Need to also show work but confused

====================================================

Explanation:

Set A = {4,5,6,7,8,9} since these values are larger than 3 and smaller than 10. We only consider whole numbers in this range.

Set B = {1,2,3,4,5,6,7} represents positive whole numbers less than 8

To find the set [tex]A \cap B[/tex] we need to see which values are in both A and B at the same time. Those values are {4,5,6,7}

So [tex]A \cap B = \{4,5,6,7\}[/tex]

--------

side note: the notation [tex]A \cap B[/tex] means "A intersect B", so we're looking at where the two sets intersect or overlap (ie what they have in common).

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{2}}}}}[/tex]

Option D is the correct option.

Step-by-step explanation:

Given, x = 2 and y = 4

[tex] \sf{(2x + 3y) \div 4 - 2}[/tex]

plug the value of x and y

⇒[tex] \sf{ (2 \times 2 + 3 \times 4) \div 4 - 2}[/tex]

Multiply the numbers which are inside the bracket

⇒[tex] \sf{(4 + 12) \div 4 - 2}[/tex]

Add the numbers which are inside the bracket

⇒[tex] \sf{16 \div 4 - 2}[/tex]

Divide 16 by 4

⇒[tex] \sf{4 - 2}[/tex]

Subtract 2 from 4

⇒[tex] \sf{2}[/tex]

Hope I helped!

Best regards! :D

Answer:

2 (D)

Step-by-step explanation:

(2x+3y)÷4-2 you replace the variables with the matching numbers, and then multiply them by the number next to them.

(4+12)÷4-2 you add the numbers together

16÷4-2 you divide 16 by 4

4-2 you subtract to

2 this is your answer

Answer:

you can make 8 vest

Step-by-step explanation:

2 of them are green and 3 are blue

Answer:

x = 12

Step-by-step explanation:

they are virtical menaing they are the same value

6x + 7 = 8x - 17

6x + 24 = 8x

24 = 2x

12 = x

Answer:

x = 12

Step-by-step explanation:

Opposite angles are equal, so 6x + 7 = 8x - 17.

6x + 7 = 8x - 17

7 = 2x - 17 (take away 6x from both sides)

2x = 24 (Add 17 to Both Sides)

x = 12 (answer)

Answer:

He needs to sell approximately 4331 books to break even

Step-by-step explanation:

Let the number of books to be produced be = y

Total cost of production ($)

= 55000+2.3(x)

Price of the book sold($)= 15

Total money from sales= 15(x)

For the publisher to break even, the cost must be equal to the total money from sales.

55000+2.3(x)= 15x

55000= 15x-2.3x

55000= 12.7x

55000/12.7= x

4330.71= x

He needs to sell approximately 4331 books to break even

Answer:

d 9 years, 11 months

Step-by-step explanation:

Rachel deposited $5,960.32 into a savings account with an interest rate of 4.2% compounded twice a year.

P = $5,960.32

Rate = 4.2%

Number of years = x

Final amount=$9000

Number of times compounded= x/2

A= p(1+r/n)^(nt)

9000= 5960.32(1+(0.042*2)/x)^(x/2 *x)

9000= 5960.32(1+0.084/x)^x²/2

2(9000/5960.32)=(1+0.084/x)^x²

3.019972=((x+0.084)/x)^x²

On trial an error

The value of x is found to be approximately 9 year, 11 months

Answer:

12 hope you understand the answer

Answer:

A-3

Step-by-step explanation:

Since Alma is 3 years older than Liz then Liz would be A-3

Answer:

a^7

Step-by-step explanation:

[tex]\frac{a^{10}}{a^3}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\frac{a^{10}}{a^3}=a^{10-3}\\\\=a^7[/tex]

Answer:

The answer is

Step-by-step explanation:

In order to convert radians to degrees multiply the the value by

So for the value above we have

We have the final answer as

Hope this helps you

Answer:

x²-7x+2

Step-by-step explanation:

x²+2-7x in standard form is

x²-7x+2

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Large eggs : ≥2 ounces

Mean of 48 large eggs = 2.1 ounces

Mean absolute deviation = 0.08 ounces

0.08 ounces here is the mean absolute deviation of the 48 large eggs weighed, meaning that:

The average of the sum of the absolute differences in each individual egg and the mean value of all eggs weighed is 0.08.

