an isosceles triangle has two vertices at ( 4 , 2 ) and ( 2 , 12 ) . what are the possible coordinates of the third vertex?

Answer:

\(5(x - 2) = x + 1 \\ 5x - 10 = x + 1 \\ 5x - x = 1 0+ 1 \\ 4x = 11 \\ x = \frac{11}{4} \)

Answer:

1,200,000

Step-by-step explanation:

hope i helped

Answer:

1.200.000

Step-by-step explanation:

\(thankyou\)

Answer: 15

Step-by-step explanation:

Since we are informed that in exchange for 5 eclaire boxes, that Luna gets, she decided to give 1 eclaire box for free.

Then, the number of eclaires boxes that they can buy from Luna using 77 claire boxes will be:

= 77 / 5

= 15 2/5

= 15 approximately

They'll get 15 boxes of eclaires from Luna.

The power of a test is measured by its capability of rejecting a null hypothesis that is false, so option C is the correct answer

what is power with respect to probability?

Power is defined as the probability of correctly rejecting the false null hypothesis. It is the measure of the capability of rejecting a null hypothesis that is false.

Power = P[ rejecting a null hypothesis that is false.]

So, option C is correct, the power of a test is measured by its capability of rejecting a null hypothesis that is false

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Answer:

the correct answer is 90•

Step-by-step explanation:

90-x =180

ATQ,

x =180-90

= 90•

Answer:

Step-by-step explanation:

plug in the points minus the constant for 7=3*4 + x and you will get -5 for your constant  

y=3x - 5

Answer:

y = 3x - 5

Step-by-step explanation:

7 = 3(4) + b

---> b = -5

y = 3x - 5

The domain of the function f(x) = log_b(x) in interval notation is (0, +∞). The range of the function depends on the base b.

The domain of the logarithmic function f(x) = log_b(x) is determined by the requirement that the argument of the logarithm, x, must be positive. Since the logarithm is undefined for zero and negative numbers, the domain excludes these values. Therefore, the domain is expressed in interval notation as (0, +∞), where the parentheses indicate that zero is not included and the positive infinity symbol indicates that the domain extends indefinitely towards positive numbers.

The range of the logarithmic function depends on the base b. If the base b is greater than 1, the function can output any real number as the exponent increases or decreases, leading to a range of (-∞, +∞), covering all possible real numbers. However, if the base b is between 0 and 1, the logarithmic function only outputs negative numbers. As the exponent increases or decreases, the value of the logarithm approaches negative infinity, resulting in a range of (-∞, 0). This signifies that the range consists of all negative real numbers, but does not include zero or positive numbers.

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Answer:

$541.90

Step-by-step explanation:

We'll start with his regular pay, 40 hours times $10.73

10.73 x 40 = 429.20

His overtime pay is 10.73 + 1/2(10.73) = 10.73 + 5.365 = 16.095, rounded to 16.10

He worked 7 hours at the rate of $16.10/hour

16.10 x 7 = 112.70

Add the two totals together for his total pay before taxes:

429.20 + 112.70 = 541.90

Please lmk if you have questions.

Answer:

D. Make the column wider

Step-by-step explanation:

The amount of footcandles on a surface located 18 feet away from the lamp can be calculated by dividing the candelas of the lamp (4,500) by the square of the distance (324). This results in 13.89 footcandles, which can be rounded to 13.90.

Footcandles = Candelas / Distance2

Footcandles = 4,500 / (18 x 18)

Footcandles = 4,500 / 324

Footcandles = 13.89

Rounded to two decimal places:

Footcandles = 13.89 → 13.90

Step 1: Calculate distance2

Distance2

= 18 x 18

Distance2

= 324

Step 2: Calculate footcandles

Footcandles = Candelas / Distance2

Footcandles

= 4,500 / 324

Footcandles = 13.89

Step 3: Round the answer

Footcandles

= 13.89 → 13.90

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Therefore, it would take approximately 10.246 hours for the satellite to fly 82000 miles.

We can use the concept of unit rate to solve this problem.

