What is the length of the hypotenuse of the triangle? Triangle A B C. Side A C is 8 centimeters and side C B is 15 centimeters. Hypotenuse A B is unknown. StartFraction 94 EndFraction cm StartFraction 161 EndFraction cm 17 cm 23 cm AWNSER ASPA!

Answer:

Amount after 12 years is $205.42

Step-by-step explanation:

Fibal amount a is not given and to be found

Principal amount p = $100

Rate r = 6% ° 0.06

Years t = 20

Number if times computed n = 20*12

n = 240

a(t)=p(1+r/n)^nt

a = 100(1+0.06/240)^(240*12)

a = 100(1+0.00025)^(2880)

a= 100(1.00025)^2880

a= 100(2.054248)

a= 205.4248

To the nearest cent

a =$ 205.42

Amount after 12 years is $205.42

Answer:

D

Step-by-step explanation:

We calculate the z-score for each

Mathematically;

z-score = (x-mean)/SD

z1 = (1.9-2.1)/0.2 = -1

z2 = (2.3-2.1)/0.2 = 1

So the proportion we want to calculate is;

P(-1<x<1)

We use the standard score table for this ;

P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%

Answer:

68

Step-by-step explanation:

Answer:

96.08% probability that their mean rebuild time is less than 8.9 hours.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]

Find the probability that their mean rebuild time is less than 8.9 hours.

This is the pvalue of Z when X = 2.9.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2.9 - 2.4}{0.2846}[/tex]

[tex]Z = 1.76[/tex]

[tex]Z = 1.76[/tex] has a pvalue of 0.9608

96.08% probability that their mean rebuild time is less than 8.9 hours.

Answer:

couldnt tell you

Step-by-step explanation:

jkj

Answer:

It's written as

[tex]2.6 \times {10}^{ - 3} [/tex]

Hope this helps you

Answer:

2.6 × 10⁻³

Step-by-step explanation:

To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.

In the decimal 0.0026, the first number that is 1 or higher is 2.

0.0026 ⇒ 2.6

When trying to figure out the exponent, here are some things to keep in mind:

- when you move the decimal to the right, the exponent is negative

- when you move the decimal to the left, the exponent is positive

You moved the decimal to the right three places. So the exponent will be -3.

The result is 2.6 × 10⁻³.

Hope this helps. :)

Answer:

B: 304in^2

Step-by-step explanation:

One triangle face: (8)(15) ÷ 2 = 60

Four triangle faces: 60 x 4 = 240

Bottom Face: (8)(8) = 64

Total Surface Area: Four triangle faces + Bottom Face

Total Surface Area: 240 + 64

Total Surface Area: 304in^2

Answer:

neither

Step-by-step explanation:

First we must determine if both x and -x are in the domain of the function

since it is a polynomial function our first condition is satisfied

Then we should calculate the image of -x :

2x(-x)^3 + 3*(-x)² = -2x^3+3x²

it is not equal to f(x) nor -f(x)

Answer:

Step-by-step explanation:

Let the length and width of the rectangular package be x and y respectively. Since end of the package is a square, the perimeter of the package will be expressed as P = 4x+y and the volume will be expressed as V = x²y

If a postal service will accept a package if its length plus its girth is not more than 96 inches, then the perimeter is equivalent to 96 inches.

96 = 4x+y

y = 96-4x

Substituting the value of x into the formula for calculating the volume, we will have;

V(x) = x²(96-4x)

V(x) = 96x²-4x³

To get the dimensions and volume of the largest package, we will find V'(x) and equate it to zero.

V'(x) = 192x-12x²

192x-12x² = 0

Factoring out x;

x(192-12x) = 0

x = 0 and  192-12x = 0

12x = 192

x = 192/12

x = 16

This shows that we have a maximum value at x = 16 and minimum at x = 0

To get y, we will substitute x = 16 into the expression y = 96-4x

y = 96-4(16)

y = 96-64

y = 32

- The dimensions of the largest package is therefore 16in by 16in by 32in

- Volume of largest package = x²y = 16²*18 = 8,192in³

(4x-16)/3 = 36

4x-16 = 108

4x = 108+16

4x = 124

x = 124/4

x = 31

Answer:

x = 31

Step-by-step explanation:

=> [tex](4x-16)\frac{1}{3} = 36[/tex]

Multiplying 3 to both sides

=> [tex]4x-16 = 36*3[/tex]

=> 4x-16 - 108

Adding 16 to both sides

=> 4x = 108+16

=> 4x = 124

Dividing both sides by 4

=> x = 31

Answer:

a) 24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%

b) 13.57% probability that the mean return will be less than 5%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 8.7, \sigma = 20.2, n = 36, s = \frac{20.2}{\sqrt{36}} = 3.3667[/tex]

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?

