Find the area of the shaded part ! ​

Answer:

x=2

Step-by-step explanation:

you first have to make the bases the same

3^2x+1=9^2x-1

3^2x+1=3^2(2x-1) if you make the bases the same you will use 3^2 because it's equal to 9

3^2x+1=3^4x-2

2x+1=4x-2

2x-4x=-2-1

-2x/-2=-4/-2

x=2

I hope this helps

9514 1404 393

Answer:

Step-by-step explanation:

a) 1/4 of 28 = 28/4 = 7 coins are quarters.

  2/3 of (28 -7) = (2/3)(21) = 14 coins are dimes

The remaining 28 -7 -14 = 7 coins are nickels

__

b) The amount of money in coins is ...

  7×$0.25 +14×$0.10 +7×$0.05 = $3.50 . . . in coins

__

c) 2 packs of cards at $1.35 each will cost 2×$1.35 = $2.70. After the purchase, the remaining money would be ...

  $3.50 -2.70 = $0.80 . . . remaining

Answer:

one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.

The answer would then be D

Step-by-step explanation:

f(x)=log(x)

     =d(log(x)/dx)

=>y=1/x

Answer:

There would be [tex]120[/tex] of them.

Step-by-step explanation:

There are [tex]6[/tex] distinct letters in the word "[tex]\verb!theory![/tex]".

Hence, there would [tex]6[/tex] possible choices for the first letter that was selected.

Since the chosen card won't be placed back in the pool, there would be only [tex](6 - 1) = 5[/tex] possible choices for the second letter.

Likewise, there would be [tex](6 - 2) = 4[/tex] choices for the third letter.

[tex]6 \times 5 \times 4 = 120[/tex]. In other words, there are [tex]120[/tex] possible ways to draw three cards out of [tex]6[/tex] one after another.

Since the question states that the order of the cards matters, it won't be necessary to eliminate repetitions such as "[tex]\verb!the![/tex]" and "[tex]\verb!het![/tex]" from the number of combinations.

Solution :

Given :

n = 221

x = 17

a). [tex]$p=\frac{17}{221}$[/tex]

       = 0.076

b). At the 95 confidence interval

   Value of z = 1.96

  Margin of error

    [tex]$=1.96 \times \sqrt{\frac{p(1-p)}{n}}$[/tex]

    [tex]$=1.96 \times \sqrt{\frac{0.076(1-0.076)}{221}}$[/tex]

   [tex]$=1.96 \times \sqrt{\frac{0.076\times 0.924 }{221}}$[/tex]

   = 1.96 x 0.017

   = 0.03332

c). confidence interval

   = ( 0.076-0.033,  0.076+0.033)

   = ( 0.043, 0.109 )

d). The confidence interval does not contain null value, so it is significant.

Answer:

C) SQRT(65)

Step-by-step explanation:

the magnitude of 1-8i is given by the following:

sqrt(a^2+b^2)  

sqrt(1^2+8^2)

=sqrt(1+64)

=sqrt(65)

It is to be noted that the magnitude of   |1 − 8i| is √(65) (Option C)

To find the magnitude (or absolute value) of a complex number, we use the formula |a + bi| = √(a² + b²). In this case, the complex number is 1 - 8i.

Using the formula, we have  -

|1 - 8i| = √(1² + (-8)²)

= √(1 + 64)

= √65

Hence, the magnitude of 1 - 8i is √65.

So the correct answer is C) √65.

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Answer:

Imaginary roots

Step-by-step explanation:

The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].

Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:

[tex]7x^2-5x+1=0[/tex]

Now assign variables:

The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].

What does this tell us about the roots?

Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.

Answer:

28 seconds ..............

Answer:

PW, BW,  GW, PY,  BY, GY

Step-by-step explanation:

We need to determine the sample space

pink(P), blue (B), and green (G) cards,   (W) and yellow (Y) envelopes

Each color card can match with each color envelope

Start with the white envelopes and each color card

and then the yellow envelopes with each color card

PW   BW  GW

PY  BY   GY

9514 1404 393

Answer:

  $11,680.58

Step-by-step explanation:

Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.

__

The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.

The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...

  0.205×21,465 = 4400.325 ≈ 4400.33

The the total tax due on $70,000 is ...

  $7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000

_____

Additional comments

The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.

__

Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.

  ≤ 48535 -- income × 0.15

  ≤ 97069 -- income × 0.205 -2669.425

  ≤ 150,473 -- income × 0.26 -8008.22

  ≤ 214,368 -- income × 0.29 -12,522.41

  > 214,368 -- income × 0.33 -21,097.13

In this case, the second row of this simpler table would give the tax on $70,000 as ...

  tax = 70,000 × 0.205 -2669.425

  tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above

Answer:

D

Step-by-step explanation:

(x^2+3)(x-5)

That's the answer

9514 1404 393

Answer:

Step-by-step explanation:

Let L represent the length of the rectangle. Then the width is W=5+3L, and the perimeter is ...

