Find the value of z /2 that corresponds to a confidence level of 89.48%.

The GCF (Greatest Common Factor) of the terms in the algebraic expression 4a^4+6a^2 is found by observing the numerical coefficients (4 and 6) and the variables (a^4 and a^2). The GCF of 4 and 6 is 2, and the GCF of a^4 and a^2 is a^2, so the GCF of the terms in the expression is 2a^2.

The GCF (Greatest Common Factor) of two or more terms is the greatest number that divides each of the terms without any remainder. The GCF of the terms in the algebraic expression 4a^4+6a^2 can be found by observing the numerical coefficients and the variables.

1. The numerical coefficients of the terms are 4 and 6. The GCF of 4 and 6 is 2.

2. The variables in the terms are a^4 and a^2. The GCF of a^4 and a^2 is a^2, because a^2 is the factor that appears in both terms to the smallest power.

By combining the GCF of the numerical coefficients with the GCF of the variables, we find that the GCF of the terms in the algebraic expression 4a^4+6a^2 is 2a^2.

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To find the balance after 10 years when $20,000 is invested at 5% interest compounded annually, we can use the formula for compound interest:

A = P(1+r)ⁿ

Where:

*A is the complete volume of money obtained after

*n years, including interest.

*P embodies the initial investment, or the principle amount.

*The yearly interest rate, calculated by decimal, is r.

*n is the number of periods the money has been put into investments for.

Given:

*P = $20,000

*r = 5% = 0.05

*n = 10 years

Taking appropriate values to carry out the calculation:

A = 20000(1 + 0.05)¹⁰

A = 20000(1.05)¹⁰

Now, let's calculate:

A ≈ 20000 × (1.05)¹⁰

A ≈ 20000 × 1.62889462677744

A ≈ 32577.89

So, the balance after 10 years will be approximately $32,577.89.

After 10 years, the balance of the investment can be calculated using the formula for compound interest: A = P(1+r)ⁿ

Where:

*A is the amount of money accumulated after

*n years, including interest.

*P is the principal amount (the initial investment).

*r is the annual interest rate (in decimal).

*n is the number of times the interest is compounded per year.

In this case, the principal (P) is $20,000, the annual interest rate (r) is 5%, and the investment is compounded annually. Substituting these values into the formula:

A = 20000(1.05)¹⁰

A ≈ 20000 × (1.05)¹⁰

After computation, the balance after 10 years is approximately $32,577.89. This represents the accumulated amount including the initial investment and the interest earned over the 10-year period.

Complete Question:

Suppose your friend’s parents invest $20,000 in an account paying 5% interest compounded annually. What will the balance be after 10yr?

Angles 4 and 5 form a pair of vertical angles. Vertical angles are two angles that are opposite each other when two lines intersect. They have the same measure and are congruent.

Vertical angles are a pair of angles formed when two lines intersect. In this case, angles 4 and 5 are considered vertical angles because they are opposite each other at the point where the lines intersect. These angles have a special property: they are congruent, which means they have the same measure. This is a fundamental principle in geometry.

Imagine drawing two straight lines that intersect, creating four angles. Angles 4 and 5 are positioned opposite each other, and they share the same measurement. This relationship is true regardless of the lengths of the lines or the specific angles involved. It's a geometric rule that holds true in all cases where vertical angles are formed.

Understanding vertical angles is important in various mathematical and geometric applications, as it allows us to make deductions about the relationships between angles and lines in different configurations.

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circumference of a circle:-The circumference is the measurement around the circle.

The digit 4 in 6,296.04 is in the hundredths place, representing four hundredths or 4/100. This can also be expressed in scientific notation as 4 x 10⁻².

The place value of the digit 4 in 6,296.04 is in the hundredths position. This is because the digit 4 is two places to the right of the decimal point. In a decimal number, the first place to the right of the decimal point is the tenths place, the second is the hundredths place, and it continues with thousandths, ten-thousandths, and so on. Therefore, in the number 6,296.04, the 4 represents four hundredths, or 4/100, which can also be written in scientific notation as 4 × 10⁻².

Final Answer:

The probability that at least one of the four randomly selected people has been vaccinated is approximately 0.9606.

Explanation:

To find the probability that at least one of the four randomly selected people has been vaccinated, we can use the complement rule. The complement of "at least one person vaccinated" is "none of the people vaccinated." Then, we subtract the probability of none of them being vaccinated from 1.

Given that 61% of the population has been vaccinated, the probability that a randomly selected person has been vaccinated is [tex](P(\text{vaccinated}) = 0.61\)[/tex].

