Question
In △ABC, AB=7.8 ft, BC=10.7 ft, and m∠B=27°.



What is the area of △ABC?



Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.


ft²

Given statement "f the null hypothesis is correct, the probability of getting a sample mean greater than $189,500 is .0668" is true. Because, It's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.

The null hypothesis is a general statement that there is no significant effect or difference between the considered groups or variables.

In this case, the null hypothesis would be that the true mean valuation of homes is equal to or less than $189,500.
The probability of 0.0668, mentioned in the question, represents the likelihood of getting a sample mean greater than $189,500 if the null hypothesis is true.

In other words, it's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.

This probability (0.0668) is also known as the p-value.

The p-value helps to determine the significance of the results.

If the p-value is less than a predetermined significance level (usually 0.05), the null hypothesis is rejected in favor of the alternative hypothesis.
In this case, the p-value of 0.0668 is higher than the common significance level of 0.05.

We cannot reject the null hypothesis, meaning the probability of getting a sample mean greater than $189,500 is indeed 0.0668 if the null hypothesis is correct

Hence, the statement is true.
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The arch has a width of 6 - (-6) = 12 feet at ground level.

To find the width of the arch at ground level, we need to find the x-values where y = 0, since the width of the arch is the distance between these two x-values.

So, we set y = 0 and solve for x:

0 = − 1/3(x + 6)(x − 6)

Either x + 6 = 0 or x - 6 = 0

If x + 6 = 0, then x = -6.

If x - 6 = 0, then x = 6.

To find the width of the arch at ground level, we need to find the x-values where y=0.

y = − 1/3(x + 6)(x − 6)

Setting y=0:

0 = − 1/3(x + 6)(x − 6)

We can solve for x using the zero product property:

0 = x + 6 or 0 = x - 6

x = -6 or x = 6

The arch intersects the ground at x = -6 and x = 6.

Therefore, the arch has a width of 6 - (-6) = 12 feet at ground level.

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Answer:

The first step is to convert the annual interest rate to a monthly rate. We divide 14% by 12 months to get a monthly interest rate of 1.17%.

Next, we need to calculate the total number of months for the loan. Since the loan is for 2 years, or 24 months, we will make 24 payments.

To calculate the interest paid, we can use the formula:

I = P[(1 + r)^n - 1]

where:

I = interest paid

P = principal (amount borrowed) = $1200

r = monthly interest rate = 0.0117

n = total number of compounding periods = 24

Plugging in these values, we get:

I = 1200[(1 + 0.0117)^24 - 1]

I = $357.72

Therefore, the interest paid is $358.

Hope This Helps!

Therefore, the expression that can be used to find the probability that a boy will be chosen, and the arrow will land on "Free assignment" is 2/13.

Which expression can be used to find the probability that this week a boy will be?

chosen and the arrow will land on "Free assignment"?

The probability of a boy being chosen is the ratio of the number of boys to the total number of students, which is:

[tex]P(boy) = 12 / (12 + 14) = 12/26 = 6/13[/tex]

The probability of the arrow landing on "Free assignment" is 1/3, since there are 3 equal sectors on the spinner.

To find the probability that both events occur (i.e., a boy is chosen and the arrow lands on "Free assignment"), we multiply the probabilities:

[tex]P(boy and "Free assignment") = P(boy) x P("Free assignment")[/tex]

[tex]P(boy and "Free assignment") = (6/13) x (1/3) = 2/13[/tex]

Therefore, the expression that can be used to find the probability that a boy will be chosen, and the arrow will land on "Free assignment" is 2/13.

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Answer:

C

Step-by-step explanation:

About 16 days because 0.58 x 28 is 16.24

The estimated coefficient for x1 in the multiple linear regression equation is 2.3529.

To estimate the coefficient for x1 in the multiple linear regression equation, we can use the following formula:

where n is the number of data points, x and y are the respective variables, and Σ denotes the sum of the values.

Using the provided data, we can calculate the coefficient for x1 as follows:

= 2.3529 (rounded to 4 decimal places)

In this problem, we are given data on the amount of wear of a type of bearing, as well as the oil viscosity and load that the bearing was subject to. We want to estimate the coefficient for oil viscosity (x1) in the multiple linear regression equation for this data.

