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$16,000 was invested in the account earning 6% interest and

$10,500 was invested in the account earning 5% interest.

Given that, Ngoc invests a total of $26,500 in two accounts. The first account earned an annual interest rate of 6% and the second account earned an annual interest of 5%. At the end of one year, the total amount of money gained was $1485.

We need to find how much was invested into each account.

A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.

Now,

Let x be the amount of money invested at 6% interest.

Let y be the amount of money invested at 5% interest.

Thus, x +y = 26,500-----(1) and 0.06X + 0.05Y = 1485-----(2)

Multiply 0.06 to the equation x +y = 26,500, so we get 0.06x+0.06y=1,590-----(3)

By subtracting equation (2) from (3), we get

0.01y=105

⇒y=10,500

Substituting y=$10500 in equation (1), we get x=$16,000

Therefore, $16,000 was invested in the account earning 6% interest and

$10,500 was invested in the account earning 5% interest.

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Therefore, the annual annuity payment can be approximately $6,069,727.

To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:

PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]

Where:

PMT = Annual annuity payment

PV = Present value of the annuity

r = Annual interest rate

n = Number of periods

Given:

PV = $230 million

r = 8% = 0.08

n = 40 years

Using the formula, we can calculate the annual annuity payment:

PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]

PMT ≈ $6,069,727

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Answer:

335/1000

Step-by-step explanation:

33.5% is .335 so 335/1000 is 33.5%

Arizona Department of Health used a option (d) cluster sampling method to obtain data on teen birth rates in rural and urban areas.

Sampling is a crucial technique used in research to obtain data that accurately represents the population of interest.

The Arizona Department of Health randomly selected 5/13 rural counties and 1/2 urban counties to obtain the data on teen birth rates. This type of sampling method is called a cluster sampling method. In cluster sampling, the population is divided into smaller groups, called clusters, and a random sample of clusters is selected.

Cluster sampling is often used when it is impractical or too costly to sample individuals from the population.

It reduces costs and time required to obtain the required data. In this case, if the department chose to sample each individual from the rural and urban areas, it would have taken a lot of time and resources to obtain the data.

Therefore, selecting a few clusters from each area provides a representative sample, which saves both time and resources.

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The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%

Z- Score gives an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , mean = 80beats/minute

standard deviation = 10 beats/minute

x = 86 beats/minute

Applying z score formula :

z-score = (x-mean)/standard deviation

P(x>86) = P(z > 86-80/10)

=P(z>6/10)

=P(z>0.6) = 1 - P(z<0.6)

= 1 -0.7257

= 0.2742

Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742

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True. If A is an n × n matrix and A = \(PDP^{T}\) where P is an n × n invertible matrix and D is a diagonal matrix, then A is a symmetric matrix.

To see why this is true, note that since D is a diagonal matrix, its transpose is equal to itself. That is, \(D^{T}\) = D. Using this fact, we can show that A is symmetric:

\(A^{T}\) = (\(PDP^{T}^\))\(^{T}\) = (\(P^{T}\))^\(^{TP}\)^\(TP^{T}\) = \(PDP^{T}\) = A

Therefore, A is a symmetric matrix

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Answer:

Step-by-step explanation:

x+4y+68

Step-by-step explanation:

15x - 31 = 9x + 11

6x =42

x = 7

15(7) - 31 = 9(7) + 11

74 = 74

74 × 2 = 148

180-148=32

Answer: x=t

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

\(\frac{1}{2}\)\(e^{2t-2}\)+1

Step-by-step explanation:

rewrite the equation: \(e^{2t-2}\) = 2x-2

Isolate the x: \(e^{2t-2}\)+2\(\frac{e^{2t-2} +2}{2}\)

Simplify

Answer:

unlikely

Step-by-step explanation:

If there 10 numbers, each number has a 10% chance of being chosen, and there are 3 generated number.

1/10 x 1/10 x 1/10 = 1/1000

Therefore the percent of this happening is 0.001%

That's very low.

That's why it's unlikely.

Each month we have to deposit 1389 of amount and we get interest of 30000

percentage, a relative value indicating hundredth parts of any quantity.

Given 500000 to be in our account in retirement of 30 years.

We need to find how much we have to deposit each month.

We know that in a year there are 12 months.

