What is the area of the triangle?

3/5kg + 760g

3/5kg = 3/5×1000

= 600g

Now

600g + 760g = 1360g

Or 1.36kg

Answered by Gauthmath must click thanks and mark brainliest

The power to which a number or expression is raised is called the exponent.

1. An exponent is a mathematical notation that represents the power to which a number or expression is raised. It is written as a superscript number or variable placed above and to the right of the base number or expression.

2. The base number or expression is the number or expression that is being multiplied repeatedly by itself, raised to the power of the exponent.

3. The exponent tells us how many times the base number or expression should be multiplied by itself. For example, in the expression \(2^3\), the base is 2 and the exponent is 3. This means that 2 should be multiplied by itself three times: 2 * 2 * 2 = 8.

4. The exponent can be a positive whole number, a negative number, zero, or a fraction. Each of these cases has different interpretations:

  - Positive exponent: Indicates repeated multiplication. For example, \(2^4\)means 2 multiplied by itself four times.

  - Negative exponent: Indicates the reciprocal of the base raised to the positive exponent. For example, \(2^{-3\) means 1 divided by \(2^3\).

  - Zero exponent: Always equals 1. For example, \(2^0\) = 1.

  - Fractional exponent: Represents a root. For example, \(4^{(1/2)\)represents the square root of 4.

5. Exponents follow certain mathematical properties, such as the product rule \((a^m * a^n = a^{(m+n)})\), the quotient rule \((a^m / a^n = a^{(m-n)})\), and the power rule \(((a^m)^n = a^{(m*n)})\).

Remember to use these rules and definitions to correctly interpret and evaluate expressions involving exponents.

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The probability that at least one woman will receive a positive result if 100 unrelated women with normal pregnancies are tested with the first-trimester screen is 99.52%.

Suppose that two unrelated women, Devondra and Miranda, who are having normal pregnancies, are given the first-trimester screen.

This screen is a prenatal test that evaluates the risk of the fetus having certain chromosomal abnormalities, including Down syndrome.

The probability that Devondra gets a positive result and Miranda gets a negative result will be determined below.

For this purpose, the probability of getting a positive result on a first-trimester screen is 0.03, and the probability of getting a negative result is 0.97.

Therefore, the probability of Devondra getting a positive result and Miranda getting a negative result is:

P(Devondra gets a positive result AND Miranda gets a negative result) = P(Devondra gets a positive result) * P(Miranda gets a negative result)= 0.03 * 0.97

= 0.0291

= 2.91%.

Therefore, the probability that Devondra gets a positive result and Miranda gets a negative result is 2.91%.

Now, let's find out the probability that at least one woman will receive a positive result if 100 unrelated women with normal pregnancies are tested with the first-trimester screen.

The probability of getting a positive result is 0.03, and the probability of getting a negative result is 0.97.

We want to find the probability of at least one woman receiving a positive result.

It means that we will calculate the probability of no woman receiving a positive result and subtract it from 1.

Let's denote this probability by P(no woman receives a positive result).

P(no woman receives a positive result)

= P(first woman gets a negative result AND second woman gets a negative result AND ... AND hundredth woman gets a negative result)

= P(first woman gets a negative result) * P(second woman gets a negative result) * ... * P(hundredth woman gets a negative result) = 0.97 * 0.97 * ... * 0.97 (100 times)≈ 0.0048.

The probability that at least one woman will receive a positive result is:

P(at least 1 woman receives a positive result)= 1 - P(no woman receives a positive result)

= 1 - 0.0048

= 0.9952

= 99.52%.

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The effective annual rate for a 8.65% interest compounded monthly is 9.14%.

To calculate the effective annual rate, we need to take into account the compounding frequency. In this case, the interest is compounded monthly.

We can use the formula for compound interest to calculate the effective annual rate:

Effective Annual Rate = (1 + (interest rate / compounding frequency))^compounding frequency - 1

Plugging in the given values:

Effective Annual Rate = (1 + (8.65% / 12))^12 - 1

                     = (1 + 0.0072083)^12 - 1

                     = 1.0072083^12 - 1

                     ≈ 0.0914 or 9.14%

Therefore, the effective annual rate for a 8.65% interest compounded monthly is approximately 9.14%.

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Answer:

B.

Step-by-step explanation:

-\(\frac{3}{4}\) = -0.75

-0.75 is less than -0.5 but more than -1.

A shows -1.75.

B shows -0.75.

C shows -0.25.

D shows 0.75.

Note: Each mark is 0.25.

I would advise Rolf to take advantage of the Section 179 deduction for the current year to maximize his tax savings. By doing so, he can deduct the full cost of the equipment purchased and placed into service, up to the Section 179 limit.

Rolf should consider utilizing the Section 179 deduction, which allows business owners to deduct the full cost of qualifying equipment purchased and placed into service during the year, instead of depreciating it over several years. The current Section 179 limit is $1,050,000. Since Rolf purchased equipment worth $1,080,000, he can fully deduct this amount, subject to the limit. By taking advantage of this deduction, Rolf can significantly reduce his taxable income for the current year, thereby lowering his tax liability in the highest marginal tax bracket.

