Joes is making salary $62,000. He recieves a 3% cost of living increase and a 10% merit bonus. what is his new salary?

Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

Answer:

(2, 1)

Step-by-step explanation:

To solve by substitution, we solve one equation for one of its variables and then substitute the solved value for that variable into the other equation. Because this system of equations already has one solved for the variable, this makes our job much easier. We only need to implement the solved value for y into the other equation and solve for x.

y = 6x - 11

-2x - 3(6x - 11) = -7 Distribute.

-2x - 18x + 33 = -7 Combine like terms.

-20x + 33 = -7 Subtract 33 from both sides of the equation.

-20x = -40 Divide by -20 on both sides of the equation.

x = 2

Then, with this value, we will place it into the equation that was already solved for y in order to get a definite value for y.

y = 6(2) - 11

y = 12 - 11

y = 1

Using this information, the coordinate pair for this equation (the point of intersection between the two lines) is (2, 1).

The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

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Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

If cos < 0 and cot > 0, then the terminal point is determined by

C. quadrant 3.

In quadrant I the referece angle Ф is Ф.

In quadrant II the referece angle Ф is (π - Ф).

In quadrant III the referece angle Ф is (π + Ф).

In quadrant IV the referece angle Ф is (2π - Ф).

We know, cos is -ve on III and IV quadrants, and cot = 1/tan is +ve on I and III quadrant.

Therefore, The combined condition cos < 0 and cot > 0 satisfies on the II quadrant.

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Answer:

29

he area of the pool is 34 ft * 48 ft = <<34*48=1632>>1632 ft2.

Thus, the total area of the pool and the border strip is 1632 ft2 + 344 ft2 = <<1632+344=1976>>1976 ft2.

Hence, the border strip is 1976 ft2/34 ft = <<1976/34=58>>58 ft long.

Therefore, the border strip can be 58 ft/2 = <<58/2=29>>29 ft wide. Answer: {29}.

Answer:

u > 7

Step-by-step explanation:

-2u -6 < -20  Add 6 to both sides

-2u - 6 + 6 < -20 + 6

-2u < -14  Divide both sides by -2.  When you multiply or divide both sides by a negative number, you must flig the sign.

\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)

u > 7

Helping in the name of Jesus.

The answer is:

u > 7

In-depth explanation:

You haven't told me what the values of u are, but I'll solve the equation for u.

Add 6 on each side:

\(\bf{-2u-6 < -20}\)

\(\bf{-2u < -14}\)

Divide each side by -1 and reverse the sign:

\(\bf{2u > 14}\)

Now divide each side by 2

\(\bf{u > 7}\)

Answer:

5. To find the time in which the loan of N3,900 at the rate of 5% yields N585, we can use the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed), r is the interest rate (as a decimal), and t is the time (in years).

Plugging in the given values, we get:

585 = 3900 * 0.05 * t

Solving for t, we get:

t = 3 years

Therefore, it will take 3 years for the loan to yield N585 in interest.

6. To find the time it will take for the simple interest on N70,000 at the rate of 7% to be N20,000, we can again use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

20000 = 70000 * 0.07 * t

Solving for t, we get:

t = 4 years

Therefore, it will take 4 years for the simple interest on N70,000 at the rate of 7% to be N20,000.

7. To find the time it takes for N300 to amount to N390 at the rate of 3%, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

where A is the final amount, P is the principal (the initial amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).

Plugging in the given values, we get:

390 = 300 * (1 + 0.03/1)^(1*t)

Simplifying, we get:

1.3^t = 1.3

Taking the logarithm of both sides, we get:

t = log(1.3) / log(1.3)

t ≈ 1.82

Therefore, it takes approximately 1.82 years for N300 to amount to N390 at the rate of 3%.

8. To find the rate percent per annum for a simple interest of N80 on N5600 in 1 year, we can use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

80 = 5600 * r * 1

Solving for r, we get:

r = 0.0143 or 1.43%

Therefore, the rate percent per annum is 1.43%.

9. To find the year in which N5100 will yield an interest of N170 at the rate of 2 1/2 per annum, we can use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

170 = 5100 * 0.025 * t

Solving for t, we get:

t = 2/3 years

Since the question asks for the year, we need to add 2/3 years to the current year. Assuming the current year is 2021, we get:

2021 + 2/3 ≈ 2022.67

Therefore, N5100 will yield an interest of N170 at the rate of 2 1/2 per annum in the year 2022.

10. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can again use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

230 = 4600 * r * 2

Solving for r, we get:

r = 0.025 or 2.5%

Therefore, the rate per annum is 2.5%.

