During a certain day, a worker made 81 parts. He usually does 45 parts per day. What was the percent by which he increased the number of parts he usually makes?

Answer:

Step-by-step explanation:

The formula of a sum of a geometric sequence:

[tex]S_n=\dfrac{a_1(1-r^n)}{1-r}[/tex]

We have

[tex]a_1=1,\ a_2=-6,\ a_3=36,\ ....\\\\r=\dfrac{a_2}{a_1}\to r=\dfrac{-6}{1}=-6[/tex]

Substitute:

[tex]a_1=1,\ n=7,\ r=-6:\\\\S_7=\dfrac{1(1-(-6)^7)}{1-(-6)^7}=\dfrac{1-(-279936)}{1+6}=\dfrac{279937}{7}=39991[/tex]

This is the order you need to use to solve this problem: PEMDAS

(Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

So you start with P and make your way down to S

(2x + 3)(x - 6) - 2x² + 3x + 30    First multiply (2x + 3)(x - 6) (distribute)

(2x)x - (2x)6 + (3)x - (3)6 = 2x² - 12x + 3x - 18 = 2x² - 9x - 18

(2x²- 9x - 18) - 2x² + 3x + 30    Simplify by combining like terms

-6x + 12

Answer:

- 6x + 12

Step-by-step explanation:

Expand the product of factors

= 2x² - 12x + 3x - 18 - 2x² + 3x + 30 ← collect like terms

= (2x² - 2x²) + (- 12x + 3x + 3x) + (- 18 + 30) ← simplify parenthesis

= 0 + (- 6x) + (12)

= - 6x + 12

24$ I believe is the answer You divide the total number of miles driven, to the number of miles per gallon . 180 divided by 30 = 6. Then multiply the answer 6 times dollars per gallon 4$ • 6 = 24 Your answer is 24 :)

Ethan's trip cost $24 in gasoline expenses, calculated by dividing the distance by the fuel economy to find the gallons used and then multiplying that by the cost per gallon.

To calculate the total cost of gasoline for Ethan's trip, we need to know two things: the fuel economy of the car and the distance traveled. The fuel economy is given as 30 miles per gallon, and the distance traveled is 180 miles.

First, we calculate how many gallons of gas were used during the trip:

Therefore, the total cost of gasoline for the trip was $24.

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Answer:

5u - 30y + 10

Step-by-step explanation:

To convert George the giraffe's height from feet to inches, multiply 18 feet by the conversion factor of 12 inches per foot, resulting in George being 216 inches tall.

If George the giraffe is 18 feet tall and you want to convert his height to inches, you need to know that one foot is equal to 12 inches. To find out how many inches tall George the giraffe is, you multiply his height in feet (18 feet) by the number of inches in one foot.

Here's the calculation step by step:

Therefore, George the giraffe is 216 inches tall.

Answer:

9 on ED2020

Step-by-step explanation:

The simplified value of the expression [tex]\frac{27^2}{27 ^{4/3}}[/tex]  using properties of exponents is 3² or 9.

Given Expression: [tex]\frac{27^2}{27 ^{4/3}}[/tex]

To Simplify the expression, use the following Exponents properties

Now, let's factorize the number of prime factors

27 = 3 x 3 x 3 or 3³

So, the Expression [tex]\frac{27^2}{27 ^{4/3}}[/tex] can  be written as

[tex]\frac{27^2}{27 ^{4/3}}[/tex] = [tex]\frac{(3^3)^2}{(3^3)^{4/3}}[/tex]

Using Power Rule: [tex](a^m)^n = a^{(m*n)[/tex]

[tex]\frac{27^2}{27 ^{4/3}}[/tex] = [tex]\frac{3^{(3*2)}}{3^{3*(4/3)}}[/tex]

       = [tex]\frac{3^6}{3^4}[/tex]

Using Quotient Rule: [tex]a^m / a^n = a^{m-n}[/tex]

[tex]\frac{27^2}{27 ^{4/3}}[/tex]  = [tex]\frac{3^6}{3^4}[/tex]

         =[tex]3^ {6-4}[/tex]

         = 3²

         = 9

Therefore, the simplified expression is 3² or 9.

Learn more about Exponents and power here:

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Answer:

b

Step-by-step explanation:

The square of 2 and the resultant is multiplied by 3 then subtract by 2. Then the correct option is B.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = 3x² - 2

The value of the function at x = 2 will be given as,

f(2) = 3(2)² - 2

The square of 2 and the resultant is duplicated by 3 then, at that point, taken away by 2. Then, at that point, the right choice is B.

