nate and laura picked 20 apples laura picked 1/2 of what nate picked
how many did nate pick?

Answer:

[tex]\frac{1}{2^{n} }[/tex]

Step-by-step explanation:

The rules of exponents state that

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] and [tex]a^{0}[/tex] = 1

Thus

[tex]2^{-5}[/tex] = [tex]\frac{1}{2^{5} }[/tex] = [tex]\frac{1}{32}[/tex]

[tex]2^{-4}[/tex] = [tex]\frac{1}{2^{4} }[/tex] = [tex]\frac{1}{16}[/tex]

[tex]2^{-3}[/tex] = [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]

and so on , to

[tex]2^{0}[/tex] = 1

Answer:

15.52 ft

Step-by-step explanation:

the length of the rope can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√15² + 4²

= √225 + 16

=√ 241

= 15.52 ft

Answer:

the answer is b the square root of 160

Step-by-step explanation:

i did it on the assignment

Answer:

14 units is the answer

Step-by-step explanation:

^_^^_^^_^^_^^_^

Answer:

1,568 customer

Step-by-step explanation:

Find the lowest common multiple of 98, 112, and 224

98 = 98, 196, 294, 392, 490, 588, 686, 784, 882, 980, 1078, 1176, 1274, 1372, 1470, 1568, 1666

112 = 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120, 1232, 1344, 1456, 1568, 1680, 1792, 1904

224 = 224, 448, 672, 896, 1120, 1344, 1568, 1792, 2016, 2240

The lowest common multiple of 98, 112, and 224 is 1568

Therefore, the 1,568th customer will be the first to receive all 3 iitem

The question is incomplete. The complete question is :

Cylinders A and B are similar. The length of the cylinder A is 4 mm and the length of cylinder B is 6 mm. The volume of cylinder A is 20mm3. Calculate the volume of cylinder B.

Answer:

67.5 [tex]mm^3[/tex]

Step-by-step explanation:

Given that :

Cylinder A and cylinder B are similar.

Let volume of cylinder A = 20 [tex]mm^3[/tex]

We know the volume of a cylinder is given by V = [tex]$\pi r^2 h$[/tex]

where, r is the radius of the cylinder

            h is the height of the cylinder

We have to find the scale factor.

The length scale factor is = [tex]$\frac{6}{4}$[/tex]

                                          [tex]$=\frac{3}{2}$[/tex]

Area scale factor [tex]$=\left(\frac{3}{2}\right)^2$[/tex]

                           [tex]$=\frac{9}{4}$[/tex]

∴ Volume scale factor [tex]$=\left(\frac{3}{2}\right)^3$[/tex]

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

Therefore, the volume of cylinder B is [tex]$=20 \times \frac{27}{8}$[/tex]

                                                               = 67.5 [tex]mm^3[/tex]

Answer:

D

Step-by-step explanation:

(4ab)^2 = 4^2a^2b^2 = 16a^2b^2

Answer:

(b) 30.25 feet

Step-by-step explanation:

Given

[tex]v = \sqrt{64h[/tex]

Required

Find [tex]h[/tex] when [tex]v = 44[/tex]

Substitute [tex]v = 44[/tex] in [tex]v = \sqrt{64h[/tex]

[tex]44 = \sqrt{64h[/tex]

Take square of both sides

[tex]44^2 = 64h[/tex]

[tex]1936 = 64h[/tex]

Divide both sides by 64

[tex]30.25 = h[/tex]

Rewrite as:

[tex]h = 30.25[/tex]

Answer:

the answer with the salad and dressing that has 100 calories per oz.

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

Given

[tex]\frac{x}{5}[/tex] = 5 ( multiply both sides by 5, the reciprocal of [tex]\frac{1}{5}[/tex] to clear the fraction )

x = 25

Answer:

30.44 pounds.  

Step-by-step explanation:

to find the answer you have to subtract 45.33 and 14.89

so 45.33-14.89= 30.44

so now you would have to round. the number after the decimal is NOT greater then 5 so Therefore, we simply remove the 4 an d the the whole number as: 30

SO your answer ROUNDING wise is 30

Hope this helps

Answer:

well your answer should be "F"

Step-by-step explanation:

we have

Y<-2x+10  -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

Y = -2x+10

The y-intercept of the dashed line is (0,10)

The x-intercept of the dashed line is (5,0)

