Simplify:6 to the power of 5/6to the power of 2.
A.1/6 to the power of 3
B.6 ttpo 7
C.6ttpo 2
D.6ttpo 3

$18,750 was invested in the 4% fund, and $6,250 was invested in the 6% fund, resulting in a total interest of $1,300.

To find the amounts invested in each fund, we set up an equation based on the interest earned.

The interest from the 4% fund is 0.04x, and the interest from the 6% fund is 0.06(25,000 - x).

The total interest earned is 1300, so we have the equation 0.04x + 0.06(25,000 - x) = 1300.

Solving this equation, we find x = 18,750, which represents the amount invested in the 4% fund. Therefore, the amount invested in the 6% fund is 25,000 - 18,750 = 6,250.

Hence, $18,750 was invested in the 4% fund, and $6,250 was invested in the 6% fund.

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The coordinates of the image of the triangle ABC after the dilation with center (0,0) and a scale factor of 1/2 are:

A' = (1/2 * x₁, 1/2 * y₁)

B' = (1/2 * x₂, 1/2 * y₂)

C' = (1/2 * x₃, 1/2 * y₃)

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To find the image of triangle ABC after a dilation with center (0,0) and a scale factor of 1/2, we need to multiply the coordinates of each vertex by the scale factor.

Let's suppose that the coordinates of the vertices of the original triangle ABC are:

A = (x₁, y₁)

B = (x₂, y₂)

C = (x₃, y₃)

Then, the coordinates of the image of A, B, and C after the dilation are:

A' = (1/2 * x₁, 1/2 * y₁)

B' = (1/2 * x₂, 1/2 * y₂)

C' = (1/2 * x₃, 1/2 * y₃)

Therefore, the coordinates of the image of the triangle ABC after the dilation with center (0,0) and a scale factor of 1/2 are:

A' = (1/2 * x₁, 1/2 * y₁)

B' = (1/2 * x₂, 1/2 * y₂)

C' = (1/2 * x₃, 1/2 * y₃)

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The magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

The value of the net electrostatic force on the 5.0-nC

charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0),

charge Q2 = −1.0 nC is at (0, 0.10 m), and

charge Q3 = 5.0 nC is at (0, 0) can be calculated as follows:

Given data,Charge Q1 = 6.0 nC is at (0.30 m, 0),

Charge Q2 = -1.0 nC is at (0, 0.10 m),

Charge Q3 = 5.0 nC is at (0, 0)

The formula to find out the force on the third charge Q3 is:

                      F = k * |Q1 * Q3| / r1^2 + k * |Q2 * Q3| / r2^2

Here, k = 8.99 × 10^9 N·m^2/C^2, Q1 = 6.0 nC, Q2 = -1.0 nC, Q3 = 5.0 nC

For the third charge Q3, the distance from Q1 is:

                                r1 = √(0.3^2 + 0^2) = 0.3 m

And the distance from Q2 is: r2 = √(0^2 + 0.1^2) = 0.1 m

Substituting all the given values in the formula:

                               F = 8.99 × 10^9 * [ (6.0 × 10^-9 * 5.0 × 10^-9) / 0.3^2 ] + 8.99 × 10^9 * [ (-1.0 × 10^-9 * 5.0 × 10^-9) / 0.1^2 ]F = 6.21 N

Therefore, the magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

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Answer:

45 mph

Step-by-step explanation:

3/4x60=45

Answer:

look at the picture I have sent

Answer:

D

Step-by-step explanation:

Using the sine ratio or the cosine ratio in the right triangle.

Choosing the sine ratio with the exact value

sin45° = \(\frac{\sqrt{2} }{2}\) , then

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{10}\) = \(\frac{\sqrt{2} }{2}\) ( cross- multiply )

2x = 10\(\sqrt{2}\) ( divide both sides by 2 )

x = 5\(\sqrt{2}\) → D

Total amount paid over the next year including the initial down payment and finance charge = $856

The difference between paying in cash for the laptop and this financial arrangement = $106

Cost of laptop=$750

Down payment=$150

Finance charges = $25

Remaining amount =$600

Amount for 1 month including 13.5 % interest=600/12*13.5/100+600/12

                                                                       =$56.75

Total amount paid over the next year including the initial down payment and finance charge =  56.75*12+150+25 = $ 856

The difference between paying in cash for the laptop and this financial arrangement = $106

Benefits of financing laptop:

A costly laptop can be yours without having to pay in full.

Bank loans and conventional credit card services are not required.

Numerous retailers provide rewards, flexible payment plans, zero-interest rates, and other benefits.

Downsides of financing laptop:

It's dangerous to borrow money because late payments might result in fees and excessive interest rates.

A credit score may suffer if there is no interest charged.

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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.

Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.

In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.

Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.