Given that the satellite flies 73680 miles in 9.21 hours, we can calculate the unit rate of the satellite's speed:

Unit Rate = Distance / Time

= 73680 miles / 9.21 hours

≈ 8004.55 miles/hour

Now, to find out how long it would take for the satellite to fly 82000 miles, we can use the unit rate:

Time = Distance / Unit Rate

= 82000 miles / 8004.55 miles/hour

Calculating this value:

Time ≈ 10.246 hours

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The rate of change of the volume of a spherical ball is equal to the derivative of its volume with respect to time.  The rate of change of the volume of the ball when the radius is 5 cm is given by:dV/dt = 4π(5)²(-3) = -300π cubic cm/s

Given, the radius of a spherical ball is decreasing at a constant rate of 3 cm per second. Find, in cubic centimeters per second, the rate of change of the volume of the ball when the radius is 5 cm.To solve the problem, we need to find the rate of change of the volume of the spherical ball when the radius is 5 cm.The formula for the volume of a sphere is given by V = (4/3)πr³. So, the volume of the spherical ball is proportional to the cube of the radius of the ball.

This means that the rate of change of the volume of the ball is also proportional to the square of the radius. So, if the radius of the ball decreases at a constant rate, then the rate of change of the volume of the ball also decreases at a constant rate.To find the rate of change of the volume of the ball when the radius is 5 cm, we need to differentiate the volume with respect to time. Using the formula for the volume of a sphere, we getV = (4/3)πr³Differentiating both sides of the equation with respect to time, we get:dV/dt = 4πr² (dr/dt)where r is the radius of the sphere and dr/dt is the rate of change of the radius with respect to time. Since the radius of the ball is decreasing at a constant rate of 3 cm/s, we have dr/dt = -3 cm/s. Therefore,dV/dt = 4πr² (-3) = -12πr² cubic cm/sWhen the radius is 5 cm, we have r = 5 cm. Thus,dV/dt = -12π(5)² = -300π cubic cm/sTherefore, the rate of change of the volume of the ball when the radius is 5 cm is -300π cubic cm/s.

Therefore, option (B) -3001 is the correct answer.

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Answer:

469.9 ft^2

Step-by-step explanation:

The rate at which soil covers the garden is:

  125.3 ft^2  /  (1 bag)

If Stephanie has 3 3/4 bags of soil to start with, the area she can cover with this soil is (rate)(number):

   125.3 ft^2          15 bags

------------------- * ---------------- = 469.9 ft^2 can be covered with 3 3/4 bags

        1 bag                  4

The approximate breakeven points of the given functions are 15 and 47.

The breakeven point is the point where the total revenue equals to total expenses.

At this point, there is no profit or loss. That is the net profit is zero and he net loss is zero.

From the given graph, the dashed line represents the expense function while the solid line represents the revenue function.

Thus, the approximate breakeven points of the given functions are 15 and 47.

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Answer: 15 and 47

Step-by-step explanation:

Answer:

\(\frac{11}{15} =0.733333333333\)

Step-by-step explanation:

• Here The sample space S is the set of possible outcomes (ordered pairs of marbles) that we can draw at random (without replacement) from the bag.

Then

\(\text{cardS} =P^{2}_{10}=10\times 9=90\)

……………………………………………

Drawing two marbles where the marbles are different colors

means

drawing (1green ,1 yellow) or (1green ,1 red) or (1yellow ,1 red)

Remark: the order intervene

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

•• Let E be the event “Drawing two marbles where the marbles are different colors”.

CardE = 2×3×3 + 2×3×4 + 2×3×4 = 66  (2 is for the order)

Conclusion:

\(p\left( E\right) =\frac{66}{90} =\frac{11}{15} =0.733333333333\)

Method 2 :

\(p\left( E\right) =2\times \frac{3}{10} \times \frac{3}{9} +2\times \frac{3}{10} \times \frac{4}{9} +2\times \frac{3}{10} \times \frac{4}{9} =0.733333333333\)

Answer:

\(\sf \dfrac{11}{15}\)

Step-by-step explanation:

The bag of marbles contains:

⇒ Total marbles = 3 + 3 + 4 = 10

Probability Formula

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

First draw

\(\implies \sf P(green)=\dfrac{3}{10}\)

\(\implies \sf P(yellow)=\dfrac{3}{10}\)

\(\implies \sf P(red)=\dfrac{4}{10}\)

Second draw

As the first marble is not replaced there are now 9 marbles in the bag.

If the first marble was green, the probability of drawing a yellow is now 3/9 and the probability of drawing a red is now 4/9.

