$11,335
is invested, part at 9%
and the rest at 6%
. If the interest earned from the amount invested at 9%
exceeds the interest earned from the amount invested at 6%
by $865.35
, how much is invested at each rate? (Round to two decimal places if necessary.)

The simplified expression of [tex]\sqrt[4]{567(x^9)(y^{11})}[/tex] is [tex]3x^2y^2\sqrt[4]{7xy^3}[/tex].

Given expression:

[tex]\sqrt[4]{567(x^9)(y^{11})}[/tex].

We can simplify the expression using the property that says for any non-negative numbers a and b, and any integer n ≠ 0,

[tex](a\times b)^{n} = a^n \times {b^n}[/tex]

Using this property, we can simplify the expression as follows:

[tex](567x^9y^{11})^{1/4} = (567)^{1/4} \times (x^9)^{1/4} \times (y^{11})^{1/4}[/tex]

Now we need to simplify,

[tex](81\times 7)^{1/4}x^{9/4}y^{11/4}\\=(81)^{1/4}(7)^{1/4}(x^{\frac{8}{4}+\frac{1}{4})(y^{\frac{8}{4}+\frac{3}{4})[/tex]

Also,

[tex]{3^4}^{1/4}(7)^{1/4}(x^{2+\frac{1}{4}})(y^{2+\frac{3}{4}})\\=3^1 7^{1/4}x^2x^{1/4}y^2y^{1/4}\\=3x^2y^2(7^{1/4}x^{1/4}y^{3/4})\\=3x^2y^2(7xy^3)^{1/4}\\=3x^2y^2\sqrt[4]{7xy^3}[/tex]

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This shaded region represents the solution to the system of inequalities.

We have,

The inequalities:

y ≤ -1 and x ≥ 1

To graph y ≤ -1, we first draw the horizontal line y = -1.

Since we want y to be less than or equal to -1, we shade the area below the line.

To graph x ≥ 1, we draw the vertical line x = 1.

Since we want x to be greater than or equal to 1, we shade the area to the right of the line.

The shaded regions of both inequalities overlap in the area to the right of x = 1 and below y = -1.

Thus,

This shaded region represents the solution to the system of inequalities.

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The required standard error of the mean is 2.4 units.

The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is 36 units and the sample size is 225. Therefore, the standard error of the mean is:

SE = σ / √n = 36 / √225
     = 36 / 15 = 2.4 units

Therefore, the standard error of the mean is 2.4 units.

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We can simplify the square roots:

√2 = √(2 × 1) = √2 × √1

√18 = √(9 × 2) = √9 × √2 = 3√2

√50 = √(25 × 2) = √25 × √2 = 5√2

Now we can find the mean:

(mean) = (sum of numbers) / (number of numbers)

(mean) = (√2 + 3√2 + 5√2) / 3

(mean) = (9√2) / 3

(mean) = 3√2

Therefore, the mean of the numbers √2, √18, and √50 is 3√2.

The function of the graph is f(x) = x²-3x -10

A quadratic function is a function in which the highest power of it's variable is 2. quadratic equation is given in the form f(x) = ax²+ bx +c

To form the quadratic function from a graph, we need to find the roots of the function from the graph. The root is the point where the curve intercept the x axis.

Therefore the roots are -2 and 5.

f(x) = x² -( z+y)x +zy

where z and y are the roots

z+y = -2 +5 = 3

zy = -2 × 5 = -10

f(x) = x²-3x -10

therefore the function of the graph is f(x) = x²-3x -10

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Answer:

-2x^2 - 2x + 5

Step-by-step explanation:

Combine like terms (same variable and degree) to simplify

3x^2-5x^2+5x-7x+3+2

-2x^2-2x+5

Answer:

Combining like terms, we get:

-2x² - 2x + 6

The sum of their ages if the son’s age is X is 3X.

We are given that;

x=A father is twice as old as his son

Now,

If the son’s age is X,

Then the father’s age = 2X.

The sum of their ages

= X + 2X

= 3X.

Therefore, by algebra the answer will be 3X.

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12.1 Alternative Hypothesis, 12.2 The level of significance will typically be set at α = 0.05 (5%), 12.3 In terms of tails, we will perform a two-tailed test. 12.4 The rejection region is determined by the critical values corresponding to the significance level α. In a two-tailed test,

To test if there is a significant difference between the survey results and the director's claim, we will perform a hypothesis test using a one-sample proportion test.

12.1 Alternative Hypothesis: The alternative hypothesis would be that the proportion of the workforce supporting the new shift pattern is not equal to 90%. We can express this as H1: p ≠ 0.9.

