Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 15. Find the probability that a randomly selected adult has an IQ less than 130.

To start off scaling is another way of saying resizing the numbers --

Example: "1" on paper means "10" in real life   --

To predict a product of a number/fraction using scaling, you would compare the size of a product on the basis of the size of the other.

Most scaling is used in maps or something to do with rulers

I hope this helps!!

Answer:

See attachment.

Step-by-step explanation:

The equation of the function is

[tex]y=-4x+7[/tex]

The slope of this function is

[tex]m=-4[/tex] and the y-intercept is [tex]c=7[/tex].

This implies that the graph of the straight line passes through (0,7).

Let us also find the x-intercept by putting y=0 into the equation.

[tex]0=-4x+7[/tex]

[tex]-7=-4x[/tex]

Divide through by -4.

[tex]\Rightarrow x=\frac{7}{4}[/tex]

Therefore the graph also passes through [tex](\frac{7}{4},0)[/tex].

We plot these two points and draw a straight line through them.

If the room is 10 by 12 that means each wall is 10 by 12 (I'm assuming) so the area of each wall is 120 ft and since there are 4 of them the total area of the walls is 480 ft and if wallpaper costs 1.53 per ft, it costs 480 * 1.53 or $734.40

Hope this helps

Answer:

[tex]C(h)=\$30+xh[/tex]

Step-by-step explanation:

Let

C-----> the cost of having a plumber spend h hours at your house

h----> the number of hours

x----> the cost per hour of labor

we know that

The linear equation that represent the cost C is equal to

[tex]C(h)=\$30+xh[/tex]

In this linear equation in the slope-intercept form (y=mx+b)

the slope is equal to [tex]m=x\frac{\$}{hour}[/tex]

the y-intercept b is equal to [tex]b=\$30[/tex] ---> charge for coming to the house

The Answer is 0.0636 c

Answer:

(2, 8).

Step-by-step explanation:

(x - 2)^2 + (y - 6)^2 = 4

If x = 2 and y = 8 we have:

(2 - 2)^2 + (8 - 6)^2

= 0 + (2^2

= 4.

So it passes through the point (2,8).

The point through which the circle passes is:

                               (2,8)

The equation of the circle is given by:

[tex](x-2)^2+(y-6)^2=4[/tex]

We will check by putting each point in the equation and check which is equal to 4.

1)

(2,8)

when x=2 and y=8 we have:

[tex](2-2)^2+(8-6)^2=4\\\\i.e.\\\\0^2+2^2=4\\\\i.e.\\\\4=4[/tex]

Hence, the circle passes through the point (2,8).

2)

(5,6)

when x=5 and y=6 we have:

[tex](5-2)^2+(6-6)^2=4\\\\i.e.\\\\3^2+0^2=4\\\\i.e.\\\\9=4[/tex]

which is not true.

Hence, the circle does not pass through (5,6).

3)

(-5,6)

when x= -5 and y=6 we have:

[tex](-5-2)^2+(6-6)^2=4\\\\i.e.\\\\(-7)^2+0^2=4\\\\i.e.\\\\49=4[/tex]

which is not true.

Hence, the circle does not pass through (-5,6).

4)

(2,-8)

when x=2 and y= -8 we have:

[tex](2-2)^2+(-8-6)^2=4\\\\i.e.\\\\0^2+(-14)^2=4\\\\i.e.\\\\196=4[/tex]

Hence, the circle does not passes through the point (2,-8).

1. subtract 47.5 from both sides

2. divide both sides by 4.5

3. 3

Just did in edg

Answer:

1. By substitution property of inequality

5(9.5)+4.5[tex]\leq[/tex]65

2. By using multiplication  in equality then we get

47.5+4.5x[tex]\leq[/tex]65

3. The five friends will have 3 snacks to split.

Step-by-step explanation:

Given

Five friends have total money= $65

Cost of each movie ticket= $9.50

Cost of each snack item= $4.50

Let ,five friends have total snacks = x

Total movie tickets=5

Because total number of friends=5

The inequality expressionis given by

I Step: [tex]5(9.5)+4.5x\leq 65[/tex]

Reason: By using substitution property of inequality

[tex]47.5+4.5x\leq 65[/tex

2. Step :[tex]4.5x[tex]\leq[/tex]65-47.5[/tex]

[tex]4.5x\leq 17.5[/tex]  ( by subtarction 47.5  from both sides)

[tex]x\leq \frac{17.5}{4.5}[/tex]   ( by dividing 4.5 on both sides )

Because they can buy maximum 3 snacks .

