Consider the normal distribution curve.


Which statements are true about the curve? Check all that apply.

The standard deviation of the data is 64.
The variance of the data is 49.
The median is 64.
The data point 75 is less than one standard deviation from the mean.
The data point 50 is two standard deviations away from the mean.

Answer:

[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = - 8x + 4 ( add 8x to both sides )

8x + y = 4 ( subtract y from both sides )

8x = 4 - y ( divide both sides by 8 )

x = [tex]\frac{4-y}{8}[/tex]

Change y back into terms of x

[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]

Answer:

263.99 m3 (i tried my best)

Step-by-step explanation:

diameter > radius= 12/2

=6 m

v. of cone: 1/3 x 22/7 x r² x h

1/3 x 22/7 x 6² x 7

=263.99 m3

Answer:84piem^3

Step-by-step explanation:AP3X

Answer:

D. d = 5

Step-by-step explanation:

d = d² - d¹

= 5 - 0

= 5

d = d³ - d⁴

= 10 - 5

= 5

d = dⁿ - dⁿ-¹

The common difference of the given sequence will be 5, i.e. option D.

Arithmetic progression is the sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. The common difference is the value between each successive number in an arithmetic sequence

i.e. Common difference (d) = Successive term - Previous term

We have,

0, 5, 10, 15, 20, . . .

Here,

a₁ = 0

a₂ = 5

a₃ = 10

a₄ = 15

a₅ = 20

Now,

Find the common difference,

i.e.

Common difference (d) = a₂ - a₁ = 5 - 0 = 5,

Now,

Common difference (d) = a₃ - a₂ = 10 - 5 = 5

Now,

Common difference (d) = a₄ - a₃ = 15 - 10 = 5

Now,

Common difference (d) = a₅ - a₄ = 20 - 15 = 5

Now,

The Common difference is same for all i.e. 5.

Hence, we can say that the common difference of the given sequence will be 5, i.e. option D.

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Answer:

Length =12

Width= 10

Step-by-step explanation:

The difference between two consecutive integers is 2.

Thus the difference between the length and the width of the rectangle also differ by 2.

width- x

length- x+2

AREA=L×W

120=x(x+2)

x²+2x-120=0

Factorizing:

x² - 10x + 12x - 120=0

x(x-10) + 12( x-10)=0

(x-10)(x+12)=0

either x-10=0 or x+12=0

x=10 0r -12

We consider positive roots only. thus x=10

width = 10

length = 10+2 =12

Answer: y=3x+8

Step-by-step explanation:

The slope will be the same as the original equation, so 3. And to make the line go the points (0,8), you can plug in 0 into the original equation to find what needs to change. Hope this helps!

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

If lines are parallel then they have the same slope (m)

This means that the slope of the line will be 3

y = 3x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(0, 8)

8 = 3(0) + b

8 = 0 + b

8 = b

y = 3x + 8

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

16 quarters 2 dimes

Step-by-step explanation:

16 quarters is 4 dollars

2 dimes is 20 cents

Step-by-step explanation:

If D is number of dimes and Q is number of quarters:

D + Q = 21

10D + 25Q = 420

Solve the system of equations through either substitution or elimination.

10D + 25(21 - D) = 420

10D + 525 - 25D = 420

105 = 15D

D = 7

Q = 14

There are 7 dimes and 14 quarters.

Answer:

Step-by-step explanation:

setup a proportion

                               Big Triangle             Small Triangle

corresponding              15                              3

corresponding               x                               6

so you are trying to solve 15/x=3/6

cross multiply 6(15)=3(x)

last step divide both sides by 3 giving x=30 ft

If the triangles are similar, value of x in the drawings is Option(B) 30 ft.

Similar triangles are triangles that have the same shape, but their sizes may vary. If two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

The given two triangles are similar .

In the diagram, it is mentioned that one side is 3 and its corresponding other side of the similar triangle is 15 .

Thus the proportion is 15/3 = 5

Therefore if the other side of the same triangle is 6 then its corresponding other side of the similar triangle will be 6*5 = 30

Thus x = 30 ft.

Therefore, if the triangles are similar, value of x in the drawings is Option(B) 30 ft.

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Because this expression is a difference of squares, meaning both terms have square roots, the factors would be 12+7x and 12-7x

Answer:12+7x and 12-7x

Answer:

-15/2

Step-by-step explanation:

For this case we have by definition, that each of the four internal angles of a square measure 90 degrees.

If we draw the diagonals of the square then the angles are divided by two, that is:

[tex]\frac {90} {2} = 45[/tex]

Thus, angle 3 measures 45 degrees.

[tex]A3 = 45[/tex]

By definition, the sum of the internal angles of a triangle is 180 degrees.

So:

[tex]A2 + A3 + 90 = 180\\A2 = 180-90-A3\\A2 = 180-90-45\\A2 = 45[/tex]

Thus, angle 2 measures 45 degrees.

