Find the probability that the number is in set A’ giving your answer as a decimal

Answer :

(1) [tex][(\frac{1}{3})^{-3}\times (\frac{1}{2})^{-3}]\div (\frac{1}{4})^{-3})=3.375[/tex]

(2) [tex]x=\frac{45}{56}[/tex]

Step-by-step explanation :

Part 1:

The given expression is:

[tex][(\frac{1}{3})^{-3}\times (\frac{1}{2})^{-3}]\div (\frac{1}{4})^{-3})[/tex]

[tex]=[(\frac{1}{(\frac{1}{3})^3})\times (\frac{1}{(\frac{1}{2})^3})]\div (\frac{1}{(\frac{1}{4})^3})[/tex]

[tex]=[27\times 8]\div (64)[/tex]

[tex]=[216]\div (64)[/tex]

[tex]=\frac{27}{8}[/tex]

[tex]=3.375[/tex]

Part 2:

The given expression is:

[tex](7-3)2\times (7x+4)=77[/tex]

[tex](4)2\times (7x+4)=77[/tex]

[tex]8\times (7x+4)=77[/tex]

[tex]56x+32=77[/tex]

[tex]56x=77-32[/tex]

[tex]56x=45[/tex]

[tex]x=\frac{45}{56}[/tex]

Thus, the value of x is [tex]\frac{45}{56}[/tex]

Answer:

(-2, 2)

Step-by-step explanation:

When an image is dilated by a factor of 2, we can simply multiply the x and y coordinates by 2.

Therefore, the coordinates will become (-2, 2).

This is a answer of this question.

Answer:

Hi there!

The correct choices are: A, B, C

Step-by-step explanation:

π in radians equals to 180°

A is correct because 180/3 = 60

C is correct because 180/4 = 45

The measure angles π and π/4 is true

Radian, When we rotate the radius completely around the circle, it completes one rotation. The angle subtended at the center of the circle by the radius after one complete rotation is 2π radians. The angle in radians subtended by the radius at the center of the circle is the ratio of the length of the arc to the length of the radius. When the length of the arc becomes equal to the length of the radius, the angle subtended at the center becomes 1 radian. We denote the unit radian as rad. Radians is the SI unit of measuring angles.

Degree  Angles are measured in degrees. One revolution is divided into 360 equal parts and each part is called a degree. The angle subtended at the center of the circle after one complete rotation of the radius is 360°. The symbol for degrees is denoted by '°'. Degrees is not an SI unit to measure angles but it is an accepted unit to measure. Hence, while solving problems, it is preferred to convert the unit of angle from radians to degrees to understand it better. The instrument used to measure an angle in degrees is a protractor. Comparing the measures of the angle for a complete rotation, we observe,360 Degrees = 2π Radians180 Degrees = π Radians

According to the question

To convert radians to degrees, multiply by 180/p,

like this: degrees = radians x (180 / π )

To convert degrees to radians,

multiply by p/180, like this

radians = degrees x ( π/180)

(A)

This will use the formula for radians to degrees. π/3 x (180/π) The pi's cancel, leaving you with: 180/3 = 60 degrees False

(B)

An angle that measures π/6 radians also measures 30°π/6 x (180/π) = 30 degrees. True

(C)

An angle that measures π/3 radians also measures 60°π/3 x (180/π) = 60 degrees. True

(D) An angle that measures 180 degrees also measures π/2π/2 x (180/π) = 90 degrees. False

hence, measure angles π and π/4 is true, therefore option B and C are true

To learn more about radian and degree from here https://brainly.in/question/3390676

#SPJ2

Answer:

Time t = 3.02 hours

Step-by-step explanation:

Given;

Distance d = 350 km

Speed v = 72 mi/h

Since 1 mile ≈ 1.61 km

Converting the speed to km/h

Speed v = 72 mi/h × 1.61km /mi

Speed v = 115.92 km/h

Speed = distance/time

Time t = distance/speed = d/v

Substituting the values;

Time t = 350 km/115.92 km/h

Time t = 3.019 hours

Time t = 3.02 hours (to the nearest hundredth.)

Answer:

Principal amount (P) = $6000

Rate (R) = 12%

Time = 2 years

Simple interest, I = P X R X T / 100

= 6000 X 12 X 2 / 100

= 144000 / 100

= 1440

=> Simple interest, I = $1440

Amount they would owe at the end of 2 years,

= P + I

= 6000 + 1440

= $7440

Answer:

The area of the circle is 12.6 m2

DIVIDE the area of the circle by 2 to find area of the semicircle.

To find the area of the composite figure, ADD the area of the rectangle and the area of the semicircle.

Step-by-step explanation:

Hope this helps

Correct me if this is wrong

Answer:

12.6

Divide

Add

Step-by-step explanation:

Answer:

the answer is [tex]\frac{13}{12}[/tex] or 1 [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

First, you have to make all the denominators the same, which is the least common multiple of the 3 numbers, (6, 3, and 4). That would be 12.

So you change all the denominators to 12, keeping in mind that whatever you multiply the denominator by, you MUST multiply by the numerator.

You will end up with 2/12+8/12+3/12. Adding those together you get 13/12, or written as a mixed number, 1 [tex]\frac{1}{12}[/tex]

Answer:

13/12

Step-by-step explanation:

I used a calculator

to crazy moderators (like gmany), I used a calculator so there is no work

Answer:

the answer is

z is equal to 12 units. Side RS measures 9 units longs

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

x = kendalls money

98 = 7x

Divide each side by 7

98/7 = 7x/7

14=x

Kendall had 14 dollars

Answer:

D

Step-by-step explanation:

94 divided by 7 = 14 also

7x (x is 14) = 94

Answer:

B, π:(4-π).

Step By Step:

With a side of length 12, we have an area of 144. The circle's radius is 3, so their area is 9π, per circle. All four circles have a total combined area of 36π  - green. The area that is left of the square after the circles are painted green  is  144-36π - White

So, the ratio of Green:White is (36π) : (144-36π), which simplifies to π:(4-π), B

Answer:

No, the answer is not correct

Step-by-step explanation:

In the second step, the student didn’t use the quotient of powers property correctly. They should have subtracted inside the parentheses instead of dividing. This would have left them with x^(4/5). They should have then multiplied this power by ^(1/2) resulting in x^(4/10) which simplified is x^(2/5) which is the correct answer.

The resulting answer that the student got was wrong this was due to the wrong miscalculation when applying the division rule according to the law of indices. The difference between 6/5 and 2/5 is not 3 but 4/5

The expression simplified by the student is an indicinal expression

Indices are mathematical expressions that show the number of times a number or variable is being multiplied by itself.

According to the law of indices

where a, and n are integers or fractions

Given the expression simplified by the student expressed as:

[tex](\dfrac{x^\frac{2}{5} \times x^\frac{4}{5} }{x^{\frac{2}{5} }})^\frac{1}{2}[/tex]

Using the laws above:

[tex]=(\dfrac{x^{\frac{2}{5}+\frac{4}{5} } }{x^{\frac{2}{5} }} )^\frac{1}{2} \\=(\dfrac{x^\frac{6}{5} }{x^\frac{2}{5} })^\frac{1}{2} \\[/tex]

Based on the law of division,

[tex]=(x^{\frac{6}{5}-\frac{2}{5} })^\frac{1}{2} \\=(x^{\frac{6-2}{5} })^\frac{1}{2} \\=(x^\frac{4}{5})^\frac{1}{2} \\=x^{\frac{2}{5} }[/tex]

Hence the resulting answer that the student got was wrong this was due to the wrong miscalculation when applying the division rule according to the law of indices. The difference between 6/5 and 2/5 is not 3 but 4/5.

Learn more about indices here: https://brainly.com/question/24160371

Answer:

Minimum: 63

Lower quartile: 67

Median: 80

Upper quartile: 89

Maximum: 92

I hope this helped!

Answer:5x+10

Step-by-step explanation:

2x+3x+9+1=5x+10

Answer: D’ (3, -6), E’ (4, -2), F’ (5, -5)

Step-by-step explanation:

If it’s reflected across the x-axis, the y coordinates become negative. Then move each coordinate 2 units to the right.

(x, y) — (x + 2, -y)

D (1, 6) — D’ (3, -6)

E (2, 2) — E’ (4, -2)

F (3, 5) — F’ (5, -5)

Answer:

$5.46

Step-by-step explanation:

Total = 3*1.29 + 1.59

= 5.46

Answer:

2.88

Step-by-step explanation:

that is total amount

Answer:

They are not similar

Step-by-step Explanation:

For two polygons to be considered similar, two conditions must be met:

1. The ratio of their corresponding sides must be equal, and must have the same scale factor.

2. Their corresponding angles must be the same. That is, the corresponding angles must be congruent.

Now let us examine the two polygons ( ∆AYP and ∆BOX) given to ascertain if they are similar.

First, we can observe that only two of their corresponding sides were given. The third corresponding side, "YP/OX" is not given. This makes it difficult for us to tell if the polygons are similar, if we are to base our conclusion on merely considering the ratio of their corresponding sides.

Although, the two given corresponding sides (AY/BO & AP/BX), both have equal ratio ⅖, i.e. AY/BO = AP/BX = ⅖. This is not enough to tell both polygons are similar, as we cannot tell if the third corresponding side would give us same ratio, since it wasn't given in the diagram.

==>Next is to examine the interior angles of the polygons, whether the measure of their corresponding angles are the same.

Thus, from the diagram, we can see that two angles of the each triangle were given. We can find the measure of the third angle not given since we know that sum of the interior angles of a triangle = 180°

Thus, <P in ∆AYP = 180 - (90+20) = 180 - 110

<P = 70°

Thus, <B in ∆BOX = 180 - (90+80) = 180 - 170

<B = 10°

From the above calculation, comparing both polygons having known the measures of their corresponding angles, we can conclude that both polygons given in the question are not similar.

This is because the measure of their corresponding angles are not congruent.

<A is not congruent to <B, so likewise with <P and <X.

Answer:

x=3

z=112

Step-by-step explanation:

9x-27 needs to be solved for x.

Set the equation equal to zero.

9x-27=0

Now add 27 to both sides.

9x=27

Divide both sides by 9

x=3

Plug 3 into 5x+53 to find the angle.

5(3)+53=15+53=68.

Since 5x+53 and Z are  on the same line, that means, when added together, they equal 180 degrees. Subtract 68 from 180.

z=112

Answer:

Bottom Left

Step-by-step explanation:

Break up the numbers to 7,  and -8.

Break up the fractions to 1/5 and -3/5.

Answer:

An apple costs £0.25

A banana costs £0.34

Step-by-step explanation:

Let a be apples and b be bananas.

10a+5b=4.2

8a+10b=5.4

Solve for a:

10a+5b=4.2

Subtract 5b from both sides

10a=4.2-5b

Subtract 4.2 from both sides

10a-4.2= -5b

Multiply both sides by -1

-10a+4.2=5b

8a+10b=5.4

Subtract 10b from both sides

8a=5.4-10b

Subtract 5.4 from both sides

8a-5.4= -10b

Multiply both sides by -1

-8a+5.4= 10b

Divide both sides by 2

-4a+2.7=5b

Combine equations:

-4a+2.7= -10a+4.2

Add 10a to both sides

6a+2.7=4.2

Subtract 2.7 from both sides

6a=1.5

Divide both sides by 6

a=0.25

An apple costs £0.25

Solve for b:

10a+5b=4.2

Subtract 10a from both sides

5b= -10a+4.2

Subtract 4.2 from both sides

5b-4.2= -10a

Multiply both sides by -1

-5b+4.2=10a

8a+10b=5.4

Subtract 8a from both sides

10b= -8a+5.4

Subtract 5.4 from both sides

10b-5.4= -8a

Divide both sides by 4

2.5b-1.35= -2a

Multiply both sides by 5

12.5b-6.75= -10a

Multiply both sides by -1

-12.5b+6.75=10a

Combine equations:

-12.5b+6.75= -5b+4.2

Add 12.5b to both sides

6.75=7.5b+4.2

Subtract 4.2 from both sides

2.55=7.5b

7.5b=2.55

Divide both sides by 7.5

b=0.34

A banana costs £0.34

If you would like to check and see if it is true, (I already checked, it is) you can use the formulas I gave at the start of the explanation.

10a+5b=4.2

8a+10b=5.4

a=0.25

b=0.34

Answer:

Step-by-step explanation:

(-8+2)/(8-8)= -6/0= undefined

Answer:

1

3

Step-by-step explanation:

The equation of a graph is normally written in form Mx+c.

So, here there is x+3.

Thus, m = 1

C = 3

Hope this helps

Answer:

y = -2x - 13

Step-by-step explanation:

Answer:

y = - 2x - 13

Step-by-step explanation:

First, distribute out the two on the right side of the equation.

y + 7 = - 2x - 6

Next, subtract 7 from both sides to isolate the y variable on the left side.

y = - 2x - 13

That is your answer in slop-intercept form.

Answer: 270g of butter

225g of flour

300g of sugar

6 eggs

Step-by-step explanation:

Answer: A_a^3

B_c^1

Step-by-step explanation:they work like integers therefore vlby sharing the same base and Having the division sign u just subtract the powers

Answer:

15 in - (1.25 in/hr)t

Step-by-step explanation:

L(t) is a function of time, t:  L(t) = 15 in - (1.25 in/hr)t

Note that when the candle has burned down to nothing, L(t) = 0.  How long does that take?  Set 15 in - (1.25 in/hr)t equal to zero and solve for t:

(1.25 in/hr)t = 15 in, or

         15 in

t = ---------------- = 12 hrs

     1.25 in/hr

Answer:

x=29.9 degrees

Step-by-step explanation:

Sides we are given: x and side length of 92.

Angle we are given: angle of measure 18.

Relative to the angle we are given, we have the opposite and adjacent sides, so we use TOA, as O is opposite and A is adjacent.

Tangent 18= x/92

Tangent 18 (92)=x

x=29.9 degrees

Answer:

29.9 to one decimal place

Step-by-step explanation:

To work out X you can find the missing angle by doing;

[tex]180 - (90 + 18) = 72[/tex]

Then use Sine rule to work out X;

[tex]x = \frac{92}{ \sin(72)} \times \sin(18) \\ x = 29.89261.....[/tex]

Answer:

x = 5,  AB = 5 inches, BC = 15 inches

Step-by-step explanation:

The segment addition postulate states that for line AC having point B between point A and point C, the distances between the point satisfy the equation:

AB + BC = AC

Given that AB = x and BC = 3x, also AC = 20 inches

AB + BC = AC

x + 3x = 20

4x = 20

Dividing through by 4:

4x/4 = 20/4

x = 5

Therefore AB = x = 5 inches, BC = 3x = 3 * 5 = 15 inches