Which of the following are negative integers? Select all that are correct

A the sum of two positive integers

B. The sum of two negative integers

C different of a positive integer that is greater than it

D the difference of a negative integer and an integer and an integer that is greater than it but that is not its opposite

The number we are looking for is N = 2 × 2^3 × 3^2 = 72.

Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say

n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k

then the number of divisors of n is given by

d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).

Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form

N = p_1^2 × p_2^2, or N = p_1^7,

where p_1 and p_2 are distinct prime numbers.

Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that

N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,

and

N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,

where q_1, q_2, r_1, and r_2 are distinct prime numbers.

To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by

p_1 = q_1^a × q_2^b,

p_2 = r_1^c × r_2^d,

N/2 = q_1^e × q_2^f,

N/3 = r_1^g × r_2^h.

Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:

a + 1 × (b + 1) = e + 1 × (f + 1) = 4,

c + 1 × (d + 1) = g + 1 × (h + 1) = 4,

2a × 2b = ef,

2c × 2d = gh.

We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get

(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.

We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.

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Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation:

The compound interest on ₹4000 at a rate of 5% p.a. for 3 years is ₹631.03.

The formula to calculate compound interest is:

[tex]A= P(1+\frac{R}{N} )^{nt}[/tex]

Where:

A = Final amount (including interest)

P = Principal amount

r = Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

In this case, P = ₹4000, N = 3 years, R = 5% per annum (p.a.), which means r = 0.05 and n = 1 (compounded annually).

So, plugging in the values in the formula:

[tex]A= 4000(1+\frac{0.05}{1} )^{1*3}[/tex]

[tex]A= 4000(1.05)^{3}[/tex]

[tex]A = 4631.03[/tex] (rounded to 2 decimal places)

Compound interest is a type of interest that is calculated not only on the initial amount of money borrowed or invested but also on the accumulated interest from previous periods. In other words, the interest earned in each period is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.

This compounding effect can result in significant growth in the value of an investment or debt over time, especially if the interest rate is high and the period of investment or debt repayment is long. For example, if you invest $1,000 at an annual interest rate of 5% compounded annually, you will earn $50 in interest at the end of the first year, and your new total will be $1,050.

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Answer:

3m

Step-by-step explanation:

red wire = 27

black wire= 12

so, we take HCF (highest common factor)

which would be 3 so all the wires would be cut into 3m long.

I hope it helps.

Answer:2m

Step-by-step explanation:

as the factors of 12 are:1, 2, 3, 4, 6 and 12

and the factors of 26 are:1, 2, 13 and 26

so if you are talking meters 2 would be the longest

i hope you get this right x

We can graph this solution on the number line by placing a point at 7.6.

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20

80 10x + 4 = 20

80 - 4 = 10x

76 = 10x

7.6 = x

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We can graph this solution on the number line by placing a point at 7.6.

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x

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How does cellular respiration help maintain homeostasis in animals?

Answer: Cellular respiration helps animals maintain homeostasis by breaking down glucose to produce ATP, which is the energy currency of the cell. ATP is necessary for many cellular processes that help maintain homeostasis such as active transport and protein synthesis.

Explain why cells separate and expel waste.

Answer: Cells separate and expel waste to prevent the accumulation of toxic substances that can disrupt cellular function and lead to disease. The waste products are transported out of the cell and into the bloodstream where they are filtered and excreted by organs such as the kidneys.

Why do cells in organisms such as animals reproduce?

Answer: Cells in organisms such as animals reproduce to replace damaged or dying cells, and to enable growth and development. Reproduction ensures that the organism maintains the proper balance of cells and that there is enough tissue to perform necessary functions.

Explain how plant cells use photosynthesis to maintain homeostasis?

Answer: Plant cells use photosynthesis to maintain homeostasis by converting light energy into chemical energy in the form of glucose. This glucose is then used to produce ATP, which is necessary for cellular processes such as active transport and protein synthesis. Additionally, plants use photosynthesis to produce oxygen, which is necessary for respiration.

I hope this helps :)

The probability that the jury makes the correct decision is approximately 0.7063.

To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.

We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.

