What is the value of X ?
A-17
B-26
C-39
D-41

Answer:

d) [tex]8.97*10^{-3}[/tex]

Step-by-step explanation:

Move the decimal 3 spaces to the right so that way the decimal can be between the first two numbers. When you move the decimal to the right, it makes the exponent negative, when it moves to the left, it makes it positive

Answer:

A

Step-by-step explanation:

We can use the trigonometric ratios. Recall that sine is the ratio of the opposite side to the hypotenuse:

[tex]\displaystyle \sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side with respect to ∠C is 24 and the hypotenuse is 26.

Hence:

[tex]\displaystyle \sin(C)=\frac{24}{26}=\frac{12}{13}[/tex]

Our answer is A.

Answer:

x = -2

y = -5

Step-by-step explanation:

You can use either substitution or elimination for this problem. I will be using elimination,

Step 1: Add the 2 equations together

-8y = 40

y = -5

Step 2: Plug y into an original equation to find x

-3 (-5) + 10x = -5

15 + 10x = -5

10x = -20

x = -2

And you have your final answers!

Answer:

[tex]X \sim Exp (\mu = 49)[/tex]

But also we can define the variable in terms of [tex]\lambda[/tex] like this:

[tex]X \sim Exp(\lambda= \frac{1}{\lambda} = \frac{1}{49})[/tex]

And usually this notation is better since the probability density function is defined as:

[tex] P(X) =\lambda e^{-\lambda x}[/tex]

Step-by-step explanation:

We know that the random variable X who represents the waiting time to see a shooting star during a meteor shower follows an exponential distribution and for this case we can write this as:

[tex]X \sim Exp (\mu = 49)[/tex]

But also we can define the variable in terms of [tex]\lambda[/tex] like this:

[tex]X \sim Exp(\lambda= \frac{1}{\lambda} = \frac{1}{49})[/tex]

And usually this notation is better since the probability density function is defined as:

[tex] P(X) =\lambda e^{-\lambda x}[/tex]

Answer:

(a) The first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.

The second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.

The third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.

(b) The 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.

Step-by-step explanation:

The first, second the third quartile are the values that let a probability of 0.25, 0.5 and 0.75 on the left tail respectively.

So, to find the first quartile, we need to find the z-score for which:

P(Z<z) = 0.25

using the normal table, z is equal to: -0.67

So, the value x equal to the first quartile is:

[tex]z=\frac{x-m}{s}\\ x=z*s +m\\x =-0.67*119 + 462\\x=382.27[/tex]

Then, the first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.

At the same way, the z-score for the second quartile is 0, so:

[tex]x=0*119+462\\x=462[/tex]

So, the second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.

Finally, the z-score for the third quartile is 0.67, so:

[tex]x=z*s +m\\x =0.67*119 + 462\\x=541.73[/tex]

So, the third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.

Additionally, the z-score for the 99th percentile is the z-score for which:

P(Z<z) = 0.99

z = 2.33

So, the 99th percentile is calculated as:

[tex]x=z*s +m\\x =2.33*119 + 462\\x=739.27[/tex]

So, the 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.

Answer:

The total number of houses are "9". The further explanation is given below.

Step-by-step explanation:

The given values are:

height,

h =  28h - h²

Housing profit of developers will be:

⇒  [tex]\pi^h=28h-h^2-hf[/tex]

If airport won't pay any cost for the damage,

⇒  [tex]\pi^A=20f-f^2[/tex]

then,

⇒  [tex]\frac{\partial \pi^A}{\partial f}[/tex] = [tex]20-2f =0[/tex]

                      [tex]20=2f[/tex]  

                       [tex]f=\frac{20}{2}[/tex]

                       [tex]f=10[/tex]

On putting the value of "f", we get

⇒  [tex]\pi^h=28h-h^2-10h[/tex]

         [tex]=18h-h^2[/tex]

⇒  [tex]\frac{\partial \pi h}{\partial h}=18-2h=0[/tex]

                      [tex]2h=18[/tex]

                        [tex]h=\frac{18}{2}[/tex]

                        [tex]h=9[/tex]

So that the total number of house built by the developers will be "9".

Answer:

[tex] y =y_o e^{kt}[/tex]

Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.

For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:

[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]

And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235

Step-by-step explanation:

We can assume that the following model can be used:

[tex] y =y_o e^{kt}[/tex]

Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.

