If a normal distribution has a mean of 132 and a standard deviation of 20 what is the value that has a z score of 2.4?

Answer:

B

Step-by-step explanation:

Answer:

(x, y ) = (3 , - 4 )

Step-by-step explanation:

given the 2 equations

2x - 3y = 18 → (1)

4x + y = 8 → (2)

multiply (2) by 3

12x + 3y = 24 → (3)

add (1) and (3) term by term to eliminate the term in y

(2x + 12x) + (- 3y + 3y) = (18 + 24)

14x = 42 ( divide both sides by 14 )

x = 3

substitute x = 3 in (1) or (2) to evaluate for y-coordinate

(2) → 12 + y = 8 ⇒ y = 8 - 12 = - 4

solution is (3, - 4 )

The set of angle measures could be the measures of the interior angles of a triangle are,

⇒ 55°, 90°, and 35°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

To find the set of angle measures could be the measures of the interior angles of a triangle.

Now, We know that;

Sum of all interior angles of a triangle is 180 degree.

A) 60°, 45°, and 70°

⇒ 60 + 45 + 70

⇒ 175 ≠ 180

Hence, It is not possible.

B) 30°, 85°, and 25°

⇒ 30 + 85 + 25

⇒ 140 ≠ 180

Hence, It is not possible.

C) 55°, 90°, and 35°

⇒ 55 + 90 + 35

⇒ 180

Hence, It is possible.

Thus, The set of angle measures could be the measures of the interior angles of a triangle are,

⇒ 55°, 90°, and 35°

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Answer:

A [tex]\alpha ,\beta[/tex]

Step-by-step explanation:

Step 1

The first step is to notice that the graphs of II and iv have the same y intercept. This means that we are looking for functions that match the condition that when t=0, the two functions have the same value.  The functions [tex]10(1.02)^t,10(1.05)^t[/tex] meet that condition. Additionally the functions  [tex]30(0.95)^t,30(1.05)^t[/tex] meet this condition.

Step 2

The other condition that must be met by the 2 functions is that they should both increase with the increase in increasing values of t.  the function  [tex]30(0.95)^t[/tex] does not meet this condition. This means that only the functions [tex]\alpha ,\beta[/tex] are the only functions that meet this condition.

Answer:

a. α and β

Step-by-step explanation:

One way to solve this exercise is by analyzing the y - intercept of the functions.

By looking at the graph, we can see that II and IV have the same y - intercept.

All the formulas below depend of the variable ''[tex]t[/tex]'' so if we want to find the y - intercept we only need to replace by ''[tex]t=0[/tex]'' in the formulas.

We can also see that the y - intercept of II and IV will be the lower that the another y - intercept of the functions.  

If we replace by [tex]t=0[/tex] :

(α)(t) = [tex]10.(1.02)^{t}[/tex] ⇒ [tex]10.(1.02)^{0}=10[/tex]

(β)(t) = [tex]10.(1.05)^{t}[/tex] ⇒ [tex]10.(1.05)^{0}=10[/tex]

(χ)(t) = [tex]20.(1.02)^{t}[/tex] ⇒ [tex]20.(1.02)^{0}=20[/tex]

(δ)(t) = [tex]30.(0.85)^{t}[/tex] ⇒ [tex]30.(0.85)^{0}=30[/tex]

(ε)(t) = [tex]30.(0.95)^{t}[/tex] ⇒ [tex]30.(0.95)^{0}=30[/tex]

(Φ)(t) = [tex]30.(1.05)^{t}[/tex] ⇒ [tex]30.(1.05)^{0}=30[/tex]

We find that the lowest y - intercept (also equal) are the y - intercept of α and β. Therefore, the correct option is a. α and β

Answer:

Width of the rectangular side of that prism is, 9cm

Step-by-step explanation:

The formula for Perimeter of pentagonal prism is given by:

[tex]P = 5b[/tex]

where

P represents the perimeter of the pentagonal prism and

b is the base length of the pentagonal prism.

Given: Perimeter of pentagonal prism(P) is 45 cm.