We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:

P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x [tex]p^i \times (1-p)^{(n-i)}[/tex] ]

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Plugging in the values, we get:

P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x [tex]0.80^i \times (1-0.80)^{(12-i)}[/tex]]

Using a calculator or software, we can calculate this to be approximately 0.7063.

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Thus, the total area of composite figure (circle on a rectangle) is found as  29.91 m².

Area of sector of the circle = (Ф/360°) *π*r²

r is the radius = 5.5 m

π = 3.14

Area =  (30/360°) *3.14 * 5.5²

Area = 7.91 m²

Area of rectangle = width × length

Area = 4 × 5.5 = 22 m²

Total area of composite figure = area of the circle's sector + area of the rectangle

Total area of composite figure =  7.91 m² + 22 m² = 29.91 m²

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Answer:

a. 6

b. 6

Step-by-step explanation:

A. mean proportion

3:x::x:12

product of mean = product of extreme

3 x 12 = x^2

x^2= 36

now take square root on both sides

x = 6

as sqaure root will cancel the square on x and square root of 36 is 6.

B. the geometric mean is the product of all

the numbers in a set, with the root of how many numbers there are. here, there are two numbers, so a square root is used. the value of the geometric mean of 3 and 12 is 6.

Hope's it helps...

Answer:

Step-by-step explanation:

You want to make 5.4 in three different ways.

You can add, subtract, multiply, or divide numbers to obtain a result of 5.4:

  2.9 +2.5 = 10.0 -4.6 = 2.0×2.7 = 10.8÷2 = 5.4

  √29.16 = ∛157.464 = 5.4

  [tex]\displaystyle\sum_{n=1}^\infty{10.8(3^{-n})}=5.4[/tex]

The factorizations of these integers above represent their factorizations into their respective prime numbers.

(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.

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The solution to the differential equation y" - 8y' + 16y = 24x + 2 is y = (c1 + c2 x) e^(4x) - 3x + 1 plus any constants determined by initial or boundary conditions.

To solve the given differential equation y" - 8y' + 16y = 24x + 2 using the method of undetermined coefficients, we first find the complementary solution of the homogeneous equation y" - 8y' + 16y = 0:

The characteristic equation is r^2 - 8r + 16 = 0, which has a double root of r = 4. Therefore, the complementary solution is y_c = (c1 + c2 x) e^(4x).

Next, we need to find a particular solution for the non-homogeneous equation. Since the right-hand side has two terms, we can try a particular solution of the form y_p = Ax + B for the homogeneous term and y_p = C for the constant term.

Substituting this form into the differential equation, we get:

y_p" - 8y_p' + 16y_p = 24x + 2

Taking the derivatives and plugging them back into the equation, we get:

-8A + 16B + 16C = 2

0 + 0 + 16C = 24

Solving for A, B, and C, we get A = -3, B = -1/2, and C = 3/2.

Therefore, the particular solution is y_p = -3x - 1/2 + 3/2 = -3x + 1.

The general solution is then y = y_c + y_p = (c1 + c2 x) e^(4x) - 3x + 1.

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Answer:

28 is the ans of 252÷9here we go

252 divided by 9 equals 28.

To divide 252 by 9, you can use long division, which involves dividing the number in steps until there is no remainder left.

Here's the step-by-step process:

Write down the dividend (252) and the divisor (9), and set up the long division format:

9 | 252

Look at the leftmost digit of the dividend (2) and see if it's divisible by the divisor (9). Since 2 is less than 9, we bring down the next digit (5) to the right of 2, making it 25.

9 | 252

2

Divide the new number (25) by the divisor (9). The result is 2, which is the first digit of the quotient. Multiply this result by the divisor (2 x 9 = 18) and write it below the 25, then subtract it from 25:

9 | 252

25

18

--

7

Bring down the next digit (2) from the dividend to the right of the remainder (7), making it 72. Now, divide 72 by 9, which gives you 8. Multiply this result by the divisor (8 x 9 = 72) and write it below the 72, then subtract it from 72:

9 | 252

25

18

--

72

72

---

0

There is no remainder left, and the dividend has been completely divided. The quotient is the result of the division, which is 28.

Therefore, 252 divided by 9 equals 28.