If the first marble was yellow, the probability of drawing a green is now 3/9 and the probability of drawing a red is now 4/9.

If the first marble was red, the probability of drawing a green is now 3/9 and the probability of drawing a yellow is now 3/9.

To find the individual probabilities of picking 2 different colors, multiply the probability of the first draw by the probability of the second draw:

\(\implies \sf P(green)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}\)

\(\implies \sf P(green)\:and\:P(yellow)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}\)

\(\implies \sf P(yellow)\:and\:P(green)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}\)

\(\implies \sf P(yellow)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}\)

\(\implies \sf P(red)\:and\:P(green)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}\)

\(\implies \sf P(red)\:and\:P(yellow)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}\)

To find the probability of drawing two marbles at random and the marbles being different colors, add the individual probabilities listed above:

\(\begin{aligned}\implies \sf P(2\:different\:color\:marbles) &=\sf \dfrac{12}{90}+\dfrac{9}{90}+\dfrac{9}{90}+\dfrac{12}{90}+\dfrac{12}{90}+\dfrac{12}{90}\\\\ & = \sf \dfrac{66}{90}\\\\ & =\sf \dfrac{11}{15}\end{aligned}\)

The equation y = x - 8 is expressed as a slope-intercept form.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

The slope-intercept form is y = mx+c, where the slope is m and the y-intercept is c.

The equation is given in the question, as follows:

x - y = 8

We have to write it in the slope-intercept form,

As per the question, we have

x - y = 8

Rearrange the variables in the above equation, and we get

y = x - 8

This equation is in the slope-intercept form.

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Answer:

[C] 29 Miles

Step-by-step explanation:

Given that the vessel sails 41 miles S 45° E.

We need to determine the how far south the vessel has sailed.

Let us use the Pythagorean theorem to find the distance of the vessel has sailed.

Thus, we have,

\(Cos 0= \frac{adj}{hyp}\)

Substituting \(0 = 45\)° , \(adj = x\), and \(hyp = 41\)

Hence, we get,

\(cos\) \(45 = \frac{x}{41}\)

Simplifying, we have,

\(0.71 = \frac{x}{41}\)

Multiplying both sides by 41, we have,

\(29.11 = x\)

Rounding off to the nearest integer, we have,

\(29 = x\)

Thus, the vessel has sailed 29 miles South.

Therefore, Option C is the correct answer.

[RevyBreeze]

Answer:

$110 is what she started with

Step-by-step explanation:

Answer:

Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero (which has one double square root).

Step-by-step explanation:

The measure of one interior angle of a regular 16-gon is 157.5 degrees. This is obtained by using the formula (n-2) * 180° / n, where "n" represents the number of sides of the polygon. In this case, (16-2) * 180° / 16 = 157.5°..

To find the measure of one interior angle of a regular 16-gon, we can use the formula for the measure of an interior angle of a regular polygon:

Interior Angle = (n-2) * 180° / n

where "n" is the polygon's number of sides.

For a regular 16-gon, substituting the value of "n" into the formula, we get:

Interior Angle = (16 - 2) * 180° / 16

= 14 * 180° / 16

= 2520° / 16

= 157.5°

Therefore, the measure of one interior angle of a regular 16-gon is 157.5 degrees.

To understand the calculation, let's break it down. Equal interior angles and sides define a regular polygon. The sum of the interior angles of any polygon is given by the formula (n-2) * 180°, where "n" is the number of sides. In a regular polygon, all the interior angles are congruent, so to find the measure of one angle, we divide the sum by the number of sides.

In the case of a regular 16-gon, we subtract 2 from 16 to get 14, multiply it by 180°, and then divide by 16 to find that each interior angle measures 157.5°.

Therefore, the measure of one interior angle of a regular 16-gon is 157.5 degrees.

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To find the probability that a participant selected at random found the products favorable, we can calculate the weighted average of the favorable responses from both the industry-sponsored and non-industry-funded studies.

