1. GE lighting claims that their lightbulbs last exactly 2,000 hours before needing to be replaced. I am suspicious of this claim and believe that they last less than 2,000 hours. What are the null and alternate hypotheses? a.) HA = 2,000 hours; H0 < 2,000 hours b.) H0 ≠ 2,000 hours; HA > 2,000 hours c.) H0 = 2,000 hours; HA < 2,000 hours d.) H0 ≠ 2,000 hours; HA = 2,000 hours

The total area of the shaded region is 4 ln(2) square units.

To find the total area of the shaded region, we need to integrate the function \(y = x(4 - (x^2)^{(1/2)})\) with respect to x over the interval [0, 2].

First, let's graph the function to visualize the shaded region:

|        *

|      *   *

|    *       *

|  *           *

|*_____________*

0               2

The shaded region is the area between the x-axis and the function y = \(x(4 - (x^2)^{(1/2)})\) from x = 0 to x = 2.

To integrate this function, we can use the substitution \(u = 4 - (x^2)^{(1/2),\) which gives us \(du/dx = -x/(x^2)^{(1/2)\). Solving for dx, we get dx = -\(du/(x/(x^2)^{(1/2)}) = -2du/u.\)

Substituting \(u = 4 - (x^2)^(1/2)\)and dx = -2du/u into the integral, we get:

\(A = \int [0,2] x(4 - (x^2)^(1/2)) dx\\ = \int [4,2] (4 - u) (-2du/u)\\ = 2 \int [2,4] (u - 4)/u du\\ = 2 (\int [2,4] 1 du - \int [2,4] 4/u du)\\ = 2 [u|2^4 - 4 ln(u)|2^4]\\ = 2 [(4 - 2) - (0 - 4 ln(2))]\\ = 4 ln(2)\)

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The total area of the shaded region of y=x(4-((x^2))^(1/2)) is 10 square units.

To find the total area of the shaded region of y = x(4 - ((x^2))^(1/2)), we need to integrate the function from its intersection points with the x-axis.

First, we find the x-intercepts by setting y = 0:

x(4 - ((x^2))^(1/2)) = 0

This means that either x = 0 or 4 - ((x^2))^(1/2) = 0. Solving for the second equation, we get x^2 = 16, so x = ±4.

Therefore, the shaded region is bounded by the x-axis and the curve y = x(4 - ((x^2))^(1/2)) from x = -4 to x = 0, and from x = 0 to x = 4.

To find the area of the shaded region, we integrate the function from x = -4 to x = 0 and add the absolute value of the integral from x = 0 to x = 4.

∫(-4)^0 x(4 - ((x^2))^(1/2)) dx + |∫0^4 x(4 - ((x^2))^(1/2)) dx|

Using substitution, we can simplify the integrals:

= 2∫0^4 u^2/16 * (4 - u) du

where u = ((x^2))^(1/2).

Simplifying this expression, we get:

= (1/24) * [32u^3 - 3u^4] from 0 to 4

= (1/24) * [(512 - 192) - 0]

= 10

Therefore, the total area of the shaded region is 10 square units.

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Answer:

if u feel like u find the value that is correct but if u didn't find it it can be 1 the power of x can be 1

Answer:

B.9

all done  hope it help

Answer:

x = 7°

Step-by-step explanation:

The sum of all octogon's angles equals 1080°

Let's solve your equation step-by-step.

8(16x + 23) = 1080

Step 1: Simplify both sides of the equation.

8(16x + 23)=1080

(8)(16x) + (8)(23) = 1080(Distribute)

128x + 184 = 1080

Step 2: Subtract 184 from both sides.

128x + 184 − 184 = 1080 − 184

128x = 896

Step 3: Divide both sides by 128.

128x/128 = 896/128

x = 7°

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:(7,6)

Equation Form: x=7, y=6

2x+y=20

6x-5y=12

First get y by its self

2x+y=20

y= -2x+20

Now plug into second equation for y

6x-5(-2x+20)=12

6x+10x-100

16x-100=12

16x=112

x=7

now plug in x value into first equation and solve for y

2(7)+y=20

14+y=20

y= 6

Now check by plugging x and y values back into equation

2(7)+6=20

6(7)-5(6)=12

They both work so x=7 and y =6

Answer:

there are 96 4 oz servings in a 24 pound bag

Step-by-step explanation:

Solution. To graph f, we graph the equation y=f(x).

