o put on Your Thinking Cap!
$ Challenging Practice
1.
Michelle got an average score of 80 on two tests. What score must
she get on the third test so that her average score for the three tests
is the same as the average score for the first two tests?

Answer:

39

Step-by-step explanation:

8(4) + 11 -2(2)

32 + 11 - 4

43 - 4

39

Answer:

EF is 109

DAB is 54.5

Step-by-step explanation:

Applying the central angle theorem, the correct statement would be:

The central angle theorem states that:

Thus:

Measure of minor arc EF = m∠ECF = 109°

m∠DAB = 1/2(109°) [m∠ECF = m∠BAD = 109°]

m∠DAB = 54.5°

Therefore, applying the central angle theorem, the correct statement would be:

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Let X be a random variable denoting pulse rates of females as described, with mean µ = 74.0 bpm and standard deviation σ = 12.5 bpm. Then

P(70 < X < 78) = P((70 - µ)/σ < (X - µ)/σ < (78 - µ)/σ)

… = P(-0.32 < Z < 0.32)

… = P(Z < 0.32) - P(Z < -0.32)

… ≈ 0.6255 - 0.3745

… ≈ 0.2510

where Z is normally distributed with mean 0 and s.d. 1.

• • •

Next, you sample 25 females from the population and want to find the probability that their average falls between 70 and 78 bpm. Let [tex]X_i[/tex] denote the pulse rate of the i-th woman from the sample, and let Y be the random variable for the sample mean; that is,

[tex]Y=\displaystyle\sum_{i=1}^{25}\frac{X_i}{25}[/tex]

Recall that a sample of size n taken from a normal distribution with mean µ and s.d. σ has a mean that is also normally distributed with mean µ and s.d. σ/√n.

The mean stays the same, µ = 74.0, but now the s.d. is σ/√n = σ/5 = 2.5. So we have

P(70 < Y < 78) = P((70 - µ)/(σ/5) < (Y - µ)/(σ/5) < (78 - µ)/(σ/5))

… = P(-1.6 < Z < 1.6)

… = P(Z < 1.6) - P(Z < -1.6)

… ≈ 0.9452 - 0.0548

… ≈ 0.8904

Answer:

Area of the actual room = 288 m²

Step-by-step explanation:

Given:

Scale factor = 2cm to 4 m

Dimension of rectangle ball room = 6 cm and 12 cm

Find:

Area of the actual room

Computation:

Actual dimension of rectangle ball room;

⇒ [6/2]4 = 12 m

⇒ [12/2]4 = 24 m

Area of rectangle = Length x Width

⇒ Area of the actual room = Actual length x Actual width

⇒ Area of the actual room = 12 x 24

Area of the actual room = 288 m²

Answer:v= x a h add then multiply

Step-by-step explanation:

Answer:

Oops, didn't mean to answer because I already answered this one.

Step-by-step explanation:

Answer:

85/100*x=51

Step-by-step explanation:

85x=5100

Answer:

x=10

Step-by-step explanation:

Because of the two parallel lines, the ratio between the sides must be the same.  Since the bottom is 12 to 18 (a ration of two to three) we know that x and x+5 would have the same ratio.  Logically, x would have to equal 10 so that x+5 would equal 15 and a ratio of two to three would exist there too.  If you go to solve a problem and the answer isn’t obvious, jut set up a ratio.

12/18=x/(x+5)

then cross multiply and solve

12(x+5)=18x

12x+60=18x

60=18x-12x

60=6x

10=x

Answer:

x=10

Step-by-step explanation:

You can set it up as a proportion, since the lines are parallel, the sections are proportionate to each other.

[tex]\frac{x}{12} = \frac{x+5}{18} \\18x=12(x+5)\\18x=12x+60\\6x=60\\x=10[/tex]

The probability of winning the jackpot is 1/32728332.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 43) and matching the number on the gold ball (1 through 34).

Total number of white balls = 43

Number of combinations of selecting 5 from 43 = 43C₅  

                                                                                = 43! / (5! × 38!)

                                                                                = 962598

Total number of gold balls = 34

Number of combinations of selecting 1 from 34 = 34C₁

                                                                               = 34

Total number of ways of selecting 5 white balls and 1 gold ball = 962598 × 34 = 32728332

There is only 1 way for which the player wins the jackpot.

Probability of winning the jackpot = 1/32728332

Hence the required probability is 1/32728332.