More about the function link is given below.

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Corresponding angles are the ones that occupy the same relative position where a third line intersects two other lines. If lines FH and IK are parallel, the corresponding angles are FHB and IKB; and BHJ and BKL. They are always equal in measure if the lines are parallel.

In geometry, lines that are parallel have several corresponding angles. Corresponding angles are the angles that occupy the same relative position at each intersection where a line intersects two other lines. If lines FH and IK are parallel and intersected by another line (Let's call it line B for easier understanding), the corresponding angles would be as follows:

These pairs are known as corresponding angles. Coresponding angles are always equal in measure if the lines are parallel to each other.

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Answer:

-2 11⁄20 = -2.55

Step-by-step explanation:

Combine like-terms to get -2x - 0.2 = 4.9. So, straight off the bat, we know that -2x has to equal 5.1 [move 0.2 to the right side of the equivalence symbol]. Then you would simply divide by -2 to get the above answer.

I am joyous to assist you anytime.

Answer:

3.2

Step-by-step explanation:

it is closer to 3.2 than 3.3

Answer: 3.2

Step-by-step explanation:

2 is the the tenths place and 4 is in the hundredths. .24 rounded to .2 is now the tenths therefore 3.2 is the tenths place

Answer:

x = 7

Step-by-step explanation:

Assuming we need to solve for x, we cross multiply and do algebra to solve it. Steps shown below:

[tex]\frac{8x}{7}=8\\8x=7*8\\8x=56\\x=\frac{56}{8}\\x=7[/tex]

The correct answer is x = 7

Answer:

Step-by-step explanation:

[tex]\dfrac{8x}{7}=8\qquad\text{multiply both sides by 7}\\\\7\!\!\!\!\diagup^1\cdot\dfrac{8x}{7\!\!\!\!\diagup_1}=7\cdot8\\\\8x=56\qquad\text{divide both sides by 8}\\\\x=7[/tex]

answer:

y=5.5x

explanation:

rise over run=rise/run= x/y

for every t shirt or "y" multiply 5.5 and it will give u the total cost or"x"

for president, we have 12 possible options

12_

Once we’ve decided on a president we only have 11 possible people to choose from for vice president

12_11

multiplying these options together gives us:

12•11= 132

So the answer is C.132

The correct answer is C 132

The answer would be 3.175 kg

Answer:knee r

Step-by-step explaning

Answer:

C. P= 1000M

Step-by-step explanation:

[tex]log(\frac{M}{N} )=4[/tex]

Using the quotient rule of logs we can write:

log(M) - log(N) = 4

or

log(M) - 4 = log(N)                                       (Equation 1)

[tex]log(\frac{P}{N} )=4[/tex]

Using the quotient rule of logs we can write:

log(P) - log(N) = 7

or

log(P) - 7 = log(N)                                         (Equation 2)

Comparing equation 1 and 2, we can write:

log(M) - 4 = log(P) - 7

-4 + 7 = log(P) - log(M)

log(P) - log(M) = 3

[tex]log(\frac{P}{M} )=3[/tex]

Converting the log to exponential form we get:

[tex]\frac{P}{M}=10^{3}\\\\\frac{P}{M}=1000\\\\P=1000M[/tex]

Thus, option C gives the correct answer.

Final answer:

The relationship between M and P is that P is 1000 times greater than M; hence, the correct option is P = 1000M.

Explanation:

Given the two equations log(M/N) = 4 and log(P/N) = 7, we need to find the relationship between M and P.

To understand this relationship, we use the property of logarithms that equates to a multiplication by 10 for each unity increase in logarithmic value.

From the first equation, M/N = 10⁴, and from the second equation, P/N = 10⁷. Simplifying these, M = 10⁴ N and P = 10⁷ N.

To find the relationship between M and P, we can divide the equation for P by the equation for M:

P/M = (10⁷ N) / (10⁴ N) = 10³ = 1000.

Therefore, P is 1000 times M, which means P = 1000M

Answer:

33

Step-by-step explanation:

Each holds 2.5*12 = 30 eggs.

1000/30 = 33.333333

So he fills 33 flats.

