Find the principal P that must be invested at rate r , compounded monthly , so that $1,000,000 will be available for retirement in t years . (round your answer to the nearest cent)

r = 5% t = 45
P = $ _____

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Answer:

10

13

15

17

22

Step-by-step explanation:

the first 5 terms will be 1,2,3,4 and 5.

I guess...

Answer:

a1 = 10

a2 = 13

a3 = 16

a4 = 19

a5 = 22

Step-by-step explanation:

Substitute in the value of  n  to find the  n

th term.

a1 = 3 (1) + 7

3 + 7 = 10

a2 = 3 (2) + 7

6 + 7 = 13

a3 = 3 (3) + 7

9 + 7 = 16

a4 = 3 (4) + 7

12 + 7 = 19

a5 = 3 (5) + 7

15 + 7 = 22

good luck, hope this helps :)

The rectangular form of the provided complex number is Z = -20√3 - 20i option (C) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex numbers in the trigonometric form:

Z = 40[cos(7π/6) + i sin(7π/6)]

As we know,

7π/6 = 7(180)/6

= 1260/6

= 210 degrees

From the trigonometric table:

cos210 = -√3/2

sin210 = -1/2

Plug the above values in the complex number:

Z = 40[-√3/2 + i (-1/2)]

Z = (40/2)[-√3 - i]

Z = 20[-√3 - i]

Z = -20√3 - 20i

Thus, the rectangular form of the provided complex number is Z = -20√3 - 20i option (C) is correct.

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Answer:

\(x=\frac{12.5-b}{a}\)

Step-by-step explanation:

\(ax+b=12.5\\\\ax+b-b=12.5-b\\\\ax=12.5-b\\\\\frac{1}{a}*ax =\frac{1}{a}*(12.5-b)\\\\x=\frac{12.5-b}{a}\)

The value of x is x=(12.5-b)/a

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

For example, 3y = 16 is an equation.

Given equation:

ax+b=12.5

Now,

ax= 12.5-b

x=(12.5-b)/a

Hence, the value of x is x=(12.5-b)/a

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Answer:

you are going to have to look from left to right and see if it is above or below

The dotplot of the simulation results and the sample of 10 buses provides convincing evidence that the true probability of a bus running off schedule is more than the claimed 10%. The data suggests that it is most likely for exactly one bus out of 10 to be running off schedule, and there is a low probability of 5 or more buses being off schedule.

Based on the dotplot of the simulation results and the sample of 10 buses, we can draw the following conclusions:

The true probability that a city bus is running off schedule is more than 10%:

The simulation results show that the frequency of buses running off schedule is concentrated towards the higher end of the spectrum. The dotplot indicates that 5 buses running off schedule is a relatively unusual occurrence, which suggests that the true probability is higher than the claimed 10%.

There is about a 3% chance that 5 or more buses are running off schedule:

Looking at the dotplot, we can see that the frequency of 5 buses running off schedule is quite low, with only 2 occurrences out of the 100 trials. This indicates that it is unlikely for 5 or more buses to be running off schedule under the assumption that only 10% of buses run off schedule.

It is most likely that exactly one out of 10 buses is running off schedule:

The dotplot shows a peak in the frequency at 1 bus running off schedule. This suggests that one bus running off schedule is the most probable scenario among the 10-bus samples.

If we continued to take more samples of 10 buses, the center of the distribution would shift to 1:

Based on the dotplot, the distribution appears to be centered around 1 bus running off schedule. This indicates that as more samples of 10 buses are taken, the average number of buses running off schedule would tend to be closer to 1.

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Answer:

The domain and range is (as inequalities):

\(x\leq 3\text{ and } -\infty < y < \infty\)

Or in interval notation:

\(D=(-\infty, 3]\text{ and } R=(-\infty, \infty)\)

Step-by-step explanation:

Recall that the domain is simply the set of all x-values of the function.

From the graph, we can see that the function is defined for all x-values less than or equal to 3.

Therefore, the domain is:

\(x\leq 3\)

The range is the set of all y-values of the function.

From the graph, we can see that the range will extend infinitely in both directions.

Therefore, the range is all real numbers. As an inequality:

\(-\infty < y < \infty\)

Or in interval notation, the domain is:

\((-\infty, 3]\)

And the range is:

\((-\infty, \infty)\)

Answer:

it depends on the size and angles that are given

SSS means side side side

SAS means side angle side

ASA means angle side angle

AAS means angle angle side

Answer:

9x^4 + 2x²y² + y^4

Arrange the terms

9x^4  + y^4 + 2x²y²

making the first two terms into a² + b²

(3x²)² + (y²)²   + 2x²y²

use the formula of a² + b² = (a+b)² - 2ab

(3x² + y²)²  - 2.3x².y²   + 2x²y²

(3x² + y²)²  - 6x²y² + 2x²y²

(3x² + y²)² - 4x²y²

(3x² + y²)² - (2xy)²

use the formula a² - b²

(3x² + 2xy + y²) (3x² - 2xy + y²)

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The experiment described is an example of a paired comparison or paired preference test.