Answer:

45 degrees

f(-2) means replace x in the equation with -2, then solve:

-2^2 +5(-2)

Simplify:

4 + -10

Add:

-6

Answer:

150

Step-by-step explanation:

Given that;

Company A offers;

Salary= $ 17000

commission= $100 per tv set

Company B offers;

Salary= $29000

Commission = $ 20 per tv set

Let the number of tv set sold to be= x

To solve this problem, the amount obtained after selling for A option should be equal to B option

Form equations

[tex]17000 +100 x = 29000 + 20x\\\\\\100x-20x= 29000-17000\\\\\\80x=12000\\\\\\x=12000/80 = 150[/tex]

The number of televisions sold for the options to be equal = 150

Answer:

Amara needs to sell 150 televisions to make both options earnings equal.

Step-by-step explanation:

Let the number of television sold be = x

For company A:

Salary is $17,000 plus a $100 commission for each television she sells.

Equation becomes:

[tex]f(x)=17000+100x[/tex]

For company B :

Salary is $29,000 plus a $20 commission for each television she sells.

Equation becomes:

[tex]f(x)=29000+20x[/tex]

So, to calculate how many televisions would Amara need to sell for the options to be equal, we will equal both the equations.

[tex]17000+100x=29000+20x[/tex]

=> [tex]100x-20x=29000-17000[/tex]

=> [tex]80x=12000[/tex]

x = 150

So, Amara needs to sell 150 televisions to make both options earnings equal.

We can check this :

[tex]17000+100(150)=29000+20(150)[/tex]

=> [tex]17000+15000=29000+3000[/tex]

=> [tex]32000=32000[/tex]

Answer:

420

Step-by-step explanation:

Each of the 7 appetizers can be paired with one of 10 entrees, and each entree can be paired with one of 6 desserts.  So the number of combinations is:

7 × 10 × 6 = 420

By combination property, there are a total of 420 different lunch specials that are possible.

The combination property is defined as the selection of items from a set that has distinct members, such that the order of selection does not matter.

It is given that a restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts.

Thus, there are 3 different items which quantities are also mentioned. '

Thus by combination property, the total number of lunch specials that are possible -

7 * 10 * 6 = 420 .

Therefore, by combination property, there are a total of 420 different lunch specials that are possible.

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Answer:

The height of the lighthouse is [tex]742.5\ ft[/tex]

Step-by-step explanation:

Let

h -----> the height of the lighthouse

we know that

The tangent of angle of 68 degrees is equal to divide the height of the lighthouse by the horizontal distance from the buoy to the base of lighthouse

so

[tex]tan(68\°)=\frac{h}{300}[/tex]

Solve for h

[tex]h=(300)tan(68\°)=742.5\ ft[/tex]

False.

[tex]\sec{\dfrac{\pi}{2}}=undefined[/tex]

Hope this helps.

r3t40

Answer:

TRUE APEX dont trust the other guy!!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

We need to find the value of log4(768).

768 can be written as 3*256

which further can be simplified to 3*4^4

so using the log property log(AB)=log A+ log B

we can write

log4(768) = log4(3)+log4(4^4)

                 =0.7925+4log4(4)

                 =0.7925+4

                  =4.7925

ANSWER

5.2387 and 5.2437

EXPLANATION

To round a decimal to the nearest hundredth means we should round to two decimal places.

To round to two decimal places we consider the third decimal place.

When we round 5.2387 to the nearest hundredth, we obtain 5.24 because the third decimal place is greater than or equal to 5 so we round up.

When we round 5.2437 to the nearest hundredth, we get 5.24 because the third decimal place less than 5 so we round off.

In fact there are infinitely many decimals that will round to 5.24 when rounding to the nearest hundredth.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y< 8[/tex]

The solution is the interval -----> (-∞,8)

[tex]y\geq3[/tex]

The solution is the interval -----> [3,∞)

The solution of the system is equal to

[3,∞)∩ (-∞,8)-------> [3,8)

All real numbers greater than or equal to 3 and less than 8

The graph in the attached figure

Answer:

B.

Step-by-step explanation:

Let's find g(f(x)) for each choice for fun and so you can have more examples:

A) f(x)=3x and g(x)=sqrt(x)+1

so g(f(x))=g(3x)=sqrt(3x)+1

So definitely not this choice

B) f(x)=x+1 and g(x)=sqrt(3x)

so g(f(x))=g(x+1)=sqrt(3(x+1))

So this one works! :)

C) f(x)=sqrt(x)+1 and g(x)=3x

so g(f(x))=g(sqrt(x)+1)=3(sqrt(x)+1)

Not this one!

D) f(x)=sqrt(3x) and g(x)=1

g(f(x))=g(sqrt(3x))=1

Answer:

Sorry if its wrong i hope it helps!

Answer:

Step-by-step explanation:

[tex]\text{Use the Pythagorean theorem to calculate the length of the CB:}\\\\CB^2+BA^2=AC^2\\\\CB^2+6^2=12^2\\\\CB^2+36=144\qquad\text{subtract 36 from both sides}\\\\CB^2=108\to CB=\sqrt{108}\\\\CB=\sqrt{36\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\CB=\sqrt{36}\cdot\sqrt3\\\\CB=6\sqrt3[/tex]

[tex]\text{Use sine to calculate the length of CD:}\\\\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\theta=55^o\\opposite=6\sqrt3\\hypotenuse=CD\\\\\sin55^o\approx0.8192\qquad(look\ at\ the\ picture)\\\\\text{Substitute:}\\\\0.8192=\dfrac{6\sqrt3}{CD}\\\\0.8192=\dfrac{10.3923}{CD}\qquad\text{multiply both sides by}\ CD\\\\0.8192CD=10.3923\qquad\text{divide both sides by 0.8192}\\\\CD\approx12.7[/tex]

Answer: 6x+18

Step-by-step explanation: Because of the Distributive property, you would multiply the 6 by the’x’ and 3, as they are in the parenthesis.

