Ken has just retired. His Roth IRA has a present value of $524,856.00 and has an interest rate of 3.4%, compounded annually. In addition, he receives a yearly pension of $32,615.12. Given that Ken plans to draw from his Roth IRA for the next fifteen years, find his total annual income.

Answer:

Step-by-step explanation:

4x + 9 = x + 30

3x + 9 = 30

3x = 21

x = 7

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

To know more about probability

https://brainly.com/question/30625528

#SPJ4

The obtuse angle θ which has the same value of sin(-275) is 95°, which is in the second quadrant.

What are the different quadrants of trigonometric identities?

The first quadrant has angles between 0 and 90 degrees. The second quadrant has angles between 90 and 180 degrees. The third quadrant contains angles between 180 and 270 degrees. The fourth quadrant contains angles between 270 and 360 degrees. All six trigonometric functions have positive values in the first quadrant.  The only positive values in the second quadrant are sine and cosecant. The only positive values are tangents and cotangents in the third quadrant. The only positive values in the fourth quadrant are cosine and secant.

We are asked to find an obtuse angle θ such that 0 ≤ θ ≤ 2π and has the same sine as -275°.

The value of sin(-275°) = 0.996

Since the value of sin(-275°) is positive, the angle θ should be in the first or second quadrant, because the sine of angles in the first and second quadrants is positive.

But the θ should be an obtuse angle.

So θ should be in the second quadrant.

sin(-275) = sin(360-275) = sin 85° = 0.996

sin(180 - 85) = sin(95)  = 0.996

Therefore the obtuse angle θ which has the same value of sin(-275) is 95°, which is in the second quadrant.

To learn more about quadrants, follow the link.

https://brainly.com/question/28471977

#SPJ1

Step-by-step explanation:

here, 4 days = 20 miles

so, 1 day = 5 miles

hence, x miles = 5x miles

The dot product of two vectors [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex]  in terms of the positive scalar quantities a, b, c, and d is:

[tex]\vec{A}.\vec{B}=-ab[/tex]

The scalar product of two vectors [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex] is given by the formula:

[tex]\vec{A}.\vec{B}=(a_1*b_1) + (a_2*b_2) + (a_3*b_3)[/tex]

Where a₁, a₂, and a₃ are the components of vector [tex]\vec{A}[/tex] and b₁, b₂, and b₃ are the components of vector [tex]\vec{B}[/tex].

In this case, vector A = (ai - bk) and vector B = (- cj + dk), so the components of vector A are a₁ = a, a₂ = 0, and a₃ = -b, and the components of vector B are b₁ = 0, b₂ = -c, and b₃ = d.

Plugging these values into the formula for the dot product, we get:

[tex]\vec{A}.\vec{B}=(a*0) + (0*-c) + (-d*b)\\\\\vec{A}.\vec{B}= 0 + 0 + (-bd) \\\\\vec{A}.\vec{B}=-bd[/tex]

More information on the scalar product here:

https://brainly.com/question/17401277

#SPJ11

The answer is 1.25 ft-lb. This can be calculated by multiplying 15 ft-lb by (9 in. / 12 in. per ft), which equals 1.25 ft-lb. The amount of work needed to stretch a spring 9 inches beyond its natural length is 1.25 ft-lb.

1. Convert 9 in. to feet by dividing 9 in. by 12 in. per ft.

2. Multiply the result (0.75 ft) by 15 ft-lb, which equals 1.25 ft-lb.

The amount of work needed to stretch a spring 9 inches beyond its natural length is 1.25 ft-lb. This can be found by taking the given work required to stretch the spring 1 foot (15 ft-lb) and multiplying it by the ratio of the desired distance (9 in.) to 1 foot (12 in. per ft). First, the desired distance of 9 inches must be converted to feet by dividing it by the conversion factor of 12 inches per foot. This results in 0.75 feet. This number is then multiplied by the given work of 15 ft-lb to yield 1.25 ft-lb of work. This is the amount of work needed to stretch the spring 9 inches beyond its natural length.