  P = 2(L+W)

  240 = 2(L +(5 +3L))

  120 = 5 +4L

  115 = 4L

  115/4 = L = 28.75 . . . . cm

  W = 5+3L = 5 +3(28.75) = 91.25 . . . . cm

The length and width of the rectangle are 28.75 cm and 91.25 cm.

Answer:

40

Step-by-step explanation:

Based on the Proportional Transversal Theorem, the three parallel lines hat intersects the two transversals, divides the transversal lines proportionally.

Therefore, we would have the following ratio:

28/35 = ?/50

Cross multiply

35*? = 50*28

35*? = 1,400

Divide both sides by 35

? = 1400/35

? = 40

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The imaginary value is plotted on the vertical axis in the same way that the y-coordinate would be for an ordered pair (x, y). Similarly, the real value is plotted on the horizontal axis.

__

I find it helpful to think of the complex number a+bi as equivalent to the ordered pair (x, y) = (a, b) when it comes to graphing.

Answer:

Im pretty sure its 1,000 miles (dont forget the unit)

Step-by-step explanation:

Determine if this problem is a inverse variation or direct variation problem! This means that:

equation would be:

1=40

25=x

cross multiply*

x=25*40

x=1,000 miles apart! (dont forget the unit)

If this doesnt work then try this equation!

1=40

25=x

Multiply 1*40 and 25 *x

40=25x......    

40/25= 1.6

x=1.6! (Extra step)

Cheers!

Answer: 100 Miles

Step-by-step explanation: took the miles and got it correct.

(Also it's 2.5 inches apart, not 25.)

Answer:

White

6

Red

9

Green

Total number of balls =5+6+9

=20

(i) Probability =

Total cases

favourable cases

P(Green) =

20

9

(ii) P(White or red) =

20

5+6

=

20

11

(iii) P(neither green nor white) = P(Red)

=

20

6

=

10

3

The probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.

The probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.

(a) Probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls:

Total number of balls = 29

Total number of balls to be pulled = 8

Number of ways to choose 1 green out of 8 = C(8, 1) = 8

Number of ways to choose 1 yellow out of the remaining 7 = C(7, 1) = 7

Number of ways to choose 2 red out of the remaining 6 = C(6, 2) = 15

Total favorable outcomes = 8 x 7 x 15 = 840

Total possible outcomes = C(29, 8) = 2,765,905

Probability

= favorable outcomes / possible outcomes

= 840 / 2,765,905

= 0.000303

Therefore, the probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.

(b) Total number of balls = 29

Total number of balls to be pulled = 6

Number of ways to choose 1 green out of 8 = C(8, 1) = 8

Number of ways to choose another green out of the remaining 7 = C(7, 1) = 7

Number of ways to choose 2 yellow out of the remaining 5 = C(5, 2) = 10

Number of ways to choose 2 red out of the remaining 3 = C(3, 2) = 3

Total favorable outcomes = 8 x 7 x 10 x 3 = 1,680

Total possible outcomes = C(29, 6) = 593,775

Probability

= favorable outcomes / possible outcomes

= 1,680 / 593,775

= 0.00283

Therefore, the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.

(c) Probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls:

Total number of balls = 29

Total number of balls to be pulled = 8

Number of ways to choose the first green = C(8, 1) = 8

Number of ways to choose the last green = C(7, 1) = 7

Number of ways to choose 2 yellow out of the remaining 6 = C(6, 2) = 15

Number of ways to choose 2 red out of the remaining 4 = C(4, 2) = 6

Number of ways to choose the remaining 2 balls (either blue or black) = C(5, 2) = 10

Total favorable outcomes = 8 x 7 x 15 x 6x 10 = 50,400

Total possible outcomes = C(29, 8) = 2,765,905

Probability

= 50,400 / 2,765,905 ≈ 0.0182

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Each child will get 9 pieces with 13 pieces left.

'Division is a method of distributing a group of things into equal parts.'

According to the given problem,

Number of beads Kesley has = 157

Number of children to be shared between = 16

Number of beads in possession of each child = 157 ÷ 16

                                                                             = 9

Number of beads divided equally = 144

Remaining beans = 157 - 144

                              = 13

Hence, we can conclude that out of 157 beans, 144 is divided equally among 16 children with each child getting 9 pieces.