Furthermore, Rolf's plan to semi-retire in the future and potentially drop into lower marginal tax brackets should be considered when deciding whether to utilize cost recovery deductions such as depreciation. If Rolf expects to be in a lower tax bracket in the coming years, it may be more advantageous to spread the deductions over the useful life of the equipment through depreciation. This would allow him to offset income in future years when his tax rate is lower. However, since Rolf plans to keep the business open for another three to five years before fully retiring, it is important to assess the potential tax implications during this period. Consulting with a tax professional would be beneficial in determining the most suitable strategy for Rolf's specific circumstances.

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Answer:

Area

Step-by-step explanation:

That's the definition of area.

Answer:

9 for each row

Step-by-step explanation:

Answer:

I think that :

A and B : 464

C and D : 132

Step-by-step explanation:

For A and B

Surface area = (2(5+4)*8) + ( 2( 5*4*8)) = 464

For C and D

Surface area = (2(3+2)*6) + ( 2( 3*2*6)) = 132

I hope that is useful for you

To determine the number of aardvarks that were there last year, we will have to use the formula for exponential growth. Exponential growth is a type of growth that increases in size exponentially over time.

The formula for exponential growth is given by the equation:

\(Nt = N\times(1 + r)^t,\)

where N₀ is the initial population, r is the annual growth rate, t is the time in years, and Nt is the population after t years.Let's use this formula to find the number of aardvarks last year. Given that the current population of aardvarks is 756, and the growth rate is 8%, we can write the equation as

\(:Nt = N \times (1 + r)^t756 = N \times(1 + 0.08)^1So, N = 756 / (1 + 0.08)^1\)

Now, we need to find the population of aardvarks last year, which is t = 1 year before.

Thus, plugging in t = 1, we get

:\(N = 756 / (1 + 0.08)^1N= 700\)

Hence, there were 700 aardvarks last year.

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Answer:

b

Step-by-step explanation:

just move the shape with cordinantes of b

The rule that maps figure 1 onto figure 2 is B. (x,y)→(x-5, y+11)

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, therefore,

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

The correct option is B.

(x,y)→(x-5, y+11)

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We have that the equation for this is

So we have that the length of one side of the figure is

So the answer is that one side of the figure have a length of 15.

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.

Property of Equality:

The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.

That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.

Multiplicative Property of Equality:

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.

The formula for this property can be expressed as for the real numbers a, b, and c.

If a × b, then, a × c = b × c.

In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.

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On solving the provided question we can say that - the probability of the event will be there are two red sides, thus multiplying 16.6667 by two results in 33.3333%.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

Each side would be 50%, and if one side were divided among three people, it would equal 16.6667 per person.

Given that there are two red sides, you can multiply 16.6667 by 2 to get 33.3333%.

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Answer:

-17-7=-24

-10-7=-17

-6-7=-13

-5-7=-12

-1-7=-8

Step-by-step explanation:

Answer:

Step-by-step explanation:

The graph starts at x = - 3 and ends x = 2. For all x between -3 and 2, there points on the graph. Hence the domain, in interval notation, is written as

[-3 , 2]

We have closed circles at x = - 3 and x = 2 because -3 and 2 are included in the domain which is indicated by the closed brackets at x = - 3 and x = 2.

The range is the set of possible output values, which are shown on the y-axis.

This is why our graph goes from (-3,8) to (2,3)

Answer:

90 minutes or 1 hour and 30 minutes

Step-by-step explanation:

Hey there!

In order to find out how long Amy studied for her math test, all we need to do is divide 3 hours by 2

First of all, we can convert 3 hours to 180 minutes since there are 60 minutes in 1 hour

Now, we divide 180 and 2

180/2 is 90

This means, Amy studied 90 minutes or 1 hour and 30 minutes for her math test

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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If both p and 2p+1 are prime, then 2p+1 is a safe prime and p is a Sophie Germain prime.

Sophie Germain was a French mathematician who used these primes to investigate Fermat's Last Theorem, a famous mathematical conjecture that was finally proved in 1994 by Andrew Wiles. A safe prime is a prime number of the form 2p+1, where p is also a prime number, and it is called "safe" because it has some cryptographic properties that make it useful in certain encryption schemes.                                                                                                                                          In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.

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Answer:

89

Step-by-step explanation:

The factored form of the quadratic function is (n - 10)(n - 1) and the zeros of the function are 10 and 1.

The factored form of the quadratic function is calculated as follows;

f(n) = n²- 11n + 10

Multiply 10 and n² = 10n²

Find two numbers whose sum will be -11n and product will be 10n².