12.2 The level of significance for testing the difference between the director's claim and the survey results will typically be set at α = 0.05 (5%).

12.3 In terms of tails, we will perform a two-tailed test. This is because we are testing if the proportion is significantly different from the claimed value (90%), which could be either higher or lower.

12.4 The rejection region is determined by the critical values corresponding to the significance level α. In a two-tailed test, we divide α equally between the two tails. So, the rejection region will be split into two parts, one in the left tail and one in the right tail.

12.5 The rejection region is determined by the critical values. In this case, the critical values will be based on the standard normal distribution and the significance level α. The values that indicate the rejection region are the critical values of the standard normal distribution associated with α/2 (in each tail) based on the sample size.

12.6 Let's calculate the test statistic. The sample proportion in favor of the new shift pattern is 85/100 = 0.85. The expected proportion under the null hypothesis is 0.9. The standard error can be calculated using the formula: SE = sqrt(p * (1-p) / n), where p is the expected proportion and n is the sample size. Plugging in the values, we have SE = sqrt(0.9 * 0.1 / 100) ≈ 0.03. The test statistic can be calculated as (sample proportion - expected proportion) / SE, which gives (0.85 - 0.9) / 0.03 ≈ -1.67.

12.7 Referring to the rejection region and the test statistic, if the test statistic falls within the rejection region (i.e., if it is beyond the critical values), we will reject the null hypothesis. If the test statistic is not in the rejection region, we will fail to reject the null hypothesis.

12.8 Based on the calculated test statistic of -1.67 and the critical values associated with α/2, we would compare the test statistic with the critical values to determine if it falls within the rejection region. If it does, we would reject the null hypothesis and conclude that there is a significant difference between the survey results and the director's claim.

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A bag of chips costs $0.95, a bottle of Water Costs 2*$0.95 = $1.90, and a gallon of milk costs 2*$0.95 + $1.90 = $3.80.

Let x be the cost of a bag of chips in dollars.

Since a bottle of water costs twice as much as a bag of chips, a bottle of water costs 2x dollars.

A gallon of milk costs $1.90 more than a bottle of water, so a gallon of milk costs 2x + $1.90 dollars.

Using the given information, we can set up the following equation to represent the total cost:

3(2x + $1.90) + 5(2x) + 8x = $28.50

Simplifying the equation, we get:

6x + $5.70 + 10x + 8x = $28.50

24x + $5.70 = $28.50

Subtracting $5.70 from both sides, we get:

24x = $22.80

Dividing both sides by 24, we get:

x = $0.95

Therefore, a bag of chips costs $0.95, a bottle of water costs 2*$0.95 = $1.90, and a gallon of milk costs 2*$0.95 + $1.90 = $3.80.

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1. The area of the fort is 27 square feet.

2. No, Carlos was not correct

3.  The correct way to determine the area is to multiply the length and width, not add them. Carlos' mistake was in incorrectly calculating the area of the fort.

1. The area of the fort can be calculated by multiplying the length and width of the rectangle. In this case, the length is 6 feet and the width is 4.5 feet. Therefore, the area can be calculated as:

Area = Length × Width

= 6 feet × 4.5 feet

= 27 square feet

So, the area of the fort is 27 square feet.

2. No, Carlos was not correct. The actual area of the fort is 27 square feet, not 13.5 square feet as he determined.

3. Carlos made a mistake in his calculation. Instead of multiplying the length and width together, he likely mistakenly multiplied them as if he was finding the perimeter or added them together. The correct way to determine the area is to multiply the length and width, not add them. Carlos' mistake was in incorrectly calculating the area of the fort.

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Answer:

A = 36π units²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

here r = 6 , then

A = π × 6² = 36π units²

The average response time for the ambulance company is 13 minutes, with 95% of response times falling between 10 and 16 minutes.

The response times for a specific ambulance company follow a normal distribution with a mean of 13 minutes. This means that the majority of response times will cluster around the average of 13 minutes.

Furthermore, we know that 95% of the response times fall within the range of 10 to 16 minutes. This suggests that the response times are relatively consistent, with only a small percentage of outliers falling outside this range.

In summary, the average response time for this ambulance company is 13 minutes, and 95% of their response times fall between 10 and 16 minutes.

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The graph of the polynomial function with a positive leading coefficient and zeros at x = 4, 2, and -1 (multiplicity 2) is given by the image presented at the end of the answer.

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the zeros of the function, the linear factors are given as follows:

Considering the leading coefficient of a = 1, the function is defined as follows:

f(x) = (x - 4)(x - 2)(x + 1)²

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The value of x using Tangent - Secant theorem is: 16

The tangent-secant theorem states that when a tangent and secant possess a common endpoint outside the circle the product of the secant and the external part of the secant is equal to the square of the tangent.