11. To find the time it takes for N8100 to yield an interest of N729 at the rate of 9% per annum, we can use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

729 = 8100 * 0.09 * t

Solving for t, we get:

t = 1 year

Therefore, it takes 1 year for N8100 to yield an interest of N729 at the rate of 9% per annum.

12. To find the rate of interest per annum for an interest of N23 on N2300 for 2 years, we can use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

23 = 2300 * r * 2

Solving for r, we get:

r = 0.005 or 0.5%

Therefore, the rate of interest per annum is 0.5%.

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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Using the given restrictions we can see that there are 37 balls on the box.

Let's assume that the total number of balls is B.

We know that in the box there are more than 25 and fewer than 40 tennis balls, so we have the inequality.

25 < B < 40

If we count in 3's, then there is one left over, so we can write:

B = 3*n + 1   (where n is an integer number)

And if we count in 5's there are 2 leftovers:

B = 5*m + 2  (where m is an integer, from this we conclude that the number ends in a 2 or a 7)

Then we have 3 restrictions:

25 < B < 40

B = 3*n + 1

B = 5*m + 2

notice that if n = 12

B = 3*12 + 1 = 37

if m = 7

B = 5*7 + 2 = 37

and 37 is a solution of the inequality, then we conclude that there are 37 balls on the box.

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The expression expressed as a difference is (a - 2) - (-7).

We have,

We can express a + 5 as a difference by subtracting a suitable term from it.

One way to do this is to subtract 2 and add 2, like this:

a + 5 = a + 5 - 2 + 2   (adding and subtracting 2)

     = (a - 2) + 7     (rearranging)

Now,

We can express a + 5 as the difference between a - 2 and -7, like this:

a + 5 = (a - 2) - (-7)

Thus,

The expression expressed as a difference is (a - 2) - (-7).

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Answer:

So, 3 households would use 20 4/5 x 3 = 62 1/5 L of water per day.

Step-by-step explanation:

Each household uses 613 1/5 ÷ 10 = 61 3/5 L of water in 3 days.

Therefore, each household uses an average of 61 3/5 ÷ 3 = 20 4/5 L of water per day.

Answer:

Step-by-step explanation:

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Answer: (3,1)

Step-by-step explanation: Use the midpoint formula

Answer: 16j^3+2

Step-by-step explanation:

The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled.

Arrows pointing from the selected cell to cells that depend on the selected cell are generated by using the Trace dependents button of the Formula Auditing group.

nodes in an influence diagram represent part of the model

The Trace Precedents button, located in the Formula Auditing group, creates arrows pointing to the selected cell from cells that are part of the formula in that cell

The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

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Answer:

11

Step-by-step explanation:

Answer:

38.5

Step-by-step explanation:

rectangle = (2.5x2)+1.5=6.5

6.5x5=32.5

both triangle = 4/2 = 2

(1.5x2)x2=6

total area = 32.5 + 6 = 38.5

The probability of observing such an extreme result by chance alone is 0.0124.

To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.

Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:

P-value = 2 * 0.0062

P-value = 0.0124

This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.

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The area between the solid line (y=x+4) and the dotted line (y=-2x-2) represents the system of inequalities solution set.

Two linear inequalities system on a coordinate plane. The first has a solid line graphed with a negative slope of one, a negative y-intercept, and a shaded origin area. The area encompassing the origin is shaded, and the second is a dashed vertical line 3 units to the left of the origin.

x ≥ –3; y ≥ x – 2

x > –3; 5y ≥ –4x – 10

x > –3; y ≥ –x + 1

x > –2; y ≥ –x – 1

The solution set for the system of inequalities is represented by the region between the solid line (y=x+4) and the dotted line (y=-2x-2).

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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After solving;

(a) P(40.5<Y<48.9) = 0.3721

(b) P(40.5<Y<48.9|X=68.6) = 0.6075

(c) P(40.5<Y<48.9∣X>=68) = 0.3925

(d) In b and c we use conditional probability in bi-variate case. In a it is uni-variate normal distribution.

Given that;

μ(x) = 60.6  

σ(x) = 11.2  

μ(y) = 46.8  

σ(y) = 8.4  

ρ = 0.94  

That is (X,Y) follows BVN(60.6,46.8,11.2,8.4,0.94)

(a) We have to find P(40.5<Y<48.9).

