Consider triangle ABC. The legs have a length of 5 units each. Triangle A B C is shown. Angle A C B is a right angle. The lengths of sides A C and C B are 5. The length of the hypotenuse c is unknown. What is the length of the hypotenuse of the triangle? 5 units 5 StartRoot 2 EndRoot units 10 units 10 StartRoot 2 EndRoot units

Answer:

The price for 3.75 pounds of cherries is $17.775.

Step-by-step explanation:

The price las week was $ 4.99 and it got a discount of 15% for this week, this means that the price for this week is 100% of the one prior minus 15%, therefore it is 85% of the last price. We need to calculate the price per pound with this discount as shown below:

[tex]\text{this week} = \text{last week}*\frac{95}{100}\\\\\text{this week} = 4.99*0.95 = 4.74 \text{ per pound}\\[/tex]

Since the price is $4.74 per pound and we want to buy 3.75 pounds, then the total amount we need to pay is:

[tex]\text{total amount} = 3.75*4.74 = 17.775[/tex]

The price for 3.75 pounds of cherries is $17.775.

Answer:

a

The average cost is [tex]E(C) = 66[/tex]

b

The standard deviation of  cost is  [tex]\sigma = 9.798[/tex]

Step-by-step explanation:

From the question we are told that

          [tex]E(X) = 4[/tex]

          [tex]E(Y) = 2[/tex]

          [tex]E(X^2) = 24[/tex]

           [tex]E(Y^2) = 8[/tex]

The cost of replacing the two component is  C =  50 + 2 X + 4 Y

The variance   of X is mathematically represented as

           V(X) =  [tex]E(X^2) - [E(X)]^2[/tex]

Substituting values  

              [tex]V[X] = 24 - 4^2[/tex]

               [tex]V[X] =8[/tex]

The variance  of Y is mathematically represented as

           V(Y) =  [tex]E(Y^2) - [E(Y)]^2[/tex]

Substituting values  

              [tex]V[Y] = 8 - 2^2[/tex]

               [tex]V[X] =4[/tex]

The average of  replacing the two component is  

        [tex]E(C) = 2 * E(X) + 4* E(Y)[/tex]

substituting value

         [tex]E(C) = 50 + 2 * (4) + 4* (2)[/tex]

         [tex]E(C) = 66[/tex]

The variance  of replacing the two component is  

        [tex]V(C) = V(50 + 2X +4Y)[/tex]      Note: The variance of constant is zero

                                                                  and X and  Y are independent  

=>      [tex]V(C) = 2^2 * V(X) + 4^2 * V(Y)[/tex]

substituting values

=>       [tex]V(C) = 4 * 8 + 16 * 4[/tex]        

=>         [tex]V(C) = 32 + 64[/tex]

=>         [tex]V(C) = 96[/tex]

The standard deviation is

         [tex]\sigma = \sqrt{V(C)}[/tex]  

substituting values

           [tex]\sigma = \sqrt{96}[/tex]

           [tex]\sigma = 9.798[/tex]

Answer:

A and C

Step-by-step explanation:

3 - 4 - 5

6 - 8 - 10

7 - 24 - 25

5 - 12 - 13

are some basic right triangle

(about more, look picture)

Just use hypotenuse formula :

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

Option C is correct

[tex] {5}^{2} + { \sqrt{6} }^{2} = { \sqrt{31} }^{2} [/tex]

Option A is correct

[tex] {5}^{2} + {5}^{2} = { \sqrt{50} }^{2} [/tex]

But B isn't correct

Hope this helps ^-^

The integral is path-independent if we can find a scalar function f such that grad(f ) = A. This requires

[tex]\dfrac{\partial f}{\partial x}=2x-y[/tex]

[tex]\dfrac{\partial f}{\partial y}=x+y[/tex]

Take the first PDE and integrate both sides with respect to x to get

[tex]f(x,y)=x^2-xy+g(y)[/tex]

where g is assumed to be a function of y alone. Differentiating this with respect to x gives

[tex]\dfrac{\partial f}{\partial y}=-x+\dfrac{\mathrm dg}{\mathrm dy}=x+y\implies\dfrac{\mathrm dg}{\mathrm dy}=2x+y[/tex]

which would mean g is *not* a function of only y, but also x, contradicting our assumption. So the integral is path-dependent.

Parameterize the unit circle (call it C) by the vector function,

[tex]\mathbf r(t)=\cos t\,\mathbf i+\sin t\,\mathbf j[/tex]

with t between 0 and 2π.