The two numbers are -1 and -10

The quadratic equation is factorized as follows;

= n²- 11n + 10

= n²- n - 10n + 10

= n(n - 1) - 10(n - 1)

= (n - 10)(n - 1)

So the zeros of the function are;

n - 10 = 0 or n - 1 = 0

n = 10 or 1

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Answer:

17.A 18.A

Step-by-step explanation:

The constants a and b are 2 and -π/4 respectively, and the integral of (1/sin(x) + cos(x)) dx is given by -2cos(x - π/4) - cos(x) + C.

The constants a and b are 2 and -π/4 respectively, and the integral of (1/sin(x) + cos(x)) dx is given by -2cos(x - π/4) - cos(x) + C.

To determine the constants a and b such that sin(x) cos(x) = a sin(x + b), we can use the double-angle formula for sine: sin(2x) = 2sin(x)cos(x). By comparing this with the given equation, we can see that a = 2 and b = -π/4.

Now, let's proceed to the integration of ∫(1/sin(x) + cos(x)) dx using the result we obtained. First, we rewrite the integral as ∫(1/sin(x) + cos(x)) dx = ∫(csc(x) + cos(x)) dx.

We can rewrite csc(x) as 1/sin(x), and since a = 2 and b = -π/4, we can rewrite cos(x) as sin(x - π/4). Therefore, the integral becomes ∫(2sin(x - π/4) + sin(x)) dx.

Now, using the linearity property of integration, we split the integral into two parts: ∫2sin(x - π/4) dx + ∫sin(x) dx.

The integral of 2sin(x - π/4) dx can be easily evaluated using the substitution method, where u = x - π/4. The integral becomes ∫2sin(u) du = -2cos(u) + C.

The integral of sin(x) dx is -cos(x) + C.

Putting it all together, the result of the integration is -2cos(x - π/4) - cos(x) + C.

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The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

here, we have,

Given data:

{1 ,2, 3 ,4, 5}

Formula for combinations is used since the order does not matter and repetition is allowed.

nCr = (n + r -1) /(r! * (n-1)!)

where n is the total number of items and r is the items to be picked

now, we get,

5C3 = (5 + 3 - 1)! /(3! * (5 -1)!

5C3 = 7!/(3! *4!) Simplifying the factorials)

5C3 = 5040/(6*24)

5C3 =5040/144

5C3 = 35

Hence, The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.

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Answer:

They walk a total amount of 819 laps.

Answer:

16!

Step-by-step explanation:

4 x 3 = 12 + 4 = 16

a. The diagonal 3 times 3 matrices: This is a subspace of r3x3 because it is closed under addition and scalar multiplication. The sum of two diagonal matrices is another diagonal matrix, and multiplying a diagonal matrix by a scalar yields another diagonal matrix.

b. The 3 times 3 matrices whose entries are all greater than or equal to 0: This is not a subspace of r3x3 because it is not closed under scalar multiplication. If we multiply a matrix in this set by a negative scalar, the resulting matrix will have entries that are negative, which violates the condition of the set.

c. The 3 times 3 matrices with trace 0: This is a subspace of r3x3 because it is closed under addition and scalar multiplication. The sum of two matrices with trace 0 is another matrix with trace 0, and multiplying a matrix with trace 0 by a scalar yields another matrix with trace 0.

d. The 3 times 3 matrices whose entries are all integers: This is not a subspace of r3x3 because it is not closed under addition. If we add two matrices in this set, the resulting matrix may have entries that are not integers, which violates the condition of the set.

e. The 3 times 3 matrices with all zeros in the second row: This is a subspace of r3x3 because it is closed under addition and scalar multiplication. The sum of two matrices with all zeros in the second row is another matrix with all zeros in the second row, and multiplying a matrix with all zeros in the second row by a scalar yields another matrix with all zeros in the second row.

f. The 3 times 3 matrices in reduced row-echelon form: This is not a subspace of r3x3 because it is not closed under addition. If we add two matrices in reduced row-echelon form, the resulting matrix may not be in reduced row-echelon form, which violates the condition of the set.

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Answer:(2, 3)

Step-by-step explanation:

Because we are reflecting the point across the y axis, we know that we are changing the X coordinate. Reflecting across in this case, since there is no other given rule means we are changing the current X coordinate to be the negative version of itself, since it is already negative, this makes the new point a positive one.

This can be explained as moving the point across the given axis at the same distance as the original point from the axis, but in the opposite direction. If it is on the left of the axis, we move it the same distance from the axis to the right, and vice-versa.

We do not change the y coordinate, because we are reflecting the point across the Y axis, which is the vertical line that has an x origin of 0.

All of this means that the new coordinate for our point will be (2, 3).

Answer: 28x+8y+2 .

= -2 (-14x-4y-1)

= 28x + 8y + 2

Step-by-step explanation:

Answer: 28x + 8y + 2

Step-by-step explanation:

-2(3x+12y-5-17x-16y+4)

= -2(3x-17x+12y-16y-5+4)

= -2(-14x-4y-1)

= -2(-14x) -2(-4y) -2(-1)

= 28x+8y+2