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Answer: 30

Step-by-step explanation: So what you do is,

1) Add the 25 to the 8

2) Find the sum

3) Subtract 3 from the sum

4) Done!

I hope this helps!

Best,

Abigail H

8th Grade

The value of x in the right triangle when calculated is approximately 13.8 units

Given the right-angled triangle

The side length x can be calculated using the following sine ratio

So, we have

sin(39) = x/22

To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.

First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.

Then, we can set up the equation:

0.6293 = x/22

To solve for x, we can multiply both sides by 22:

0.6293 * 22 = x

13.8446 = x

Rewrite as

x = 13.8446

Approximate the value of x

x = 13.8

Therefore, x is approximately 13.8 in the triangle

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The number of bacteria in a second study is modeled by the function, the growth rate r for the equation is 0.017, since the equation is [tex]A(t) = 2500e^{(0.017t)}[/tex].

To find the growth rate r of an exponential function, use the following formula:[tex]A = Pe^{(rt)}[/tex] Where:

To determine r, divide both sides by P and take the natural logarithm of both sides. It yields: ln(A/P) = rt Therefore: r = ln(A/P) / tNow, given that the number of bacteria in a second study is modeled by the equation: [tex]A(t) = 2500e^{(0.017t)}[/tex] Compare the given equation with [tex]A = Pe^{(rt)}[/tex]. The initial amount (P) is 2500, since that is the starting amount. The final amount (A) is [tex]2500e^{(0.017t)}[/tex], since that is the amount after a certain period of time (t).Thus, [tex]r = ln(A/P) / t= ln(2500e^{(0.017t)} / 2500) / t= ln(e^{(0.017t))} / t= 0.017[/tex] (rounded to 3 decimal places)Therefore, the growth rate r for the equation is 0.017.

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The cost per ounce of the juice is $0.0.9 using unitary method.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary method, in its most basic form, is used to calculate the value of a single unit from a specified multiple. The unitary technique can be used to complete it. Additionally, after determining the value of a single unit, we can increase that value by the number of units needed to determine the value of the additional units. What is division?One of the four fundamental arithmetic processes, or how numbers are combined to create new numbers, is division. The other processes are addition, subtraction, and multiplication. The reverse of multiplying is division.

In this question,

64-ounce container of juice costs $5.76. I

ounce of juice costs = 5.76/64= $0.09

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Answer:

30 minutes

Step-by-step explanation:

Use ratios. This is an inverse function, as speeding up makes the time traveling go down. So, when dividing the speed by 3 (done so 15 can get to 5), we multiply the time traveled by 3.

10 minutes * 3 = 30 minutes

The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.

The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.

The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.

A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.

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For the first question, the indefinite integral of [tex]16x³ - 15x² + 6[/tex] is [tex]4x⁴ - 5x³ + 6x + C[/tex], where C is the constant of integration.

For the second question, the indefinite integral of 7cos(x) + 5sin(x) is [tex]7sin(x) + 5cos(x) + C,[/tex]where C is the constant of integration.

1)To check the result, differentiate the indefinite integral using the power rule and product rule: [tex](16x³ - 15x² + 6)' = 64x² - 30x + 6.[/tex]

2)To check the result, differentiate the indefinite integral using the sum rule and product rule: [tex](7sin(x) + 5cos(x))' = 7cos(x) - 5sin(x).[/tex]

In summary, to find the indefinite integral of a function, use the power rule and product rule to integrate the individual terms. To check the result, differentiate the indefinite integral.

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The combined ratio of x : y : z from x ; y = 4 : 3 and y : z = 5 ; 2 is x:y:z = 20:15:6

Given the following ratios

x ; y = 4 : 3

y : z = 5 ; 2

To find the ratio of x:y:z, we need to combine the two given ratios and simplify:

x:y = 4:3

y:z = 5:2

To combine these ratios, we need to have a common term for y.