This means that the average difference, variability or deviation in the weight of large eggs weighed is 0.08 ounces around the mean value of all eggs weighed.

Mean Absolute Deviation (MAD) :

Σ|xi - mean| / n

xi = each individual value

n = number of values

Answer:

Step-by-step explanation:

(3-6)/(5-2) = -3/3= -1

y - 6 = -1(x - 2)

y - 6 = -x + 2

y = -x + 8

Answer: luis is 28

Step-by-step explanation:

first you need to set up an equation. if luis age is equal to four years added to colleens age we can substitute colleens age with a variable (i’m gonna use the letter c) and luis’s age for a different variable (i’ll use L). your equation would be C + 4 = L. our second equation would be both of their ages is equal to 52, giving us C + L = 52 as our equation. since our other equation tells us that what L equals (it would equal C plus 4), we can substitute out the L in the second equation for C + 4. the equations would change from C+L= 52, to C + C + 4 = 52. then we would solve like any regular equation for our variable. first we can simplify the 2 c’s together to get

2c + 4 = 52. next you would take your + four and do the opposite sign to both sides of the equation. so you do + 4 minus 4 and then 52 minus four. this leaves you with the equation 2c = 48. lastly you do the opposite function to both sides with your coefficient. you would do 2c divides by 2 (to cancel out your two because it’s being multiplied by c). and then 48 divided by 2 leaving you with C = 24. that tells us that colleens age is 24, and then you plug this into your first equation to get 24 + 4 = L telling you that luis’s age is 28. to fact check you would just add the two ages together to see if you got your total

number. these are called like two step equations with substitution i believe

Answer:

50 seconds in order to assemble 20 pizza boxes

Step-by-step explanation:

there are two ways to solve this the first way is divide 20 by 2 which is 10 and then multiply 10 by 5 the reason to this is because we know that for every 2 it takes 5 seconds.

the second way takes longer but you write:

2, 2, 2, 2, 2, 2, 2, 2, 2, 2,

5, 5, 5, 5, 5, 5, 5, 5, 5, 5,

so here were basically writing the number 2 10 times because when u count that u can see that it equals 20 and then since for every 2 boxes it takes 5 seconds u put the 5 under each 2 so then you would count the 5s, like 5, 10 15, 20... and so on and u will see that its 50 which means 50 seconds.

Answer:

22 fourth graders

Step-by-step explanation:

Set up an equation, with the total amount on one side and the amount per cone on the other. Let x represent the unknown number of students:

[tex]1.47x=32.34[/tex]

Now we need to solve for x. Do this by isolating it:

Undo the multiplication on the left side by dividing both sides by 1.47:[tex]\frac{1.47x}{1.47} =\frac{32.34}{1.47}[/tex]

The 1.47 on the left now cancels each other out. Simplify:

[tex]x=22[/tex]

x equals 22, so there are 22 fourth graders in the class.

:Done

Answer:

w = -6

Step-by-step explanation:

Adding 4 to both sides (we do this to get rid of the -4) gives us:

-4 + w + 4 = -10 + 4

w = -6

Answer:

[tex]\Huge \boxed{w=-6}[/tex]

Step-by-step explanation:

[tex]-4+w=-10[/tex]

To solve for [tex]w[/tex], we need to isolate the variable on one side of the equation.

Adding 4 to both sides.

[tex]-4+w+4=-10+4[/tex]

Simplifying the equation.