We are given:

internal part of the secant = (x + 9),

external part of the secant = 9,

tangent = 15,

According  to Tangent-secant Theorem:

(x + 9) * 9 = 15²

9x + 81 = 225

9x = 144

x = 144/9

x = 16

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The value of given expression is 57.

We are given that;

|—15u| + |3v| + 3

u=3, v = 3

Now,

To evaluate the expression, you need to substitute the values of u and v and simplify. The absolute value of a number is the distance from zero on the number line, so it is always positive or zero. You can write your solution as:

|—15u| + |3v| + 3 = |—15(3)| + |3(3)| + 3 = |—45| + |9| + 3 = 45 + 9 + 3 = 57

Therefore, by the given expression the answer will be 57.

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The inequality 2|x - 3| + 6 > 10 has the solution set:

x < 1 or x > 5

To solve the inequality 2|x - 3| + 6 > 10, we need to isolate the absolute value expression |x - 3|.

We can do this by subtracting 6 from both sides of the inequality:

2|x - 3| > 4

Then we can divide both sides by 2:

|x - 3| > 2

Now we need to consider two cases, one where x - 3 is positive, and another where it is negative:

When x - 3 is positive, the inequality |x - 3| > 2 becomes:

x - 3 > 2

Solving for x gives:

x > 5

When x - 3 is negative, the inequality |x - 3| > 2 becomes:

-(x - 3) > 2

Solving for x gives:

x < 1

Therefore, the solution set for the inequality 2|x - 3| + 6 > 10 is:

x < 1 or x > 5

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The complete question:

Match each absolute value inequality on the left side with its solution set on the right

2|x - 3| + 6 > 10 - 2

Answer:

15

Step-by-step explanation:

I'm going to be very honest with you; one of my kids had this problem recently and I remember the answer is 15.

99=15+14+13+12+11+10+9+8+7

So the largest number is 15.

The way we solved it:

Call the 1st number x. Each number after x is x+(a number) all the way up to x+8 (the 9th number in the series of 9 consecutive whole numbers):

  x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6, x + 7 and x + 8

Add up those consecutive numbers (I know, it's kind of messy):

             x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 + x + 8

Combine the like terms:

           9x + 36 = 99

Subtract 36 from both sides:

            9x = 63

Divide by 9 on both sides:

            x = 7

So the largest number will be: x + 8

            7+8 = 15

And then check that it works:

99=15+14+13+12+11+10+9+8+7

The value of angle ABC in the equilateral triangle formed by points D, E, and C, given angle EAB is 80°, is 50°.

Let's solve the problem step by step:

In an equilateral triangle, all three angles are equal. Let's denote the measure of angle ABC as x.

Since the triangle is equilateral, angle BAC is also equal to x.

The sum of angles in a triangle is

=180°

Therefore, we can write the equation:

= x + 80 + x = 180.

Simplifying the equation, we have:

= 2x + 80 = 180.

Subtracting 80 from both sides:

= 2x = 100.

Dividing both sides by 2:

=x = 50.

Thus, angle ABC measures 50°.

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The complete question is:

The shaded triangle formed by points D, E and C is equilateral. If angle EAB is 80°, then what is the value of angle ABC? Give your answer in degrees (°).

Answer:

The answer to this question is vertical angles

Step-by-step explanation:

angle 5 and 8

 Those are vertical angles formed by two crossing lines and they are equal

After considering all the given data we conclude that the total distance traveled by the car is 285m, under the condition that the given car starts from rest and moves with an acceleration of 1m/s2 for 15.

The distance traveled during this time can be evaluated using the formula

[tex]s = ut + (1/2)at^2[/tex]

Here,

s = distance traveled,

u =  initial velocity (0),

a = acceleration (1m/s2)

t = time (15s).

Placing in these values we get

s = 0 + (1/2) × 1 × 15²

= 112.5m .

After this, the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. The distance traveled during this time can be evaluated applying  the formula

[tex]s = ut + (1/2)at^2[/tex]

Here,

s = distance traveled,

u = initial velocity (the final velocity of the previous step),

a = acceleration (-0.05m/s2)

t = time (10s).

Placing in these values we get

s = 112.5 + (1/2) × (-0.05) × 10²

= 87.5m.

Finally, brakes are applied and it stops after 5s. The distance traveled during this time can be evaluated using the formula [tex]s = ut + (1/2)at^2[/tex]

Here,

s = distance traveled,

u = initial velocity (the final velocity of the previous step),

a = acceleration (-0.05m/s2)

t = time (5s).