So, the probability that a randomly selected person has not been vaccinated is [tex]\(P(\text{not vaccinated}) = 1 - P(\text{vaccinated}) = 1 - 0.61 = 0.39\).[/tex]

Now, we can find the probability that none of the four randomly selected people has been vaccinated:

[tex]\[P(\text{none vaccinated}) = (0.39)^4\][/tex]

And the probability that at least one of them has been vaccinated is the complement of this:

[tex]\[P(\text{at least one vaccinated}) = 1 - P(\text{none vaccinated}) = 1 - (0.39)^4\][/tex]

Let's calculate it:

[tex]\[P(\text{at least one vaccinated}) = 1 - (0.39)^4\][/tex]

[tex]\[P(\text{at least one vaccinated}) \approx 1 - 0.0394179 \][/tex]

[tex]\[P(\text{at least one vaccinated}) \approx 0.9605821\][/tex]

So, the probability that at least one of the four randomly selected people has been vaccinated is approximately 0.9606.

The probability that at least one of the 4 randomly selected people has been vaccinated is calculated using the complement rule and is found to be 0.9769.

To determine the probability that at least one of the 4 randomly selected people has been vaccinated, we can use the complement rule. The probability of an individual not being vaccinated is 1 - 0.61 = 0.39.

We need to calculate the probability that none of the 4 selected people are vaccinated and subtract this from 1:

Thus, the probability that at least one of them is vaccinated is:

1 - 0.0231 = 0.9769

Therefore, the probability that at least one of the 4 randomly selected people has been vaccinated is 0.9769.

Kyle scored a total of 923 points after playing all the three games.

Addition is defined as combining two or more number together.

Given is Kyle who is playing a new video game. He scored 128 points on his first game, 305 points on his second and 490 points on his third game

The total points scored by Kyle will be the sum of the individual points in each game. Therefore, adding each set of points, we get -

P[T] = 128 + 305 + 490 = 923 points.

Therefore, Kyle scored a total of 923 points after playing all the three games.

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The number of  students enrolled this year are 17,360.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, the number of students enrolled at a community college increase by 12% from last year to this.

The enrollment last year to this year was 15,500.

Increased number of students are

12% of 15500

= 12/100 ×15500

= 12×155

= 1860

Number of students enrolled this year are 15,500+1860

= 17360

Therefore, the number of  students enrolled this year are 17,360.

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volume of the rectangular prism = base area * height

base area = length * breadth

volume of the rectangular prism = length * breadth * height

volume of the rectangular prism = 5*8*2 = 80 inches ^3

volume of taken up by the eraser = 5.5 inches^3

volume that is not take-up by the eraser = 80-5.5 = 74.5 inches^3

we have

[tex]f(x)=6x^{3}-35 x^{2} +26x-5[/tex]

we know that

The zeros of the function are the values of x when the value of the function is equal to zero. The zeros of the function are the x-intercepts of the function

Using a graphing tool

see the attached figure  

the answer is the option

[tex](5,\frac{1}{2}, \frac{1}{3})[/tex]

The dimensions of the wall are found by defining variables based on the given ratio and area, resulting in a height of 16 ft and a length of 24 ft.

The question involves finding the dimensions of a wall given the ratio of its height to length and its total area. To solve this, let's denote the height of the wall as 2x and the length of the wall as 3x, based on the ratio 2:3. The area of the wall is the product of its height and length, which means (2x) ×(3x) = 384 sq. ft.

Now, by simplifying the equation, we get [tex]6x^2[/tex] = 384. Dividing both sides by 6 gives us [tex]x^2[/tex] = 64. Taking the square root of both sides, we find x = 8. Therefore, the height of the wall is 2x = 16 ft and the length of the wall is 3x = 24 ft.

Answer:
The shorter side is 5 inches and the longer side is 8 inches.

Explanation:
We start by listing formulas for solving for the area and perimeter of a rectangle, which will then determine how we find the dimensions we are looking for.

The area of a rectangle is length (l) times width (w), often represented as:
A = l(w), or A = lw

The perimeter of a rectangle is the sum of twice the length and twice the width, often represented as:
P = 2l + 2w

If product of length and width is 40 inches per the rectangle's given area, then a factor pair of 40 must be the dimensions of the rectangle. These values can then be checked to see if they also satisfy the perimeter of the rectangle.

So first, list factors of 40:
1, 40; 2, 20; 4, 10; 5, 8

Now, we plug these pairs into the perimeter equation.
2(1) + 2(40) = 2 + 80 = 82
82 > 26

2(2) + 2(20) = 4 + 40 = 44
44 > 26

2(4) + 2(10) = 8 + 20 = 28
28 > 26

2(5) + 2(8) = 10 + 16 = 26
26 = 26
Therefore, the factors 5 and 8 are what we use. 5 inches by 8 inches are the dimensions.

Final answer:

Linda has completed 60% of her deliveries for the week.

Explanation:

Linda has completed 24 deliveries out of a total of 40 deliveries for the week. To find the percentage of deliveries Linda has completed, we can divide the number of completed deliveries by the total number of deliveries and multiply by 100.

Percent of deliveries completed = (Number of completed deliveries / Total number of deliveries) * 100

Percent of deliveries completed = (24/40) * 100 = 60%