[tex]w=-6[/tex]

Answer:

Step-by-step explanation:

[tex]d=\sqrt{(x-2)^2+(10-10)^2} =\sqrt{(x-2)^2}=x-2[/tex]

The required expression is [tex]x^2-4x+4[/tex]

The given coordinates are (2,10) and (x,10)

The formula for finding the distance between two points is,

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

Now, substituting the given points into the above formula we get,

[tex]\sqrt{(x-2)^2+(10-10)^2}\\=(x-2)^2\\=x^2-4x+4[/tex]

Learn More:https://brainly.com/question/11495758

Answer:

8a+2

Step-by-step explanation:

[tex]6a + 8 + 2a – 6\\\\\mathrm{Group\:like\:terms}\\=6a+2a+8-6\\\\\mathrm{Add\:similar\:elements:}\:6a+2a=8a\\=8a+8-6\\\\\mathrm{Add/Subtract\:the\:numbers:}\:8-6=2\\=8a+2[/tex]

Answer:

6a + 8 + 2a – 6

we calculate the unknowns of the same type alone (x with x, a with a, y with y ...) and the digits / numbers alone .

6a+2a=8a

8-6=+2

So 8a+2

Answer:

[tex]x=12[/tex]

Step-by-step explanation:

First, note that the angles shown are vertical angles. In other words, the two equations are equivalent to each other.

Therefore, set the equations equal to each other and solve for x;

[tex]6x+7=8x-17[/tex]

Add 17 to both sides:

[tex]6x+24=8x[/tex]

Subtract 6x from both sides:

[tex]24=2x[/tex]

Divide both sides by 2:

[tex]x=12[/tex]

Therefore, the value of x is 12.

And we're done!

Answer:

12

Step-by-step explanation:

Answer:

A simple random technique used to choose let's say 100 students can be adopted

Step-by-step explanation:

Because it give each student equal opportunity of being selected to avoid bias

Answer:

A is yes, and B is no

Step-by-step explanation:

Yes is a key word of A which means it is infact 48 and B is in fact no or 18 because of the discrete maths of espanol you can deprecate george washingtons face. And yes yes, it is gerla no yes maybe

Answer:

Step-by-step explanation:

Given:

u = 1, 0, -4

In unit vector notation,

u = i + 0j - 4k

Now, to get all unit vectors that are orthogonal to vector u, remember that two vectors are orthogonal if their dot product is zero.

If v = v₁ i + v₂ j + v₃ k is one of those vectors that are orthogonal to u, then

u. v = 0                    [substitute for the values of u and v]

=> (i + 0j - 4k) . (v₁ i + v₂ j + v₃ k)  = 0               [simplify]

=> v₁ + 0 - 4v₃ = 0

=> v₁ = 4v₃

Plug in the value of v₁ = 4v₃ into vector v as follows

v = 4v₃ i + v₂ j + v₃ k              -------------(i)

Equation (i) is the generalized form of all vectors that will be orthogonal to vector u

Now,

Get the generalized unit vector by dividing the equation (i) by the magnitude of the generalized vector form. i.e

[tex]\frac{v}{|v|}[/tex]

Where;

|v| = [tex]\sqrt{(4v_3)^2 + (v_2)^2 + (v_3)^2}[/tex]

|v| = [tex]\sqrt{17(v_3)^2 + (v_2)^2}[/tex]

[tex]\frac{v}{|v|}[/tex] = [tex]\frac{4v_3i + v_2j + v_3k}{\sqrt{17(v_3)^2 + (v_2)^2}}[/tex]

This is the general form of all unit vectors that are orthogonal to vector u

where v₂ and v₃ are non-zero arbitrary real numbers.

[tex]\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]

A vector is a quantity that has both magnitude and direction.

Two vectors are said to be orthogonal if they are perpendicular to each other.

Unit vectors orthogonal to [tex]u=\left ( a,b,c \right )[/tex] are given by [tex]\left ( \frac{a}{\sqrt{a^2+b^2+c^2}},\frac{b}{\sqrt{a^2+b^2+c^2}},\frac{c}{\sqrt{a^2+b^2+c^2}} \right )[/tex]

So, vectors orthogonal to [tex]u=\left ( 1,0,-4\right )[/tex] are [tex]\left ( \frac{1}{\sqrt{1^2+0^2+(-4)^2}},\frac{0}{\sqrt{1^2+0^2+(-4)^2}},\frac{-4}{\sqrt{1^2+0^2+(-4)^2}} \right )[/tex]

[tex]\left ( \frac{1}{\sqrt{1^2+0^2+(-4)^2}},\frac{0}{\sqrt{1^2+0^2+(-4)^2}},\frac{-4}{\sqrt{1^2+0^2+(-4)^2}} \right )=\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]

So, unit vector orthogonal to [tex]u[/tex] is [tex]\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]

For more information:

https://brainly.com/question/17108011?referrer=searchResults

The rate of the slower hiker is 1.1 mph and the rate of the faster hiker is 6.6 mph

Explanation

One hiker walks 5.5 mph faster than the other.