We can do this by multiplying the first ratio by 5 and the second ratio by 3:

5(x:y) = 5(4:3) = 20:15

3(y:z) = 3(5:2) = 15:6

Now we have a common term of 15 for y, so we can combine the ratios:

x:y:z = 20:15:6

Therefore, the ratio of x:y:z is 20:15:6

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Answer:

D) he did not multiply -3 with -2 to get +6 instead of -6

Step-by-step explanation:

-3(x - 2)

-3x + 6

Compare the two

-3x + 6 ≠ -3x - 6

They are not equal! Looking at the options, D is the answer.

Answer:

The correct answer is D) he did not multiply -3 with -2 to get +6 instead of -6.

To expand -3(x-2), we need to distribute -3 to both terms inside the parentheses, which gives us:

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

Therefore, the correct equivalent expression is -3x + 6, not -3x - 6 as Rob wrote. He made a mistake in multiplying -3 and -2, which should have given him +6 instead of -6.

(please mark my answer as brainliest)

Answer:

This is not my own answer it is a copied one.

If h (x) represents the amount of money spent and x the amount of friends, then we can write it as in a pair as (x, h (x)) Then the pair given is (6.5, $92.25) Here you see a problem, x is 6.5, knowing that x represents the amount of friends, this is a problem because you need to have a whole number ( you can't have a 0.5 of a friend)

Answer:

see explanation

Step-by-step explanation:

(a)

the scale factor is the ratio of corresponding sides, shape B to shape A

scale factor = [tex]\frac{12}{15}[/tex] = [tex]\frac{4}{5}[/tex]

(b)

t is then [tex]\frac{4}{5}[/tex] of 7 = [tex]\frac{4}{5}[/tex] × 7 = [tex]\frac{28}{5}[/tex]

Step-by-step explanation:

40 Years is the right answer

Answer:

son is 10 , father is 40

Step-by-step explanation:

let x be the sons age then father is x + 30

in 5 years

son is x + 5 and father is x + 30 + 5 = x + 35

at this time the father is three times as old as his son , then

x + 35 = 3(x + 5)

x + 35 = 3x + 15 ( subtract x from both sides )

35 = x + 15 ( subtract 15 from both sides )

20 = x

then sons age = x = 10 and fathers age = x + 30 = 10 + 30 = 40

In conclusion  the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.  The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Why it is?

The expression for how much money Elena saves after selling p pens is:

Total money saved = 5 + (1.5)p

The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Solving the equation:

5 + (1.5)p = 20

(1.5)p = 15

p = 10

We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.

If Elena wants to have some money left over, we can write the inequality:

5 + (1.5)p > 20

Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.

To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:

5 + (1.5)p > 20

(1.5)p > 15

p > 10

Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.

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Answer: The expression is undefined.

Step-by-step explanation:

Division by zero is undefined in mathematics. In this expression, there is a division by zero in the term 0/7. Therefore, the entire expression is undefined.

It is correct to state that if there is a sample, the standard error is used in the denominator of the z stat or t stat formula.

The t-distribution is used when we have the standard deviation for the sample instead of the population, hence the equation is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The standard error is modeled as follows:

[tex]s_e = \frac{s}{\sqrt{n}}[/tex]

Which is the denominator of the formula for the test statistic, hence the statement is true.

When we have the standard deviation for the population, we use the z-distribution, however the formula for the standard error is similar.

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Answer:

We need to prove that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.

Let's consider an isosceles triangle ABC where AB = AC. We draw the altitude from A to BC and call the point where it intersects BC as D.

Now, we need to prove that AD is the angle bisector, median, and altitude to the base BC.

To prove AD is the angle bisector:

We need to prove that the angle ADB and ADC are equal. We know that angle ABD and angle ACD are right angles because BD and CD are altitudes. We also know that AB = AC because the triangle is isosceles. Therefore, the triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion.

Thus, angle ADB = angle ADC, which means that AD is the angle bisector of angle BAC.

To prove AD is the median:

We need to prove that BD = CD. Since AB = AC and AD is perpendicular to BC, triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion. Therefore, BD = CD, which means that AD is also the median to the base.

To prove AD is the altitude:

We need to prove that angle BAD and angle CAD are right angles. This is true because AD is perpendicular to BC, and BD and CD are also perpendicular to BC. Therefore, AD is also the altitude to the base BC.

Hence, we have proved that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.