Y<1/2x-2 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line

Y= 1/2x-2

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution

therefore

The solution are the points

E, F and G

i hope this helps

Answer:

a) The greatest number that divides 36, 45, and 63 without leaving a remainder is 9

b) The greatest number which exactly divides 90, 120, and 150 is 30

c) The greatest capacity of the bucket is 10 liters

d) The greatest number of people to whom the items can be distributed equally is 40 people

ii) 2 kg of wheat flour, 3 kg of corn and 4 kg of rice

e) The greatest number of children to whom the 48 orange, 80 bananas, and 144 apples can be distributed equally is 16

ii) 3 oranges, 5 bananas and 9 apples each

f) 5 mangoes at a time from the basket containing 120 mangoes

7 mangoes at a time from the basket containing 168 mangoes

g) The greatest length of each squared marble is 2 m

Step-by-step explanation:

a) The greatest number that divides 36, 45, and 63 without leaving a remainder = The highest common factor of 36, 45, and 63, which is given as follows;

36 = 9 × 4

45 = 9 × 5

63 = 9 × 7

Therefore, The greatest number that divides 36, 45, and 63 without leaving a remainder  = The highest common factor of 36, 45, and 63 = 9

b) 90 = 30 × 3

120 = 30 × 4

150 = 30 × 5

The greatest number which exactly divides 90, 120, and 150 is 30

c) The factors of the volumes are;

50 l = 10 × 5 l

60 l = 10 × 6 l

70 l = 10 × 7 l

Therefore, the greatest capacity of the bucket = 10 liters

d) The masses of the items are

The factors of 80 = 40 × 2

120 = 40 × 3

160 = 40 × 4

Therefore the items can be distributed equally to 40 people

ii) Each person gets 2 kg of wheat flour, 3 kg of corn and 4 kg of rice

e) 48 = 16 × 3

80 = 16 × 5

144 = 16 × 9

Therefore, the greatest number of children = 16

ii) Each child gets 3 oranges, 5 bananas and 9 apples

f) The factors of 120 = 24 × 5

168 = 24 × 7

Therefore;

The greatest number of mangoes which is to be taken out of the basket with 120 mangoes = 5 mangoes each (24 times)

The greatest number of mangoes which is to be taken out of the basket with 168 mangoes = 7 mangoes each (24 times)

g) The area of the floor = 12 m × 10 m = 120 m²

The factor of 120 m² which is a perfect square is 4 therefore, we have;

The side length of each squared marble, s = √4 = 2

The side length of each squared marble, s = 2 m

Answer:

commutative property of addition.

a sequence of additions can be done in any order and the total remains the same.

Step-by-step explanation:

so, we can actually do

27 + 3 + 15 + 5

and now it is easy to combine 27+3 to 30 and 15+5 to 20, and to make the final calculation of 30 + 20 = 50 in our minds.

Answer:

If Cathy ran at a constant speed of 10 meters in 2 seconds, it took Cathy 20 seconds to run 100 meters.

Step-by-step explanation:

Hope this helps.

Answer:

If Cathy run at constant speed of 10 meters in 2 seconds, it took Cathy 20 second to run 100 meters.

Answer:

the answer is going to be 1/3

Answer:

$2,400

Step-by-step explanation:

Note: The correct years is 4 not 44

The Principal  = $10,000

Time period = 4 years

Rate = 6 % p.a.

Simple Interest = Principal * Rate * Time

Simple Interest = $10,000 * 6% * 44

Simple Interest = $2,400

So, the amount of interest Diego earned after four years is $2,400

Answer:

x>-1.25

Step-by-step explanation:

0.2x+4-3>-7-6.2x

0.2x+1>-7-6.2x

0.2x+6.2x>-7-1

6.4x>-8

x>-1.25

or x>-5/4,x>-1 1/4, xE(-1.25, infinite)

The solution to the inequality is x > -1.25.

The complete steps are:

the distributive property: 0.2x+4-3>-7-6.2x

Combine like terms: 0.2x+1>-7-6.2x

the addition property of inequality: 0.2x+6.2x +1 >-7 => 6.4x + 1 > –7

the subtraction property of inequality: 6.4x > -7 - 1 => 6.4x>-8

the division property of inequality: (6.4x)/6.4 > (-8)/6.4 => x>-1.25

Here, we have,

To solve the inequality 0.2(x + 20) - 3 > -7 - 6.2x,

let's go through the steps:

Step 1: Use the distributive property:

0.2x + 4 - 3 > -7 - 6.2x

Step 2: Combine like terms:

0.2x + 1 > -7 - 6.2x

Step 3: Use the addition property of inequality:

0.2x + 1 + 6.2x > -7

6.4x + 1 > -7

Step 4: Use the subtraction property of inequality:

6.4x > -7 - 1

6.4x > -8

Step 5: Use the division property of inequality:

Divide both sides of the inequality by 6.4 to isolate x:

(6.4x)/6.4 > (-8)/6.4

x > -8/6.4

Simplifying further, we have:

x > -1.25

Therefore, the solution to the inequality is x > -1.25.

To learn more on inequality click:

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Answer:

54

Step-by-step explanation:

It is the answer to this question

Wait waaaait Hol' up.

Answer:

Its 18.

Answer: C

Step-by-step explanation: A straight angle is 180 degrees:

180-130 = 50

Triangle angles equal up to 180.

50 + 2y =180

y =65

SUM OF INTERIOR OPPOSITE ANGLES = EXTERIOR ANGLE .

[tex]130 = y + y \\ 130 = 2y \\ \frac{130}{2} = y \\ \frac{ \cancel{130}^ { \tiny \: \: \: \: 65} }{ \cancel{2}} = y \\ y = 65 \degree[/tex]

Answer:

Step-by-step explanation:

Cross multiplication can be used but not in the beginning. First x should be isolated.

[tex]3 +\frac{5}{x}=\frac{7}{x}\\\\[/tex]

Now subtract [tex]\frac{5}{x}[/tex] from both sides

[tex]3 = \frac{7}{x}-\frac{5}{x}\\\\3=\frac{7-5}{x}\\\\3=\frac{2}{x}[/tex]

In this stage, cross multiplication can be used.

[tex]\frac{3}{1}=\frac{2}{x}\\\\3*x=2*1\\\\x = \frac{2}{3}[/tex]

Answer:

x =0 and x =2/3

Step-by-step explanation:

as is no

but if you put an x under the 3 to make 3x/x

then you'd have 3x+5/x = 7/x

to make

3x^2 + 5x = 7x

this makes

3x^2 -2x =0

using the quadratic formula

answers

x =0 and x =2/3

Answer:

Step-by-step explanation:

Step 3:

Let LM = x

OK = KP = 12 units [Radii of circle K]

LN = LP = 8 units [Radii of circle L]

Therefore, KL = KP + PL

KL = 12 + 8

     = 20 units

Step 4:

Since, ΔKOM and ΔLNM are the similar triangles,

By the property of two similar triangles, corresponding sides of these similar triangles will be proportional.

[tex]\frac{OK}{NL}=\frac{KM}{LM}[/tex]

[tex]\frac{12}{8}=\frac{x+20}{x}[/tex]

12x = 8(x + 20) [By cross multiplication]

12x = 8x + 160

12x - 8x = 160

4x = 160

x = 40

Answer:

A

Step-by-step explanation:

Answer:

Volume of sphere = 4/3 * π * r³

Since 36π = 4/3 * π * r³, r³ = 27 and r = 3.

Step-by-step explanation:

Answer: The answer is (D) Reflection across the line y = -x.

Step-by-step explanation: In figure given in the question, we can see two triangles, ΔABC and ΔA'B'C' where the second triangle is the result of transformation from the first one.

(A) If we rotate ΔABC 180° counterclockwise about the origin, then the image will coincide with ΔA'B'C'. So, this transformation can take place here.

(B) If we reflect ΔABC across the origin, then also the image will coincide with ΔA'B'C' and so this transformation can also take place.

(C) If we rotate ΔABC through 180° clockwise about the origin, the we will see the image will be same as ΔA'B'C'. Hence, this transformation can also take place.

(D) Finally, if we reflect ΔABC across the line y = -x, the the image formed will be different from ΔA'B'C', in fact, it is ΔA'D'E', as shown in the attached figure. So, this transformation can not take place here.

Thus, the correct option is (D).

Answer:

5^4x+3 ×100^-2x+1=50000

5^4x×100^-2x=49996

isolate the variable by dividing each side by factors that don't contain the variable. Exact Form: x = 8 √ 12499 ,  Decimal Form: x = 894.39141319 …

From one of the trigonometric ratios, tan(x), it is possible to find that x is equal to 52.1°.

The main trigonometric ratios for a right triangle are presented below.

                [tex]sin(x)= \frac{opposite\; side}{hypotenuse} \\ \\ cos(x)= \frac{adjacent\; side}{hypotenuse} \\ \\tan(x)= \frac{sin(x)}{cos(x)} =\frac{opposite\; side}{hypotenuse}* \frac{adjacent\; side}{hypotenuse}=\frac{opposite\; side}{adjacent\; side}[/tex]

For solving this question, you need to apply the a trigonometric ratio . You have the dimensions of two sides and you need to find the angle x.

Thus, you can apply the tan(x).

                       [tex]tan(x)= \frac{opposite\; side}{adjacent\; side}=\frac{36}{28} =\frac{9}{7}[/tex]

After that, you should calculate the arctan(x).

                           [tex]arctan\left(\frac{9}{7}\right)=52.1^{\circ \:}[/tex]

Then x= 52.1°

Learn more about trigonometric ratios here:

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