In △ABC , point D is between points A and B, and point E is between points B and C. Point Y is the incenter of the triangle, YD¯¯¯¯¯⊥AB¯¯¯¯¯ , and YE¯¯¯¯¯⊥BC¯¯¯¯¯ . DB=45 and YB=51 . What is YE ? Enter your answer in the box.

Answer:

a) 24 square feet

b) $12

Step-by-step explanation:

You want to make a retangular prism out of cardboard. The base is 3 feet by 4 feet. The height is 2 feet. You have $5.00 and cardboard costs .10 per square foot.

a) What is the surface area of the rectangular prism?

Length × Width × Height

3 feet × 4 feet × 2 feet

= 24 square feet

b).How much will it cost to make the rectangular prism out of cardboard?

1 ft² = $0.5

24 ft² = x

Cross Multiply

x = 24ft² × $0.5/1 ft²

x = $12

It would cost $12 to make the rectangular prism out of the cardboard. You do not have sufficient money to make it

Answer:

Because <CBD is an inscribed angle and <CAD is a central angle with the same intercepted arc, m<CBD = 55°, or half of the measure of <CAD.

Step-by-step explanation:

The Inscribed Angle Theorem proves that an inscribed angle is half the measure of a central angle, if both the inscribed angle and the central angle intercepts the same arc.

Also, according to the inscribed angle theorem, an inscribed angle is ½ of the measure of the arc it intercepts.

Therefore, m<CBD is half of m<CAD, or half of the measure of the arc CD that they both intercept together.

Thus, m<CBD = 55°, which is ½ of m<arc CD.

m<arc CD = 110° = m<CAD.

m<CBD = ½ of m<CAD = 55°.

The statement that best describes the relationship between <CBD and <CAD is "Because <CBD is an inscribed angle and <CAD is a central angle with the same intercepted arc, m<CBD = 55°, or half of the measure of <CAD."

Using the Bisector Theorem, the length of DE is 4y + 13 if we bisect (Line Over DE) at point R, DR = 2y + 9, and RE = 3y – 1.

Since l bisects DE at point R, we can use the segment bisector theorem, which states that the ratio of the lengths of the two segments is equal to the ratio of the lengths of the two other segments:

DR/RE = DE/ER

Substituting DR = 2y + 9 and RE = 3y - 1, we get:

(2y + 9)/(3y - 1) = DE/ER

Since R is the midpoint of DE, we have ER = DR = 2y + 9. Substituting this into the equation above, we get:

(2y + 9)/(3y - 1) = DE/(2y + 9)

Cross-multiplying, we get:

DE = (2y + 9)²/(3y - 1)

Expanding the numerator, we get:

DE = (4y² + 36y + 81)/(3y - 1)

Simplifying the expression, we get:

DE = 4y + 13

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Answer:

1 and 5

Step-by-step explanation:

first category and fifth one up

If the engineer wants to be 95% confident that the error in estimating the mean life is less than 15 hours, with confidence interval of +/- 5%, and standard deviation of 0.5, The sample size should be 385 samples.

Accordingly, the Necessary Sample Size is calculated as follows:

Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²

For example, given a 95% confidence level, 0.5 standard deviation, and a margin of error (confidence interval) of +/- 5%. Necessary Sample Size =

((1.96)² x 0.5(0.5)) / (0.05)²

(3.8416 x 0.25) / .0025

0.9604 / 0.0025

384.16

So in order to get 95% confidence level, with confidence interval of +/- 5%, and standard deviation of 0.5, The sample size should be 385 samples.

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Answer:

Hello! answer: 80

Step-by-step explanation:

When doing the Pythagorean theorem you do...

a^2+b^2=c^2 which is just A multiplied byitself + B multiplied byitself that will equal the number that C multiplied by itself would equal then you just figure out what multiplied byitself equals that number and thats the answer so...

64 × 64 = 4096 48 × 48 = 2304

4096 + 2304 = 6400 80 × 80 = 6400 therefore c = 80 hope that helps!

Answer:

c = 80 inches

Step-by-step explanation:

The length of the hypotenuse can be found by using the following formula in which "c" is the length of the hypotenuse, and "a" and "b" are the legs of the right angles triangle.

\(c = \sqrt{a^{2} + b^{2} }\)

\(c= \sqrt{64^{2} + 48^{2} } \\c= \sqrt{4096 + 2304} \\c = \sqrt{6400} \\c = 80 inches\)

Answer:

12.5% profit

Step-by-step explanation:

By combinations, there are 210 10 bit strings which contains exactly 4 ones.