Learn more about amount here

https://brainly.com/question/8082054

#SPJ4

If you multiply the left side of an equation by 4, what must you multiply the right side of the equation by 4

Here you you multiply the left side of an equation by 4.

According to the solving for unknow rule you must perform same function to both side of the equation. If you multiply the left side of an equation by any integer then you must multiply the same integer on right hand side of the equation

To maintain equality, you must multiply the right side of the equation by 4 as well.

This is because the left side of the equation represents the same quantity as the right side, so any operation that is performed on one side must also be performed on the other side to preserve the equality.

Therefore, you must multiply the right side of the equation by 4

Learn more about multiplication here

brainly.com/question/5992872

#SPJ4

If a 0.10 significance level is used in place of a 0.05 significance level, the power of the test will generally increase. As we are increasing the probability of rejecting the null hypothesis.

The significance level (alpha) of a hypothesis test determines the probability of making a Type I error, which is the probability of rejecting the null hypothesis when it is actually true. The power of a test, on the other hand, is the probability of correctly rejecting the null hypothesis when it is actually false (i.e., the probability of detecting a true effect).

By using a higher significance level (0.10 instead of 0.05), we are increasing the probability of rejecting the null hypothesis, which means we are more likely to detect a true effect. This results in an increase in the power of the test. However, it's worth noting that using a higher significance level also increases the risk of making a Type I error, which means we have to be careful when interpreting the results of the test.

In summary, increasing the significance level generally increases the power of the test, but it also increases the risk of making a Type I error

To know more about null hypothesis:

https://brainly.com/question/28920252

#SPJ4

Vertices :

Edges:

Step-by-step explanation: A vertex is a corner on shape. And edge is a line segment between faces. A face is singular flat surface.

The slope of the given straight line passing through the coordinates given would be -8.

       By + C = - Ax

       By = - Ax - C

       y = -(A/B)x - (C/B)

Given are the coordinate points lying on the line.

We can write the slope as -

m = (y₂ - y₁)/(x₂ - x₁)

m = {12 - 36}/{11 - 8}

m = -24/3

m = -8

Therefore, the slope of the given straight line passing through the coordinates given would be -8.

To solve more questions on slopes, visit the link below

https://brainly.com/question/26650172

#SPJ9

Answer:

Step-by-step explanation:

3x- (3x-2)=7

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

3x-3x=0x

so the answer is zero or imposible becasue nothing can be times by zero

Gold costs less than platinum per ounce because the slope of the graph for gold is less than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars per ounce.

In Mathematics, a slope is sometimes referred to as rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Mathematically, the slope (rate of change) can be calculated by using this mathematical expression;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph of the weight of gold and platinum, we can reasonably infer and logically deduce that the slope (unit rate) of the graph for gold is less than the slope (unit rate) of the graph for platinum.

Read more on slope here: https://brainly.com/question/29470973

#SPJ1

Complete Question:

Use the drop-down menus to complete the statements to match the information shown by the graph.

A graph has weight (ounces) on the x-axis, and cost (dollars) on the y-axis. A line labeled gold starts at (0, 0) and has a positive slope. A line marked platinum starts at (0, 0) and has a greater positive slope than gold.

Gold costs ---------------- platinum per ounce because the ----------- of the graph for gold is -------------that of the chart for platinum. The --------of the graph tells you the unit rate in _____.

Answer: Check down below!!!

Step-by-step explanation:

   8x² = 6x² + 5x²

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

8x² = 6x² + 5x²

8x² = 11x²

Now, we can isolate x² by subtracting 11x² from both sides of the equation:

8x² - 11x² = 11x² - 11x²

-3x² = 0

Finally, we can divide both sides of the equation by -3 to get:

(-3x²)/(-3) = 0/(-3)

x² = 0

So the solution is x = 0.

   -7x² + 6 = x² - 7x²

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

-7x² + 6 = x² - 7x²

-7x² + x² = -7x² + 6

-6x² = 6

Now, we can isolate x² by dividing both sides of the equation by -6:

(-6x²)/(-6) = 6/(-6)

x² = -1

So the solution is x = ±√(-1), which is an imaginary number.