Suppose, the speed of the slower hiker is (x) mph.

So, the speed of the faster hiker will be:

(x+5.5)mph

Both hikers are walking toward each other and meet in 10 hours.

We know that, Distance = speed * time

So, the distance walked by the slower hiker in 10 hours = 10x miles and the distance walked by the faster hiker in 10 hours = 10(x + 5.5) miles.

Given that, they were 77 miles apart in the beginning. So the equation will be ...

10x + 10(x + 5.5) = 77

10x + 10x + 55 = 77

20x = 77 - 55 = 22

x = 22/20 = 1.1

Thus, the rate of the slower hiker is 1.1 mph and the rate of the faster hiker is (1.1 + 5.5) mph = 6.6 mph

Answer:

each peice will be 1/15 m long.

Step-by-step explanation:

Answer:

you got this

Step-by-step explanation:your smart try to figure it out by yourself

Step-by-step explanation:

The domain and target set of functions f and g given is expressed as;

f(x) = 2x+3 an g(x) = 5x+7 on R. To calculate the given functions, the following steps must be followed.

a) f◦g

f◦g = f(g(x)]) = f(5x+7)

To solve for the function f(5x+7), the variable x in f(x) will be replaced with 5x+7 as shown;

f(x) = 2x+3

f(5x+7) = 2(5x+7)+3

f(5x+7) = 10x+14+3

f(5x+7) = 10x+17

Therefore the function f◦g is equivalent to 10x+17

b) For the composite function g◦f  

g◦f = g(f(x)])

g(f(x)) = g(2x+3))

To drive the functon g(2x+3), the variable x in g(x) will be replaced with 2x+3 as shown;

g(x) = 5x+7

g(2x+3) = 5(2x+3)+7

g(2x+3) = 10x+15+7

g(2x+3) = 10x+22

This shoes that the composite function g◦f = 10x+22

c) To get the inverse of the composite function f◦g i.e (f◦g)⁻¹

Given (f◦g) = 10x+17

To find the inverse, first we will replace (f◦g) with variable y to have;

y = 10x+17

Then we will interchange variable y for x:

x = 10y+17

We will then make y the subject of the formula;

10y = x-17

y = (x-17)/10

Hence (f◦g)⁻¹ = (x-17)/10

d) For the function f⁻¹◦g⁻¹

First we need to calculate for the inverse of function f(x) and g(x) as shown:

For f⁻¹(x):

Given f(x)= 2x+3

To find the inverse, first we will replace f(x) with variable y to have;

y = 2x+3

Then we will interchange variable y for x:

x = 2y+3

We will then make y the subject of the formula;

2y = x-3

y = (x-3)/2

f⁻¹(x) = (x-3)/2

Similarly for the function g⁻¹(x):

Given g(x)= 5x+7

To find the inverse, first we will replace g(x) with variable y to have;

y = 5x+7

Then we will interchange variable y for x:

x = 5y+7

We will then make y the subject of the formula;

5y = x-7

y = (x-7)/5

g⁻¹(x) = (x-7)/5

Now to get f⁻¹◦g⁻¹

f⁻¹◦g⁻¹= f⁻¹(g⁻¹(x))

f⁻¹(g⁻¹(x)) = f⁻¹((x-7)/5)

Since f⁻¹(x) = (x-3)/2

f⁻¹((x-7)/5) = [(x-7)/5)-3]/2

= [(x-7)-15/5]/2

= [(x-7-15)/5]/2

= [x-22/5]/2

= (x-22)/10

Hence f⁻¹◦g⁻¹= (x-22)/10

e) For the composite function g⁻¹◦f⁻¹

g⁻¹◦f⁻¹= g⁻¹[f⁻¹x)]

g⁻¹[f⁻¹(x)] = g⁻¹((x-3)/2)