For the industry-sponsored studies, 65% of participants found the products favorable, and for the non-industry-funded studies, 47% found the products favorable. Since there were 65 industry-sponsored studies and 35 non-industry-funded studies, the overall probability is:

(65/100) * 0.65 + (35/100) * 0.47 = 0.4225 + 0.1645 = 0.587 or 58.7%

If a randomly selected participant found the product favorable, we can use Bayes' theorem to calculate the probability that the study was sponsored by the food industry given this favorable response. The calculation is:

P(Industry-sponsored | Favorable) = (P(Favorable | Industry-sponsored) * P(Industry-sponsored)) / P(Favorable)

P(Favorable | Industry-sponsored) = 0.65

P(Industry-sponsored) = 65/100

P(Favorable) = 0.587

P(Industry-sponsored | Favorable) = (0.65 * (65/100)) / 0.587 ≈ 0.719 or 71.9%

Similarly, if a randomly selected participant found the product unfavorable, we can use Bayes' theorem to calculate the probability that the study had no industry funding given this unfavorable response. The calculation is:

P(No industry funding | Unfavorable) = (P(Unfavorable | No industry funding) * P(No industry funding)) / P(Unfavorable)

P(Unfavorable | No industry funding) = 0.36

P(No industry funding) = 35/100

P(Unfavorable) = 1 - P(Favorable) = 1 - 0.587 = 0.413

P(No industry funding | Unfavorable) = (0.36 * (35/100)) / 0.413 ≈ 0.305 or 30.5%

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Answer:

1)

\(L=18 \frac{1}{2} in\)

\( W= 9 \frac{1}{4} in\)

2)

\(T_{1}=14 balls\)

\(T_{2}=7 balls\)

\(T_{3}=3 balls\)

Step-by-step explanation:

In order to solve this problem, we need to build the equations we need. Since there are two values we want to figure out (length and width) we will then need two equations to solve simultaneously.

First, the problem tells us that the perimeter is 55 1/2 in, which can be rewritten as an improper fraction:

\(55 \frac{1}{2}= \frac{55*2+1}{2}= \frac{111}{2}\)

Next, we also know the perimeter of a rectangle is found by using the following formula:

P=2L+2W

where L is the length of the rectangle and W is its width.

So our first equation will look like this:

\(2L+2W=\frac{111}{2}\)

Next, the problem tells us that the width of the rectangle is twice its width, so our second equation will look like this:

L=2W

which can be substituted into our first equation:

\(2L+L=\frac{111}{2}\)

Now, we can solve this for L, so we get:

\(3L=\frac{111}{2}\)

\(L=\frac{111}{2*3}\)

\(L=\frac{111}{6}=18 \frac{3}{6}=18 \frac{1}{2}\)

so we can now use this information to find its width:

L=2W

\( \frac{111}{6}=2W\)

so

\(W=\frac{111}{6*2}\)

\(W=\frac{111}{12}=9\frac{3}{12}=9\frac{1}{4}\)

2)

When solving this problem it is a good idea to split it into little chunks of information. The first sentence says:

"... "teacher 1" shoots twice as many airballs as "teacher 2"."

This can be translated as an equation like this:

\(T_{1}=2T_{2}\)

The next sentence says:

""teacher 3" shoots 4 airballs less than "teacher 2"."

This can be written as an equation like this:

\(T_{3}=T_{2}-4\)

and finally, the problem states: "... they shot 24 airballs together,..."

This can be written as an equation like this:

\(T_{1}+T_{2}+T_{3}=24\)

so now we can do substitutions. We can take the first and second equations and write them into the third equation so we get:

\(2T_{2}+T_{2}+T_{2}-4=24\)

so now we can solve this equation for \(T_{2}\), so we get:

\(2T_{2}+T_{2}+T_{2}=24+4\)

\(4T_{2}=28\)

\(T_{2}=\frac{28}{4}\)

\(T_{2}=7\)

and once we got this answer, we can find the remaining two answers:

\(T_{1}=2T_{2}\)

\(T_{1}=2(7)\)

\(T_{1}=14\)

and

\(T_{3}=T_{2}-4\)

so we get:

\(T_{3}=7-4\)

\(T_{3}=3\)

Answer:

1)

Step-by-step explanation:

1)

The 95% confidence interval for the mean is (1.6048, 1.6352).Hence, option (d) is the correct answer.