   7x² + 9x² = -6x² - 7x

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

7x² + 9x² = -6x² - 7x

16x² = -6x² - 7x

Now, we can isolate x² by adding 6x² to both sides of the equation:

16x² + 6x² = -6x² + 6x² - 7x

22x² = -7x

Finally, we can divide both sides of the equation by 22 to get:

22x²/22 = -7x/22

x² = -7x/22

So the solution is x = ±√(-7/22), which is a complex number.

Answer: We know that the volume of a cuboid is given by the product of its length, width and height, or V = l * w * h. In this case, the length is 250 cm and the height and width are both x cm. So, the volume can be written as:

V = 250 * x * x

Substituting the given value of V = 4840 cm³, we get:

4840 = 250 * x * x

Dividing both sides by 250, we get:

19.36 = x * x

Taking the square root of both sides, we get:

x = ±√19.36

Since the side length of a square must be positive, we use the positive square root:

x = ±4.4 cm

Therefore, the side length of the square cross-section is 4.4 cm.

Step-by-step explanation:

Answer:

x = -2, y = -4

Step-by-step explanation:

Take the first equation-   -2y = 2 - 3x
Arrange it first-
-3x + 2y = -2

Multiply is by 5 on both sides
5(-3x + 2y) = 5(-2)
-15x + 10y = -10

Take the second equation-    -5y = 10 - 5x
Arrange it-
-5x + 5y = -10

Multiply is by 2 on both sides
2(-5x + 5y) = 2(-10)
-10x + 10y = -20

Subtract second equation from the first one-

  -15x + 10y = -10
-  -10x + 10y = -20
= -5x = 10

-5x = 10
x = 10/(-5)
x = -2

Substitute the value of x in Equation 1
-2y = 2 - 3(-2)
-2y = 2 + 6
-2y = 8
y = 8/(-2)
y = -4

Hope it helps ;)

Answer:

18.84

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

165 and 3/4 is equal to 165.75 and 4 and 1/4 is 4.25

165.75/4.25=39

39 uniforms could be made

Answer:

Step-by-step explanation:

The gardener used 5/8 of the soil, which is equal to 10 * 5/8 = 10 * 0.625 = 6.25 pounds.

So, he used 6.25 pounds of soil in the garden.

The gardener had 10 - 6.25 = 3.75 pounds of soil left.

Step-by-step explanation:

The constant in an expression is the number without any letters attached to it.

Looks like B and E are the only ones with constant. The other 3 only have numbers attached to numbers

A correlation coefficient of 0.05 indicates a very weak positive correlation between the number of bedrooms and selling price.

When Bob calculates the correlation between the number of bedrooms in a home and its selling price and obtains a value of only 0.05, he can conclude that there is little to no linear relationship between the two variables.

Correlation is a statistical measure that indicates the degree to which two variables are related and the direction of the relationship. A correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

A correlation coefficient of 0.05 is very close to 0, indicating that there is almost no linear relationship between the number of bedrooms in a home and its selling price.

However, it is important to note that a low correlation coefficient does not necessarily mean that there is no relationship between the variables, as there could be a non-linear relationship or other types of relationships that cannot be captured by a correlation coefficient.

Therefore, Bob should further analyze the data set and explore other statistical measures or techniques to fully understand the relationship between the number of bedrooms in a home and its selling price.

To learn more about correlation click on,

https://brainly.com/question/30631861

#SPJ4

Answer:

Mai spent 60% of her total spending on fruit

Step-by-step explanation:

To find the percentage of the total spent on fruit, we can divide the amount spent on fruit by the total amount paid and multiply by 100 to express the answer as a percentage.

First, let's find the amount spent on things other than fruit: $15 total spent - $9 spent on fruit = $6 spent on other things.

Next, we divide the amount spent on fruit by the total amount spent: $9 on fruit / $15 total spent = 0.6.

Finally, we multiply by 100 to express the answer as a percentage: 0.6 * 100 = 60%.

So Mai spent 60% of her total spending on fruit.