To this end, we use the techniques outlined in Section 1.2.1. Specifically, we check for intercepts, test for symmetry, and plot additional points as needed. To find the x -intercepts, we set y=0. Since y=f(x), this means f(x)=0.

\($$\begin{aligned}f(x) & =x^2-x-6 \\0 & =x^2-x-6 \\0 & =(x-3)(x+2) \quad \text { factor } \\x-3=0 & \text { or } x+2=0 \\x & =-2,3\end{aligned}$$\)

So we get (-2,0) and (3,0) as x-intercepts. To find the y-intercept, we set x=0. Using function notation, this is the same as finding f(0) and f(0)=0^2-0-6=-6. Thus the y-intercept is (0,-6). As far as symmetry is concerned, we can tell from the intercepts that the graph possesses none of the three symmetries discussed thus far. (You should verify this.) We can make a table analogous to the ones we made in Section 1.2.1, plot the points and connect the dots in a somewhat pleasing fashion to get the graph below on the right.

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Answer:

1. Josie needs 21 litres of fruit juice need 28 litres of lemonade.

2. Josie can make an extra of 35 litres of punch.

3. 5:8

Step-by-step explanation:

a) The ratio of the fruit juice to lemonade = 3:4

Total litres of punch to be made = 49

Amount of fruit juice needed = \(\frac{3}{7}\) x 49

                                                 = 21 litres

Amount of lemonade needed = \(\frac{4}{7}\) x 49

                                                  = 28 litres

Thus, she would need 21 litres of fruit juice need 28 litres of lemonade.

b) She has 15 litres of fruit juice left. Let the litres of punch to be made be represented by s.

\(\frac{3}{7}\) x s = 15

s = 35

Josie can make an extra of 35 litres of punch.

c) For the second batch, she needs;

15 litres of fruit juice needs 20 litres of lemonade.

But adding 4 more litres to the lemonade makes the total litres of lemonade to be 24.

Thus the ratio of the juice to lemonade = 15:24

                                                                 = 5:8

my man your answer is b

srry if im wrong

The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2. 3(10 + 2) = ? According to this property, you can add the numbers and then multiply by 3.

Answer:

the answer is a

Step-by-step explanation:

a is .75 shaded in then there are 5 sections in the shaded area

Answer:

D is the correct option.

Step-by-step explanation:

I used the elimination method to solve this. so we can see that there is 100 boxes and we need to 75 to be shaded. only C and D have 75 squares shaded so we can eliminate A and B. now we have to divide by 5. Square C is divided 3 times while square D is divided 5 times, so square D is correct.

Have a nice day! :-)

Answer:

x = 44

Step-by-step explanation:

4+4+2x+2x= 96

-(add like terms)

8+4x=96

-(subtract 8 from both sides)

4x=88

-(divide by 4 on both sides to get you x alone)

x=44

Answer:

x = 8

Step-by-step explanation:

2 x+ 4

2 x 4 = 8

8 ÷ 2 = 4

Answer:

x = 8

In the parallelogram DEFG, value of x is,

⇒ x = - 31

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

The parallelogram DEFG is shown,

And, m ∠FHG = 58° , m ∠DHE=(−2x−4)°

Now, By figure we get;

⇒ m ∠FHG = m ∠DHE

⇒ 58° = (- 2x - 4)°

⇒ 58 = - 2x - 4

⇒ 58 + 4 = - 2x

⇒ 62 = - 2x

⇒ x = - 31

Thus, In the parallelogram DEFG, value of x is,

⇒ x = - 31

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Asia is a chef in a restaurant. To prepare for dinner service, she chops 7 1/2 onions in 1/6 of an hour. Asia's rate of chopping onions is 30 onions per hour.

From the information given;

So, the onion is given in mixed fraction which can be converted to an improper fraction as: \(\mathbf{\dfrac{15}{2}\ onions}\)

Now,

We can cross multiply the above two equations to determine the number of onions Asia will chop per hour as follows:

\(\mathbf{(x) \times \dfrac{1}{6} \ hours = \dfrac{15}{2} \ onions \times 1 \ hour}}\)

Making (x) the subject of the formula:

\(\mathbf{(x)=\dfrac{ \dfrac{15}{2} \ onions \times 1 \ hour}{ \dfrac{1}{6} \ hours }}}\)

\(\mathbf{(x)={ \dfrac{15}{2} \ onions } \times { \dfrac{6}{1} }}}\)

(x) = 15 onions × 3

(x) = 30 onions per hour.