Then;

45 = 5b

Divide both sides  by 5 we get;

[tex]b = \frac{45}{5} = 9 cm[/tex]

Therefore, the width of the rectangular side of that prism is, 9cm

Answer:

Width of the rectangular side of that prism is, 9cm

Step-by-step explanation:

Answer:

k = 3

Step-by-step explanation:

the equation relating x and y is

y = kx ← k is the constant of proportionality

to find use the given conditions

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{36}{12}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Answer:

1. [tex]\Delta ADC\sim \Delta RTS[/tex] because [tex]\angle A\cong \angle R[/tex], [tex]\angle C\cong \angle S[/tex] and [tex]\angle D\cong \angle T[/tex]

Step-by-step explanation:

We have been given two triangles [tex]\Delta ADC[/tex] and [tex]\Delta RTS[/tex]. We are asked to find the relationship between these triangles.

By angle sum property let us find measure of angle C of triangle ADC.

[tex]m\angle C+m\angle D+m\angle A=180^{o}[/tex]

[tex]m\angle C+51.2^{o}+96.5^{o}=180^{o}[/tex]

[tex]m\angle C+147.7^{o}=180^{o}[/tex]

[tex]m\angle C=180^{o}-147.7^{o}[/tex]

[tex]m\angle C=32.3^{o}[/tex]

Let us find measure of angle T of triangle RTS.

[tex]m\angle T+m\angle R+m\angle S=180^{o}[/tex]

[tex]m\angle T+96.5^{o}+32.3^{o}=180^{o}[/tex]

[tex]m\angle T+128.8^{o}=180^{o}[/tex]

[tex]m\angle T=180^{o}-128.8^{o}[/tex]

[tex]m\angle T=51.2^{o}[/tex]

We can see that [tex]m\angle C=m\angle S[/tex], [tex]m\angle A=m\angle R[/tex] and [tex]m\angle D=m\angle T[/tex]. Therefore, [tex]\Delta ADC\sim \Delta RTS[/tex] and 1st option is the correct choice.

Answer:

770 high-quality songs were downloaded

Step-by-step explanation:

A web music store offerst two versions:

There were 1290 for a total download size of 4403MB.

According to the information above, we have the following system of equations:

A + B =1290

2.1A + 4.3B = 4403

Where 'A' referst to the number of Standard songs and 'B' refers to the number of High Quality songs.

Solving the sistem of equations we get that:

A + B =1290 ⇒ A = 1290 - B

2.1A + 4.3B = 4403 ⇒ 2.1(1290 - B) + 4.3B = 4403

⇒ 2709 - 2.1B + 4.3B = 4403 ⇒ 2.2B = 1694 ⇒ B=770

Now, let's find the value of 'A':

A + B =1290 ⇒ A = 1290 - 770 ⇒ A = 520.

Therefore, 770 high-quality songs were downloaded.

There are 8 possibilities: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Of these 4 have at least two heads. Assuming a fair coin, the probability of tossing at least two heads is 4/8 or 1/2. The Answer would probably be 3/8 though.

C) 3/8

The probability of heads is 1/2, so the probability of not-heads is 1/2.

Then the probability of 2 heads and a tails is (1/2)²·(1/2) = 1/8.

There are 3 choose 2 = (3·2)/(2·1) = 3 ways that the pair of heads may appear among the three tosses. Thus the probability of 2 heads in 3 tosses is ...

... 3·(1/8) = 3/8

_____

Or you can simply count the favorable outcomes among the possible outcomes:

TTT TTH THT THH HTT HTH HHT HHH . . . . 3 of 8 are favorable.

Answer:

161

Step-by-step explanation:

We will use the math operation addition to find last year's number of floats. We know this year was 127 and was fewer than 34. So 127+34=last year's floats.

127+34=161

Answer:

The answer is 19.0000. 38 divided by two = t. (19)

Step-by-step explanation:

The approximate solution of an equation is simply an estimate of the solution.