For 30 years the number of months are 12×30=360

So Now divide 500000 by 360 to find each month deposit

500000/360=1388.8

So each month one has to deposit 1389 into account.

Now if account earns 6% of interest. We need to find how much amount we earned.

6% is converted to decimal by dividing 6 by 100

0.06

Now multiply with 500000

0.06×500000

30000

Hence, each month we have to deposit 1389 of amount and we get interest of 30000.

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Answer:

-3 and -4

Hope this is correct:)

Answer:

The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Probability that carbon emissions from the company’s factory exceed the permissible level = 35% = 0.35

Accuracy of the test of emissions level = 85% = 0.85

2. The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is?

These two events, carbon emissions from the company’s factory and the accuracy of the test are independent events, therefore:

Probability that carbon emissions from the factory are within the permissible level = 1 - 0.35 = 0.65

Probability that the test predicts the opposite to be true = 0..35 * 0.85 = 0.2975 (The opposite is that the carbon emissions from the company exceed the permissible level)

Probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is:

0.65 * 0.2975 = 0.193375

The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place

MARK BRAINLIEST PLS

If they are parallel it would be 105

If its right please give brainliest

The missing length in the given triangles CG is 18.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangles ABC and CFG are similar triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

AC/CG=BC/CF

66/CG=154/42

66×42=154CG

2772=154 CG

Divide both sides by 154

CG=18

Hence, the missing length in the given triangles CG is 18.

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The volume of the cone is \(\frac{1}{3} \pi r^{2} h\)

Volume =  \(\frac{1}{3} \pi *(3)^{2} *12 = 113.04ft^3\)

Hope that helps!

Answer:

134.24 in³

Step-by-step explanation:

Use the formula for the volume of a cylinder, V = \(\pi\)r²h

Plug in the radius, pi, and the height:

V = \(\pi\)r²h

V = (3.14)(1.5²)(19)

V = 134.235

= 134.24 in³

So, the volume of the cylinder is 134.24 in³

Answer:

134.24 in³

Step-by-step explanation:

Answer:

\(y^{-5}\)

Step-by-step explanation:

The Exponent Quotient Rule states that if two terms of the same base are being divided by each other, then the simplified expression is the base to the first power subtracted by the second power. As an algebraic equation, that would be \(\frac{x^{a} }{x^{b} } =x^{a-b\), where \(x\) is the common base and \(a\) and \(b\) are the exponents.

In this case, \(x=y\), \(a=2\), and \(b=7\), so we know that \(\frac{y^{2} }{y^{7} } =y^{2-7}=y^{-5}\). Hope this helps!

Answer:

y  = xt-3

i hope this will help you let me know i am only 70%

sure this is right

Answer:

t = \(\frac{y + 3}{x}\)

Step-by-step explanation:

step 1: add 3 to both sides

step 2: divide both sides by x

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:

i think 150 degrees

Step-by-step explanation:

the 30° angle and ∠1 are a linear pair, and are supplementary. therefore they add up to 180°
∠1 + 30° = 180°

Answer:

the number of tomatoes he gathered for 3 days = 3 × x = 3x  

Step-by-step explanation:

According to the question Stan gathered x number of tomatoes every single day for three days. The total number of tomatoes she gathered altogether can be calculated below.

The number of tomatoes she gathered daily = x

The number of tomatoes she gathered for 3 days will be the product of the daily number of tomatoes she gathered(x) and the number of days she gathered it(3).

Therefore,

the number of tomatoes he gathered for 3 days = 3 × x = 3x  .

Or you could calculate the number of tomatoes she gathered for that 3 days by summing the number of tomatoes she had daily for that 3 days .

The firs day she gathered x number of tomatoes , the second day another x number and finally the last day another x number of tomatoes. Therefore,

x + x + x = 3x

Zoe walks from her house to a bus stop that is 460 yards away. The varying distances would depend on where Zoe begins her walk. if she starts closer to the bus stop, she would walk a shorter distance.

The varying distances would refer to the different distances Zoe might walk on different occasions. For example, she might take different routes or make detours, causing the actual distance she walks to vary.

However, without more information about Zoe's specific routes or circumstances, it is not possible to provide more detailed information about the varying distances.

However, if she starts closer to the bus stop, she would walk a shorter distance.

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The complete table with the ordered pairs are shown in the diagram attached below.