To do this, we can use the formula for calculating the coefficient for x1 in the multiple linear regression equation. This formula takes into account the number of data points, the sums of the values for x1 and y, and the sum of the products of x1 and y, as well as the sum of the squares of x1.

Using the provided data and this formula, we find that the estimated coefficient for x1 is 2.3529. This means that, for this data, the amount of wear of the bearing is estimated to increase by 2.3529 units for every one unit increase in oil viscosity, while holding the load constant.

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The length a of the right angle triangle is 13.74 cm.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the opposite side of the right triangle a cm. The side a cm can be found using Pythagoras's theorem or trigonometric ratios.

Let's use Pythagoras's theorem,

a² + b² = c²

where

15² - 6² = a²

225 - 36 = a²

1809 = a²

square root both sides of the equation

a = √189

a = 13.7477270849

a = 13.74 cm

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The value of x in given figure is a whole number that is x = 6.6

When two tangent segment are drawn from an outside point to a circle, the sum of the dimensions of the first tangent segment and its exterior tangent segment equals the sum of the dimensions of the other secant segments and its exterior secant segment.

Given the image and the labelled measurement of two secant segments outside the predetermined circle that have a similar endpoint. We are required to determine what x's value is.

With these measurements, we can use the secant-secant theorem to solve for the value of x as we refer to and analyse the figure. We will therefore have this theorem applied.

(5) [(5) + ( x+4)] = (6) [6 + 7]

(5) [5+x+4] = (6) [13}

5 [9 + x] = 78

45 + 5x = 78

5x = 33

x = 6.6

Therefore the value of x is 6.6

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Answer:

x = y = 2√7 = 5.292

Step-by-step explanation:

We have a right isosceles triangle, so the length of the hypotenuse is √2 times the length of each leg. Since the hypotenuse is 2√14, each leg measures 2√7.

The length of the sides of the right isosceles triangle is 5.292units.

A right isosceles triangle is a special type of triangle that has two equal-length legs and a right angle between them. Because it has two equal legs, it is also an isosceles triangle. The name "right isosceles" comes from the fact that it has a right angle and two equal legs.

In the given question,

In a right isosceles triangle, the two legs are congruent, and the length of the hypotenuse can be found using the Pythagorean theorem:

a² + b² = c²

Since this is an isosceles triangle, we know that a = b, so we can simplify the equation to:

2a² = c²

Taking the square root of both sides, we get:

a√2 = c

In this case, we are given that the hypotenuse has a length of 2√14, so we can set c equal to that value and solve for a:

a√2 = 2√14

a = (2√14)/√2

Simplifying the expression by canceling the square root of 2 in the denominator, we get:

a = 2√7

Therefore, each leg of the isosceles triangle has a length of 2√7, which agrees with your answer.

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The answer is 6√5

In 3√5 and 3√5, √5 is multiplied with 3 in both terms,

∴ 3 is the common factor

∴ 3√5+3√5= 3(√5+√5)

                   = 3×2√5

                   = 6√5

Hence the answer is 6√5

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Answer:

True

Step-by-step explanation:

If you took a true if-then statement, inserted not in each clause and reversed the clauses you will have created the contrapositive. The contrapositive of an if-then statement has the same true value as the original statement.

Statement:

If p, then q.

Contrapositive:

If not q, then not p

If the statement is true, then the contrapositive is also true.

Best investment amounts are $2,000 in high-risk account, $1,000 in bank certificates of deposit, and $7,000 in municipal bonds and remaining $4,000 placed in municipal bonds to optimize return while lowering risk.

We must adhere to two criteria in order to find the best investment amounts: reducing risk and satisfying tax obligations.

Let's think about the high-risk account first. We will only put $2,000 in this account because that is the most we are ready to risk because we want to keep the risk to a minimum.

Let's go on to the tax regulations. We must invest at least $3,000 in municipal bonds to reach the three times minimum investment requirement in municipal bonds compared to bank CDs. We will therefore put $1,000 into bank CDs and $3,000 into municipal bonds.

We currently have $2,000 set aside for the high-risk account, $1,000 for bank CDs, and $3,000 set aside for municipal bonds. We are now left with $4,000 to invest.