The number of flats he could fill is 33

Peterson needed to pack 1000 eggs into flats that held 2 1/2 dozen eggs. To find out how many flats he could fill, we need to calculate the total dozen eggs in 1000 and then divide by 2.5 dozen since each flat holds 2 1/2 dozen eggs.  One dozen equals 12 eggs. Therefore, 1000 eggs would be equivalent to 1000/12 = 83.33 dozen. To find the number of flats, we divide the total dozen eggs by the capacity of each flat in dozen: 83.33 dozen / 2.5 dozen = 33.33. This means Peterson can completely fill 33 flats, with a partial amount of eggs left over not sufficient to fill another flat completely.

Answer:

17 $10s and 8 $20s

Step-by-step explanation:

Answer:

45 degrees

2 units

Step-by-step explanation:

A rotation is an Isometry so therefore the 45-45-90 Triangle is the exact same size and shape after the rotation.

Answer: $0.25

Step-by-step explanation:

Let x be the total money was in her wallet and m be the cost of each petunia,

From the given table , the money left in wallet after purchasing 2 petunia =$6.50

Then we have the following equation :-

[tex]6.50=x-2m-----(1)[/tex]

Also, the money left in wallet after purchasing 8 petunia =$5

Then, we have

[tex]5=x-8m---------(2)[/tex]

Subtracting (2) from (1) , we get

[tex]6.50-5=-2m-(8m)\\\\\Rightarrow\ -2m+8m=1.50\\\\\Rightarrow\ 6m=1.50\\\\\Rightarrow\ m=\dfrac{1.50}{6}=0.25[/tex]

Hence, the price of one petunia = $0.25

Answer:

$.25

Step-by-step explanation:

Answer:

The value of a7 is 128

Step-by-step explanation:

* Lets revise the rule of the geometric series

-There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

* General term (nth term) of a Geometric series:

# a1 = a  ,  a2  = ar  ,  a3  = ar2  ,  a4 = ar3  ,  a5 = ar4

# an = ar^n-1, where a is the first term , r is the constant ratio

   between each two consecutive terms , and n is the position

   of the term in the series

* Now lets solve the problem

∵ a = 2

∵ r = -2

* To find a7 put n = 7

∵ an = a (r)^n - 1

∴ a7 = 2 (-2)^(7 - 1) = 2 (-2)^6

∵ (-2)^6 = 64 ⇒ even power canceled the negative sign

∴ a7 = 2 (64) = 128

∴ The series is : 2 , -4 , 8 , -16 , 32 , -64 , 128 , ............

* The value of a7 is 128

Answer:

A. 1ft

Step-by-step explanation:

1 x 1 = 1 squared

So 1 foot x 1 foot = 1 square foot

Answer:

a. 1 ft

Step-by-step explanation:

The area of a square is found by using the formula

A = s^2 where s is the side length of the square

We know the area is 1 ft^2

1 = s^2

Take the square root of each side

sqrt(1) = sqrt(s^2)

1 = s

The side length is 1 ft

ax² + bx + c = 0

You know:

a = -2

b = 1

c = 3

The 1st option is your answer

-2x² + x + 3 = 0

a = -2

b = 1

c = 3

Answer:

A: 0 = –2x2 + x + 3

Step-by-step explanation:

edge

Answer:

B

Step-by-step explanation:

The range is the difference between the largest and smallest members of the data set.

largest = 25 and smallest = 17

range = 25 - 17 = 8 → B

Answer:

Step-by-step explanation:

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have r = 4 u and H = 6 u. Substitute:

[tex]V=\dfrac{1}{3}\pi(4^2)(6)=\dfrac{1}{3}\pi(16)(6)=\dfrac{1}{3}\pi(96)=32\pi\ u^3[/tex]

[tex]\pi\approx3.14\to V\approx(32)(3.14)=100.48\ u^3[/tex]

If the cylinder has the same radius and height as a cone, then the volume of the cylinder is three times larger than the volume of the cone.

Therefore, the volume of acylinder:

[tex]V\approx3(100.48)=301.44\ u^3[/tex]

Why?

The formula of a volume of a cone:

[tex]V_{cone}=\dfrac{1}{3}\pi r^2H[/tex]

The formula of a volume of a cylinder:

[tex]V_{cylinder}=\pi r^2H[/tex]

Therefore

[tex]V_{cone}=\dfrac{1}{3}V_{cylinder}\to V_{cylinder}=3V_{cone}[/tex]

If the radius and height are the same.

Answer:

A cone has a radius of 4 units and a height of 6 units.

Its volume is

[100.48]

cubic units. If a cylinder has the same radius and the same height as the cone, then its volume is

[301.44]

cubic units.