Placing in these values we get s = 87.5 + (-0.05)× 5² = 85m.

Therefore, total distance traveled by car can be calculated by adding all three distances together which gives us

112.5m + 87.5 + 85

= 285m.

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The complete question is

A car starts from rest and moves with an acceleration of 1m/s2 for 15. Then the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. then the brakes are applied and it stops 5s after calculating the total distance traveled?

Answer:

The expression -7x^0 cannot be a part of a rational expression because any non-zero number raised to the power of 0 is equal to 1. Therefore, -7x^0 is equal to -7(1) = -7, which is a constant and not a variable expression. In a rational expression, the numerator and denominator should be polynomial expressions with variables.

The other options 4, 3x^2-4rootx, and 3x^2-4x+5 can be part of a rational expression as they are polynomial expressions with variables.

We can use the exchange rate of 1 Euro = R18.32. Therefore,400 € = 400 x R18.32 = R7,328.

1.1.1 According to the table, the weakest currency is the yen with 14 yen being equivalent to only R0.14.1.1.2 R292 318 460 in words is Two hundred and ninety-two million, three hundred and eighteen thousand, four hundred and sixty Rand. 1.1.3

To determine the amount in rand that needs to be spent on ventilators in Spain, we need to find out the total amount of money raised, then use the ratio provided (1:2:4) to determine the amount to be spent on ventilators.

The ratio indicates that for every 1 unit of money, 2 units are to be spent on staff payment and 4 units on purchasing ventilators.

Therefore, if the total amount of money raised is €14 million, which is equivalent to R292 313 460, then the amount to be spent on ventilators is:4/(1+2+4) × 292 313 460 = R175 388 076.1.1.4 To find out how much 400€ would be in rand,

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Answer:

a. The probability that all 5 selected transistors are defective is 0.0024 or 0.24%.

To calculate this probability, we use the formula for the probability of the intersection of independent events:

P(all 5 defective) = P(defective) x P(defective) x P(defective) x P(defective) x P(defective)

where P(defective) = 5/12 for each transistor.

Plugging in the values, we get:

P(all 5 defective) = (5/12) x (5/12) x (5/12) x (5/12) x (5/12) = 0.0024

b. The probability that none of the selected transistors are defective is 0.163 or 16.3%.

To calculate this probability, we use the complement rule:

P(none defective) = 1 - P(at least one defective)

To calculate P(at least one defective), we can use the complement rule again:

P(at least one defective) = 1 - P(none defective)

So, we need to find P(none defective) first:

P(none defective) = P(not defective) x P(not defective) x P(not defective) x P(not defective) x P(not defective)

where P(not defective) = 7/12 for each transistor.

Plugging in the values, we get:

P(none defective) = (7/12) x (7/12) x (7/12) x (7/12) x (7/12) = 0.163

Then, we can find P(at least one defective):

P(at least one defective) = 1 - P(none defective) = 1 - 0.163 = 0.837

Finally, we can find P(none are defective) using the complement rule:

P(none defective) = 1 - P(at least one defective) = 1 - 0.837 = 0.163.

The Surface area of the composite figure is calculated as approximately: 234 sq. cm

Here, we have,

to Find the Surface Area of a Composite Figure:

The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:

Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)

Area of base = area of square = 6 * 6 = 36 sq. cm.

Surface area of the square prism = 2a² + 4ah

a = 6 cm

h = 4 cm

Plug in the values:

Surface area of the square prism = 2(6²) + 4*6*4

= 72 + 96

= 168 sq. cm.

Surface area of the square pyramid = 2bs + b²

b = side length = 6 cm

s = slant height = √(8² + 3²) = 8.5 cm

Plug in the values:

Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.

Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm

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complete question:

Find the surface area of each composite figure. Use 3.14 for π. Round to the nearest tenth. 12m. 6cm. 6cm. 4cm.​

The correct answer is: The median is the best measure of center, and it equals 19.

A box plot, also known as a box-and-whisker plot, is a graph that displays the distribution of a dataset.

The box represents the middle 50% of the data, with the bottom of the box being the first quartile (Q1) and the top of the box being the third quartile (Q3). The line inside the box represents the median.

The "whiskers" extend from the box to the dataset's minimum and maximum values or, in the case of outliers, a specific distance from the box (often 1.5 times the interquartile range).

The box plot in this instance reveals that the median number of tickets sold was 19, with the middle 50% of the data falling between 17 and 21 tickets sold.

A minimum of 10 and a maximum of 27 tickets may be sold before the whiskers are removed.

The median is the most suitable measure of the center for this dataset since it is the measure of the center that represents the middle of the dataset.

In light of this, the answer is "The median is the best measure of center, and it equals 19."

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