Beacause the number of snacks is natural number so we can't take in rational numbers.

Answer:

Step-by-step explanation:

A=l•w

=5/6•1/3

=5/18

A=0.28 mi²

Answer:

  11.55

Step-by-step explanation:

SOH CAH TOA reminds you ...

  Tan = Opposite/Adjacent

The angle at lower left is the complement of 60°, so is 30°. Then the side x satisfies the equation ...

  tan(30°) = x/20

Multiplying by 20 gives ...

  20·tan(30°) = x ≈ 11.55

Angle K is bisected which means it is actually twice the shown angle.

Angle K = 22 x 2 = 44 degrees.

Angle H = Angle K = 44 degrees.

The sum of Angle G and J is 360 - 44 - 44 = 272 degrees

Angle G and J are identical, so angle G = 272 / 2 = 136

Angle G is also bisected, so angle 1 = 136 / 2 = 68 degrees.

The answer is C. 68

Answer:

a) 0.0139; b) 0.1809; c) 0.4278

Step-by-step explanation:

We use a normal approximation to a binomial distribution for these problems.

The sample size, n, for each is 30; p, the probability of success, is 0.808.  This makes the mean, μ = np = 30(0.808) = 24.24.  The standard deviation,

σ = √(npq) = √(30(0.808)(1-0.808)) = √(30(0.808)(0.192)) = √4.65408 = 2.1573

For part a,

We are asked for P(X < 20).  Using continuity correction to account for the discrete variable, we find

P(X < 19.5)

z = (19.5-24.24)/(2.1573) = -4.74/2.1573 = -2.20

Using a z table, we see that the area under the curve to the left of this is 0.0139.

For part b,

We are asked for P(X = 24).  Using continuity correction, we find

P(23.5 < X < 24.5)

z = (23.5-24.24)/2.1573 = -0.74/2.1573 = -0.34

z = (24.5-24.24)/2.1573 = 0.26/2.1573 = 0.12

Using a z table, we see that the area under the curve to the left of z = -0.34 is 0.3669.  The area under the curve to the left of z = 0.12 is 0.5478.  The area between them is then

0.5478-0.3669 = 0.1809.

For part c,

We are asked to find P(25 ≤ X ≤ 28).  Using continuity correction, we find

P(24.5 < X < 28.5)

z = (24.5-24.24)/2.1573 = 0.26/2.1573 = 0.12

z = (28.5-24.24)/2.1573 = 4.26/2.1573 = 1.97

Using a z table, we see that the area under the curve to the left of z = 0.12 is 0.5478.  The area under the curve to the left of z = 1.97 is 0.9756.  The area between them is 0.9756 - 0.5478 = 0.4278.

Answer:

im not 100% sure but to me it looks like it could be 225

Answer:

The correct option is 3.

Step-by-step explanation:

From the given figure it is clear that the vertices of preimage are A(-4,-2), B(-2,1) and C(-2,-2).

Center of rotation is origin, i.e., (0,0).

Triangle ABC is rotated counterclockwise about the origin.

We need to find the angle of rotation.

Draw line segments OC and OC'. From the below figure it is clear that the angle of rotation counterclockwise about origin is

[tex]45^{\circ}+90^{\circ}+90^{\circ}=225^{\circ}[/tex]

Therefore the correct option is 3.

Answer:

Step-by-step explanation:

Graphs of quadratics are symmetrical about the vertex (minimum or maximum point).  

The x value of the point (-3, 11) is 3 units to the left of the vertex (0, 2), the x value that is 3 units to the right of the vertex will have the same y value, so the point

(3, 11) is also on the graph

The quadratic function has a minimum at (0, 2) and includes the point (-3, 11). Solving for the function's equation, we find y = x² + 2, and another point on the graph is (1, 3).