To complete the table with the ordered pairs, find the equation of the given line.

Slope (m) of the line = rise/run = 2/1

m = 2

The y-intercept (b) = 4 (the line intercept the y-axis at this point).

Substitute m = 2 and b = 4 into y = mx + b:

y = 2x + 4

Use the equation to find the missing ordered pairs of the given table:

When x = -1:

y = 2(-1) + 4

y = 2

When y = 5.5:

5.5 = 2x + 4

5.5 - 4 = 2x

1.5 = 2x

1.5/2 = x

0.75 = x

x = 0.75

When x = 2.6:

y = 2(2.6) + 4

y = 9.2

The image below shows the complete table with the missing ordered pairs.

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Answer:

Step-by-step explanation:

Laundry washed:

Who washed more?

Compare the fractions by bringing them to common denominator:

Compare the numerators:

It means Mrs. Stem washed more than laundry her son.

Total portion of laundry washed:

Laundry left to wash is the difference of full and the fraction of washed laundry:

Answer:

7/20 of laundry is still pending.

Step-by-step explanation:

Now the both washed is,

→ (2/5) + (1/4)

→ ((2 × 4)/(5 × 4)) + ((1 × 5)/(4 × 5))

→ (8/20) + (5/20)

→ 13/20

Forming the equation,

→ (13/20) + x = 1

Then required value of x will be,

→ (13/20) + x = 1

→ x = 1 - (13/20)

→ x = (20/20) - (13/20)

→ x = (20 - 13)/20

→ [ x = 7/20 ]

Hence, 7/20 of laundry is pending.

Answer:

sq rt 3, 3.11, 3.14, Pi, 3 2/3

Answer:

Same as the top. Got it right

There are 90 different outfits he can wear if he has to wear slacks and a shirt along with his 3 sport coats and 1 tie.

Here, we can use the multiplication principle of counting to determine the number of possible outfits a man can wear given that he must wear at least one pair of slacks and one shirt. Let us denote sport coats as A, B, and C; slacks as P1, P2, P3, P4, and P5; shirts as S1, S2, S3, S4, S5, and S6; and the tie as T.

Then, the number of outfits he can wear is given by the product of the number of choices for each item as follows: Total outfits = (Number of sport coats) × (Number of slacks) × (Number of shirts) × (Number of ties)= 3 × 5 × 6 × 1= 90. Differentiating between the cases where he wears only one shirt and one pair of slacks from those where he wears two or more of each is unnecessary because the problem statement requires that he wears at least one of each.

Therefore, we can calculate the total number of outfits directly using the multiplication principle of counting, which gives us the answer of 90 different outfits he can wear if he has to wear slacks and a shirt along with his 3 sport coats and 1 tie.

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x = 108

y = 36

z = 72

=============================================================

Explanation:

Check out the diagram below. I have added letters of x, y and z in places to help find the values of y and z. Note the triangle on top is isosceles (since a regular polygon has all sides equal; therefore the triangle on top has the top diagonal sides equal).

Before we find either y or z, let's find x.

For any regular polygon, the interior angles are all the same measure. They sum to 180(n-2). In this case, n = 5, so the angles sum to 180(5-2) = 540. Each individual interior angle is 540/n = 540/5 = 108 degrees

x = 108

Another way to find this interior angle is to first find the exterior angle. For any convex polygon (regular or not), the exterior angles always add to 360. When we talk about regular polygons, each individual exterior angle is 360/n. So in this case, we have 360/5 = 72 as one exterior angle. The adjacent interior angle is therefore x = 180-72 = 108. So there are two ways to find the measure of an interior angle.

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Referring to the diagram, specifically the isosceles triangle on top, we can see that it has angles of x, y and y. They add to x+y+y = x+2y. Set this equal to 180, plug in x = 108 and solve for y

x+2y = 180

108+2y = 180

2y = 180-108

2y = 72

y = 72/2

y = 36

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The bottom most triangle is a congruent copy of the triangle on top. We have another isosceles triangle with the same side lengths as before. This triangle also has x, y and y as mentioned above.

Notice the adjacent angles of y and z in the bottom left corner. They must add to 108 as this was the measure of the interior angle of a regular pentagon. So,

y+z = x

36+z = 108

z = 108-36

z = 72