Factor the following expressions completely. Show and check all work on your own paper.
x^2+169

Factor the following expressions completely. Show and check all work on your own paper.
5x^2-50x+125

Factor the following expressions completely. Show and check all work on your own paper.
100x^2-25y2

Answer:

5x

Step-by-step explanation:

(75b x)x×2

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

(10b x)×3

=75b x×x×2

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

10b x×3

=25x

-------

5

=5x

Answer:

gang nem

Step-by-step explanation:

Answer:

total = m/n * c

m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid

Answer:

a) 0.0156 = 1.56% probability that all children will develop the disease.

b) 0.4219 = 42.19% probability that only one child will develop the disease.

c) 0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they carry the disease, or they do not. The probability of a children carrying the disease is independent of any other children, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

The probability that their offspring will develop the disease is approximately .25.

This means that [tex]p = 0.25[/tex]

Three children:

This means that [tex]n = 3[/tex]

Question a:

This is P(X = 3). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]

0.0156 = 1.56% probability that all children will develop the disease.

Question b:

This is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{3,1}.(0.25)^{1}.(0.75)^{2} = 0.4219[/tex]

0.4219 = 42.19% probability that only one child will develop the disease.

c. The third child will develop Tay–Sachs disease, given that the first two did not.

Third independent of the first two, so just multiply the probabilities.

First two do not develop, each with 0.75 probability.

Third develops, which 0.25 probability. So

[tex]p = 0.75*0.75*0.25 = 0.1406[/tex]

0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.

Answer:

48 ÷ 60 = 4/5

Step-by-step explanation:

4/5 is the answer

Answer:

[tex]\frac{1}{30}[/tex]

Step-by-step explanation:

We require the number of minutes in a day.

i hour = 60 minutes

24 hours = 24 × 60 = 1440 minutes ( 24 hours in 1 day )

Then

fraction = [tex]\frac{48}{1440}[/tex] ( divide numerator/ denominator by 12 )

            = [tex]\frac{4}{120}[/tex] ( divide numerator/ denominator by 4 )

            = [tex]\frac{1}{30}[/tex]

Answer:

5≤x≤7

Step-by-step explanation:

For a given function f(x), the average rate of change in a given interval:

a ≤ x ≤ b

is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Here we have:

f(x) = 4*log(x + 2)

And we want to see which interval has the smallest average rate of change, so we just need fo find the average rate of change for these 4 intervals.

1)  1≤x≤3

here we have:

[tex]r = \frac{f(3) - f(1)}{3 - 1} = \frac{4*log(3 + 2) - 4*log(1 + 2)}{2} = 0.44[/tex]

2)  5≤x≤7

[tex]r = \frac{f(7) - f(5)}{7 - 5} = \frac{4*log(7 + 2) - 4*log(5 + 2)}{2} = 0.22[/tex]

3) 3≤x≤5

[tex]r = \frac{f(5) - f(3)}{5 - 3} = \frac{4*log(5 + 2) - 4*log(3 + 2)}{2} = 0.29[/tex]

4) −1≤x≤1

[tex]r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{4*log(1 + 2) - 4*log(-1 + 2)}{2} = 0.95[/tex]

So we can see that the smalles average rate of change is in 5≤x≤7

Answer:

y  ≤  9

Step-by-step explanation:

3y - 11 ≤ 2y - 2

Subtract 2y from each side

3y-2y - 11 ≤ 2y-2y - 2

y - 11 ≤  - 2

Add 11 to each side

y - 11+11 ≤  - 2+11

y  ≤  9

Answer:

[tex]y \leqslant 9[/tex]

Step-by-step explanation:

[tex]3y - 11 \leqslant 2y - 2 \\ 3y - 2y \leqslant 11 - 2 \\ y \leqslant 9[/tex]

Answer:

Time and rate is 4 years and 4% respectively.

Step-by-step explanation:

P = Rs 66000

so

T = R

I = 10560

so

I = PTR/100

Rs 10560 = (66000*T^2)/100

or, Rs 1056000 = 66000*T^2

or. 1056000/66000 = T^2

or, 16 = T^2

OR, T =√16

so T = 4

Then

T = R

so, R = 4

Answer:

60

Step-by-step explanation:

15kilometers into 1 hour

60 minutes in 1 hour

so Amir ran 15 kilometers in 60 minutes

Answer:

0.25 km

step explanation:

that was the anwser on khan

Answer:

z=9

Step-by-step explanation:

z-5=4. /+5

z=4+5

z=9

Answer:

z<-1

Step-by-step explanation:

5<z=4

collect like terms

z=<4-5

z<-1

Answer:

B. The mean GPA of the university honors students

Step-by-step explanation:

Parameter in statistical parlance simply refers to numerical characteristics obtijed from the population dataset or observations. The population itself refers to all observations belonging to a particular or specific experiment or research. Here, the population is the all students belonging to the university's honors programme. The measured characteristic is the mean of the student's GPA. THEREFORE, the parameter will be the mean GPA of the honors student.