This $4,000 can be invested in a way that strikes a compromise between the need to reduce risk and the desire for great returns. We have the choice of investing the final $4,000 in either municipal bonds or CDs from a nearby bank, depending on our investment alternatives.

Our total investment would be $5,000 in bank CDs, $3,000 in municipal bonds, and $2,000 in the high-risk account if we choose to invest the additional $4,000 in the local bank CDs. The expected return from this is:

($5,000 x 8%) + ($3,000 x 7%) + ($2,000 x 12%) = $400 + $210 + $240 = $850.

If we choose to invest the $4,000 in municipal bonds, our overall investment will consist of $2,000 in the high-risk account, $1,000 in bank CDs, and $7,000 in municipal bonds. The expected return from this is:

($1,000 x 8%) + ($7,000 x 7%) + ($2,000 x 12%) = $80 + $490 + $240 = $810.

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The required probability of the candies in the bag having width between 1200 and 1225 is given by 16.67%.

The range of the number of skittles in the bag is 1150 to 1300 candies and is uniformly distributed.

This implies that the probability density function is a horizontal line over this interval.

The width of the interval we are interested in is 1225 - 1200 = 25 candies.

The total width of the interval is 1300 - 1150 = 150 candies.

The probability that the bag contains between 1200 and 1225 candies is equals to,

= ( Width of the required interval ) / (Total width of the interval )

= 25 / 150

= 0.1667

This means that the probability is 16.67% accurate to two decimal places.

Therefore, the probability of the bag contains candies between 1200 and 1225 is equal to 16.67%.

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Answer:

The appropriate domain for the function is [0, ∞).

Step-by-step explanation:

Given function: f(x) = 120 (0.86)x

To find the function values, we can substitute the given value of x into the function:

f(0) = 120 (0.86)^0 = 120 (1) = 120

Interpretation: When the medication is first taken, there are 120 milligrams of medicine in the person's bloodstream.

f(2) = 120 (0.86)^2 ≈ 84.24

Interpretation: After 2 hours, there are approximately 84.24 milligrams of medicine remaining in the person's bloodstream.

f(6) = 120 (0.86)^6 ≈ 34.17

Interpretation: After 6 hours, there are approximately 34.17 milligrams of medicine remaining in the person's bloodstream.

The domain of the function is all non-negative real numbers, since the amount of medicine in the bloodstream can't be negative and time is measured in non-negative hours. So the appropriate domain for the function is [0, ∞).

Answer:

They are 50 and 20 years old.

Step-by-step explanation:

5 years ago jack was 45 and his son was 15, which makes jack 3 times older than his son and has a 30 year difference.

The quadratic function graphed is defined as follows:

C) y = x² - x - 2.

The factored format of a quadratic function is given as follows:

y = a(x - x*)(x - x**)

In which the parameters are given as follows:

From the graph, we have that it crosses the x-axis at x = -1 and x = 2, hence the x-intercepts are given as follows:

x* = -1, x** = 2.

Hence:

y = a(x + 1)(x - 2)

y = a(x² - x - 2).

When x = 0, y = -2, hence the leading coefficient a is given as follows:

-2a = -2

a = 1.

Thus the equation is:

y = x² - x - 2.

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Now, we can construct the confidence interval: [tex]0.4 ± 1.96 * 0.0157 ≈ 0.4 ± 0.0308. [/tex]The resulting interval is 0.3692 to 0.4308, which is closest to option e. 0.374 to 0.426

5. To calculate the sample proportion, divide the number of consumers who shop online at least once a week (121) by the total number of consumers surveyed (484). So, the sample proportion is[tex] 121/484 = 0.25.[/tex] The correct answer is c. 0.25.

6. A sample proportion is a statistic because it is a measure derived from a sample of the population. The correct answer is a. statistic.

7. To construct a 95% confidence interval for the proportion of OSU undergraduates with full-time jobs, we first find the sample proportion:[tex] 368/920 = 0.4[/tex].

Next, we find the standard error (SE) for the sample proportion: SE = sqrt(0.4 * (1 - 0.4) / 920) ≈ 0.0157. For a 95% confidence interval, the critical value (z-score) is approximately 1.96.

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The probability that exactly one of three randomly selected high school students graduate, given an 85% graduation rate, is 0.057. This calculation was based on the combination formula and the binomial probability distribution.