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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.

Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.

In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.

Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.

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The distances from the midpoint M to the vertices are all the same and equivalent to 5·√2, therefore, the diagonals of the quadrilateral bisect each other.

What in math is a quadrilateral?

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. Four non-collinear points are connected to produce it. Quadrilaterals' internal angles add up to a constant 360 degrees.

The vertices of the quadrilateral are;

P(1, -1), Q(3, -7), R(-9, -11), and S(-11, -5)

The midpoint of the side PR = ((-9 + 1)/2, (-11 + (-1))/2) = (-4, -6)

Midpoint of the diagonal SQ = ((3 + (-11))/2, (-7 - 5)/2) = (-4, -6)

Let M represent the point of intersection of the diagonals, we get;

PM = √((1 - (-4))² + (-1 - (-6))² = 5·√2

MR = √((-9 - (-4))² + (-11 - (-6))² = 5·√2

The length of PM = The length of MR, therefore, the diagonal SQ bisects PM

Similarly, we get;

SM = √((-9 - (-4))² + (-11 - (-6))²) = 5·√2

MQ = √((3 - (-4))² + (-7 - (-6))²) = 5·√2

The length PM = MR and the lengths SM = MQ, therefore, the diagonals bisect each other.

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Answer:

5

Step-by-step explanation:

H                       15                          J

------------------------------------------------

         5           I                10

15-10 =5

Step-by-step explanation:

..............

=> 3x + 4y = 12

area of rectangle = l×b

So, area of drawing = l×b = 8cm×4cm = 32cm²

Answer: (-0.75, 309)

Step-by-step explanation:

To find the vertex, first we will complete the square.

Given:

     h(t) = - 16t² + 24t + 300

Factor out -16:

     h(t) = -16(t² - 1.5t) + 300

Add and subtract \(\frac{b}{2} ^2\):

     h(t) = -16(t² - 1.5t + 0.5625 - 0.5625) + 300

Regroup:

     -16 * -0.5625 = 9; 9 + 300 = 309

     h(t) = -16(t² - 1.5t + 0.5625) + 309

Factor:

     h(t) = -16(t² - 1.5t + 0.5625) + 309

     h(t) = -16(t - 0.75)² + 309

Now, this equation is in vertex form. The vertex is (h, k) in the form y = a(x - h)² + k, meaning that our vertex is;

          (-0.75, 309)

I have also graphed this, see attached.

Answer:

7=6

Step-by-step explanation:

since it is times 1 plus 6 = 6 times 6 divided by 6

1+6=6x6/6

1+6 is 7

6 times 6 is 36  then 36 divided by 6 is 6

then you get  7=6  

The height of the tower from the point of observation is 118.7 feet. Now, let's calculate ZRPQ.ZRPQ = tan-1(FRP/RP)ZRPQ = tan-1(152.32/183.5)ZRPQ = 39.6°.

A famous leaning tower was originally 183.5 feet high.

At a distance of 124 feet from the base of the tower, the angle of elevation to the top of the tower is found to be 57° and FRP is the perpendicular distance from R to PQ. Now, we have to find ZRPQ using the given information.

Let's consider the following diagram to solve the given problem:In the above diagram, RP represents the leaning tower and ZRPQ represents the angle of elevation. Let's apply the given information in the diagram.

According to the problem,Base of the tower, PQ = 124 feetHeight of the tower, RP = 183.5 feet ZRPQ = 57° Let FRP be the perpendicular distance from R to PQ.ZRPQ = tan-1(FRP/RP).

On substituting the given values,57° =

tan-1(FRP/183.5)

Now, apply tangent on both sides to obtain,

tan 57° = FRP/183.5tan 57° × 183.5 = FRPFRP = 152.32 feet.

Therefore, the perpendicular distance from R to PQ is 152.32 feet.Using the Pythagorean Theorem,

QR² = RP² - PQ²QR² = (183.5)² - (124)²QR = 118.7 feet.

Therefore, the height of the tower from the point of observation is 118.7 feet. Now, let's calculate ZRPQ.

ZRPQ = tan-1(FRP/RP)ZRPQ = tan-1(152.32/183.5)ZRPQ = 39.6°.

Therefore, ZRPQ is 39.6° (rounded to one decimal place).

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we have that

P+0.50=0.8554

so

P=0.3554

using the tables of z-score

For P=0.3554

the value of z is

Answer:

x = 84/5 = 16.8

Step-by-step explanation:

The angle bisector theorem said that

21/15 = x/12

==> 7/5 = x/12

==> x = 84/5

Answer: 9 × 6 = 54

Step-by-step explanation:

In the Product Game, we need to multiply the both number of factor markers.

Chris and Katie were playing The Product Game. Their factor markers were on 9  and 2.