Step-by-step explanation:

Answer:

[tex] \frac{3}{10} [/tex]

Step-by-step explanation:

First we need to find a common denominator for the fractions.

[tex] \frac{3}{2} + \frac{ - 6}{5} \: is \: to \: \frac{15}{10} + \frac{ - 12}{10} [/tex]

Now we just need to work out the result by adding the numerators.

[tex] \frac{15}{10} + \frac{ - 12}{10} = \frac{3}{10} [/tex]

Answer: First graph

Step-by-step explanation:The lines wont intersect

Answer:

The answer is option A.

Answer: First option.

Step-by-step explanation:

Marta needs to subtract [tex]2\pi r^2[/tex] from  both sides of the equation:

[tex]s=2\pi rh+2\pi r^2[/tex]

[tex]s- 2\pi r^2=2\pi rh+2\pi r^2- 2\pi r^2[/tex]

[tex]s- 2\pi r^2=2\pi rh[/tex]

Now she needs to divide both sides of the equation by [tex]2\pi r[/tex], then:

[tex]h=\frac{s- 2\pi r^2}{2\pi r}[/tex]

Rewriting:

[tex]h=\frac{s}{2\pi r}-\frac{2\pi r^2}{2\pi r}[/tex]

Simplifying, she should get:

[tex]h=\frac{s}{2\pi r}-r[/tex]

This matches with the first option.

Answer:

[tex]\frac{s}{2\pi r}-r=h[/tex]

Step-by-step explanation:

Given equation is [tex]s=2\pi rh+2\pi r^2[/tex].

Now we need to solve this equation for "h" and match with the given choices to find the correct choice.

[tex]s=2\pi rh+2\pi r^2[/tex]

[tex]s-2\pi r^2=2\pi rh[/tex]

[tex]2\pi rh=s-2\pi r^2[/tex]

[tex]h=\frac{s-2\pi r^2}{2\pi r}[/tex]

[tex]h=\frac{s}{2\pi r}-\frac{2\pi r^2}{2\pi r}[/tex]

[tex]h=\frac{s}{2\pi r}-r[/tex]

[tex]\frac{s}{2\pi r}-r=h[/tex]

Hence first choice [tex]\frac{s}{2\pi r}-r=h[/tex] is correct choice.

Answer:

28

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6, hence

sum = 180° × 4 = 720°

Each exterior angle plus it's interior angle = 180°

Subtract each exterior angle from 180 to obtain interior angle

180 - 80 = 100, 180 - 56 = 124, 180 - 61 = 119, 180 - 43 = 137, 180 - 92 = 88

The 6 th interior angle is the sum of the 5 interior angles subtracted from 720

6 th angle = 720° - (100 + 124 + 119 + 137 + 88)° = 720° - 568° = 152°

The 6 th angle and 2x sum to 180 ( same reason as given above )

2x + 152 = 180 ( subtract 152 from both sides )

2x = 28 ( divide both sides by 2 )

x = 14

Answer:

120 in^2

Step-by-step explanation:

Split the shape into a square and a rectangle, like you did. A square has all equal sides, so you know that 9 x 9= 81. If the whole length of the square and the triangle combined is 15, then you know the triangle base is 6. Multiply the height of the triangle by the base and .5 to get that area. Add everything together for the answer

Answer:

C. 2 cups

Step-by-step explanation:

So since it says for every 1/2 cup of whole milk, you need 1/4 of heavy cream, that means you will need twice as much whole milk as you do heavy cream.

So for every one cup of heavy cream, that means you need 2 cups of whole milk.

This is because 1/2 is twice as much as 1/4.

To scale up the given ratio of 1/2 cup of whole milk to 1/4 cup of heavy cream to 1 cup of cream, you need to multiply the quantity of milk by 4. This gives you 2 cups of milk for 1 cup of cream.

The question asks us to calculate the quantity of whole milk that should we used for every cup of heavy cream, based on a given ratio. The ratio given is 1/2 cup of milk for every 1/4 cup of cream. Ratios can be scaled up or down while keeping the same relationship between quantities. In this case, we want to know how much milk to use for 1 cup of cream. Since 1 cup is 4 times larger than 1/4 cup, we simply multiply the quantity of milk by 4 as well, which gives us 1/2 cup * 4 = 2 cup. Hence, the answer is C. 2 cups of milk should be used for every cup of heavy cream.

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