Therefore, Asia's rate of chopping onion is 30 onions per hour.

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If Asia chops 7 1/2 onions in 1/6 hour, therefore, using proportion, the rate of chopping onions per hour is: 45 onions per hour.

Applying the knowledge of proportion and fractions, we can determine Asia's chopping rate of onions per hour.

Given:

Using proportion, we have the following:

\(7\frac{1}{2} = \frac{1}{6} \\\\x = 1\)

\(\frac{1}{6} \times x = 7\frac{1}{2} \times 1\\\\\frac{x}{6} = \frac{15}{2}\)

\(\frac{x}{6} = \frac{15}{2}\\\\x = \frac{15}{2} \times 6\\\\x = 45\)

Therefore, if Asia chops 7 1/2 onions in 1/6 hour, therefore, using proportion, the rate of chopping onions per hour is: 45 onions per hour.

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Step-by-step explanation:

Since area = length(width) = l(w)

We need to multiply 15 and 9.

15(9) = 135

Therefore, the area of the rectangle is 135 ft

Area of the rectangle is 135 feet square

A rectangle is a quadrilateral with four right angles.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface

Given,

Length of the rectangle = 15 feet

Width of the rectangle = 9 feet

Area of the rectangle = Length × Width

=15×9

=135 feet square

Hence, the area of the Rectangle is 135 feet square

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The height of the ground from the base of the window is 144 inches.

One angle of a right angle triangle is equals to 90 degrees.

Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.

tan x = WY / XY

tan x  = opposite / adjacent

tan x = 24 / 8

x = tan⁻¹ 3

x = tan⁻¹ 3

x = 71.5650511771

x = 71.60°

tan 71.60 = h / 48

cross multiply

h = 48 tan 71.60

h = 48 × 3

h = 144 inches

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Answer:

52.1 is the percentage of employees that are men

Step-by-step explanation:

(a) Using the Russian peasant method, 29 x 15 is computed to be 435.(b) Employing ancient Egyptian division, 17 + 12 is determined to be 1 remainder 5. .

(a) The Russian peasant method involves halving and doubling numbers to perform multiplication. To compute 29 x 15, we start by writing the numbers in two columns: 29 and 15. We repeatedly halve the first column and double the second column until the number in the first column reaches 1. Then we add the values in the second column corresponding to the odd numbers in the first column. In this case, the calculations would be as follows:

29  15

14  30

7   60

3   120

1   240

Adding the values in the second column corresponding to the odd numbers in the first column (15 + 60 + 240), we get the result 435.

(b) Ancient Egyptian division involves finding the remainder and quotient through repeated subtraction. To compute 17 + 12 using this method, we repeatedly subtract the smaller number (12) from the larger number (17) until the remainder is less than the smaller number. In this case, the calculations would be as follows:

17 - 12 = 5 (remainder)

Since the remainder (5) is less than the smaller number (12), the result is 1 remainder 5.

(c) The Sylvester method is a method used to express a given number as the sum of distinct unit fractions. It involves finding a series of distinct unit fractions (fractions with a numerator of 1) whose sum equals the desired number. The method starts by expressing the number as the sum of two distinct unit fractions, and then each fraction is expressed as the sum of two smaller fractions, and so on. The process continues until all the fractions in the series are distinct. However, without a specific number to express in this format, it is not possible to provide a detailed calculation.

(d) The sexagesimal system is a base-60 numeral system used by ancient civilizations, including the Babylonians and the Sumerians. To represent 1/8 in sexagesimal notation, we divide the base (60) by the denominator (8), which gives us 7 with a remainder of 30. Therefore, the sexagesimal representation of 1/8 is 0; 0, 7, 30. In this representation, the first zero represents the whole number part, followed by two digits representing the fractional part in base-60 (7 and 30, respectively).