For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:

[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]

And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235

Answer:

[tex]\frac{d y}{d x} = \frac{2}{\sqrt{(2 x+1)^{2} -1} } + (\frac{-x}{|x|\sqrt{1-x^2}) }) + (1) Sec h^{-1} (x)[/tex]

Step-by-step explanation:

Step(i):-

Given function

               [tex]y = cosh^{-1} (2 x +1) - x Sec h^{-1} (x)[/tex]   ....(i)

we will use differentiation formulas

i) y = cos h⁻¹ (x)

   Derivative of cos h⁻¹ (x)

           [tex]\frac{d y}{d x} = \frac{1}{\sqrt{x^2-1} }[/tex]

ii)

      y = sec h⁻¹ (x)

   Derivative of sec h⁻¹ (x)

           [tex]\frac{d y}{d x} = \frac{-1}{|x|\sqrt{(x^2-1} }[/tex]

Apply U V formula

[tex]\frac{d UV}{d x} = U V^{l} + V U^{l}[/tex]

Step(ii):-

Differentiating equation (i) with respective to 'x'

[tex]\frac{d y}{d x} = \frac{1}{\sqrt{(2 x+1)^{2} -1} } X \frac{d}{d x} (2 x+1) + x (\frac{-1}{|x|\sqrt{1-x^2}) }) + (1) Sec h^{-1} (x)[/tex]

[tex]\frac{d y}{d x} = \frac{1}{\sqrt{(2 x+1)^{2} -1} } X (2) + (\frac{-x}{|x|\sqrt{1-x^2}) }) + (1) Sec h^{-1} (x)[/tex]

Conclusion:-

[tex]\frac{d y}{d x} = \frac{2}{\sqrt{(2 x+1)^{2} -1} } + (\frac{-x}{|x|\sqrt{1-x^2}) }) + (1) Sec h^{-1} (x)[/tex]

Answer:

the math problem is incomplete

Answer:

  [tex]\dfrac{x^2+8x+16}{x-1}[/tex]

Step-by-step explanation:

In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...

  [tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]

Answer:

96 degrees

Step-by-step explanation:

Since x is half of 168, its angle measure is 84 degrees. Since x and y are a linear pair, their angle measures must add to 180 degrees, meaning that:

y+84=180

y=180-84=96

Hope this helps!

Answer:

x+7)^2=x^2+2*7x+7^2= x^2+14x+49

Step-by-step explanation:

Answer:

2x-14

From: iOE your friend :D :)

* Be awesome Be you*

Answer:

Raspberry: 30%

Strawberry: 15%

Apple: 20%

Lemon: 35%

Step-by-step explanation:

18 + 9 + 12 + 21 = 60 (there are 60 gummy worms)

18 out of 60 = 30%

9 out of 60 = 15%

12 out of 60 = 20%

21 out of 60 = 35%

Please mark Brainliest

Hope this helps

Answer:

Raspberry Worms: 30%

Strawberry Worms: 15%

Apple Worms: 20%

Lemon Worms: 35%

Step-by-step explanation:

Raspberry Worms: [tex]\frac{18}{18+9+12+21}=\frac{18}{60}=\frac{30}{100}[/tex] or 30%

Strawberry Worms: [tex]\frac{9}{18+9+12+21}=\frac{9}{60} =\frac{15}{100}[/tex] or 15%

Apple Worms: [tex]\frac{12}{18+9+12+21} =\frac{12}{60} =\frac{20}{100}[/tex] or 20%

Lemon Worms: [tex]\frac{21}{18+9+12+21} =\frac{21}{60} =\frac{35}{100}[/tex] or 35%

Answer:

0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51

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, we have that:

[tex]\mu = 50, \sigma = 1.5, n = 10, s = \frac{1.5}{\sqrt{10}} = 0.4743[/tex]

What is the probability that the sample mean hardness for a random sample of 10 pins is at least 51

This is 1 subtracted by the pvalue of Z when X = 51. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{51 - 50}{0.4743}[/tex]

[tex]Z = 2.11[/tex]

[tex]Z = 2.11[/tex] has a pvalue of 0.9826

1 - 0.9826 = 0.0174

0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51

Answer:

a) three eigenvalues, all of them real.

d) one real eigenvalue and two complex eigenvalues.

Step-by-step explanation:

A  3x3 matrix with real entries can have : (a) three eigenvalues, all of them are real and (d) one real eigenvalue and two complex eigenvalues.

Let consider the equation for a  3x3 matrix with real entries :

[tex]\lambda^3+a\lambda^2+b \lambda +c = 0[/tex]

From above ; we will notice that the polynomial is of 3°; as such there will be three eigenvalues in which all of them real.

Also ; complex values shows in pairs, a  3x3 matrix cannot have a three complex eigenvalues but one real eigenvalue and two complex eigenvalues.

Answer:

Distance = 0.3

Step-by-step explanation:

We have two point in a line (one dimension).

One point is at 2.1 units and 1.8 units.

The distance between two points can be calculated as the absolute value of the difference between the position of each point.

This can be derived from the distance formula for two dimensions:

[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\y_1=y_2=0\\\\d=\sqrt{(x_2-x_2)^2}\\\\d=|x_2-x_1|[/tex]

Then, for this case, the distance is:

[tex]d=|1.8-2.1|=|-0.3|=0.3[/tex]

Answer:

225º or 3.926991 radians

Step-by-step explanation:

The area of the complete circle would be π×radius²: 3.14×8²=200.96

The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.

[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).

There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.

We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.

Answer:

225º

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Example:

Consider A vertex. A is connected  with two other vertices  C and B.