Answer:

You dind't include the answer choices but it should look something like

[tex]50000(.8)^t[/tex]

Answer:

A

Step-by-step explanation:

in the question given, the goal is to rationalize the denominator, or in other words get rid of any square roots.

recall this formula :

(a-b)(a+b) = a^2 - b^2

in this case, to rationalize the denominator of 3 - [tex]\sqrt{6x}[/tex] , we will multiply it and the numerator by its conjugate. the conjugate of    3 -

after multiplying the denominator by its conjugate, we get:

(3 - [tex]\sqrt{6x}[/tex]) (3 +

at this point there is no need to solve the numerator as there is only one answer with this denominator.

hope this helps  :)

Answer:

Step-by-step explanation:

Answer:

0.5145

Step-by-step explanation:

Mean is also known as average. It is expressed as:

Mean  = Sum of data/Sample size

Sum of data = 0.33+0.33+0.54+0.46+0.30+0.77+0.42+0.44+0.60+0.32+0.47+0.64+0.61+0.69+0.41+0.39+0.66+0.60+0.61+0.70

Sum of data = 10.29

Sample size = 20

Mean = 10.29/20

Mean = 0.5145

Hence the mean of the data is 0.5145

Taking into account the definition of axis of simmetry and vertexn the axis of symmetry is x = 5.

So, first of all, you must know what a quadratic function is. Every quadratic function can be expressed as follows:

f(x) = a*x² + b*x + c

where a, b and c are real numbers.

The graph of a quadratic function is a parabola. Every parabola is a symmetric curve with respect to a horizontal line called the axis of symmetry.

That is, the axis of symmetry is an imaginary line that passes through the middle of the parabola and divides it into two halves that are equal of each other.

In other words, the axis of symmetry of a parabola is a vertical line that divides the parabola into two equal halves and always passes through the vertex of the parabola.

The point of intersection of the axis of symmetry with the parabola is called the vertex.

The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Being the vertex of the quadratic function (5,7), where the vertex on the x-axis has a value of 5 and on the y-axis a value of 7, the axis of symmetry is x = 5.

Learn more with this examples:

Answer:

[tex]x = 2[/tex]

[tex]S_n = 63[/tex]

Step-by-step explanation:

Given

[tex]a_1 = x + 1[/tex]

[tex]a_2 = 4x -2[/tex]

[tex]a_3 = 6x -3[/tex]

[tex]a_n = 18[/tex]

Solving (a): x

To do this, we make use of common difference (d)

[tex]d = a_2 - a_1[/tex]

[tex]d = a_3 - a_2[/tex]

So, we have:

[tex]a_3 - a_2 = a_2 - a_1[/tex]

Substitute known values

[tex](6x - 3) - (4x - 2) = (4x - 2) - (x + 1)[/tex]

Remove brackets

[tex]6x - 3 - 4x + 2 = 4x - 2 - x - 1[/tex]

Collect like terms

[tex]6x - 4x- 3 + 2 = 4x - x- 2 - 1[/tex]

[tex]2x- 1 = 3x- 3[/tex]

Collect like terms

[tex]2x - 3x = 1 - 3[/tex]

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

[tex]x = 2[/tex]

Solving (b): Sum of progression

First, we calculate the first term

[tex]a_1 = x + 1[/tex]

[tex]a_1 = 2 + 1 = 3[/tex]

Next, calculate d

[tex]d = a_2 - a_1[/tex]

[tex]d = (4x - 2) - (x +1)[/tex]

[tex]d = (4*2 - 2) - (2 +1)[/tex]

[tex]d = 6 - 3 = 3[/tex]

Next, we calculate n using:

[tex]a_n = a + (n - 1)d[/tex]

Where:

[tex]a_n = 18[/tex]

[tex]d = 3; a = 3[/tex]

So:

[tex]18 = 3 +(n - 1) * 3[/tex]

Subtract 3 from both sides

[tex]15 = (n - 1) * 3[/tex]

Divide both sides by 3

[tex]5 = n - 1[/tex]

Add 1 to both sides

[tex]6 = n[/tex]

[tex]n = 6[/tex]

The sum of the progression is:

[tex]S_n = \frac{n}{2} * [a + a_n][/tex]

So,, we have:

[tex]S_n = \frac{6}{2} * [3 + 18][/tex]

[tex]S_n = 3 * 21[/tex]

[tex]S_n = 63[/tex]

Answer:

sorry bhanxchu ma tha timro sathi hola bhandai thiye yata dehrai garmi xcha ki xaina tha man parauxchu tha man parauxchu tme maile man paraudinayou hola yesto handsome bhayera janu xchu ki xaina delete

To produce 35 gallons of a 45% disinfectant solution, you would need to mix 15 gallons of the 50% disinfectant solution with 20 gallons of the 40% disinfectant solution.