To find out how many 10-bit strings there are that contain exactly 4 ones, we can use the binomial coefficient formula.

The binomial coefficient formula is given by `C(n, k) = n! / (k! * (n-k)!)`,

where,

n is the total number of items, and k is the number of items

we want to choose from n. In this case, we want to choose 4 ones from 10 bits, so n = 10 and k = 4. Therefore, the number of 10-bit strings that contain exactly 4 ones is:

`C(10, 4) = 10! / (4! * (10-4)!) = 210`.

Hence, there are 210 10-bit strings that contain exactly 4 ones.

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The logarithm of (789.5) elevated to the power 1/8 is given as follows:

log(789.5)^(1/8) = 0.36216901679.

The logarithm in this problem is defined as follows:

log(789.5)^(1/8).

It has a power, hence the power can be moved to the front of the logarithm expression applying the power rule, as follows:

log(789.5)^(1/8) = 1/8 x log(789.5).

Then a calculator is used to obtain the logarithm of 789.5, which is the number that is elevated to the base 10 to obtain 789.5, hence:

log(789.5) = 2.89735213434.

Thus the numeric value of the logarithmic expression in this problem is calculated as follows:

log(789.5)^(1/8) = 1/8 x log(789.5) = 1/8 x 2.89735213434 = 0.36216901679.

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The division of 16 - 8x - 7x² + 2x³ by x - 4 will have a quotient of 2x² + x - 4 and a remainder of 0 using synthetic division.

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall rearrange 16 - 8x - 7x² + 2x³ to become 2x³ - 7x² - 8x + 16 and then divide by x - 4 as follows;

2x³ divided by x equals 2x²

x - 4 multiplied by 2x² equals 2x³ - 8x²

subtract 2x³ - 8x² from 2x³ - 7x² - 8x + 16 will give x² - 8x

x² divided by x equals x

x - 4 multiplied by x equals x² - 4x

subtract x² - 4x from x² - 8x will give us -4x + 16

-4x divided by x equals -4

x - 4 multiplied by -4 equals -4x + 16

subtract -4x + 16 from -4x + 16 will result to a remainder of 0

Therefore by synthetic division, 16 - 8x - 7x² + 2x³ divided by x - 4 is equal to the quotient of 2x² + x - 4 with a remainder of 0.

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91% confidence interval of true proportion of workers who belong to a union is between 22.71% and 29.29%.

The formula for a proportion's confidence interval is: p z* (p(1-p) / n) where: P is the sample proportion (p = sample size / number of unionised employees).

z is the z-score that corresponds to the desired level of confidence; for example, a 91% confidence level corresponds to a z-score of roughly 1.645.

The sample size is n.

Therefore, the sample proportion for the given case is p = 26% = 0.26, and the sample size is n = 434.

We obtain the following numbers by substituting them in the formula: 0.26 1.645 * (0.26 * 0.74 / 434)

figuring out the standard error

√(0.26 * 0.74 / 434) = 0.0199

Therefore, 0.26 1.645 * 0.0199 = 0.26 0.0329 represents the 91% confidence interval.

Therefore, 0.26 - 0.0329 = 0.2271 are the lower and upper boundaries of the 91% confidence interval.

0.26 + 0.0329 = 0.2929

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Answer:

Hey Desmariesin7587, the median of the data set that you gave is  15.9

Step-by-step explanation:

Since the amount of values in the data set was not even, I could not find a middle number. Instead, I added up all of the values and divided the total sum by the amount of values that there were; in this case, 10.

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

Have a great day,

Nish

Answer:

Over 2 up 4

Step-by-step explanation: I just learned this so I am not a pro but, 5 would be X for A, So to the right, down 2, 3 right for B, down 6

Yes, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.

A vector is a mathematical object that represents a quantity with both magnitude and direction. In the case of ℝ5, this set includes all possible lists of five real numbers, which can be thought of as five-dimensional vectors. Each number in the list represents a component or coordinate of the vector, indicating how far it extends in each of the five dimensions.

Therefore, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.


In mathematics, a vector is an element of a vector space, which is a set of objects that can be added together and multiplied by scalars (real numbers). The set ℝ⁵ is a vector space consisting of all 5-tuples (lists) of real numbers, written as (a₁, a₂, a₃, a₄, a₅), where each element aᵢ is a real number. Any list of five real numbers forms a vector in ℝ⁵ because it satisfies the required conditions to be an element of the vector space.