The distributive property is the ability of one operation to "distribute" over another operation contained inside a set of parenthesis. So, all we (you) need to do is "distribute" the 6 to the x and 3. Observe.

6(x + 3) =

6x + 18 is the rewritten equation using the distributive property.

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \cline{1-1} r=6\\ \theta =\frac{\pi }{3} \end{cases}\implies s=6\left( \frac{\pi }{3} \right)\implies s=2\pi \implies \stackrel{\textit{rounded up}}{s=6.3}[/tex]

Answer: [tex]arc\ length=6.3\ ft[/tex]

Step-by-step explanation:

You  need to use the following formula for calculate the arc lenght:

[tex]arc\ length=r\theta[/tex]

Where  "r" is the radius and [tex]\theta[/tex] is the central angle in radians.

You know that the central angle in radians s:

[tex]\theta=\frac{\pi }{3}[/tex]

And the radius is:

[tex]r=6\ ft[/tex]

Therefore, the final step is to substitute the values into the formula. Then you get:

[tex]arc\ length=(6\ ft)(\frac{\pi }{3})[/tex]

[tex]arc\ length=6.3\ ft[/tex]

Answer:

B.  9/4 <x <= 4

Step-by-step explanation:

5x - 19 <= 1

5x <= 20

 x <= 4

-4x + 3 < - 6

-4x < - 9

  x > 9/4

Answer

9/4 <x <= 4

Answer:

x ≤ 4

Step-by-step explanation:

1. 5x - 19 ≤ 1

Add: 5x ≤ 20

Divide: x ≤ 4

2. -4x + 3 > -6

Subtract: -4x > -9

Divide: x < ⁹/₄

3. Or means the union of the two sets, or all values that are in either set.

x ≤ 4 ∪ x < ⁹/₄ is x ≤ 4, since they both inequality signs point left, and 4 is larger than ⁹/₄, so x ≤ 4 also includes x < ⁹/₄.

I see here that x ≤ 4 is not one of the options. I'm not sure what to do then.

Answer:

7x+y=37

Step-by-step explanation:

You basically just add the numbers, So you add 5 and 2 and then you subtract 2 from 3 which is 1 and then you add 21 and 16

Answer:

Step-by-step explanation:

Notice that for each unit increase in x, y increases by 1 unit.  Thus, the parent function is y = x.

Answer:

f(x)=x

Step-by-step explanation:

We are given with a table, Lets look at the value of x  and y

The value of y is constantly increasing and the value of x is also increasing constantly. So it is a table for a linear equation.

the value of x  and y are same, so the equation of the line is

y=x

when x=-2  the value of y=-2

when x=1 the value of y=1

Hence , the parent function is  [tex]f(x)=x[/tex]

Answer:

Properties of Real Numbers ...

Step-by-step explanation:

Commutative Property of Multiplication (Numbers) 2 • 10 = 10 • 2

Associative Property of Addition (Numbers) 5 + (6 + 7) = (5 + 6) + 7

Associative Property of Multiplication (Numbers) 6 • (3 • 2) = (6 • 3) • 2

Additive Identity (Numbers) 6 + 0 = 6

The equation demonstrates the Associative Property of Addition, stating that the grouping of numbers being added does not affect the sum.

The property shown in the equation 3 + (5 + 7) = (3 + 5) + 7 is the Associative Property of Addition. According to this property, the grouping of numbers being added does not affect the sum. In other words, when adding three or more numbers, it doesn't matter how they are grouped in parentheses.

In this specific equation, we are adding 5 and 7 first, which gives us 12. Then, adding 3 to 12 gives us a sum of 15. On the other side of the equation, we first add 3 and 5 to get 8, and then add 8 to 7 to get the same sum of 15.

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Answer:

Equation of line: y=3x-18

Step-by-step explanation:

Point: (5,7) and slope=-13

y-7=-13(x-5)

y=-13x+72

Answer:

Yep the answer is C bro. I very much appreciate your help :D

congruency statement applies to the trapezoids is CDEF ≅ NMOP.

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid

From question, we have

Hence, Trapezoid CDEF and trapezoid NMOP are congruent.

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[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$1040\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years \end{cases} \\\\\\ 1040=1000(1+0.04t)\implies \cfrac{1040}{1000}=1+0.04t\implies \cfrac{26}{25}=1+0.04t \\\\\\ \cfrac{26}{25}-1=0.04t\implies \cfrac{~~\frac{26}{25}-1~~}{0.04}=t\implies \cfrac{~~\frac{1}{25}~~}{0.04}=t\implies 1=t[/tex]