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Answer:

( - 1, 17 ) and ( 6, 3 )

Step-by-step explanation:

- 2(x - 2)² + 35 = - 2x + 15

- 2x² + 8x - 8 + 35 = - 2x + 15

2x² - 10x - 12 = 0

x² - 5x - 6 = 0

(x - 6)(x + 1) = 0

\(x_{1}\) = - 1

\(y_{1}\) = - 2( - 1) + 15 = 17

( - 1, 17 )

\(x_{2}\) = 6

\(y_{2}\) = - 2( 6 ) + 15 = 3

( 6, 3 )

Answer:

The first number: 14

The second number: 16

The third number: 18

Step-by-step explanation:

Equations

Let's assume:

x=the first even number.

x+2=the second even number

x+4=the third even number

The sum of all three is: x + x + 2 + x + 4

The condition states the sum decreased by 34 equals the first number:

x + x + 2 + x + 4 - 34 = x

Moving all the variables to the left side and the numbers to the right side:

x + x + 2 + x + 4 - 34 - x = 34 - 2 - 4

Simplifying:

2x =  28

Solving:

x = 28 / 2 = 14

The first number: 14

The second number: 16

The third number: 18

Answer:

y = 1/3x -4

Step-by-step explanation:

Solve for y

3x-9y = 36

Subtract 3x

3x -3x-9y = -3x +36

-9y = -3x +36

Divide by -9

-9y/-9 = -3x/-9 + 36/-9

y = 1/3x -4

This is in slope intercept form ( y = mx+b) where m is the slope and b is the y intercept

Slope intercept form: y = mx + b

Solve for y:

3x - 9y = 36

~Subtract 3x to both sides

3x - 3x - 9y = 36 - 3x

~Simplify

-9y = 36 - 3x

~Divide -9 to both sides

-9y/-9 = 36/-9 - 3x/-9

~Simplify

y = -4 + 1/3x

Therefore, the answer is y = 1/3x - 4

Best of Luck!

The pharmacist should use 5.25 ounces of 1% hydrocortisone ointment and 1.75 ounces of 5% hydrocortisone ointment.

Let x be the number of ounces of 1% hydrocortisone ointment required and y be the number of ounces of 5% hydrocortisone ointment required to make a 7-ounce tube of 2% hydrocortisone ointment.

Since we want a total of 7 ounces of ointment, we have the equation:

x + y = 7

We also know that the amount of hydrocortisone in the final ointment must be equal to 2% of 7 ounces, or 0.14 ounces. The amount of hydrocortisone in x ounces of 1% ointment is 0.01x ounces, and the amount of hydrocortisone in y ounces of 5% ointment is 0.05y ounces. So, we have the second equation:

0.01x + 0.05y = 0.14

To solve for x and y, we can use the method of substitution. Rearranging the first equation to solve for x, we get:

x = 7 - y

Substituting this expression for x into the second equation, we get:

\(0.01(7 - y) + 0.05y = 0.14\)

Simplifying and solving for y, we get:

0.07 - 0.01y + 0.05y = 0.14

0.04y = 0.07 - 0.14

0.04y = -0.07

y = -0.07/0.04

y = -1.75

This negative value for y doesn't make sense, so we need to check our work. We made a mistake in the equation above, the correct equation should be:

0.01x + 0.05y = 0.02(7)

0.01x + 0.05y = 0.14

Using this corrected equation, we can solve for y:

0.01x + 0.05y = 0.14

0.05y = 0.14 - 0.01x

y = (0.14 - 0.01x)/0.05

Substituting this expression for y into the first equation, we get:

x + (0.14 - 0.01x)/0.05 = 7

Multiplying both sides by 0.05 to eliminate the denominator, we get:

0.05x + 0.14 - 0.01x = 0.35

0.04x = 0.21

x = 5.25

So, the pharmacist should use 5.25 ounces of 1% hydrocortisone ointment and 1.75 ounces of 5% hydrocortisone ointment to make a 7-ounce tube of 2% hydrocortisone ointment.

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For a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)

Given,

The conditions

We know,

Median is the middle number of ordered data set.

Consider the number of observations as x

Then the median is located at \(\frac{x+1}{2}\)

Hence, for a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)

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Answer:

42 sq ft

Step-by-step explanation:

L x W x H

3 x 7 x 2

21 x 2

42 sq ft

You would compare the proportion of simulated samples with a proportion as extreme or more extreme than your sample proportion to estimate the p-value.

For one repetition of a simulation of the proportion of high school students who followed the Egyptian Revolution using blue and yellow poker chips, you would first need to determine the total number of high school students in your sample and the estimated proportion of them who followed the Egyptian Revolution.

