = 3.375Answer: 3.375 feet.

The problem states that a rectangular garden that measures 50 feet wide and 45 feet long is enclosed by a uniform width of x feet paved path. To solve the problem,

we can use the formula of the combined area of the garden and the paved path and equate it to 2646 square feet. The combined area is computed by adding the area of the garden and the area of the paved path.

Garden area:Length of garden = 45 ftWidth of garden = 50 ftArea of garden = Length x Width= 45 x 50= 2250 square feet

Paved path:

If the garden has a uniform width of x feet paved path, then the width of the paved path would be x + 2x + x= 4x. The width is multiplied by 2 because there are two widths surrounding the garden.

Length of paved path = length of garden + 2 (width of paved path)= 45 + 2 (4x)= 8x + 45Width of paved path = width of garden + 2 (width of paved path)= 50 + 2 (4x)= 8x + 50

The area of the paved path is computed by subtracting the area of the garden from the combined area.Area of paved path = Combined area - Garden area2646 square feet

= (8x + 45) (8x + 50) - 2250= 64x² + 760x + 675

We then solve for the value of x by factoring the quadratic equation.2646 square feet = 64x² + 760x + 6752646 - 2646

= 64x² + 760x + 675 - 264664x² + 760x - 1971

= 0(8x - 27) (8x + 73) = 0

The value of x cannot be negative,

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Answer:

Step-by-step explanation:

hello :

P(E and F)=0.7×0.6 =0.42

Answer:

(-2,1)

Step-by-step explanation:

Since this is an upwards opening parabola, the minimum point is at the vertex

We can find the x coordinate of the vertex by

y = 2x^2 +8x +9

where a=2  b =8 and c =9

x = -b/2a

x = -8/(2*2)

  = -8/4 = -2

The x coordinate is -2

Now substitute this in to find the y coordinate

y = 2(-2)^2 +8(-2)+9

  = 2*4 -16+9

  8-16+9

  =1

The vertex = (-2,1), which is the minimum point

Answer:

Step-by-step explanation:

y=2x²+8x+9

to find the minimum or maximum point x=-b/2a

x=-8/4=-2

y=2(-2)²+8(-2)+9

y=8-16+9

y=1

minimum point is (-2,-1)

Answer:

the formula to use is A

hope it helps

The probability of choosing 6 people at random from the group and having all of them be left-handed is approximately 0.00002599 or 0.0026%.

We can approach this problem using the binomial distribution, which models the probability of a certain number of successes (in this case, choosing left-handed people) in a fixed number of trials (choosing 6 people).

Let p be the probability of choosing a left-handed person, which is given as 15% or 0.15. Then, the probability of choosing all 6 people to be left-handed can be calculated as:

P(6 left-handed) = (0.15\()^6\) * (1 - 0.15)\(^(6 - 6) * C(6, 6)\)

where C(6, 6) represents the number of ways to choose 6 items from a set of 6, which is equal to 1.

Plugging in the values, we get:

P(6 left-handed) = (0.15\()^6\) * (0.85)^0 * 1

= 0.00002599

Therefore, the probability of choosing 6 people at random from the group and having all of them be left-handed is approximately 0.00002599 or 0.0026%.

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Answer:

B. -5

Step-by-step explanation:

multiply the opposite number than the denominator

hope this helps :3

pls mark brainliest

Answer:

The answer is B. -5.

Step-by-step explanation:

i did it on edge

Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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Correct arrangement of the question is;

Rewrite the rational exponent as a radical: five to the three fourths power all raised to the two thirds power

A) the cube root of 5 squared

B) the twelfth root of 5

C) the square root of 5

D) the cube root of 5 the fourth power

Answer:

Option C) the square root of 5

Step-by-step explanation:

We are given: five to the three fourths power all raised to the two thirds power

Translating that statement means 5 is raised to ¾ raised to ⅔.

In indices, when we have two powers attached to a number, the two powers will multiply each other.

Thus, 5 is raised to; ⅔ × ¾ = 2/4 = ½

Thus, 5 is raised to power ½.

Now, when a number is raised to the power ½, it is said to be square root of that number.

Thus, the right answer is square root of five.

Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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Answer:

good questiion

Step-by-step explanation:

Step-by-step explanation:

slant height (l)=25cm

There are 1,764 ways to select the hockey team.

To determine the number of ways a hockey team can be selected containing 5 men and 6 women from a group of 7 men and 9 women, we can use the combination formula.

The combination formula calculates the number of ways to choose r objects from a group of n objects, where order does not matter.

The formula is given by:

nCr = n! / (r! * (n-r)!)

In this case, we need to select 5 men from a group of 7 and 6 women from a group of 9.

Therefore, the number of ways to select the team is:

7C5 * 9C6 = (7! / (5! * 2!)) * (9! / (6! * 3!))

= (7 * 6 / 2) * (9 * 8 * 7 / (3 * 2))

= 21 * 84

= 1764

Therefore, there are 1764 ways to select a hockey team containing 5 men and 6 women from a group of 7 men and 9 women.

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Answer:

hi

Step-by-step explanation:

if x is equal to 2 then 3×5×2 is 30

have a nice day

bye

The value of the expression 3·5x when x = 2 is 30

The expression is given as:

3·5x

Rewrite properly as:

3 * 5x

When x = 2, the expression becomes

3 * 5 * 2

Evaluate

30

Hence, the value of 3·5x when x = 2 is 30

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Answer:

x = 8

Step-by-step explanation:

Given

- 2(- 3x + 3) + 2x = 58 ← distribute and simplify left side

6x - 6 + 2x = 58

8x - 6 = 58 ( add 6 to both sides )

8x = 64 ( divide both sides by 8 )

x = 8

Step-by-step explanation:

Suppose the cost of each t-shirt is x

and the cost of each hat is y

according to question

\(\Rightarrow 2x+3y=12\quad \ldots(i)\\\Rightarrow 5x+4y=23\quad \ldots(ii)\\\text{solving (i) and (ii) we get}\)

\(x=3\ \text{and}\ y=2\)

So, the cost of a t-shirt is £3

the cost of a hat is £2

Answer:

30, 80

Step-by-step explanation:

Let the smaller number be \(x\). Then, the other number is \(2x+20\). The sum is 110, so

\(x+(2x+20)=110.\)

Simplifying gives

\(3x+20=110\).

Subtracting 20 from both sides gives

\(3x=90\).

Dividing by 3 gives

\(x=30\).

The smaller number is 30 and the larger number is 2(30)+20=80.

Answer:

There are 4 terms

Step-by-step explanation:

“Terms are single numbers, variables, or the product of a number and variables. Examples of terms: 9 a 9a 9a. y y y.”

A. The width of the rectangle is 32 centimeters. and B. solving for the width, we get the answer of 32 cm.

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

A. Let's use the formula for the perimeter of a rectangle:

Perimeter = 2 × (Length + Width)

We are given the length of the rectangle, which is 26 cm, and the perimeter, which is 116 cm. We can substitute these values into the formula and solve for the width:

116 cm = 2 × (26 cm + Width)

Divide both sides by 2:

58 cm = 26 cm + Width

Subtract 26 cm from both sides:

32 cm = Width

Therefore, the width of the rectangle is 32 centimetres.

B. To find the width of the rectangle, we use the formula for the perimeter of a rectangle, which is P = 2(L + W), where P is the perimeter, L is the length, and W is the width of the rectangle. We substitute the given values into the formula and solve for the width. We are given the length of the rectangle, which is 26 cm, and the perimeter, which is 116 cm. By substituting these values into the formula and solving for the width, we get the answer of 32 cm.

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