Since g⁻¹(x) = (x-7)/5

g⁻¹(x-3/2) = [(x-3/2)-7]/5

= [(x-3)-14)/2]/5  

= [(x-17)/2]/5

= (x-17)/10

Therefore the composite function g⁻¹◦f⁻¹= (x-17)/10

Answer:

16

Step-by-step explanation:

Given the equation, [tex] 200 + 10x = 120 + 15x [/tex], let's solve for x as follows,

Subtract 200 from both sides

[tex] 200 + 10x - 200 = 120 + 15x - 200 [/tex]

[tex] 10x = - 80 + 15x [/tex]

Subtract 15x from both sides

[tex] 10x - 15x = - 80 + 15x - 15x [/tex]

[tex] -5x = - 80 [/tex]

Divide both sides by -5

[tex] \frac{-5x}{-5} = \frac{-80}{5} [/tex]

[tex] x = 16 [/tex]

Answer:

3.) (x + 5) (x - 6)

Step-by-step explanation:

Factor the following:

x^2 - x - 30

Hint: | Factor x^2 - x - 30 by finding two numbers whose product is -30 and whose sum is -1.

The factors of -30 that sum to -1 are 5 and -6. So, x^2 - x - 30 = (x + 5) (x - 6):

Answer: (x + 5) (x - 6)

Answer:

p=-3

Step-by-step explanation:

Answer:

-4/2=2p

Step-by-step explanation:

5p - 8/2 = 7p +4/2

-5p           -5p

        -8/2 = 2p + 4/2

        -4/2            -4/2

Answer:

For x = 0, P(x = 0) = 0.35

For x = 1, P(x = 1) = 0.54

For x = 2, P(x = 2) = 0.11

For x = 3, P(x = 3) = 0

Step-by-step explanation:

We are given that the Sky Ranch is a supplier of aircraft parts. Included in stock are 6 altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected, one at a time, without replacement.

Let X = the number that are not correctly calibrated.

Number of altimeters that are correctly calibrated = 6

Number of altimeters that are not correctly calibrated = 2

Total number of altimeters = 6 + 2 = 8

(a) For x = 0: means there are 0 altimeters that are not correctly calibrated.

This means that all three selected altimeters are correctly calibrated.

Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]

The number of ways of selecting 3 altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_3[/tex]

So, the required probability = [tex]\frac{^{6}C_3}{^{8}C_3}[/tex]  

                                              = [tex]\frac{20}{56}[/tex]  = 0.35

(b) For x = 1: means there is 1 altimeter that is not correctly calibrated.

This means that from three selected altimeters; 1 is not correctly calibrated and 2 are correctly calibrated.

Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]

The number of ways of selecting 2 correctly calibrated altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_2[/tex]

The number of ways of selecting 1 not correctly calibrated altimeters from a total of 2 altimeters that are not correctly calibrated = [tex]^{2}C_1[/tex]

So, the required probability = [tex]\frac{^{6}C_2 \times ^{2}C_1 }{^{8}C_3}[/tex]  

                                                = [tex]\frac{30}{56}[/tex]  = 0.54

(c) For x = 2: means there is 2 altimeter that is not correctly calibrated.

This means that from three selected altimeters; 2 are not correctly calibrated and 1 is correctly calibrated.

Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]

The number of ways of selecting 1 correctly calibrated altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_1[/tex]

The number of ways of selecting 2 not correctly calibrated altimeters from a total of 2 altimeters that are not correctly calibrated = [tex]^{2}C_2[/tex]

So, the required probability = [tex]\frac{^{6}C_1 \times ^{2}C_2 }{^{8}C_3}[/tex]  

                                                = [tex]\frac{6}{56}[/tex]  = 0.11

(d) For x = 3: means there is 3 altimeter that is not correctly calibrated.

This case is not possible, so this probability is 0.