This problem involves calculating the probability of a specific outcome (exactly one of the three students graduating) in a binomial distribution. We know that the probability of any one student graduating is 0.85, so the probability of one student not graduating is 0.15. Using the binomial probability formula, we can calculate the probability of exactly one student graduating out of three as:

P(X = 1) = (3 choose 1) * (0.85)^1 * (0.15)^2 = 3 * 0.85 * 0.0225 = 0.057

Therefore, the answer is 0.057, or approximately 5.7%. This means that if we randomly select three high school students from different schools, there is a 5.7% chance that exactly one of them will graduate.

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Answer:

The area of rectangle is Length × Breadth

Step-by-step explanation:

You have already learnt that perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around a closed figure while area is the part of plane or reason occupied by the closed figure.

[tex] \sf \: Squares \: and \: Rectangles[/tex]

Ananya and samira made pictures. Ananya made her picture on a rectangular sheet of length 60 cm and breadth 20 cm while samira made hers on a rectangular seat of length 40 cm and breadth 35 cm. Both these pictures have to be separately framed and laminated.

Who has to pay more for farming is the cost of farming is $3.00 per cm?

If the cost of lamination is $2.00 per cm², who has to pay more for lamination?

For finding the cost of farming, we need to find perimeter and then multiply it by the rate for farming. For finding the cost of lamination we need to find area and then multiply it by the rate of lamination.

Find the area of the rectangle whose Length is 4 cm and breadth/width is 6 cm .

Answer:

The area of the rectangle is 24 cm²

Step-by-step explanation:

Length of rectangle = 4 cm

Breadth of rectangle = 6 cm

[tex] \bf \: Formula \: used[/tex]

[tex] \sf \: Area_ { \{Rectangle \}} = Length × Breadth[/tex]

Now put values

[tex] \sf \: Length = 4 cm [/tex]

[tex] \sf \: Breadth = 6 cm[/tex]

[tex] \sf \: Length × Breadth = 4 × 6 \: cm [/tex]

[tex] \sf \implies 24 \: cm \ {}^{2} [/tex]

Always remember if we find area :-

After units like centimetres,metres we always put (²) on these units.

Like :- 26 cm², 56 m ²

In words = Twenty six centimetre square, Fifty six centimetre square

The area of rectangle is 24 cm²

Perimeter

Area

♦ Area of Rectangle

[tex] \underline{ \rule{140pt}{4pt}}[/tex]

Area - Region occupied by figure is called area.

[tex] \large \bf{ \mathfrak{{More \: Formulas \: \red{( Area)}}}}[/tex]

[tex] \large \sf \leadsto \: triangle = \frac{1}{2} \times bh[/tex]

[tex]\large \sf \leadsto \: \: Rectangle \: = \: lb[/tex]

[tex]\large \sf \leadsto \: \: Square \: = {s}^{2} [/tex]

[tex]\large \sf \leadsto \: \: Parallelogram \: = \: bh[/tex]

[tex]\large \sf \leadsto \: \: Rhombus \: = \: \frac{1}{2} \times \: d1 \times d2[/tex]

[tex]\large \sf \leadsto \: \: Trapezium \: = \frac{1}{2} \times (x + y) \times h[/tex]

[tex]\large \sf \leadsto \: \: Quadrilateral \: = \: \frac{1}{2} \times d(h1 + h2)[/tex]

[tex]\large \sf \leadsto \: Circle \: = {\pi \: r}^{2} [/tex]

[tex]\large \sf \leadsto \: \: Equilateral \triangle \: = \frac{ \sqrt{3} }{4} \times {s}^{2} [/tex]

D) Between 0 and 100.


The best system to measure the likelihood of an event occurring would be option D between 0 and 100. This system allows for a greater level of granularity and precision in the measurement of probability, as it provides a wider range of possible values to represent different levels of likelihood. The other options may not provide enough resolution to accurately capture and distinguish between different probabilities.

Answer:

The amount of discount is 35% of � x, which is (35/100)� x = 0.35� x. So, the discounted price is � x minus the discount, which is � x - 0.35� x = 0.65� x.

Then, the tax is added to the discounted price, which is 8% of the discounted price, or (8/100)(0.65� x) = 0.052� x.