The approximate solution of 2t = 38 is (d) 19.0000

The equation is given as:

[tex]\mathbf{2t =38}[/tex]

Start by dividing both sides of the equations by 2

[tex]\mathbf{\frac{2t}{2} =\frac{38}2}[/tex]

Divide 2t by 2, to give 2

So, we have

[tex]\mathbf{t =\frac{38}2}[/tex]

Divide 38 by 2 to give 19

[tex]\mathbf{t =19}[/tex]

From the list of given options, 19.0000 approximates to 19.

So, the solution of the equation can be rewritten as:

[tex]\mathbf{t =19.0000}[/tex]

Hence, the approximate solution is (d) 19.0000

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Answer:

16

D is correct.

Step-by-step explanation:

Coefficient: The coefficient is a number front of variable.

[tex]Expression: x^2+16y[/tex]

In the given expression there are two terms

x² and 16y

First term: x²

The coefficient of x² is 1

Second term: 16y

The coefficient of 16y is 16

Hence, The coefficient of 16 of the given expression.

Answer: The price of each shirt she bought was $22.95.

Step-by-step explanation:

Hi, to answer this, first, we have to add to the discounted price (52.22) the amount of the credit (39.58), to obtain the original total cost (without discount).

So:

52.22+39.58 = $91.8

Since she bought 4 shirts, we have to divide the total cost by 4:

91.8 /4 = $22.95

The price of each shirt she bought was $22.95.

Given:

A motorist traveled 250 miles on 11 gallons of gas.

To Find:

In the same vehicle, the distance that can be traveled in 16 gallons.

Answer:

Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.

Step-by-step explanation:

We first find the number of miles that can be traveled on 1 mile of gas.

We do this by using the unitary method.

Given that in 11 gallons, 250 miles can be traveled in a certain vehicle.

So in 1 gallon, 250 ÷ 11 miles can be traveled. This is roughly equal to 22.72.

Next we will calculate how much distance he can go in 16 gallons. We multiply the distance traveled in 1 gallon by 16.

That is, in  16 gallons, the number of miles that can be traveled is 22.72 x 16 = 363.52.

Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.

Answer:363.6miles

Step-by-step explanation:

so, if you checked the link above, you know what we'll be doing, lemme run through it without much fuss.

[tex]\bf \stackrel{\textit{firstly some grouping}}{(x^2-4x)+(y^2+4y)=0}\implies (x^2-4x+\boxed{a}^2)+(y^2+4y+\boxed{b}^2)=0 \\\\[-0.35em] ~\dotfill\\\\ 2\cdot x\cdot \boxed{a}=4x\implies \boxed{a}=\cfrac{4x}{2x}\implies \boxed{a}=2 \\\\\\ 2\cdot y\cdot \boxed{b}=4y\implies \boxed{b}=\cfrac{4y}{2y}\implies \boxed{b}=2[/tex]

now, let's recall, we're simply borrowing from our very good friend Mr Zero, 0, so if we add whatever, we also have to subtract whatever.

[tex]\bf (x^2-4x+2^2-2^2)+(y^2+4y+2^2-2^2)=0 \\\\\\ (x^2-4x+2^2)+(y^2+4y+2^2)-4-4=0 \\\\\\ (x-2)^2+(y+2)^2-8=0\implies (x-2)^2+(y+2)^2=8 \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-2)^2+(y+2)^2=(\sqrt{8})^2\qquad \impliedby radius=\sqrt{8}[/tex]

Answer: D. an angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive x-axis.

D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive [tex]x-[/tex]axis.

A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.

An angle can be defined as the figure formed by two rays meeting at a common end point.

D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive [tex]x-[/tex]axis.