Next, assign one color of poker chip (e.g. blue) to represent students who followed the revolution and the other color (e.g. yellow) to represent students who did not.

Then, mix the chips thoroughly and draw a sample of the specified size.

Count the number of blue chips in the sample and divide by the total sample size to calculate the proportion of students who followed the revolution in your sample.

Repeat this process several times to simulate multiple samples from the same population.

To estimate the p-value, you would need to compare the proportion of students who followed the revolution in your sample to the null hypothesis value.

If your null hypothesis is that the true proportion of students who followed the revolution is equal to some hypothesized value (e.g. 0.5), then you would calculate the probability of observing a proportion as extreme or more extreme than your sample proportion, assuming the null hypothesis is true.

To do this, you would need to calculate the difference between your sample proportion and the hypothesized value, divide this by the standard error of the proportion, and then look up this calculated value in a t-distribution table with n-1 degrees of freedom (where n is the number of samples you simulated).

The p-value would be the area under the curve of the t-distribution beyond the calculated value.

Alternatively, you could simulate a large number of samples from a null distribution assuming the hypothesized value for the proportion of students who followed the revolution.

Then, you would compare the proportion of simulated samples with a proportion as extreme or more extreme than your sample proportion to estimate the p-value.

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If g ( x ) is the f ( x ) = x after a vertical compression by 1 4 , a shift left by 3, and a shift up by 1, c) the vertical intercept of this line is 7/4.

To find the vertical intercept of the line after the given transformations, we need to determine the value of the function when x is equal to 0.

Let's break down the transformations step by step:

Vertical compression by 1/4: This means the vertical coordinates of the points on the graph will be multiplied by 1/4. Since the original function is f(x) = x, the compressed function becomes f(x) = (1/4)x.

Shift left by 3: This means the graph will shift horizontally to the right by 3 units. The function becomes f(x) = (1/4)(x + 3).

Shift up by 1: This means the graph will move vertically upwards by 1 unit. The function becomes f(x) = (1/4)(x + 3) + 1.

Now, to find the vertical intercept, we substitute x = 0 into the function:

g(0) = (1/4)(0 + 3) + 1

g(0) = (1/4)(3) + 1

g(0) = 3/4 + 1

g(0) = 3/4 + 4/4

g(0) = 7/4

Therefore, the vertical intercept of the line after the given transformations is 7/4.

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Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer: 1) linear pairs are supplementary

2) subtraction property

3) transitive property

Step-by-step explanation:

transitive property is also vertical angles showing that angle 4 and angle 2 are equal

both angles 1 and 2 lay on the same line causing them to be supplementary angles.

Answer:

Hi. The answer is $59.40

Step-by-step explanation:

Divide $46.20 into the hours she works, so 46.20/5.25 = 8.80

She earns $8.80 per hour.  Multiply this by 6 3/4 hours...8.80x6.75 = $59.40

Answer:

$59.40

Step-by-step explanation:

The probability that the mean weight of the 17 fruits will be between 489 grams and 500 grams is approximately 0.0322 - 0.0322 = 0.0000 (rounded to four decimal places).

The probability that the mean weight of 17 randomly picked fruits falls between 489 grams and 500 grams can be calculated using the Central Limit Theorem.

The mean weight of the 17 fruits will follow a normal distribution with a mean equal to the population mean (494 grams) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (√17).

First, we calculate the z-scores for the lower and upper bounds:

Lower z-score:

z_lower = (489 - 494) / (8 / √17)

Upper z-score:

z_upper = (500 - 494) / (8 / √17)

Then, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability that the mean weight falls between 489 grams and 500 grams is equal to the difference between these two probabilities.

Let's calculate the probabilities:

z_lower = (489 - 494) / (8 / √17) ≈ -1.8409

z_upper = (500 - 494) / (8 / √17) ≈ 1.8409

Using a standard normal distribution table or a calculator, we find that the probability corresponding to z_lower is approximately 0.0322 and the probability corresponding to z_upper is also approximately 0.0322.

The problem presents a normal distribution of fruit weights, with a given mean of 494 grams and a standard deviation of 8 grams. When we randomly select a sample of 17 fruits, the mean weight of this sample will also follow a normal distribution. According to the Central Limit Theorem, as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

In this case, since the range is relatively narrow and the sample size is moderate, the probability of the mean weight falling between 489 grams and 500 grams is quite low, approximately 0.0000.

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