Number = 9 × 2 = 18

Chris decided to move the marker from 2 to 6.

Now, one maker is on 9 and other is on 6. So,

Number = 9 × (2 + 4)

Number = 9 × 6 = 54

Therefore, 9 × 6 = 54 is a numerical expression  to represent his move.​

Answer:

Hey there

It is 60466176

Answer:

60,466,176

Step-by-step explanation:

6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6

The series converges for x values that satisfy 2 < x < 6. This indicates that the series converges for all x values between 2 and 6, excluding the endpoints.

To determine the values of x for which the series converges, we need to examine the behavior of the series as n approaches infinity. The given series is:

∑ [n=0 to ∞] (x - 4)^n 2^n

This is a geometric series with a common ratio of (x - 4)/2. The series converges if the absolute value of the common ratio is less than 1. So we have:

|(x - 4)/2| < 1

Now, we can solve this inequality to find the values of x that satisfy the convergence condition.

1. When the common ratio is positive:

(x - 4)/2 < 1

x - 4 < 2

x < 6

2. When the common ratio is negative:

-(x - 4)/2 < 1

x - 4 > -2

x > 2

Therefore, the series converges for x values that satisfy 2 < x < 6.

In interval notation, we can express the values of x as (2, 6). This indicates that the series converges for all x values between 2 and 6, excluding the endpoints.

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Answer:

It's already there or it's not then put in 100

Step-by-step explanation:

Answer:

\(W=\frac{A}{2}\)

Step-by-step explanation:

\(A=2W\)

Divide 2 from both sides

\(\frac{A}{2}=W\)

Hope this is helpful.

Answer:

A/2

hope this helps

Figure J is transformed to figure K by the rotation of 90° clockwise followed with the translation of 5 units right.

A point, line, other geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

rotation of 90° clockwise: When a figure is rotated 90 degrees anticlockwise, each point must be converted from (x, y) to (y, -x) before the rotated figure may be graphed.

Before Rotation - (x, y)

After Rotation - (y, -x)

Translation of points is 5 units to the right.

Thus, Figure J is transformed to figure K by the rotation of 90° clockwise followed with the translation of 5 units right.

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Answer:

1st box=18 days

2nd box= 4 miles

Step-by-step explanation:

1st box is the number of dots

=18 days

2nd box is the dot that is on the max value

= 4 miles

Production: 168,500 units.

Direct materials: 337,000 pounds.

Direct labor: Calculated based on units produced.

Factory overhead: Calculated based on direct labor hours.

1. Production Budget for the Third Quarter:

BLACK DIAMOND COMPANY Production Budget (in units) Third Quarter

Budgeted sales units: 170,000

Add: Desired ending inventory units: 5,500

Total required units: 175,500

Less: Beginning inventory units: 7,000

Units to produce: 168,500

2. Direct Materials Budget for the Third Quarter:

BLACK DIAMOND COMPANY Direct Materials Budget Third Quarter

Units to produce: 168,500

Materials needed for production (pounds): 2 pounds per snowboard

Total materials required (pounds): 337,000 pounds

Materials to purchase (pounds): Total materials required - Beginning inventory pounds - Desired ending inventory pounds

3. Direct Labor Budget for the Third Quarter:

BLACK DIAMOND COMPANY Direct Labor Budget Third Quarter

Units to produce: 168,500

Direct labor hours needed: 0.5 hour per snowboard

Cost of direct labor: Direct labor hours needed * Direct labor rate

4. Factory Overhead Budget for the Third Quarter:

BLACK DIAMOND COMPANY Factory Overhead Budget Third Quarter

Direct labor hours needed: Calculated from the direct labor budget

Budgeted variable overhead: Direct labor hours needed * Variable overhead rate

Budgeted total factory overhead: Budgeted fixed overhead + Budgeted variable overhead

Note: The specific rates for direct materials, direct labor, and variable overhead were not provided in the given information and would need to be included in the calculations based on the company's specific cost structure.

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The theorem used to prove both triangles are similar is AAA (angle, angle, angle)

AAA theorem:

If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or porportion) and hence, the two triangles are similar.

To make your data more conclusive by conceding some sources of experimental error, you can acknowledging and accounting for potential sources of experimental error, such as measurement uncertainties, instrument limitations, and environmental factors.

In scientific experiments, acknowledging and conceding potential sources of experimental error means recognizing and accepting factors that could introduce uncertainty or variation in the data. This includes factors like imprecise measurements, limitations of the instruments or equipment used, and environmental conditions that may affect the results.

By openly acknowledging these potential errors, researchers can demonstrate transparency and a thorough understanding of the limitations of their study, leading to more robust and conclusive data analysis.

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Answer:

C.

Step-by-step explanation:

A repeating decimal is always rational I think.

I hope this helps!