Since the quadratic function has a minimum at (0, 2), it means the vertex form of the quadratic function is y = a(x - 0)² + 2, or simply y = ax² + 2. We know another point on the graph is (-3, 11), so we can use this point to find the value of 'a'.

So, the equation of the quadratic function is y = x² + 2. To find another point on the graph, choose any x-value and compute the corresponding y-value. For example, let x = 1:

Thus, another point on the graph is (1, 3).

Answer:

  a = -3/2

Step-by-step explanation:

You can set x=0 and solve for y to find the y-intercept in each case.

  first equation: y-intercept = -3/2

  second equation: y-intercept = a

To make these equal, we must have ...

  a = -3/2

Answer: option a.

Step-by-step explanation:

 By definition we know that:

 [tex]log_a(a^n)=n[/tex]

Where a is the base of the logarithm.

 We also know that:

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

Then you can rewrite the logarithm given in the problem, as you can see below:

[tex]log_{17}(\sqrt{17})[/tex]

And keeping on mind the property, you obtain:

[tex]=log_{17}(17^{\frac{1}{2}})=\frac{1}{2}[/tex]

Therefore, you can conclude that the answer is the option a.

Answer:

The answer is 1/2 ⇒ answer (a)

Step-by-step explanation:

*The logarithm function is the inverse of the exponential function

- Ex: If 2³ = 8 ⇒  then [tex]log_{2}(8) = 3[/tex]

 Vice versa : If [tex]log_{5}(125)=3[/tex] ⇒ 5³ = 125

* In logarithm function:

- If [tex]log_{a}a=1[/tex] because [tex]a^{1}=a[/tex]

- If [tex]log_{a}a^{n}=(n)log_{a}a=n[/tex]

∵ [tex]log_{17}\sqrt{17}=log_{17}(17)^{\frac{1}{2}}[/tex]

- √b = [tex]b^{\frac{1}{2}}[/tex]

∴ [tex]log_{17}(17)^{\frac{1}{2}}=\frac{1}{2}log _{17}(17)=\frac{1}{2}(1) = \frac{1}{2}[/tex]

∴ The answer is 1/2 ⇒ answer (a)

Answer:

A. seems to be the BEST choice from the information you have provided.

Answer:

A is the most practical answer with the info you have given

Step-by-step explanation:

It’s the third one C)

Answer:

B

Step-by-step explanation:

The limit of quotient of two functions is the quotient of their limits, provided that the limit in the denominator function is not zero:

[tex]\lim_{x\to x_0}\dfrac{g(x)}{h(x)}=\dfrac{ \lim_{x \to x_0} g(x) }{ \lim_{x \to x_0} h(x) }, \text{ where }\lim_{x \to x_0} h(x)\neq 0.[/tex]

In your case,

[tex]\lim_{x \to 4} h(x)=-2\neq 0,[/tex]

then

[tex]\lim_{x\to 4}\dfrac{g(x)}{h(x)}=\dfrac{ \lim_{x \to 4} g(x) }{ \lim_{x \to 4} h(x) } =\dfrac{0}{-2}=0.[/tex]

Answer:

It is B.

Step-by-step explanation:

Substitute x = 0 into the function

y = -2(0) - 4 = -4

x = 1:

y = -2(1) - 4 = -6.

x = 2 and 3 give y = -8 and - 10.

Answer:

The correct answer is B.

Step-by-step explanation:

Answer: [tex]\frac{y}{z^3}[/tex]

Step-by-step explanation:

To simplify the expression given in the problem, you must apply the proccedure shown below:

1- According the Exponents Rules, you know the following:

[tex]a^0=1\\\\a^{-n}=\frac{1}{a^n}[/tex]

2- Therefore, keeping the above on mind, you can simplify the expression given in the problem as you can see below:

[tex]x^0yz^{-3}=(1)yz^{-3}\\\\=yz^{-3}\\\\=y\frac{1}{z^3}\\\\=\frac{y}{z^3}[/tex]

1)

x + 2y = 21

+ -x + 3y = 29

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

5y = 50

y = 10

x + 2(10) =21

x = 1

2)