P(40.5<Y<48.9) = P[(40.5-μ(y))/σ(y) < (Y-μ)/σ(y) < (48.9-μ(y))/σ(y)]

Here Z = (Y-μ)/σ(y) follows N(0,1)

P(40.5<Y<48.9) = P{(40.5-46.8)/8.4 < Z < (48.9-46.8)/8.4}

P(40.5<Y<48.9) = P( -6.3/8.4 < Z < 2.1/8.4)

P(40.5<Y<48.9) = P(-0.75 < Z < 0.25)

P(40.5<Y<48.9) = p(0<Z<0.75)+p(0<Z<0.25)

P(40.5<Y<48.9) = 0.2734+0.0987

P(40.5<Y<48.9) = 0.3721

b) We have to find P(40.5<Y<48.9∣X=68.6).

We know that Y|X follows N(μ(y)+ρ σ(y)/σ(x) (x-μ(x)),σ^2(y)(1-ρ^2))

μ(y)+ρ σ(y)/σ(x) (x-μ(x)) = 46.8+0.94* 8.4/11.2 (X-60.6)

μ(y)+ρ σ(y)/σ(x) (x-μ(x)) = 46.8+0.705(X-60.6)

σ^2(y)(1-ρ^2) = 8.4^2(1-0.94^2)

σ^2(y)(1-ρ^2) = 70.56(1-0.8836)

σ^2(y)(1-ρ^2) = 70.56*0.1164  

σ^2(y)(1-ρ^2) = 8.2132

Y|X follows N(46.8+0.705(X-60.6),8.2132)  

X = 68.6

Y|X follows N(46.8+0.705(68.6-60.6),8.2132)  

N(46.8+5.64,8.2132)

N(52.44,8.2132)

P(40.5<Y<48.9|X=68.6)=p{(40.5-52.44)/√(8.2132)<Z<√(48.9-52.44)/√(8.2132)

P(40.5<Y<48.9|X=68.6) = P(-11.94/2.8658 < z < -3.54/2.8658)

P(40.5<Y<48.9|X=68.6) = p(-4.17 < z < -1.24)

P(40.5<Y<48.9|X=68.6) = 1-0.3925

P(40.5<Y<48.9|X=68.6) = 0.6075

c) Now we have to find the P(40.5<Y<48.9∣X>=68)

P(40.5<Y<48.9∣X>=68) = 1-0.6075

P(40.5<Y<48.9∣X>=68) = 0.3925

d) In b and c we use conditional probability in bi-variate case. In a it is uni-variate normal.

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The right question is given below:

Answer:

the answer is B) 24.

Step-by-step explanation:

To find the lateral surface area of the triangular prism, we need to find the perimeter of the base and then multiply it by the height of the prism.

Looking at the net, we can see that the base is a triangle with sides of length 3 cm, 4 cm, and 5 cm. So the perimeter of the base is:

3 cm + 4 cm + 5 cm = 12 cm

The height of the prism is given as 2 cm. Therefore, the lateral surface area is:

12 cm x 2 cm = 24 cm²

So the answer is B) 24.

IF THIS HELPED, CAN YOU PLEASE GIVE 5⭐? thank you

This process required 3 to be subtracted 5 consecutive times, so again we see that 15 ÷ 3 = 5. The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.

Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

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The intervals of each behavior of the function are given as follows:

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Answer:759

Step-by-step explanation:

Answer:

YEs

Step-by-step explanation:

He is correct. as long as his coin has 2 sides

I answered so the other guy could get brainlest

627 x 26 equals 16,302 when solved using the standard algorithm.

The steps below can be used to solve the multiplication issue 627 x 26 using the conventional algorithm:

627 and 26 should be written one above the other, with the larger number appearing above and the smaller number beneath.

Start by adding each digit of the top number to the ones digit of the bottom number (six). Write the answers below the line after multiplying 6 by 7 and then by 2.

1254 -- a 6 x 7 partial product

1254 -- a half 6 x 2 product

Repeat the process by moving the bottom number one position to the left after that. Multiply 2 by 7 and then by 2, and then write the results one space to the left of the line below the line.

1254 x 627

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There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.

Consider the possible digits in the hundreds, tens, and one's places.

Thousands of places: There is only one possibility, which is 7.

Hundreds place: Any digit from 0 to 9 is possible.

Tens place: Any digit from 0 to 9 is possible.

One place: Any digit from 0 to 9 is possible.

Since the number is less than 54,000, the digit in the hundreds place cannot be 5.

So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.

So, the total number of such numbers is:

9 x 10 x 10 x 10 = 9,000

Therefore, there are 9,000 numbers that satisfy the given condition.

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