Note that this parameterization takes C to have counter-clockwise orientation; if we compute the line integral of A over C, we can multiply the result by -1 to get the value of the integral in the opposite, clockwise direction.

Then

[tex]\mathrm d\mathbf r=-\sin t\,\mathbf i+\cos t\,\mathbf j[/tex]

and the (counter-clockwise) integral over C is

[tex]\displaystyle\int_C\mathbf A\cdot\mathrm d\mathbf r[/tex]

[tex]\displaystyle=\int_0^{2\pi}((2\cos t-\sin t)\,\mathbf i+(\cos t+\sin t)\,\mathbf j)\cdot(-\sin t\,\mathbf i+\cos t\,\mathbf j)\,\mathrm dt[/tex]

[tex]\displaystyle=\int_0^{2\pi}1-\sin t\cos t\,\mathrm dt=2\pi[/tex]

and so the integral in the direction we want is -2π.

By the way, that the integral doesn't have a value of 0 is more evidence of the fact that the integral is path-dependent.

Step-by-step explanation:

Area=Length×width

=6 5/7×7 3/5

change the improper fraction to proper

=47/7 ×38/5

=1786/35

=51.03ft²

Answer:

D

Step-by-step explanation:

2(x+b) = ax+c

2x+2b = ax+c

c = 2b

Answer:

54°

Step-by-step explanation:

The overall angle degrees of a trinangle 180°

Since we know that once of the angles is 72° we subract that from 180°

That equals 108°

Then we divide 108° since that is the sum of both the angles.

108/2= 54, so y= 54°

Answer:

12 boxes.

Step-by-step explanation:

We need to find the greatest common factor of 251 and 180:

First find the prime factors :

252 = 2*2*3*3*7

180 =  2*2*3*3*5

So the GCF = 2*2*3*3 = 36.

So id each box is identical, there could be 7 boxes of dark chocolates and 5 boxes of milk chocolates each containing 36 chocolates.

Total number of boxes = 12.

Answer:

please please please please show please

The diameter of a circle is twice the radius.

Diameter = radius x 2

                = 6.5 x 2

                = 13 cm

Answer:

13

Step-by-step explanation:

diameter is two times the radius

6.5 x 2 = 13

Answer:

Step-by-step explanation:

Put the values of x and y in the equations and solve the resulting system.

  A(2) +(-3) = 5

  A(2) +B(-3) = 20

__

The first equation tells the value of A:

  2A = 8 . . . . add 3

  A = 4 . . . . . .divide by 2

This and the second equation tells the value of B:

  (4)(2) -3B = 20

  -3B = 12 . . . . . subtract 8

  B = -4 . . . . . . . divide by -3

The values of A and B are 4 and -4, respectively.

Answer:

Step-by-step explanation:

morning mean: 14 mins

afternoon: 14 mins

both morning and afternoon have the same mean time

Answer: A. The average midterm score for those who listen to classical music while studying is higher than the average midterm score for those who don't listen to music while studying.

Step-by-step explanation:

An Alternative Hypothesis is one that disproves the Null Hypothesis in that it believes that indeed there is a change in the dependent variable due to a change in the independent variable.

The Alternative Hypothesis essentially aims to prove the assertion of the Researcher that there is an effect as a result of the introduction of a variable.

Null Hypothesis on the other hand believes that no significant difference exists between a change in a dependant Variable as a result of a change in an independent one.

The correct answer above therefore is that indeed music while studying inspires people to do better in exams than those who do not listen to music while studying. This is the alternative hypothesis because it believes that there was a change in the exam results due to reading while studying.

Answer:

Step-by-step explanation:

[tex]\mathrm{Slope-Intercept\:form\:of}\:2x+3y=12:\quad y=-\frac{2}{3}x+4\\\mathrm{Domain\:of\:}\:-\frac{2}{3}x+4\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\mathrm{Range\:of\:}-\frac{2}{3}x+4:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

[tex]\mathrm{Parity\:of}\:-\frac{2}{3}x+4:\quad \mathrm{Neither\:even\:nor\:odd}\\\mathrm{Axis\:interception\:points\:of}\:-\frac{2}{3}x+4:\quad \mathrm{X\:Intercepts}:\:\left(6,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:4\right)\\\mathrm{Inverse\:of}\:-\frac{2}{3}x+4:\quad -\frac{3x-12}{2}\\\mathrm{Slope\:of\:}-\frac{2}{3}x+4:\quad m=-\frac{2}{3}[/tex]

Answer:

[tex]10\dfrac{5}{8}[/tex]

Step-by-step explanation:

The perimeter of a shape is the sum of the lengths of the sides.