Thus 3 line segments are formed. At A, two pair of intersecting lines are formed, AC & AE ;   AE and AB

Each vertex form two pair of intersecting line segments. Totally , there are 8 verteces. So, 8*2 = 16 pair of  intersecting lines

Answer:

[tex]f(x)=3x^2+2[/tex] and the limit is 12

Step-by-step explanation:

we know that the derivative of the function f in x=a is the limit of this

[tex]\dfrac{f(a+h)-f(a)}{a+h-a}=\dfrac{f(a+h)-f(a)}{h}[/tex]

as the expression is

[tex][3(a+h)^2+2 ]-14[/tex]

we can say that

     [tex]f(a+h)=3(2+h)^2+2 \\\\f(a)=14[/tex]

from the first equation we can identify a = 2 and then

[tex]f(x)=3x^2+2[/tex]

to verify that we are correct, we can compute f(2)=3*4+2=14

f'(x)=6x

so f'(2)=12

we can estimate it from the fraction as well

so the limit is 12

Answer:

1. 120 ways

2. 720 ways

Step-by-step explanation:

When the order is important, we have a permutation.

When the order is not important, we have a combination.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

1. If the jobs are all the same.

Same jobs means that the order is not important. So

3 from a set of 10.

[tex]C_{10,3} = \frac{10!}{3!(10-3)!} = 120[/tex]

120 ways

2. If the jobs are all different.

DIfferent jobs means that the order matters.

[tex]P_{(10,3)} = \frac{10!}{(10-3)!} = 720[/tex]

720 ways

Answer:

Volume of liquid which freezes to ice is 1620. 37 .

Expression to find this is 108x/100 = 1750

Step-by-step explanation:

Let the volume of liquid be x cubic inches

It is  given that volume of liquid increases by 8% when it freezes to ice

increase in volume of x  x cubic inches liquid = 8% of x = 8/100 * x = 8x/100

Total volume of ice = initial volume of liquid + increase in volume when it freezes to ice  = x + 8x/100 = (100x + 8x)/100 = 108x/100

Given that total volume of liquid which freezes is 1750

Thus,

108x/100 = 1750

108x = 1750*100

x = 1750*100/108 = 1620. 37

Volume of liquid which freezes to ice is 1620. 37 .

Expression to find this is 108x/100 = 1750

Answer:

41

Step-by-step explanation:

[tex]24*2-7=\\48-7=\\41[/tex]

Answer:

44.93% probability that the person will need to wait at least 7 minutes total

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional probability:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes

This means that [tex]m = 5, \mu = \frac{1}{5} = 0.2[/tex]

Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total

Event A: Waits at least 3 minutes.

Event B: Waits at least 7 minutes.

Probability of waiting at least 3 minutes:

[tex]P(A) = P(X > 3) = e^{-0.2*3} = 0.5488[/tex]

Intersection:

The intersection between waiting at least 3 minutes and at least 7 minutes is waiting at least 7 minutes. So

[tex]P(A \cap B) = P(X > 7) = e^{-0.2*7} = 0.2466[/tex]

What is the probability that the person will need to wait at least 7 minutes total

[tex]P(B|A) = \frac{0.2466}{0.5488} = 0.4493[/tex]

44.93% probability that the person will need to wait at least 7 minutes total

Answer:

Center, radius, chord, diameter... are Words related to circle

Answer:

The 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two means is:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

It is provided that:

[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]

The critical value of z for 90% confidence level is,

z = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

    [tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]

Thus, the 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

[tex]\displaystyle\bf\\\textbf{At any translation of a quadrilateral the sides remain the same,}\\\\\textbf{the angles remain the same.}\\\\\textbf{It turns out that the quadrilateral remains the same.}\\\\P_{A'B'C'D'}=P_{ABCD}=AB+BC+CD+DA=\\\\~~~~~~~~~~~~~~=2.2+4.5+6.1+1.4=\boxed{\bf14.2}[/tex]

I will use the graphing method.

To find the slope of the line using this method,

first set up a coordinate system.

Now plot both of your points.

Label a point A and label another one B.

I have chosen to label (0,2) A and (1,6) B but it doesn't matter.

Now graph a line through the 2 points.

Now the slope or m is equal to the rise over run

from point A to point B on the coordinate system.

To get from point A to point B, we rise 4 units and run 1 unit.

So our slope or rise over run is 4/1 which reduces to 4.

Answer:

C) To the right.

Step-by-step explanation:

Answer:

cos θ = -2/√29

Step-by-step explanation:

tan θ = -5/2, π/2 < θ < π

One method is to draw a triangle with the hypotenuse in quadrant II.  The height of the triangle is 5, and the base is -2.  The hypotenuse can be found using Pythagorean theorem:

c² = a² + b²

c² = (-2)² + (5)²

c = √29

Therefore, cos θ = -2/√29.

Another method is to use one of the Pythagorean identities.

tan²θ + 1 = sec²θ

(-5/2)² + 1 = sec²θ

25/4 + 1 = sec²θ

29/4 = sec²θ

cos²θ = 4/29

cos θ = -2/√29