A list of five real numbers is indeed a vector in the set of real numbers ℝ⁵, as it meets the necessary criteria to be a part of the vector space.

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Answer:

In both cases, we have similar figures.

This means that the shape of the figures is the same, but the size is different:

PQST is similar to STNR and to NRPQ

VUYZ is similar to YZWX and to VUWX

this means that, for example, in problem 18, the ratio between ST and NR must be the same as the ratio between PQ and ST. This happens because the measure increases by the same scale factor.

With this in mind, we can solve the problem:

18)

ST = 7.5

NR = 5.5

Then the quotient ST/NR is:

ST/NR = 7.5/5.5

And, as we said above:

PQ/ST = ST/NR

PQ/7.5 = 7.5/5.5

PQ = (7.5/5.5)*7.5 = 10.23

19) Here we should have:

YZ/VU = WX/YZ

Then:

22.9/35 = WX/22.9

(22.9/35)*22.9 = WX = 14.98

Answer:

\(\frac{7}{8}\)

Step-by-step explanation:

\(\frac{1}{4}\ + \frac{10}{16}\\)

\(= \frac{4}{16}\ + \frac{10}{16}\\\)

\(= \frac{14}{16} \\\)

\(= \frac{7}{8}\)

hope it helps :)

mark brainliest!

Answer: (5,3)

Step-by-step explanation:

FA is the corresponding side to SU

AR is the corresponding side to UN

RF is the corresponding side to NS

What are Corresponding Sides ?

Corresponding sides are the sides that are in the same position in any different 2-dimensional shapes. For any two polygons to be congruent, they must have exactly the same shape and size. This means that all their interior angles and their corresponding sides must be the same measure. For any two polygons to be similar, the ratios of the lengths of each pair of corresponding sides must be equal.

In the below-given images, the two triangles are congruent and their corresponding sides are color-coded.

In the above two triangles ABC and XYZ,

AB is the corresponding side to XY

BC is the corresponding side to YZ

CA is the corresponding side to ZX

Similarly , if ΔFAR is similar to ΔSUN

then ,

FA is the corresponding side to SU

AR is the corresponding side to UN

RF is the corresponding side to NS

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Probability that the drug will be ineffective in more than two cases is 0,68.

Drug is effective in 9 cases out of 10, so the drug:

If the drug is tested on 12 patients, then there are 13 possibilities, namely:

In the problem, asked to find the probability of the drug being ineffective in more than 2 patients, there are 10 possibilities, namely

The way to find out the possibility of a drug being effective in 0-9 patients is:

P(effective ≤ 9) = P(effective 9) + P(effective 8) + ... + P(effective 0)

However, quite a lot is calculated if you use the formula above, less will be calculated if you use the method below:

P(effective ≤ 9) = 1 - ( P(effective 10) + P(effective 11) + P(effective 12) )

Let's try to start by calculating P(effective 10). P(effective 10) means the probability of being effective for 10 people and ineffective for 2 people. Then the effective probability is raised to the power of 10 and multiplied by the ineffective probability raised to the power of 2.

P(effective 10) = \((\frac{9}{10})^{10} .(\frac{1}{10} )^2\)

P(effective 10) = \(\frac{9^{10} }{10^{12} }\)

P(effective 10) = \(\frac{3486784401}{1000000000000}\)

So does P(effective 11) and P(effective 12)

P(effective 11) = \((\frac{9}{10} )^{11}.(\frac{1}{10})^{1}\)

P(effective 11) = \(\frac{9^{11} }{10^{12} }\)

P(effective 11) = \(\frac{3486784401}{1000000000000}\)

P(effective 12) = \((\frac{9}{10}) ^{12} .( \frac{1}{10} )^0\)

P(effective 12) = \(\frac{9^{12}}{10^{12}}\)

P(effective 12) = \(\frac{282429536481}{1000000000000}\)

So:

P(effective ≤ 9) = 1 - ( P(effective 10) + P(effective 11) + P(effective 12) )

P(effective ≤ 9) = 1 - ( \(\frac{3486784401}{1000000000000}\)+ \(\frac{3486784401}{1000000000000}\)+ \(\frac{282429536481}{1000000000000}\))

P(effective ≤ 9) = 1 - \(\frac{317297380491}{1000000000000}\)