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9514 1404 393

Answer:

  (f•g)(x) = -16x^3 +10x^2 -14x

Step-by-step explanation:

  (f•g)(x) = f(x)•g(x) = (-2x)(8x^2 -5x +7)

Use the distributive property:

  (f•g)(x) = -16x^3 +10x^2 -14x

Answer:

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Step-by-step explanation:

There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.

At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just

[tex]\frac{4}{52}[/tex]

After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is

[tex]\frac{4}{51}[/tex]

Now to get the total probability we need to multiply the two probabilities together

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Answer:

Step-by-step explanation:

From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.

Thus, from the diagram

the length = 8 - 2x   the width = 10 - 2x  and the height = x

So, the volume V = L*w*h

Volume (V) = (8 - 2x) (10 - 2x) x

V = (80 - 16x - 20x +4x²)x

V = 80x -36x² + 4x³

By rearrangement:

V = 4x³ - 36x² + 80x

Answer:

y-3 = 2(x-1)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-3 = 2(x-1)

Answer:

3=2x+1

Step-by-step explanation:

Use the equation y=mx+b

where y is the y component, x is the variable and b is the x intercept

9514 1404 393

Answer:

  √3

Step-by-step explanation:

The ratio of the short sides to the hypotenuse in an isosceles right triangle is ...

  1 : 1 : √2

This means ...

  p·√2 = √6

  p = (√6)/(√2) = √(6/2)

  p = √3

Answer:

the answer for this would be 1

Answer:

m=[tex]7\sqrt3[/tex]

n=7

Step-by-step explanation:

Hi there!

We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14

We need to find the lengths of m and n

Firstly, let's find the measure of the other acute angle

The acute angles in a right triangle are complementary, meaning they add up to 90 degrees

Let's make the measure of the unknown acute angle x

So x+60°=90°

Subtract 60 from both sides

x=30°

So the measure of the other acute angle is 30 degrees

This makes the right triangle a special kind of right triangle, a 30°-60°-90°  triangle

In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is [tex]\frac{a}{2}[/tex], and the leg opposite from the 60 degree angle is [tex]\frac{a\sqrt3}{2}[/tex]

In this case, a=14, n=[tex]\frac{a}{2}[/tex], and m=[tex]\frac{a\sqrt3}{2}[/tex]

Now substitute the value of a into the formulas to find n and m to find the lengths of those sides

So that means that n=[tex]\frac{14}{2}[/tex], which is equal to 7

And m=[tex]\frac{14\sqrt3}{2}[/tex], which simplified, is equal to [tex]7\sqrt3[/tex]

Hope this helps!

The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.

Given:

Probability of student smoke,

P = 27.7%

  = 0.277

Number of students (n) = 632

[tex]q = 1-p[/tex]

  [tex]=1-0.277[/tex]

  [tex]=0.723[/tex]

(i)

Here,

Number of students (n) = 60

then,

⇒ [tex]n_P=60\times 0.277[/tex]

         [tex]=16.62[/tex]

⇒ [tex]n_q=60\times 0.723[/tex]

        [tex]=43.38[/tex]

We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.

Now,

[tex]\mu = n_P= 16.62[/tex]

[tex]\sigma = \sqrt{n_{Pq}}[/tex]

  [tex]= \sqrt{60\times 0.277\times 0.723}[/tex]

  [tex]=3.9664[/tex]

Now,

⇒ [tex]P(X<19) = P(X<18.5)[/tex]

                      [tex]=P(Z_{18.5})[/tex]

The Z-score is:

= [tex]\frac{18.5-16.62}{3.4664}[/tex]

= [tex]0.5423[/tex]

hence,

The probability will be:

⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]

or,

⇒ [tex]P(Z<19) = 0.7062[/tex]

(ii)

Here,

Number of students (n) = 75

[tex]\mu = n_P = 75\times 0.277[/tex]

            [tex]=20.775[/tex]

[tex]\sigma = \sqrt{n_{Pq}}[/tex]

   [tex]=\sqrt{75\times 0.277\times 0.723}[/tex]

   [tex]=3.8756[/tex]

Now,

⇒ [tex]P(X>17) = P(X> 17.5)[/tex]

                      [tex]=1-P(X \leq 17.5)[/tex]

                      [tex]=1-P(Z_{17.5})[/tex]

The Z-score is:

= [tex]\frac{17.5-20.775}{3.8756}[/tex]

= [tex]-0.9740[/tex]

then, [tex]P(Z_{17.5}) = 0.165[/tex]

hence,

The probability will be:

⇒ [tex]P(X>17) = 1-0.165[/tex]

                      [tex]=0.835[/tex]    

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Answer:

the correct answer is |x – 18| ≤ 4

just took the test

Step-by-step explanation:

Answer:

Step-by-step explanation:multiple 5 times 108 and that gives you your answer..