[tex]2\dfrac{1}{8}+3\dfrac{3}{16}+2\dfrac{1}{8}+3\dfrac{3}{16}=10\dfrac{5}{8}[/tex] yards

Hope this helps!

Answer:

10 5/8

Step-by-step explanation:

The perimeter is the sum of all sides

2 1/8 + 3 3/16 + 2 1/8 + 3 3/16

Add the whole numbers

2 + 3 + 2 + 3 = 10

Add the fractions

1/8+ 1/8 + 3 3/16 + 3 3/16

2/8 + 6/16

1/4 + 3/8

2/8+3/8 = 5/8

Put them back together

10 5/8

Answer:

75

Step-by-step explanation:

first, there are three 5's on the spinner, with a total of 12 sections. 3/12 = 0.25, so you multiply 0.25 times 300 (the total spins) and get 75

Answer:

The skeleton is approximately 18970 years old.

Step-by-step explanation:

The amount of Carbon-14 remaining after t years is given by the following equation:

[tex]N(t) = N(0)(1-r)^{t}[/tex]

In which N(0) is the initial amount and r is the decay rate, as a decimal.

Carbon-14 has a half-life of about 5700 years.

This means that [tex]N(5700) = 0.5N(0)[/tex]

So

[tex]N(t) = N(0)(1-r)^{t}[/tex]

[tex]0.5N(0) = N(0)(1-r)^{5700}[/tex]

[tex](1-r)^{5700} = 0.5[/tex]

[tex]\sqrt[5700]{(1-r)^{5700}} = \sqrt[5700]{0.5}[/tex]

[tex]1-r = 0.9999[/tex]

[tex]r = 1 - 0.9999[/tex]

[tex]r = 0.0001[/tex]

So

[tex]N(t) = N(0)(1-r)^{t}[/tex]

[tex]N(t) = N(0)(0.9999)^{t}[/tex]

He finds that the fossil contains 15% of the amount of carbon-14 anticipated when compared to a living femur of the same size.

The age is t for which N(t) = 0.15N(0). So

[tex]N(t) = N(0)(0.9999)^{t}[/tex]

[tex]0.15N(0) = N(0)(0.9999)^{t}[/tex]

[tex](0.9999)^{t} = 0.15[/tex]

[tex]\log{(0.9999)^{t}} = \log{0.15}[/tex]

[tex]t\log{0.9999} = \log{0.15}[/tex]

[tex]t = \frac{\log{0.15}}{\log{0.9999}}[/tex]

[tex]t = 18970.25[/tex]

Rounding to the nearest year.

The skeleton is approximately 18970 years old.

Answer:

Mark as Brainliest Please :)

Step-by-step explanation:

Answer:

It would be 4.v5

Answer:

GCF: 1

Step-by-step explanation:

Factors are numbers that can be evenly divided into another number. The greatest common factor of a set of numbers is the biggest number than can evenly divide into all the the numbers.

Let's list the factors of 60, 45 and 82

Factors of 60:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Factors of 45:

1, 3, 5, 9, 15, 45

Factors of 82:

1, 2, 41, 82

The greatest factor that all 3 numbers share is 1.

The right answer is 1.

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of 8.35 hours per household. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household.

(a.) what is the probability that a household views television between 6 and 8 hours a day (to 4 decimals)?

(b.) How many hours of television viewing must a household have in order to be in the top 5% of all television viewing households (to 2 decimals)?

(c.) What is the probability that a household views television more than 5 hours a day (to 4 decimals)?

Solution:

Let x be the random variable representing the television viewing times per household. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 8.35

σ = 2.5

a) the probability that a household views television between 6 and 8 hours a day is expressed as

P(6 ≤ x ≤ 8)

For x = 6,

z = (6 - 8.35)/2.5 = - 0.94

Looking at the normal distribution table, the probability corresponding to the z score is 0.1736

For x = 8

z = (8 - 8.35)/2.5 = - 0.14

Looking at the normal distribution table, the probability corresponding to the z score is 0.4443

Therefore,

P(6 ≤ x ≤ 8) = 0.4443 - 0.1736 = 0.2707

b) the top 5% means greater than 95%. It means that the sample mean is greater than the population mean and the z score is positive. The corresponding z score from the normal distribution table is 1.645. Therefore,

(x - 8.35)/2.5 = 1.645

Cross multiplying, it becomes

x - 8.35 = 2.5 × 1.645 = 4.11

x = 4.11 + 8.35 = 12.46

c) the probability that a household views television more than 5 hours a day is expressed as

P(x > 5) = 1 - P(x ≤ 5)