P(effective ≤ 9) = 1 - 0,317297380491

P(effective ≤ 9) = 0,682702619509 ≈ 0,68

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Answer:

162 bracelets

Step-by-step explanation:

1st - 82 bracelets

2nd - 98

3rd - 114

4th - 130

5th - 146

6th - 162

Answer:

x = 13.5

Step-by-step explanation:

2/11 = 3/(3 + x)

6 + 2x = 33

2x = 27

x = 13.5

The normal probability plot suggests the data is approximately normally distributed. The sample standard deviation of given data is 3.13. The 95% confidence interval for the population standard deviation is (1.85, 6.28). The investment manager's desire for a population standard deviation below 6% is validated by the confidence interval.

To construct a normal probability plot, we first need to sort the data in ascending order:

6.6, 6.7, 8.7, 9.6, 10.0, 10.3, 11.3, 12.4, 12.4, 13.8, 14.9, 15.9

Then we can plot the ordered data against the expected values of a normal distribution with the same mean and standard deviation as the sample. The plot shows that the points follow a roughly straight line, which suggests that the data is roughly normally distributed.

To determine the sample standard deviation, we can use the formula:

s = sqrt[(∑(xi - x)²) / (n - 1)]

where xi is the rate of return for each year, x is the sample mean, and n is the sample size.

Sample mean:

x = (13.8 + 15.9 + 10.0 + 12.4 + 11.3 + 6.6 + 9.6 + 12.4 + 10.3 + 8.7 + 14.9 + 6.7) / 12 = 11.433

Sample standard deviation:

s = sqrt[((13.8 - 11.433)² + (15.9 - 11.433)² + ... + (6.7 - 11.433)²) / (12 - 1)]

= 3.059

Therefore, the sample standard deviation is 3.059.

To construct a 95% confidence interval for the population standard deviation of the rate of return, we can use the formula:

CI = [(n - 1) * s² / χ²(α/2, n-1), (n - 1) * s² / χ²(1-α/2, n-1)]

where n is the sample size, s is the sample standard deviation, χ² is the chi-square distribution, and α is the level of significance (1 - confidence level).

For a 95% confidence level and 11 degrees of freedom (n - 1), α = 0.05/2 = 0.025. From the chi-square distribution table with 11 degrees of freedom, we can find the critical values as follows:

χ²(0.025, 11) = 2.201 and χ²(0.975, 11) = 23.337

Plugging in the values, we get:

CI = [(12 - 1) * 3.059² / 23.337, (12 - 1) * 3.059² / 2.201]

= [1.946, 26.557]

Therefore, we can say with 95% confidence that the population standard deviation of the rate of return is between 1.946 and 26.557.

The investment manager wants to have a population standard deviation for the rate of return below 6%. The confidence interval (1.946, 26.557) does not validate this desire, as it includes values above 6%. Therefore, based on the sample data, the investment manager cannot be confident that the population standard deviation is below 6%.

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Using Compound Interest, The population of bears would be 1851 after 8 years with 2% increase every next year.

Compound interest is defined.

Savings interest that is calculated on both the principal and the interest accrued over the course of prior periods is called compound interest. The monthly compound interest formula is used to get the compound interest every month. The formula for compound interest is as follows: CI = P(1 + (r/12)). 12t - P, where t is the passing of time, P is the total amount of the principal, and r is the interest rate in decimal form.

Formula: Amount = P(1+r/100)ⁿ

where, P is principle

r is rate of increase in the given time period

n is time in years

Given that,

P = 1580

r = 2%

n = 8 years

∴ Population of bear  = 1580(1 + 2/100)⁸

                                 = 1580(1+0.02)⁸

                                 = 1580(1.02)⁸

                                 = 1580(1.171)

                                 = 1851

Thus, the population of bears would be 1851 after 8 years.

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Answer: A - (-5, 43)

Step-by-step explanation:

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

The triangle that has the coordinates as A(0,-4) B(0,-9) C(-2,-5) is; A scalene Triangle

The formula for the distance between two coordinates is;

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus;

Distance AB = √[(-9 + 4)² + (0 - 0)²]

Distance AB = √25

Distance AB = 5

Distance BC = √[(-5 + 9)² + (-2 - 0)²]

Distance BC = √20

Distance CA = √[(-4 + 5)² + (-2 - 0)²]

Distance CA = √5

Since the three sides all have different lengths, then they the triangle is said to be a scalene triangle.

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