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Answer:

Box dimensions:

L = 3 ft

D = 6 ft

H = 1 ft

Volume  V = 18 ft³

Step-by-step explanation:

a) Each side of the future box is

L = 5 - 2*x     D = 8 - 2*x  

height of the box is   x

Then the volume of the box as function of x is:

V(x) =  ( 5 - 2*x ) * ( 8  - 2*x ) * x

V(x) = ( 40 - 10*x - 16*x + 4*x² ) * x

V(x) = 40*x - 26*x² + 4*x³

Tacking derivatives on both sides of the equation:

V´(x) = 40 - 52*x + 12x²     or     V´(x) = 20 - 26*x + 6*x²

If V´(x) = 0

6*x² - 26*x + 20  = 0

Solving for x

x₁,₂  = (-b ± √ b² - 4*a*c  ] /2*a

x₁,₂  = ( 26  ±  √ 676  - 480  ) / 12

x₁,₂  =  (26 ± 14 )/ 12

x₁  = 1

x₂ = 3,33        ( we dismiss this solution since is not feasible according to cardboard dimensions )

Then the sides of the box are:

L = 5 -2*x      L  =  5 - 2*1     L = 3 ft

D = 8 - 2*x    D  = 8 - 2*1     D = 6 ft

H = x = 1 ft

And the volume is    V = 6*3*1 = 18 ft³

Answer:

Step-by-step explanation:

Answer:

y = 4

Step-by-step explanation:

Given that,

RS= 4y+2, ST = 3y+8, and RT = 38

We need to find the value of y.

As,

RT = RS+ST

Put all the values,

38 = 4y+2+3y+8

38-2-8 = 4y+3y

28 = 7y

y = 4

So, the value of y is equal to 4.

Answer:

1/5%

Step-by-step explanation:

The percentage of the model shaded green will be 20.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

The total number of the box in the figure is 100.

The total number of shaded green = 20

So,

[tex]\dfrac{20}{100} \times 100[/tex]

20%

Therefore, The percentage of the model shaded green will be 20.

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Answer:

588000

Step-by-step explanation:

if i am wrong pls tell me cause i think there's a different answer gl g

Answer:

$103,421.88

Step-by-step explanation:

Given:

P = 70000

r = 0.05

n = 1

t = 8

Work:

[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=70000(1+\frac{0.05}{1} )^{1*8}\\\\A=70000(1.05)^8\\\\A=103421.88[/tex]

Answer:

2/8

Step-by-step explanation:

freshman=4/8

1/8 soph    1/8 jr

add all together u get 6/8

the rest is seniors so its 2/8

Answer:

Step-by-step explanation:

x/3 + 6 = 17

Bringing like terms on one side

x/3 = 17 - 6

x/3 = 11

Dividing by 3 on both sides

x = 11/3

Answer:

w = 1/2

Step-by-step explanation:

One of the ways to solve problems using log is to use these two equations that use the same variables and plug in numbers.

log b (a) = c

b^c = a

By plugging in the numbers we get this:

log 16 (4) = w

16^w = 4

w = 1/2

Answer:  The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

Answer:

where's the two graphs

Step-by-step explanation:

where are the two graphs that we need to choose from??

Answer:

[tex]y = 5x + 3[/tex]

[tex]3y = zx - 1[/tex]

Step-by-step explanation:

Answer:they pay by yeezys

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

.......

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Take half of b (6/2=3)

Square it (3^2=9)

Answer:

A. 18

Step-by-step explanation:

Sum of the measures of all the angles of a quadrilateral is 360°

Therefore,

[tex]2m \degree + 8m \degree + 6m \degree + 4m \degree = 360 \degree \\ 20m \degree = 360 \degree \\ 20m = 360 \\ m = \frac{360}{20} \\ m = 18[/tex]

Answer:

The problem is telling you to find g ( f ( x ) )

Since we know that f(x) is square root of x, we can put the function this way.

g(√x)

Then, we use  √x as our x in our g(x) function.

You plug in  √x for x and you solve.

(√x ) ^2 is just x.

Finally the answer is

x-3

hope this helps :)

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

sqrt(36)^2

36

I hope this helps

9514 1404 393

Answer:

  (x, y) = (4, 5)

Step-by-step explanation:

The solution to the matrix equation ...

  [tex]\left[\begin{array}{cc}3&-2\\6&-5\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}2\\-1\end{array}\right][/tex]

is shown in the attachment. It is found by multiplying the equation on the left by the inverse of the coefficient matrix.

  [tex]\left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}4\\5\end{array}\right][/tex]

Answer:

Step-by-step explanation:

h = 4.2 in

Volume = 3.6  cubic inches

[tex]\frac{1}{3}\pi r^{2}h = 3.6\\\\\frac{1}{3}*3.14*r^{2}*4.2 = 3.6\\\\r^{2}= \frac{3.6*3}{3.14*4.2}\\\\ = 0.81\\r=\sqrt{0.81}\\\\[/tex]

r = 0.9 in

Answer:

.... ..................

Answer:

The company manufactures about 350 canoes, obtaining $ 28,000 after selling them all.

Step-by-step explanation:

Given that a company that manufactures small canoes has a fixed cost of $ 14,000, and it cost $ 40 to produce each canoe while the selling price is $ 80 per canoe, to determine the number of canoes that the company produces and the amount of money it makes after selling them, the following calculation must be carried out:

14/000 / 40 = X

350 = X

350 x 80 = 28,000

Thus, the company manufactures about 350 canoes, obtaining $ 28,000 after selling them all.