To solve this problem, we can use the concept of mixing different concentrations of solutions to obtain a desired concentration. Let's assume we need to mix x gallons of the 50% disinfectant solution with y gallons of the 40% disinfectant solution to obtain 35 gallons of a 45% disinfectant solution.

The amount of disinfectant in the 50% solution is 50% of x gallons, which is 0.5x gallons. The amount of disinfectant in the 40% solution is 40% of y gallons, which is 0.4y gallons.

Since we want to have 35 gallons of a 45% disinfectant solution, the amount of disinfectant in the final mixture would be 45% of 35 gallons, which is 0.45 * 35 = 15.75 gallons.

Now we can set up two equations to solve for x and y:

0.5x + 0.4y = 15.75

x + y = 35

We can solve these equations to find that x = 15 and y = 20. Therefore, you would need to mix 15 gallons of the 50% disinfectant solution with 20 gallons of the 40% disinfectant solution to produce 35 gallons of a 45% disinfectant solution.

Learn more about the topic of Mixing solutions here:

https://brainly.com/question/16901629

#SPJ3

Answer:

Angle T is congruent to Angle Z

Step-by-step explanation:

Since the 2 triangles are equal, that means that each pair of angles are also congruent. To know which angles are congruent, you check th order of how the triangles are named. Ex. Angle Q is congruent to Angle A, Angle P is congruent to Angle R, and Angle T is congruent to Angle Z.

Answer:

(483.981 ; 504.019)

Step-by-step explanation:

Given :

σ = 100

Sample size, n = 661

xbar = 494

We use the Z distribution since we are working with the population standard deviation ;

C.I = xbar ± (Zcritical * σ/√n)

Zcritical at 99% = 2.576

C.I = 494 ± (2.576 * 100/√661)

C.I = 494 ± 10.019

Lower boundary = (494−10.019) = 483.981

Upper boundary = (494+10.019) = 504.019

C.I = (483.981 ; 504.019)

Answer: [tex]x=12[/tex]

Step-by-step explanation:

[tex]f(x)=16x-30\\g(x)=14x-6[/tex]  are the equations that you've given us.

Now if we plot these two equations on the graph we notice there's an intersection at (12,162). Therefore meaning that [tex]x=12[/tex].

We can prove that by doing the following calculations to prove that both sides are equal to each other.

The left side of the equal sign:

Step 1: Write the equation down:

[tex]16x-30[/tex]

Step 2: Substitute x for the numerical value we found.

[tex]16(12)-30[/tex]

Step 3: We will multiply [tex]16*20[/tex] first, giving us 192.

[tex]192-30[/tex]

Step 4: Subtract 192 from 30. Which gives us 162.

[tex]162[/tex]

The right side of the equal sign:

Step 1: Write the equation down:

[tex]14x-6[/tex]

Step 2: Substitute x for the numerical value we found.

[tex]14(12)-6[/tex]

Step 3: We will multiply [tex]14*12[/tex] first, giving us 168.

[tex]168-6[/tex]

Step 4: Subtract 168 from 6. Which gives us 162.

[tex]162[/tex]

We know that [tex]x=12[/tex] because when substituting x with 12, we get 162 on both sides. Therefore making this statement true and valid.

[tex]162=162[/tex]

Answer:

972pi in ^3

Step-by-step explanation:

We need to find the volume of the sphere

V = 4/3 pi r^3

The diameter is 18

r = d/2 = 18/2 = 9

V = 4/3 pi ( 9)^3

V = 972pi in ^3

Answer:

18

Step-by-step explanation:

(p-1/p)² = 4²

p² + 1/p² - 2(p)(1/p) = 16

p²+1/p² -2 =16

so, p²+1/p² = 16+2

= 18

Answer: y = 0 and x = -1

Answer:

Volume 1=27m³

Volume 2=13m³

Volume 3= 23m³

Answer:

the study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural laws

Answer:

3x^2+5x+1

Step-by-step explanation:

(x^2 + 3x + 1) + (2x^2 + 2x)

Combine like terms

x^2 + 2x^2  + 3x +2x   +1

3x^2+5x+1

Answer:

[tex]3x^{2} + 5x + 1[/tex]

Step-by-step explanation:

Step 1:  Combine like terms

[tex](x^{2} + 3x + 1) + (2x^{2} + 2x)[/tex]

[tex](x^{2} + 2x^{2} + (3x + 2x) + (1)[/tex]

[tex]3x^{2} + 5x + 1[/tex]

Answer:  [tex]3x^{2} + 5x + 1[/tex]

Answer:

https://brainly.com/question/24258518

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's never negative.

D is indeed correct, the function's values never go below 0, meaning never below the x-axis

Answer:

Between 79.2 and 84.8.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 82, standard deviation of 2.8.

In what range would you expect to find the FBG of 68% of your study participants?

By the Empirical Rule, within 1 standard deviation of the mean, so:

82 - 2.8 = 79.2

82 + 2.8 = 84.8

Between 79.2 and 84.8.

Answer:

400 :D

Step-by-step explanation: