Ivan's favorite colors are \blue{\text{blue}}blue and \green{\text{green}}green. He has \blue{\text{1 blue shirt}}1 blue shirt, \green{\text{1 green shirt}}1 green shirt, \blue{\text{1 blue hat}}1 blue hat, \green{\text{1 green belt}}1 green belt, \blue{\text{1 blue pair of pants}}1 blue pair of pants, and \green{\text{1 green pair of pants}}1 green pair of pants. Ivan selects one of these garments at random. Let A be the event that he selects a green garment and B be the event that he chooses a pair of pants. What is P(A\text{ or }B)P(A or B), the probability that the garment Ivan chooses is either green or a pair of pants?

Answer:

83.5 %

Step-by-step explanation:

The mean is 38 and the standard deviation is 2

38 -2 is 36

36 is one standard deviation below the mean.

43 - 38 is 5

5/2 is 2 1/2 times the standard deviation above the mean

-1< z< 2.5

P ( Z<2.5 )−P (Z<−1 )

P ( Z<−1)=1−P ( Z<1 )

P ( Z<2.5 )-1+P ( Z<1 )

Using the standard normal table

0.9938 - 1 +0.8413

0.8351

83.51%

Rounding to the nearest tenth

83.5%

Yep the answer's 83.5%

godspeed in your adventures in cheating >:)

Answer:

[tex] The\ number\ of\ 8 \frac{1}{4}\ inches\ of\ section\ of\ rope\ be\ 6. [/tex]

Step-by-step explanation:

As given

Mario is setting up a new tent during a camping trip.

The tent came with 7 feet of rope.

As 1 foot = 12 inches

Now convert 7 feet into inches.

7 feet = 7 × 12 inches

         = 84 inches

As given

The instructions were to use 34.5 inches of the rope to tie a tarp on top of the tent.

Than

Rope left after tie a tarp on top of the tent = 84 - 34.5

                                                                      = 49.5 inches

As given

[tex]The\ remaining\ rope\ should\ be\ cut\ into\ 8 \frac{1}{4}\ inch\ sections\ to\ tie\ the\ tent\ to\ stakes\ in\ the\ ground.[/tex]

i.e

[tex]The\ remaining\ rope\ should\ be\ cut\ into\ \frac{33}{4}\ inch\ sections\ to\ tie\ the\ tent\ to\ stakes\ in\ the\ ground.[/tex]

[tex]Let\ us\ assume\ the\ number\ of\ \frac{33}{4}\ inches\ section\ of\ rope\ be\ x.[/tex]

Than the  equation becomes

[tex]\frac{33\times x}{4} = 49.5[/tex]

[tex]x = \frac{49.5\times 4}{33}[/tex]

[tex]x = \frac{198}{33}[/tex]

x = 6

Answer:

6

Step-by-step explanation:

Converting 7 ft to inches:

[tex]7*12=84[/tex] inches

We set up the equation as:

[tex]34.5+8.25x=84[/tex]

Now solving for [tex]x[/tex] would give us the number of 8.25 inch sections:

[tex]8.25x=84-34.5\\8.25x=49.5\\x=\frac{49.5}{8.25}=6[/tex]

Hence, Mario can cut 6 (8.25 inch) sections from the rope

Answer:

11 minutes

Step-by-step explanation:

Do 16 mins. 30 secs. divided by 1.5, since that is what you divide the miles by to get the base amount. The answer is 11 minutes.

Answer:

D. He can increase the number of trials.

Step-by-step explanation:

Jonas is conducting an experiment using a 10-sided die. So the theoretical probability of rolling a 3 in a single trial is, [tex]\dfrac{1}{10}[/tex]

So the theoretical expected outcome of 3 in 20 roll would be,

[tex]=\dfrac{1}{10}\times 20=2[/tex]

But when he rolled the die 20 times, where four of those rolls resulted 3.

Which is 2 times more than the theoretical expectation.

Increasing the number of trials from 20, the expected outcome will increase.

As the number of trials is multiplied with [tex]\dfrac{1}{10}[/tex], so bigger the number is from 20, bigger the value.

As we know,

[tex]E(x)=n\cdot P(x)[/tex]

If we want to increase the expected value, we have to increase the number of trials.

Answer with explanation:

Number of faces of this unique Die = 10

Theoretical  probability of rolling a 3 [tex]=\frac{1}{10}[/tex]

Now, the die is rolled 20, times.

Number of times, the rolls results in 3= 4

Probability of rolling '3' [tex]=\frac{4}{20}=\frac{1}{5}[/tex]

but, if you roll the die twenty times, Probability of rolling '3' should be [tex]=\frac{2}{20}=\frac{1}{10}[/tex]

When we want, theoretical probability and experimental probability,match each other, the number of trials should be large enough to get closer and better results.

The adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer:

D: He can increase the number of trials.

Answer:

23% error since 70 more people attended then Marcus counted

Step-by-step explanation:

To calculate the percent error:

Marcus counted 230 and 300 actually came.

1. 230-300=-70 but the absolute value is 70

2. 70/300=0.23

3. 0.23(100)=23%

Marcus' estimated had a 23% error.

Answer:

Total attendance for the game at stadium last year was 612500.

Step-by-step explanation:

Each year the soccer team, Peterson United, plays 25 games at their stadium.

The owner of Peterson United claimed that last year the mean attendance per game was = 24500

Since mean of any set of data = [tex]\frac{sum of data}{Total number of data}[/tex]

When we apply this rule in this question formula becomes as

24500 = [tex]\frac{x}{25}[/tex]

x = 25 × 24500

x = 612500

Final answer:

Hannah initially has 8/9 of a pound of birdseed, and after using 2/3 of a pound, she has 2/9 of a pound remaining, which is calculated by finding a common denominator and subtracting the second fraction from the first.

Explanation:

Hannah initially has 8/9 of a pound of birdseed. After filling her bird feeders with 2/3 of a pound of birdseed, we need to subtract the amount she used from what she started with to find out how much birdseed she has left. The calculation we'll use is:

(initial amount) - (amount used) = (amount remaining)

In fractional form, this becomes:

8/9 - 2/3

To subtract these fractions, we need a common denominator. The smallest common denominator for 9 and 3 is 9. We can convert 2/3 to 6/9 by multiplying the numerator and the denominator by 3. After this step, the subtraction is straightforward:

8/9 - 6/9 = 2/9

Hence, Hannah has 2/9 of a pound of birdseed remaining.

Answer:

I got B. 24,500 as my answer.

Step-by-step explanation:

2.45 x (10^4) = 24,500

Answer:

2/3 of 450 is 300 :)

[tex]3x^2+12x-15=3(x^2+4x-5)=3(x^2+5x-x-5)\\\\=3[x(x+5)-1(x+5)]=3(x+5)(x-1)\\----------------------\\4x^2+4x-8=4(x^2+x-2)=4(x^2+2x-x-2)\\\\=4[x(x+2)-1(x+2)]=4(x+2)(x-1)\\----------------------\\2x^2-8=2(x^2-4)=2(x^2-2^2)=2(x-2)(x+2)\\----------------------\\x^2-5x=x(x-5)\\----------------------\\\\\dfrac{3x^2+12x-15}{4x^2+4x-8}\cdot\dfrac{2x^2-8}{x^2-5x}\\\\=\dfrac{3(x+5)(x-1)}{4\!\!\!\!\diagup_2(x+2)(x-1)}\cdot\dfrac{2\!\!\!\!\diagup^1(x-2)(x+2)}{x(x-5)}\\\\\text{Canceled:}\ (x-1)\ \text{and}\ (x+2)[/tex]

[tex]=\boxed{\dfrac{3(x-2)(x+5)}{2x(x-5)}}[/tex]

Answer:

Step-by-step explanation:

The ration of weight of nickel, zinc, and copper in an alloy is 4:1:2

The weight of alloy can be written as

4x + x + 2x = 35 Kg

7 x = 35 Kg

X = 35 Kg/7

X = 5kg

The weight of nickel the alloy = 4 x 5 = 20 Kg

The weight of zinc in the alloy= 1 x 5 = 5kg

The weight of copper in the alloy = 2 x 5 = 10 kg

Answer:

Let X be the amount of each metal needed to make 35 Kg of this alloy.

We know that an alloy is composed of nickel, zinc and copper in a proportion

4:1:2. Therefore, we have:

[tex]4X+1X+2X = 35[/tex]

[tex]7X = 35[/tex]

[tex]X=\frac{35}{7}[/tex]

[tex]X=5[/tex] Kg

Therefore, there are [tex]5 \times 4 =20[/tex] kg of nickel, [tex]1 \times 5 =5[/tex] kg of zinc, and [tex]2 \times 5 = 10[/tex] kg of copper needed to make 35 kg of this alloy

Answer:

C = 45.8 or C = 117.69

Step-by-step explanation:

Remark

Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.

Given

AB = 15

<A = 35

point C opposite line AB such that CB = 12 These givens give a unique answer.

Solution

Sin(35) / 12 = Sin(C) / 15                     Multiply both sides by 15

15*Sin(35) / 12 = Sin(C)                       Find 15/12

1.25*sin(35) = Sin(C)                           Write Sin(35)

1.25*0.5736 = Sin(C)                          Multiply the left

0.71697 = Sin(C)                                 Take the inverse Sin

C = 45.805 degrees                          This is the angle opposite AB

Angle B = 180 - 35 - 45.805 = 99.2

Ambiguous Case                    

If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.

I will set up the Sin law for you, and let you solve it

Sin(B) / 12 = Sin(35)/15

When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees

C = 180 - 35 - 27.31 = 117.69

So that's two values that C could have. I think that's all given these conditions.

Two Cases or None

<A = 35 degrees

AC = 15

CB = 12

This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.

The error is in Step-4.

A negative exponent does NOT mean that the number turns negative. A negative exponent means the number is in the denominator.

(4)⁻⁴ means (1/4⁴) .  That's (1/256) .  All positive numbers.

Answer:

65° and 115°

Step-by-step explanation:

let one angle be x then the other is x + 50

The sum of 2 supplementary angles = 180°, hence

x + x + 50 = 180

2x + 50 = 180 ( subtract 50 from both sides )

2x = 130 ( divide both sides by 2 )

x = 65

Thus the 2 angles are x = 65° and x + 50 = 65 + 50 = 115°

Answer:

29.  sec w csc w - sec^2 w

31.  - tan ^2 k (sin k +1)

Step-by-step explanation:

29.  (cot w -1)/ (1- sin^2 w)

We know that cot w = cos w/ sin w

and 1 - sin^2 w = cos ^2 w

Replace these identities into the expression

(cos w/ sin w -1)

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

cos ^ 2 w    

Get a common denominator on top of sin w

(cos w/ sin w -sin w/sin w)

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

cos ^ 2 w    

(cos w - sinw)/ sin w

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

cos ^ 2 w

(cos w - sinw)

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

cos ^ 2 w  sin w

Split into 2 terms

cos w                            sin w      

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

cos ^ 2 w  sin w             cos ^2 w  sin w

Cancel cos w in the first term and sin w in the second term

1                                       1    

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

cos  w  sin w             cos ^2 w  

We know that 1/cos = sec  and 1/ sin = csc

sec w csc w - sec^2 w

31.    sin k/ (1 - csc k)

We know that csc k is 1/ sin k

sin k

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

1 - 1/ sin k

Get a common denominator for the bottom

sin k

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

sin k/ sin k - 1/ sin k

sin k

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

(sin k-1)/ sin k

Multiply by sin k/sin k

sin k * sin k

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

(sin k-1)/ sin k  * sin k

sin k * sin k

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

(sin k-1)

sin^2 k

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

(sin k-1)

Multiply by (sin k +1)/ (sin k +1)  so we can get rid of the denominator

sin^2 k  (sin k +1)

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

(sin k-1) (sin k +1)

Foiling out the denominator, we get (sin^2 k-1)

sin^2 k  (sin k +1)

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

(sin^2 k-1)

Factoring out a -1 from the denominator

sin^2 k  (sin k +1)

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

-1 (1 - sin^2 k)

1 - sin ^2 k = cos ^ k

sin^2 k  (sin k +1)

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

-1 (cos ^2 k)

sin ^2k/ cos ^2 k = tan ^2 k

- tan ^2 k (sin k +1)

Answer:

20 Riyals you receive if you exchange 5 dollars .

Step-by-step explanation:

As given

The money used in Saudi Arabia is the Riyal.

The exchange rate is 4 Riyals to 1 dollar.

i.e

4 Riyals = 1 dollar.

Now calculate for 5 dollars.

5 × 4 Riyals = 5 × 1 dollars

20  Riyals = 5 dollars

Therefore 20 Riyals you receive if you exchange 5 dollars .

Answer:

her son is 20, Mrs. Johnson is 60

Step-by-step explanation:

if her son is x, Mrs. Johnson is 3x,

Ten years ago,

her son is x-10, Mrs. Johnson is 3x-10,

so:

3x-10=5(x-10)

x=20

Answer:

90

Step-by-step explanation:

Answer:

zero is your answer.

Step-by-step explanation:

Your answer for this question is 0

Answer:

D. $2.81

Step-by-step explanation:

The statement says that the price of a cantaloupe goes up 4 cents each month and that the cost of the cantaloupe was $1.25 on the first month. Tto determine the cost in the 40th month, you have to multiply 4 cents for 39 months as the price for the first month was given and then you have to add this with the price for the first month:

0,04*39= 1.56

1.56+1.25= $2.81

The price in the 40th month is $2.81.

Answer:

A

Step-by-step explanation:

We can find the surface area of the object by adding the surface areas of each part. We have many rectangle faces to count and two triangular faces. Each has a formula for the area. We will find the area of each and then add them all together.

Triangle - 0.5 *b*h

Rectangle - b*h

Triangles

There are two triangles on either side. The height is 1.5. The base is 1.8.

0.5(1.5)(1.8)=1.35 meters squared

Since there are two, we will add 1.35+1.35 in our final calculation.

Rectangles

We will start by calculating the largest rectangle on the side. It has height of 4 and a base of 2.5 (shown above left).

4(2.5)=10

Since there are two (one we can see and one we can't), we will add 10+10 in our final calculation.

Next we calculate the top and bottom. The height is 3 and the base is 2.5 on top. But the bottom sticks out more and adds 1.8 to its base.

Top - 3(2.5)=7.5

Bottom-3(2.5+1.8)=12.9

Finally, we will calculate the front side and back(not visible) as well as the slant up front. The back side has height 4 and base 3. The front side has base 3 and height 4-1.5=2.5. The slant has base 2.3 and height 3.

Back - 4(3)=12

Front- 3(2.5)=7.5

Slant - 3(2.3)=6.9

We add all together for the total surface area: 1.35+1.35+10+10+7.5+12.9+12+7.5+6.9=69.5 meters squared.

Look at the picture.

Use the Pythagorean theorem:

[tex]a^2+b^2=d^2[/tex]

A) a = 1, b = 1

[tex]d^2=1^2+1^2\\\\d^2=1+1\\\\d^2=2\to d=\sqrt2\ \text{it's not rational number}[/tex]

B) a = 4, b = 5

[tex]d^2=4^2+5^2\\\\d^2=16+25\\\\d^2=41\to d=\sqrt{41}\ \text{it's not rational number}[/tex]

C) a = 3, b = 4

[tex]d^2=3^2+4^2\\\\d^2=9+16\\\\d^2=25\to d=\sqrt{25}\to d=5\ \boxed{:)}[/tex]

D) a = 1, b = 2

[tex]d^2=1^2+2^2\\\\d^2=1+4\\\\d^2=5\to d=\sqrt5\ \text{it's not rational number}}[/tex]

Options A, B, and D do not yield a perfect square, while option C does, with a=3 and b=4 resulting in a rational diagonal length of 5.

The diagonal of a rectangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is represented as [tex]c^2 = a^2 + b^2,[/tex] where a and b are the sides of the rectangle and c is the diagonal.

Looking at the given options:

Therefore, the possible values of a and b which will make the diagonal of the rectangle a rational number are given in option C: a=3 and b=4.

Answer:

A

Step-by-step explanation:

3/24=9/72        3*3=9    24*3=72      x=3

3/9=y/12         9/3=3        12/3=4      y=4

X=3 y=4

Answer:

[tex]\frac{\frac{51}{8}} {\frac{3}{8}}[/tex]

17 bags.

Step-by-step explanation:

We are asked to find the number of bags with weight 3/8 pound can be made from [tex]6\frac{3}{8}[/tex].

To find the number of

[tex]\text{Number of bags that can be made from available mix trail}=6\frac{3}{8}\div \frac{3}{8}[/tex]  

Convert mixed fraction into improper fraction.

[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\div \frac{3}{8}[/tex]  

Since we know that dividing a fraction with another fraction is same as multiplying the 1st fraction with the reciprocal of 2nd fraction.

[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\times \frac{8}{3}[/tex]  

After cancelling out 8 from numerator and denominator we will get,

[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{3}[/tex]  

[tex]\text{Number of bags that can be made from available mix trail}=17[/tex]  

Therefore, 17 bags each of weight 3/8 pounds can be made from [tex]6\frac{3}{8}[/tex] pounds of mix trail.

[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis}[/tex]

[tex]\bf \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

with that template in mind, let's check

C = -3, three units to the right

D = -2, two units down.

[tex]\bf f(x)=2^x~\hspace{10em}\stackrel{\stackrel{C=-3\qquad D=-2}{\cfrac{}{}}}{g(x)=2^{x-3}-2}[/tex]

Answer:

g(x) = 2^(x - 3) - 2.

Step-by-step explanation:

Translating 2^x  3 units to the right .  This is done by changing it to 2^(x - 3). Then 2 units down is given by 2^(x -3) - 2.

Answer is 2^(x - 3) - 2.