An elevation of negative 25 feet is less than an elevation of 0 feet: True.

An elevation of negative 25 feet is greater than an elevation of 5 feet: False.

An elevation of negative 25 feet is less than an elevation of negative 5 feet: True.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In this context, we can reasonably infer and logically deduce that all numerical values (numbers) to the left are always less than numerical values (numbers) located to the right of a number line such as the following:

-25 < 0.

-25 < 5.

-25 < -5.

Read more on number line here: brainly.com/question/21832213

#SPJ1

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

Explanation:

2/3 of 150 = (2/3)*150 = 100 employees are male and 150-100 = 50 employees are female. This is before the resignations.

After the resignations happen, we would have:

The chances of picking a female employee at random would be 40/120 = 1/3 which is the final answer.

Notice how the chances haven't changed from earlier (male = 2/3 chance, so 1-2/3 = 1/3 are the chances of picking a woman). Why is this? Well notice the ratio of 20 men to 10 women resigning. This ratio is 2:1, meaning twice as many men resigned. Furthermore, notice how 2/3 is twice that of 1/3.

This keeps the same proportion of men to women. Therefore, the odds haven't changed.

Answer:

b = -66.

Step-by-step explanation:

[tex]18 = \frac{b}{ - 3} - 4 \\ = - 3(18) = - 3 \times \frac{b}{ - 3} - 4( - 3) \\ = - 54 = b + 12 \\ = - 54 - 12 = b \\ = - 66 = b[/tex]

Answer:

Step-by-step explanation:

To determine whether a value is greater than or less than a specific result from an equation, you would need to substitute the value into the equation and solve for the result. For example, if you want to determine if the value "a" is greater than or less than the result of the equation -2x^2 + 16x - 36, you would substitute "a" for the variable x and solve for the result:

-2x^2 + 16x - 36 = -2a^2 + 16a - 36

Then you can compare the value of the result to "a" to determine whether it is greater than or less than.

If the result is greater than "a", you would write:

-2a^2 + 16a - 36 > a

If the result is less than "a", you would write:

-2a^2 + 16a - 36 < a

And if the result is equal to "a", you would write:

-2a^2 + 16a - 36 = a

It's important to note that the comparison only holds for a specific value of "a". The equation -2x^2 + 16x - 36 could have many solutions where the result is greater than, less than, or equal to "a".

The area of the triangle is 72 units².

The area of a triangle can be found using sine as follows:

area of a triangle = 1 / 2 ab sin C

Hence,

Therefore,

area of a triangle = 1 / 2 × 12 × 24 × sin 30

area of a triangle = 1 / 2 × 288 × sin 30

area of a triangle = 1 / 2 × 288 × 0.5

area of a triangle = 1 / 2 × 144

area of a triangle = 72 units²

learn more on area here: https://brainly.com/question/11962279

#SPJ1

Answer: An incline, a slant up or down.

Step-by-step explanation:

The distance between the foot of the ladder from the bottom of the wall is 40 meters.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Here,
The distance between the foot of the ladder from the bottom of the wall can be found by using the Pythagorean theorem.

The ladder is the hypotenuse, with a length of 50m

The distance from the wall to the ground is 30m

The distance from the wall to the foot of the ladder is x

Using the Pythagorean theorem:

x² + 30² = 50²

x² + 900 = 2500

x² = 1600

x = 40

So, the distance between the foot of the ladder from the bottom of the wall is 40 meters.

Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ9

Using this formula, we find that d = 2/3, meaning Beth rode 2/3 of a mile farther than she walked. The formula to solve this problem is d = 1/2 - 1/12, where d is the difference in distance between the bus ride and the walk.

Beth rode the bus 1/2 of a mile and then walked 1/12 of a mile to get home. To calculate how much farther she rode than walked, we need to subtract the distance walked from the distance ridden. The formula to solve this problem is d = 1/2 - 1/12, where d is the difference in distance between the bus ride and the walk. Using this formula, we find that d = 2/3, meaning Beth rode 2/3 of a mile farther than she walked.

Learn more about distance here:

https://brainly.com/question/29130992

#SPJ4