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Answer:

Each Child get = 0.928 pounds of candy

Step-by-step explanation:

Total no of girls are 3

total no of boys are 4

Total no boys and girls are = 3 + 4

                                             = 7

Now it is given that Mr Reese booth have some pound of candies and he wants to distribute it equally among each children

total candy Mr Reese have is [tex]6\frac{1}{2}[/tex]

Now converting it to proper fraction

[tex]6\frac{1}{2}[/tex] =[tex]\frac{6*2+1}{2}[/tex]

                                 =  [tex]\frac{13}{2}[/tex]

Now the amount of candy have =[tex]\frac{13}{2}[/tex]

Now we have to divide it into 7 kids

so

each kid get = total candy / total children

                     =[tex]\frac{13}{2}[/tex]÷7

Changing the divide sign to multiplication  

                      [tex]=\frac{13}{2}*\frac{1}{7}[/tex]

Which becomes

                      [tex]=\frac{13}{14}[/tex]

solving it gives

Each Child get = 0.928 pounds of candy

Answer:

c

Step-by-step explanation:

sinB= 3/5 is correct

tanA= 4/3 is correct

and sinA= 4/5 is correct

hope this helps ^

Answer:

3/4

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−5, −4), B(−7, 3) and C(3, −2) to the image triangle A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25) and C' (2.25, −1.5).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A(−5, −4) ---> A' (−3.75, −3) = [tex]\frac{-3.75}{-5} , \frac{-3}{-4}=(\frac{3}{4} , \frac{3}{4})[/tex]

B(−7, 3) ---> B' (−5.25, 2.25) = [tex]\frac{-5.25}{-7} , \frac{2.25}{3}=(\frac{3}{4} , \frac{3}{4})[/tex]

C(3, −2) ---> C' (2.25, −1.5) = [tex]\frac{2.25}{3} , \frac{-1.5}{-2}=(\frac{3}{4} , \frac{3}{4})[/tex]

Therefore, the scale factor of the dilation is 3/4.

Answer:

g(-1) = -1

g(1) =5

Step-by-step explanation:

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

If x=-1  substitute this into the equation

g(-1) = (-1) ^3 + (-1+1)^2

g(-1) = 1+0  =-1

If x=1  substitute this into the equation

g(1) = (1)^3 + (1+1)^2 = 1+2^2 = 1+4 =5

Hi There!

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

Function: g(x) = x³ + (x + 1)²

Substitute: -1

Substitute: g(-1) = -1³ + (-1 + 1)²

Remember to follow PEMDAS.

Parenthese's: g(-1) = -1³ + (0)²

Exponents: g(-1) = -1 + 0

Simplify: g(-1) = -1

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

Function: g(x) = x³ + (x + 1)²

Substitute: 1

Substitute: g(1) = 1³ + (1 + 1)²

Remember to follow PEMDAS.

Parenthese's: g(1) = 1³ + (2)²

Exponents: g(1) = 1 + 4

Simplify: g(1) = 5

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

Hope This Helps :)

Answer: g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96 which is choice C

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

Explanation:

Given roots: -2, 4, 4, 3

Based on that, we know that x = -2, x = 4, x = 4, and x = 3. The repeat x value of 4 is needed to help deal with a double root (multiplicity 2)

x = -2 leads to x+2 = 0, so (x+2) is one factor

x = 4 leads to x-4 = 0, making (x-4) another factor. We have two copies of (x-4) as a factor

x = 3 leads to x-3 = 0 so (x-3) is the last factor

Overall, the four factors are: (x+2) and (x-4) and (x-4) and (x-3)

Use the distributive property to expand everything out

g(x) = (x+2)(x-4)(x-4)(x-3)

g(x) = ( (x+2)(x-4) ) * ( (x-4)(x-3) )

g(x) = ( x^2 - 2x - 8 ) * ( x^2 - 7x + 12 )

g(x) = x^2( x^2 - 7x + 12 ) - 2x( x^2 - 7x + 12 ) - 8( x^2 - 7x + 12 )

g(x) = x^4 - 7x^3 + 12x^2 -2x^3 + 14x^2 - 24x - 8x^2 + 56x - 96

g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96

which shows how I got choice C as the answer

Answer:

1. 50%

2. 30.372

3. 569.99

5. 29.99

7. 479.99

8. 65%

9. 306.33

10. 20%

11. 31,491

Answer:

The correct answer is option C

Step-by-step explanation:

Area is usually the planar lamina of a two dimensional figure and usually expressed in units square meter, square feet, square inches etc.