This is 1 subtracted by the pvalue of Z when X = 11.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{11 - 8.7}{3.3667}[/tex]

[tex]Z = 0.68[/tex]

[tex]Z = 0.68[/tex] has a pvalue of 0.7518

1 - 0.7518 = 0.2482

24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%

(b) What is the probability that the mean return will be less than 5%?

This is the pvalue of Z when X = 5.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5 - 8.7}{3.3667}[/tex]

[tex]Z = -1.1[/tex]

[tex]Z = -1.1[/tex] has a pvalue of 0.1357

13.57% probability that the mean return will be less than 5%

Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The complete question is:

Maya is solving the quadratic equation by completing the What should Maya do first? square.

4x² + 16x + 3 = 0

We have a quadratic equation:

4x² + 16x + 3 = 0

To make the perfect square

Maya should do first:

Isolate the variable x²

To make the coefficient of x² is 1.

4(x² + 4x + 3/4) = 0

x² + 4x + 3/4 = 0

x² + 4x + 2² - 2² +  3/4 = 0

(x + 2)² - 4 + 3/4 = 0

(x + 2)² = 13/4

x + 2 = ±√(13/4)

First, take the positive and then the negative sign.

x = √(13/4) - 2

x = -√(13/4) - 2

Thus, Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.

Learn more about quadratic equations here:

brainly.com/question/2263981

#SPJ5

Step-by-step explanation:

Head(H) Tails(T)

Sample space is S (HHH,HHT,HTH,THH)

Event(HHT,HTH,THH)

so the probability is 3/4

Answer:

3/4

Step-by-step explanation:

Answer:

[tex]2\frac{1}{5}[/tex]

Step-by-step explanation:

11 ÷ 5 = 2 R 1 → [tex]2\frac{1}{5}[/tex]

Hope this helps! :)

the value of x is 115°.

hope its helpful to uh..

Answer:

B. e^x+3

Step-by-step explanation:

Y=e^x

the graph is moving 3 units up

y= y+3

y=e^x+3

answer = y=e^x+3

Answer: B

Step-by-step explanation:

Answer:

$143,739

Step-by-step explanation:

We must apply the formula for P0 and solve for d, that is,

P0=d(1−(1+rk)−Nk(rk).

We have P0=$200,000,r=0.04,k=12,N=30, so substituting in the numbers into the formula gives

$200,000=d(1−(1+0.0412)−30⋅12)(0.0412),

that is,

$200,000=209.4612d⟹d=$954.83.

So our monthly repayments are d=$954.83. To calculate the total interest paid, we find out the entire amount that's paid and subtract the principal. The total amount paid is

Total Paid=$954.83×12×30=$343,738.80

and therefore the total amount of interest paid is

Total Interest=$343,738.80−$200,000=$143,738.80,

which is $143,739 to the nearest dollar.

The interest paid is 2912683 dollars.

Compound interest is calculated for the principle taken as well as previous interest paid.

According to the given question Principle amount (P) taken from the bank is 2000000 dollars.

The yearly interest rate (r) compounded monthly is 4%.

Time in years (n)  is 30.

We know, in the case of compound interest compounded yearly is  

A = P(1 + r/100)ⁿ.

So, Amount compounded monthly will be

A = P[ 1 + (r/12)/100]¹²ⁿ.

A = 2000000[ 1 + (4/12)/100]¹²ˣ³⁰.

A = 2000000[ 1 + 0.003]³⁶⁰.

A = 2000000[ 1.003]³⁰⁰.

A = 2000000(2.456).

A = 4912583.

∴ The total interest paid on the mortgage is (4912683 - 2000000) =  2912683.

earn more about compound interest here :

https://brainly.com/question/14295570

#SPJ2

Answer:

C

Step-by-step explanation:

If two lines are parallel, their slopes are the same.

Since the slope of line l is 4/9, this means that the slope of line m must also be 4/9.

Answer:

C. 4/9

Step-by-step explanation:

Parallel lines have equal slopes.

Since line l and line m are parallel, then their slopes must be the same.

[tex]m_{l} =m_{m}[/tex]

We know that the slope of line l is 4/9

[tex]\frac{4}{9} = m_{m}[/tex]

Line l has a slope of 4/9, therefore line m must also have a slope of 4/9.

The correct answer is C. 4/9

Convert the 6 seconds to hours:

5 seconds x x 1/60 ( minutes per seconds) x 1/60 (Hours per minute) = 6/3600 = 1/600 hours.