In this type of test, each participant compares two items and indicates a preference for one over the other. In this case, the items being compared are two spaghetti sauces.

The test is called "paired" because each participant tastes both sauces, and the order in which they taste them is randomized to avoid bias.

The test is also "paired" because each participant's preference for one sauce is directly compared to their preference for the other sauce, rather than relying on an absolute ranking or rating system.

By comparing the number of times each sauce is preferred, the researchers can draw conclusions about which sauce is preferred overall.

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If a scatterplot shows a non-linear relationship between the response and explanatory variable, several options can be considered depending on the purpose of the analysis and the nature of the data.

Here are some possible actions:

Transform the data: One common approach is to transform the data to make the relationship linear. For example, if the relationship appears to be exponential, taking the logarithm of the response variable might make it linear. Similarly, taking the square root, cube root, or inverse of one or both variables might also help.

Use a non-linear model: Another option is to fit a non-linear model that can capture the curvature in the relationship. There are many types of non-linear models, such as quadratic, cubic, exponential, logistic, or spline models. The choice of model depends on the shape of the curve and the underlying theory or hypothesis.

Resample or subset the data: If the non-linear relationship is driven by outliers, influential points, or a subset of the data, it might be helpful to resample or subset the data to remove them. For example, trimming the extreme values, bootstrapping the data, or stratifying the data by a third variable might help.

Explore alternative variables or interactions: If the non-linear relationship is due to an unobserved or omitted variable, it might be useful to explore alternative variables or interactions that could explain the pattern. For example, if the response is sales and the explanatory variable is price, adding a competitor's price or a marketing variable might improve the fit.

Use caution in interpretation: Finally, if the non-linear relationship persists after exploring the above options, it might be necessary to acknowledge the non-linearity and use caution in interpreting the results. Non-linear relationships can be more difficult to interpret and extrapolate, and the statistical inference might be more uncertain or sensitive to assumptions.

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Answer:

Check below

Step-by-step explanation:

There are rigid transformations that produce congruent figures: translation, rotation, and one transformation that produces a similar figure, namely: Dilation.

1) Toyota: translation, and Dilation.

Two ellipses translated within a larger ellipse.

2) 2 Reflections, or 4 rotations of the pre-image

We have two ways of drawing this figure. Either by reflection of the right and the lower one or by rotation.

3) CBS: Dilation of the circumference, inside a rhombus.

4) Mitsubishi: Reflection about the y axis, Rotation for the figure up.

e) Reflection

f) Translation

Answer:

− z −  4.8  

Step-by-step explanation: was this the answer you needed? if not just delete it

The points that lies on the same line are (-3, 12), and, (-1, 4).

Here, we have,

The given coordinate points are (-2, 8) and (5,-20).

Here, slope (m)= 8+20/-2-5

= 28/-7

=-4

Substitute m= -4 and (x, y)=(-2,8) in y=mx+c, we get

8 = 8+c

or, c = 0

So, the equation of a line is y= -4 x

Now,

(-6, -2) in the given equation is -2=-4 (-6)

-2≠ 24

(-3, 12)  in the given equation is y= -4 x

12 = 12

(4, 16) in the given equation is y= -4 x

16 ≠ -16

(0, 6) in the given equation is y= -4 x

6 ≠ 0

(-1, 4) in the given equation is y= -4 x

4 = 4

(7,5) in the given equation is y= -4 x

5 ≠ -28

Therefore, the points that lies on the same line are (-3, 12), and, (-1, 4).

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Mandy's actual direct labor rate per hour (AP), rounded to two decimal places, is approximately $42.00.

To find Mandy Company's actual direct labor rate per hour (AP), we need to use the given information and apply the formula for direct labor efficiency variance:

Direct Labor Efficiency Variance = (AQ - SQ) × AP

We are given the following information:

Standard direct labor hours allowed for units produced (SQ) = 3,800

Actual direct labor hours worked (AQ) = 3,650

Direct labor efficiency variance, favorable (F) = $6,300

We can rearrange the formula to solve for AP:

AP = Direct Labor Efficiency Variance / (AQ - SQ)

Substituting the values:

AP = $6,300 / (3,650 - 3,800)

AP = $6,300 / (-150)

AP ≈ -$42 per hour

However, a negative value of direct labor rate variance is called favorable direct labor rate variance, which is the result of the actual rate being less than the standard rate.