While Volume is the total space occupied by an object in a 3-D setting and is usually expressed in cubic meter, cubic feet, cubic inches etc.

A 2-D dimension can not represent a 3-D structure and thus units of area inappropriate to measure volume

Hello from MrBillDoesMath!

Answer:

See Discussion section below

Discussion:

We know that

m<1  = m<2          ("measure" of angle 1 = measure of angle 2)

                     and

m<3 = m< 4

Adding these two equations gives

m<1 + m<3 = m<2 + m<4

From the diagram,  m<1 + m<3 =  m<CWE and m<2+m<4= m<FZH. Substituting these in the above equation gives:

m<CWE = m<FZH

Regards,  

MrB

Given equal angles in two figures, we prove that the angles formed by CWD and FZG, as well as DWE and GZH, are equal, thus showing m∠CWE = m∠FZH.

To prove that m∠CWE = m∠FZH, we can use the information given and apply the transitive property of equality. We have the following information:

Given:

1. m∠1 = m∠2 (angles 1 and 2 are congruent)

2. m∠3 = m∠4 (angles 3 and 4 are congruent)

We want to prove:

m∠CWE = m∠FZH

Now, let's construct a table to demonstrate the proof step by step:

| Statement         | Reason                               | Lines Used       |

|-------------------|--------------------------------------|------------------|

| 1. m∠1 = m∠2     | Given                                | Given            |

| 2. m∠3 = m∠4     | Given                                | Given            |

| 3. m∠CWD = m∠FZG | Corresponding angles are congruent   | Definition of ∠   |

| 4. m∠DWE = m∠GZH | Corresponding angles are congruent   | Definition of ∠   |

| 5. m∠CWD + m∠DWE = m∠FZG + m∠GZH | Adding equal quantities to equal quantities | Addition Property of Equality |

| 6. m∠CWE = m∠FZH | Angles CWD and DWE form ∠CWE, and angles FZG and GZH form ∠FZH | Definition of ∠ |

In lines 3 and 4, we use the definition of corresponding angles to show that angles CWD and FZG are congruent and angles DWE and GZH are congruent.

In line 5, we use the addition property of equality to add the two equal quantities, m∠CWD and m∠DWE on the left side, and m∠FZG and m∠GZH on the right side.

In line 6, we use the definition of angles to establish that m∠CWE is equal to m∠FZH.

In conclusion, we have successfully proven that m∠CWE = m∠FZH using the given information and the properties of angles.

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To find the better buy, we can find how much they cost for an ounce and find it by comparison.

First option:

20/4.4

=$4.545454...

Second option:

16/3.68

=$4.3478...

As $4.3478..< $4.5454.., the second option is cheaper and therefore is the better buy.

Hope it helps!

The 20 ounces for $4.40 is the better deal at $0.22 per ounce, compared to the 16 ounces for $3.68 at $0.23 per ounce.

To determine which cereal is the better buy, we need to calculate the cost per ounce for each option. For the first option of 20 ounces at $4.40, the cost per ounce is:

[tex]\frac{0.44}{20} = 0.22 ~per ounce[/tex]

For the second option of 16 ounces at $3.68, the cost per ounce is:

[tex]\frac{3.68}{16} = 0.23[/tex]

Comparing these two costs per ounce, the 20 ounces for $4.40 is the better buy because it has a lower cost per ounce.

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

A) 9, 12, 21

9 + 12 = 21  YES :)

B) 9, 11, 12

9 + 11 = 20 > 12  NOT :(

C) 12, 14, 16

12 + 14 = 26 > 16  NOT :(

D) 16, 18, 25

16 + 18 = 34 > 25  NOT :(

Answer:

7<x<17

Step-by-step explanation:

a+b>x

5+12>x

17>x

5+x>12

x>7

12+x>5

x>-7 (ignore then since it is negative and you would use the one that makes the range smaller which is the one above)