6x + 6y = 30

+ 15x - 6y = 12

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

21x = 42

x = 2

6(2) + 6y = 30

6y = 18

y = 3

1.  The solution to the system of equations is (x, y) = (1, 10)

2. the solution to the system of equations is (x, y) = (-2, 7)

3. the solution to the system of equations is (x, y) = (5, 3)

4.  the solution to the system of equations is (x, y) = (6, 4)

5.  the solution to the system of equations is (x, y) = (2, -3)

1. To solve the system of equations using elimination, you need to add the two equations to eliminate one of the variables. Here's how you can do it:

x + 2y = 21

-x + 3y = 29

Add the two equations together:

(x + 2y) + (-x + 3y) = 21 + 29

Now, simplify the equation:

(2y + 3y) = 50

Combine like terms:

5y = 50

Now, divide both sides by 5 to solve for y:

5y/5 = 50/5

y = 10

Now that you've found the value of y, substitute it back into either of the original equations to solve for x. Let's use the first equation:

x + 2(10) = 21

x + 20 = 21

Subtract 20 from both sides:

x = 21 - 20

x = 1

So, the solution to the system of equations is (x, y) = (1, 10). The correct answer is (1, 10).

2. 15x + 6y = 12

To solve this system of equations using elimination, you can follow these steps:

Multiply both sides of the second equation by 2 to make the coefficients of y in both equations equal:

2(15x + 6y) = 2(12)

30x + 12y = 24

Now you have the system:

6x + 6y = 30

30x + 12y = 24

Multiply the first equation by -5 to make the coefficients of x in both equations equal:

-5(6x + 6y) = -5(30)

-30x - 30y = -150

Now you have the system:

-30x - 30y = -150

30x + 12y = 24

Add the two equations to eliminate the x variable:

(-30x - 30y) + (30x + 12y) = (-150 + 24)

-18y = -126

Divide both sides by -18 to solve for y:

-18y / -18 = -126 / -18

y = 7

Now that you've found the value of y, substitute it back into the first equation to solve for x:

6x + 6(7) = 30

6x + 42 = 30

6x = 30 - 42

6x = -12

x = -12 / 6

x = -2

So, the solution to the system of equations is (x, y) = (-2, 7). The correct answer is (-2, 7).

3. Subtract the first equation from the second equation to eliminate the x variable:

(2x + 6y) - (2x + 2y) = 28 - 16

This simplifies to:

4y = 12

Divide both sides by 4 to solve for y:

4y / 4 = 12 / 4

y = 3

Now that you've found the value of y, substitute it back into the first equation to solve for x:

2x + 2(3) = 16

2x + 6 = 16

Subtract 6 from both sides:

2x = 16 - 6

2x = 10

Divide both sides by 2 to solve for x:

2x / 2 = 10 / 2

x = 5

So, the solution to the system of equations is (x, y) = (5, 3). The correct answer is (5, 3).

4. Multiply the second equation by -3 to make the coefficients of x in both equations equal:

-3(2x + y) = -3(8)

-6x - 3y = -24

Now you have the system:

2x - 3y = 0

-6x - 3y = -24

Add the two equations to eliminate the y variable:

(2x - 3y) + (-6x - 3y) = 0 - 24

This simplifies to:

-4x = -24

Divide both sides by -4 to solve for x:

-4x / -4 = -24 / -4

x = 6

Now that you've found the value of x, substitute it back into the first equation to solve for y:

2x - 3y = 0

2(6) - 3y = 0

12 - 3y = 0

Subtract 12 from both sides:

-3y = -12

Divide both sides by -3 to solve for y:

-3y / -3 = -12 / -3

y = 4

So, the solution to the system of equations is (x, y) = (6, 4). The correct answer is (6, 4).

5. To solve the system of equations using elimination, you can follow these steps:

Subtract the second equation from the first equation to eliminate the y variable:

(5x + 5y) - (5x - 5y) = -5 - 25

This simplifies to:

10y = -30

Divide both sides by 10 to solve for y:

10y / 10 = -30 / 10

y = -3

Now that you ve found the value of y, substitute it back into either of the original equations to solve for x. Let's use the first equation:

5x + 5(-3) = -5

5x - 15 = -5

Add 15 to both sides:

5x = -5 + 15

5x = 10

Divide both sides by 5 to solve for x:

5x / 5 = 10 / 5

x = 2

So, the solution to the system of equations is (x, y) = (2, -3). The correct answer is (2, -3).