As given, a machine that is programmed to package 1.60 pounds of cereal is being tested for its accuracy in a sample of 40 cereal boxes, the sample mean filling weight is calculated as 1.62 pounds. The population standard deviation is known to be 0.06 pounds. We are required to find the 95% confidence interval for the mean. Here are the steps to solve this problem:

The formula to find the confidence interval is as follows;

Lower limit = x - zα/2 (σ/√n)

Upper limit = x + zα/2 (σ/√n)

Where,

x= sample mean

zα/2 = z-value of the level of significance

σ = population standard deviation

n = sample size

We are given;

x = 1.62 pounds

σ = 0.06 pounds

n = 40

We need to find the z-value of the level of significance, which can be found using the z-table or by using the calculator.Using the z-table, we get the z-value at 95% confidence interval as zα/2 = 1.96

Substituting the values, we get

Lower limit = 1.62 - 1.96(0.06/√40)

Upper limit = 1.62 + 1.96(0.06/√40)

Lower limit = 1.6048, Upper limit = 1.6352

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Answer:

Step-by-step explanation:

To calculate the price at Restaurant A, we need to find the cost of one meal at full price and the cost of the other meal at half price. One meal at full price would be £19.50, and the other meal at half price would be £19.50/2 = £9.75. So the total cost at Restaurant A would be:

£19.50 + £9.75 = £29.25

To calculate the price at Restaurant B, we need to find the cost of two meals with a 15% discount. The cost of two meals at full price would be £18 x 2 = £36. Then we can calculate the discount:

15% of £36 = £5.40

So the total cost at Restaurant B would be:

£36 - £5.40 = £30.60

The difference between the prices at the two restaurants is:

£29.25 - £30.60 = -£1.35

So Ruby would pay £1.35 less if she bought the meals at Restaurant B.

Answer: Hence the correct answer is difference between price=£1.35

Step-by-step explanation:

Ruby wants to buy two meals at Restaurant A ,price of meal=£19.5 each and get another meal at half price, Price of two meal= 19.5+9.75=£29.25.

At Restaurarant B, Price of meal=£18 each and get 15% Off the cost of both.

The price of two meal= 36-36 x 15/100= £30.6.

Differece between the price =30.6-29.25=£1.35,

Hence the correct answer is difference between price=£1.35

I hoped this helped you!<3!

If a sample size is one-fourth the original size, the margin of error will be affected. Specifically, the margin of error will be affected inversely proportional to the square root of the sample size.

Halving the sample size (from the original) will cause the margin of error to increase by a factor of square root of 2, approximately 1.41.

Doubling the sample size (from the original) will cause the margin of error to decrease by a factor of square root of 2, approximately 0.71.

Quadrupling the sample size (from the original) will cause the margin of error to decrease by a factor of square root of 4, approximately 0.5.

Therefore, if the sample size is reduced to one-fourth the original size, the margin of error will be doubled, because the square root of 4 is 2. Conversely, if the sample size is increased fourfold, the margin of error will be halved, because the square root of 1/4 is 1/2.

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Answer:

y = 5x - 13

Step-by-step explanation:

y=5x-20+7

y = 5x - 13

The length and width of the rectangle are 12.5 cm and 22 cm, respectively.

Let L be the length of the rectangle, and W be the width of the rectangle, then we have that:

L x W = 297 sq cm 1.

If the length is increased by 3 cm and width decreased by 1 cm, then we have that:

(L + 3) x (W - 1) = 297 + 3 sq cm -......(2).

Expand equation 2, we have:

LW + 2L - W = 300 sq cm-.......(3)

We have two equations from 1 and 3:

LW = 297 sq cm         LW + 2L - W = 300 sq cm 3.

Substitute equation 1 into equation 3.

297 + 2L - W = 300 sq cm

2L - W = 3 sq cm  

2L - W = 3 sq cm

2L = W + 3 sq cm

L = (W + 3)/2 sq cm

W x (W + 3)/2 = 297 sq cm

W² + 3W - 594 = 0 (W + 27) (W - 22) = 0

Therefore, the width of the rectangle is either 22 cm or -27 cm. Since the width cannot be negative, we discard the value of -27 cm. Therefore, the width of the rectangle is 22 cm. Finally, let's calculate the length of the rectangle:

L = (W + 3)/2 sq cm L = (22 + 3)/2 sq cm L = 25/2 sq cm L = 12.5 sq cm

Therefore, the length and width of the rectangle are 12.5 cm and 22 cm, respectively.

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