Therefore, the expression for the total amount that Violet paid at the register is:

0.65� x + 0.052� x = 0.702� x

Step-by-step explanation:

Look at point A ====>  A'

  x goes from 1 to 4           so X:  x + 3

  y goes from 7 to 3          so Y:   y - 4

If a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches, then (60 - 1.5 π) square inches paper is wasted.

The area of each circle is given by the formula [tex]A = \pi r^2[/tex], where r is the radius of the circle. Since all 15 circles are congruent, they all have the same radius.

Let's first find the radius of each circle. Since the circles are cut from a 6 by 10 inch sheet of paper, we know that the diameter of each circle cannot be greater than 6 inches or 10 inches. Let's take the smaller dimension (6 inches) and divide it by 15 to find the maximum possible diameter of each circle:

6 inches ÷ 15 = 0.4 inches

Therefore, the maximum possible radius of each circle is 0.2 inches.

Now we can calculate the total area of all 15 circles:

Total area of circles = [tex]15 * \pi * (0.2)^2[/tex]

[tex]= 1.5 \pi[/tex] square inches

The area of the original sheet of paper is 6 inches * 10 inches = 60 square inches. Therefore, the amount of paper wasted is:

Amount of paper wasted = Area of sheet - Total area of circles

= 60 square inches - 1.5 π square inches

= 60 square inches - 4.71 square inches (using π ≈ 3.14)

= 55.29 square inches (rounded to two decimal places)

Therefore, the answer is (60 - 1.5π) square inches.

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Answer:

336in^2

Step-by-step explanation:

6 x 4 x 14

"The buetiful thing about learning is that no one can take it away from you" :)

Answer: 336

Step-by-step explanation: I just multiplied them all

Answer:

C. ∠ZXY and D. YX

Step-by-step explanation:

C. ∠ZXY

because the middle letter is always the angle or the turning point of an angle and also it is in order based on the diagram. The angle won't change even if you look at it on a different point of view or if the diagram was flipped.

D. YX

because the line YX is a true statement because XY or YX is on the same line that goes on and on. You can tell because there's arrows on the end of the line.

If we know that f(-4) = 0, we can say that:

x + 4 is a factor of the function f(x).

This is because when we substitute x = -4 into the function, we get:

f(-4) = (-4)^4 + 2(-4)^3 - 9(-4)^2 - 2(-4) + 6 = 0

This means that (x + 4) is one of the factors of the function.

Now, we can use polynomial division or synthetic division to find the other factors. If we divide the function f(x) by (x + 4), we obtain:

           x^3 - 2x^2 - 17x + 3

We can use the Factor theorem on this cubic function f(x) = x^3 - 2x^2 - 17x + 3.

If we try to substitute a = 1 we find that f(1) = -15 which is not zero. If we try to substitute a = -1, we find that f(-1) = 23 which is not zero.

Now we can solve as follows:

Let x = t - 2/3. After substitution we get a cubic equation.

t^3 -25/3 t - 85/27 = 0

We can find one root of this cubic by rational root theorem which is t = 5 or t = -17/3.

Now, we can use synthetic division again to divide f(x) by the binomial (x - 5). This gives us:

        (x - 5)(x^2 + 3x - 1)

Therefore, the complete factorization of f(x) is:

f(x) = (x + 4)(x - 5)(x^2 + 3x - 1)

Therefore, the zeros of the function are:

x = -4, 5, (-3 ± √13)/2

Thus, these are the zeros of the polynomial.

Answer:

C)  56

Step-by-step explanation:

2(AE) = BD

AC = BD

2(2x + 6) = 6x - 10

4x + 12 = 6x - 10

-2x = -22

x = -22/-2 = 11

AC = 6(11) - 10 = 56

Answer: y= 2x-5

Step-by-step explanation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To get the equation into slope-intercept form, you need to isolate the y-term on one side of the equation and simplify the rest of the equation. So, let's start with 6x - 3y - 15:

6x - 3y - 15 = 0 (I'm assuming this equation represents a line)

Now, let's isolate the y-term by subtracting 6x from both sides:

-3y = -6x + 15

Finally, let's solve for y by dividing both sides by -3:

y = 2x - 5