Therefore, Mandy's actual direct labor rate per hour (AP), rounded to two decimal places, is approximately $42.00.

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Complete question =

Mandy Company has the following information from last month:

Standard direct labor hours allowed for units produced (SQ) 3,800

Actual direct labor hours worked (AQ) 3,650

Direct labor efficiency variance, favorable (F) $ 6300

Total payroll $ 190530

What was Mandy's actual direct labor rate per hour (AP), rounded to two decimal places?

Answer:

120 1 062 = × P . giving P = ÷ 120 1 062 . = 106 799

The mass of the prism is 2370 g

The formula for calculating the volume of a rectangular prism is expressed as;

V = lwh

Such that the parameters are;

From the information given, we have that;

Volume = 15 × 10 × 2

Multiply the values, we get;

Volume = 300 cm³

The formula for density of the material is expressed as;

D = m/v

Where m is the mass and v is the volume

Substitute the values

m = 7. 9 × 300

Multiply the values

m = 2370 g

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Answer:

Value of m = r / [p + z]  

Step-by-step explanation:

Given:

Equation:

mp + mz = r

Find:

Value of m

Computation:

⇒ mp + mz = r

⇒ m [p + z] = r

⇒ m = r / [p + z]

Value of m = r / [p + z]  

Answer: 23.22 ft

Step-by-step explanation: Multiply the base by the height to find the area. Since this is a triangle, we also have to divided by 2 before we get our answer. So that would be written like: 5.4 x 8.6 divided by 2 = area

Answer:

41.14

Step-by-step explanation:

Answer:

SA=72

Step-by-step explanation:

18+18=36

12+12=24

6+6=12

36+24+12=72

Answer:

Step-by-step explanation:

Let the capacity of tank is x

Based on the given information, there is not enough evidence at the 0.025 level to conclude that the bags are overfilled. This can be answered by the concept of Standard deviation.

To determine whether there is enough evidence to conclude that the bags are overfilled, we need to perform a hypothesis test.

Let the null hypothesis be that the bags are not overfilled, and the alternative hypothesis be that the bags are overfilled. We can set the significance level at 0.025.

We will perform a one-sample t-test since we have a small sample size and the population standard deviation is unknown. Using the formula for the t-test statistic, we obtain a t-value of 1.58. The critical t-value for a two-tailed test with 26 degrees of freedom (n-1) and a significance level of 0.025 is 2.479. Since 1.58 < 2.479, we fail to reject the null hypothesis.

Therefore, there is not enough evidence at the 0.025 level to conclude that the bags are overfilled.

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The amount of water in liters that can be used to fill the tank would be = 20L.

To calculate the volume of the rectangular prism shaped tank, the formula of volume of the rectangular prism is used. Such as;

Volume = length× width×height

where length = 40cm

width = 20cm

height = 25cm

Vol = 40×20×25 = 20000cm³

If 1,000 cm³ = 1 L

20,000 cm³ = xL

Make xL the subject of formula;

xL = 20,000/1000

= 20L

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Answer:

B

Step-by-step explanation:

this is the answer to this question

a) Counterexample: \(m\angle{P}=90^{\circ}, m\angle{Q}=45^{\circ}, m\angle{R}=45^{\circ},\)

b) Counterexample:\(m\angle{1}=45^{\circ}, m\angle{2}=45^{\circ},\)

c) Counterexample:  length=16, width=4

d) Counter example:  angle ABD= 50 degree, angle CBD=10 degree

What is the interior?

Something's interior or related to its interior; inward.

a) An acute angle is one that measures less than 90 degrees.

Counterexample: \(m\angle{P}=90^{\circ}, m\angle{Q}=45^{\circ}, m\angle{R}=45^{\circ},\)

(90 degrees is not an acute angle)

b) When the sum of two angles is 90°, then the angles are known as complementary angles

Counterexample:\(m\angle{1}=45^{\circ}, m\angle{2}=45^{\circ},\)

( None of the angles is greater than 45 degrees )

c) Area of rectangle = length*width=16*4

Counterexample:  length=16, width=4

d)  Since C is the interior of the angle ABD, then, angle ABD+angle CBD=60 degrees

Counterexample:  angle ABD= 50 degree, angle CBD=10 degree

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Answer:C 196

Step-by-step explanation:

The expression that is equivalent to 5^6 is A.125 x 125

Index forms are defined as mathematical forms of writing numbers that are too large or small in more convenient forms.

Other terms for index forms are called standard forms or scientific notations.

They are also described as numbers or variables that are raised to an exponent.

From the information given, we have that;

5⁶

This is replicating 5 in 6 places, we have the representation as;

5 × 5 × 5 × 5 × 5 × 5

Hence, the expression is 125 x 125

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