Distance = speed x time

Distance = 585 x 1/600 = 585/600 = 0.975 miles

Convert miles to feet:

0.975 x 5280 = 5,148 feet

The plane traveled 5,148 feet in 6 seconds.

Answer: The difference between the estimated and real value of 55-21 is about 4 or 5

Step-by-step explanation:

Answer:

The difference between the estimate and the real value of 55-21 is that when you estimate you're giving an educated guess and the real value is when you're actually doing the work to prove your answer and not just guess.

Step-by-step explanation:

Real Value

55-21=34

 55

- 21

 34

Estimated

55-21=32

Answer:

B

Step-by-step explanation:

Given

x² + 14x = 51

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(7)x + 49 = 51 + 49 , that is

(x + 7)² = 100 ( take the square root of both sides )

x + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )

x = - 7 ± 10

Thus

x = - 7 - 10 = - 17

x = - 7 + 10 = 3

Answer:

The actress had more extreme age when winning the​ award.

Step-by-step explanation:

We are given that for all the best​ actors, the mean age is 43.4 years and the standard deviation is 8.8 years. For all best​ actresses, the mean age is 38.2 years and the standard deviation is 12.6 years.

To find who had the more extreme age when winning the​ award, the actor or the​ actress, we will use the z-score method.

Let X = age of the winner for best actor

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean age = 43.4 years

            [tex]\sigma[/tex] = standard deviation = 8.8 years

It is stated that the age of the winner for best actor was 34, so;

   z-score for 34 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                            =  [tex]\frac{34-43.4}{8.8}[/tex]  = -1.068

Let Y = age of the winner for best actress

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{Y-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean age = 38.2 years

            [tex]\sigma[/tex] = standard deviation = 12.6 years

It is stated that the age of the winner for best actress was 62, so;

   z-score for 62 =  [tex]\frac{Y-\mu}{\sigma}[/tex]

                            =  [tex]\frac{62-38.2}{12.6}[/tex]  = 1.889

Since the z-score for the actress is more which means that the actress had more extreme age when winning the​ award.

Answer:

The upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.

Step-by-step explanation:

Compute the mean difference and standard deviation of the difference as follows:

[tex]\bar d=\frac{1}{n}\sum d_{i}=\frac{1}{15}\times [1380+3370+2580+...+3520]=2642.67\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}\\=\sqrt{\frac{1}{15-1}[(1380-2642.67)^{2}+(3370-2642.67)^{2}+...}=525.69[/tex]

The degrees of freedom is:

df = n - 1

   = 15 - 1

   = 14

Th critical value of t is:

[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 14}=2.145[/tex]

*Use a t-table.

Compute the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus as follows:

[tex]\text{Upper Confidence Bound}=\bar d+t_{\alpha/2, (n-1)}\cdot \frac{S_{d}}{\sqrt{n}}[/tex]

                                        [tex]=2642.67+2.145\cdot \frac{525.69}{\sqrt{15}}\\\\=2642.67+291.15\\\\=2933.82[/tex]

Thus, the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.

4 times 4 is 16, think of it like 4 + 4 + 4 + 4.

4 times 4 is 16, think of it like 4 + 4 + 4 + 4.

Answer:

15√20/6√125

=√20/√5

=2

Step-by-step explanation:

Two ratios that are equal to 7:6 are 14:12 and 21:18, as they are the same, but 7 and 6 are multiplied by the same number (2 in the first, and 3 in the second.)

Answer:

Hello!

________________________

5c + 16.5 = 13.5 + 10c

Exact Form:  c = 3/5

Decimal Form: c = 0.6

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you!

Answer:

3000+3d=noods

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

We can simply plug in the 3 variables to see if it forms a Pythagorean Triple:

6² + 13² = 14.32²

36 + 169 = 205.062

205 = 205 (rounded), so True.

Answer:

26 rows

Step-by-step explanation:

[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]

Answer:

  y = 640x +4760

Step-by-step explanation:

Given:

  (x, y) = (years past 1998, number of vehicles) = (0, 4760), (3, 6680)

Find:

  a slope-intercept form linear equation through these points

Solution:

The 2-point form of the equation of a line is a useful place to start:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (6680 -4760)/(3 -0)(x -0) +4760

  y = 1920/3x +4760

  y = 640x +4760 . . . . . the desired equation

Answer:

x = 7

Step-by-step explanation:

[tex] 3^{x - 5} = 9 [/tex]

[tex] 3^{x - 5} = 3^2 [/tex]

[tex] x - 5 = 2 [/tex]

[tex] x = 7 [/tex]