Learn more about Solving systems of equations using elimination here:

https://brainly.com/question/29362376

#SPJ12

Answer: [tex]=14a^3-21a^2+42a-35[/tex]

Step-by-step explanation:

You can multiply the polynomials by applying the Distributive property.

It is important to remember the Product of powers property, which states that:

[tex](b^a)(b^c)=b^{(a+c)[/tex]

Where b is the base and a and c are exponents.

It is also important to remember the multiplication of signs:

[tex](-)(-)=+\\(+)(+)=+\\(+)(-)=-[/tex]

Then:

Each term inside of the first parentheses must multiply each term inside of the second parentheses:

[tex](7a-7)(2a^2-a+5)=(7a)(2a^2)+(7a)(-a)+(7a)(5)+(-7)(2a^2)+(-7)(-a)+(-7)(5)\\\\=14a^3-7a^2+35a-14a^2+7a-35[/tex]

Finally, add like terms:

[tex]=14a^3-21a^2+42a-35[/tex]

Answer:

D. [tex]y=\frac{7}{2}x[/tex]

Step-by-step explanation:

We are asked to find the equation, which represents the direct variation that contains the ordered pair (2,7).

When two quantities are proportional to each other, they are in form [tex]y=kx[/tex], where, k represents constant of variation.

Upon substituting [tex]y=7[/tex] and [tex]x=2[/tex] in above equation, we will get:

[tex]7=k\cdot 2[/tex]

Let us solve for k by dividing both sides by 2:

[tex]\frac{7}{2}=\frac{k\cdot 2}{2}[/tex]

[tex]\frac{7}{2}=k[/tex]

Therefore, our required equation would be [tex]y=\frac{7}{2}x[/tex] and option D is the correct choice.

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point form:

(3,2), (3-2), (-3,2), (-3,-2)

Equation Form:

x = 3, y = 2.

x = 3, y = -2.

x = -3, y = 2.

x = -3, y = -2.

Hope this is helpful. <33

Answer:

but putting 24% in the calculator

Step-by-step explanation:

24% as a fraction: 6/25

24% as a mixed number: it just a fraction

24% as a whole number: 24

Doubling the number every night will result in 4,194,304. How can that girl possibly sleep now with all those magic pennies?

Answer: The girl will have $524.288 (524,288 pennies) after 19 nights.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

So, we have to write an exponential expression where the initial value (a) is 1, the multiplicative rate of growth (b) is 2, and the time period (x) is 19.

Mathematically speaking: (where "y” is the total money)

y = ab×

y = 1 x (2) ∧19 = 524,288 pennies

Since 1 dollar = 100 pennies,

524,288 / 100 = $524.288

The girl will have $524.288 (524,288 pennies) after 19 nights.

Answer:

b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

bc IM JUICE WRLD

Answer:

The width of the rectangle is 3 and the width is 9. Those are reasonable measurements.

Step-by-step explanation:

Answer:

The difference is in which in way that they can be separated.

Step-by-step explanation:

While all three of these include mixtures of two or more things, a suspension can typically be re-separated by using a centrifuge and a solution can be filtered out. A colloid on the other hand, cannot typically be separated after it is put together.  

Answer: Last option.

Step-by-step explanation:

The formula for calculate the area of the circle is the shown below:

[tex]A_c=r^2\pi[/tex]

Where r is the radius of the circle.

As you can see in the figure attached, the radius of the circle is 6 units, then:

[tex]r=6units[/tex]

Therefore, when you substitute the value of the radius into the formula shown above, you obtain the following result:

[tex]A_c=(6\ units)^2\pi[/tex]

[tex]A_c=36\pi\ units^2[/tex]

Answer:

The correct answer is 36π square units

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where r - radius of circle

From the figure we can see a circle with radius 5 units

To find the area of circle

Area = πr² = π * 6² = 36π  square units

Area of given circle = 36π  square units

Therefore the correct answer is 36π  square units