For x = 5

z = (5 - 8.35)/2.5 = - 1.34

Looking at the normal distribution table, the probability corresponding to the z score is 0.0901

Therefore,

P(x > 5) = 1 - 0.0901 = 0.9099

Answer:

50 cars and 25 bikes

Step-by-step explanation:

Given

Total wheels = 250

Required:

Number of cars and bikes

Let C represent Cars and B represents Bike

A car has 4 wheels and a bike has 2 wheels;

So,

[tex]4C + 2B = 250[/tex]

Divide through by 2

[tex]\frac{4C + 2B}{2} = \frac{250}{2}[/tex]

[tex]2C + B = 125[/tex] ---- Equation 1

The ratio of wheels of cars to wheels of bike is 1:2

Meaning that

1C = 2B

So, C = 2B

Substitute 2B for C in equation 1

[tex]2(2B) + B = 125[/tex]

[tex]4B + B = 125[/tex]

[tex]5B = 125[/tex]

Divide both sides by 5

[tex]\frac{5B}{5} = \frac{125}{5}[/tex]

[tex]B = \frac{125}{5}[/tex]

[tex]B = 25[/tex]

Recall that C = 2B

So,

[tex]C = 2 * 25[/tex]

[tex]C = 50[/tex]

Hence, Anna has seen 50 cars and 25 bikes

The equation in standard form is given by:

[tex]7x + y - 9 = 0[/tex]

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

The general equation in standard form is:

[tex]Ax + By + C = 0[/tex]

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

The first equation is:

[tex]7x + 3 = 5[/tex]

Setting equal to zero:

[tex]7x + 3 - 5 = 0[/tex]

[tex]7x - 2 = 0[/tex]

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

The second equation is:

[tex]y - 1 = 6[/tex]

[tex]y - 1 - 6 = 0[/tex]

[tex]y - 7 = 0[/tex]

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

Combining them, and placing in standard form:

[tex]7x - 2 + y - 7 = 0 + 0[/tex]

[tex]7x + y - 9 = 0[/tex]

A similar problem is given at https://brainly.com/question/14664782

Answer:

288 votes

Step-by-step explanation:

wright out what you know

Blue: 5/8

Green: 5/9 (of 3/8 because it is the remaining parts) so 5/24

Red: 1 - (5/8 + 5/24) = 1/6

Find the total amount of people

You know that 1/6 of the population is 48, so the total population is 288 (48×6)

Multiply the total population by the fractions to get the number of votes

A: Five people each paying $14.50 means that the total bill was [tex]5\cdot\$14.50=\boxed{\$72.50}.[/tex]

B: Subtract the number of people he already has from the number of people he needs to get [tex]42-29=\boxed{13}[/tex] people.

C: Divide 96 by 8 to get [tex]\boxed{12}[/tex] packs.

Arithmetic is where it all begins, y'know?

Answer:

Hope this helps though I m not sure about the first one since I got another answer 72.5 but it isn't there

Answer:

The answer is C

Answer:

[tex]x=-8[/tex]

Step-by-step explanation:

[tex]6\left(x-1\right)=9\left(x+2\right)\\\mathrm{Expand\:}6\left(x-1\right):\quad 6x-6\\6\left(x-1\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=6,\:b=x,\:c=1\\=6x-6\cdot \:1\\\mathrm{Expand\:}9\left(x+2\right):\quad 9x+18\\9\left(x+2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=9,\:b=x,\:c=2\\=9x+9\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18\\=9x+18\\6x-6=9x+18\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}[/tex]

[tex]6x-6+6=9x+18+6\\Simplify\\6x=9x+24\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\6x-9x=9x+24-9x\\Simplify\\-3x=24\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{24}{-3}\\Simplify\\\frac{-3x}{-3}=\frac{24}{-3}\\\mathrm{Simplify\:}\frac{-3x}{-3}:\quad x\\\frac{-3x}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3x}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1\\=x\\\mathrm{Simplify\:}\frac{24}{-3}:\quad -8\\\frac{24}{-3}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{3}=8\\=-8\\[/tex]

Answer:

x=-8

Step-by-step explanation:

6(x-1)= 9(x+2)

6x-6= 9x+18

6x-9x= 18+6

-3x= 24

-3x÷-3= 24÷-3

x=-8

Answer:

Step-by-step explanation:

First ,we round 1.79 to the nearest whole dollar:

since 7 ≥ 5 then 1.79 rounded to the nearest whole dollar is 2

now ,we can estimate the greatest number she can download:

26/2 = 13

Answer:

a?

Step-by-step explanation: