Find the percent change from the first value to the second.

40; 70

Answer:

k= 70

Step-by-step explanation:

The compound amount after 3 years is $2275.22.

In this case, you are given:

Principle = $2,000

rate = 0.0353

time = 3

You need to find A, the compound amount after 3 years.

To do this, you need to plug in the values of P, r and t into the formula and use a calculator:

A=P×e^rt

A=2000×(e)^0.0353×3

A≈2275.22

Therefore, by the compound interest the answer will be $2275.22.

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Answer:

\(\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|\)

Step-by-step explanation:

Cost of a bowl of salad = $5.00

Cost of a slice of pizza = $2.00

If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation:

Next, we make P the subject of the equation above.

2P=E-5S

\(P=\dfrac{E-5S}{2} \\P=0.5(E-5S)\)

Therefore, The quantity of pizza he buys can be represented by the equation:

When E=$40, we are required to complete the table below.

\(\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&\\40.00&4&\\40.00&&0\end{array}\right|\)

When S=0, E=$40

From P=0.5(E-5S)

P=0.5(40-5(0))=20

When S=4, E=$40

P=0.5(40-5(4))

=0.5(40-20)

=0.5*20

=10

When P=0, E=$40

P=0.5(E-5S)

0=0.5(40-5S)

40-5S=0

5S=40

S=8

Therefore, the completed table is:

\(\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|\)

Answer:

98 liters

Step-by-step explanation:

add 39 and 59

Answer:

Step-by-step explanation:

512 sq. ft.

Answer:

512

Step-by-step explanation:

To start off with you can take the area of the the whole rectangle with the boxes inclosed to get (32+8) times (8+8) to get

40x16= 640ft

From their, find the areas of the two boxes inclosed in the rectangle

b1= 8x8= 64ft

b2= 8x8= 64ft

then you can subtract the two boxes areas from the larger rectangles area to get your answer of

640-64-64= 512ft

The sentence that contains filler is: D. This set also includes heroes like Obi-Wan Kenobi and Anakin Skywalker, both of whom come fully-equipped with their signature lightsabers and Jedi robes. Option D

In this sentence, the phrase "also includes heroes like Obi-Wan Kenobi and Anakin Skywalker" acts as a filler. The main purpose of this phrase is to provide additional information about the set and highlight the inclusion of popular characters from the Star Wars franchise. It doesn't directly contribute to the core information about the set's features or components.

The other sentences (A, B, and C) provide specific details and descriptions about the LEGO set, such as the number of pieces, minifigures, droids, and features like the opening top hatch and cockpit. They directly convey important information about the set itself without any filler or additional unnecessary information.

In marketing or promotional contexts, fillers are often used to enhance the appeal of a product or create excitement by mentioning well-known or desirable elements that may not be directly relevant to the core features. The filler in sentence D serves to attract fans of Obi-Wan Kenobi and Anakin Skywalker by emphasizing their presence in the set and the inclusion of their iconic weapons and attire.

Option D

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Answer:D

Step-by-step explanation:

The values of (i) x A0 (ii) 0. 12 cm N 6 cm K 8 cm M in the figure are  30⁰ anf 10cm respectively

using the trigonometric ratio of sine we have

Sin∅ = 6/12

⇒sin ∅ = 1/2 = sin 30

⇒∅ 30⁰

therefore,

x² =  8²+6²

x² = 64+36

x = √100

x = 10cm

therefore, ∅ = 30⁰ and x =- 10cm

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We know that

• Maria was getting 24 mpg (miles per gallon).

• Her mileage would increase by 8% with the new tires.

First, we find 8% of 24 mpg, remember that 0.08 is equivalent to 8%.

Second, add the 8% calculated to the mileage.

The answer is D: conjecture

The key words in the description are "look for a pattern and then form an educated guess." This suggests making a hypothesis or assumption based on the observed pattern, which is the definition of a conjecture.

The other answer choices are defined as follows:

A. conjugation - the act of changing a verb to agree with its subject

B. conjunction - a connecting word

C. congruence - the state of agreeing, matching, or coinciding

D. conjecture - an opinion or conclusion formed on the basis of incomplete information

So option D, conjecture, is the best match for forming an educated guess based on an observed pattern in induction.

Answer:

P-value (t=2.58) = 0.0066.

Note: as we are using the sample standard deviation, a t-statistic is appropiate instead os a z-statistic.

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean μ exceeds 2.4.

Then, the null and alternative hypothesis are:

\(H_0: \mu=2.4\\\\H_a:\mu> 2.4\)

The significance level is 0.05.

The sample has a size n=45.

The sample mean is M=2.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.26.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.26}{\sqrt{45}}=0.0388\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.5-2.4}{0.0388}=\dfrac{0.1}{0.0388}=2.58\)

The degrees of freedom for this sample size are:

\(df=n-1=45-1=44\)

This test is a right-tailed test, with 44 degrees of freedom and t=2.58, so the P-value for this test is calculated as (using a t-table):

\(P-value=P(t>2.5801)=0.0066\)

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

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Answer:

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = 0.5445

Step-by-step explanation:

Step(i):-

Given mean of the Population μ = 5.3 days

Given standard deviation of the population 'σ' = 2 days

Let 'X' be the random variable in normal distribution

Let    x₁ = 4

\(Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{4-5.3}{2} = -0.65\)

Let    x₂ = 7

\(Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{7-5.3}{2} = 0.85\)

Step(ii):-

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = P(-0.65≤Z≤0.85)

             =  P(Z≤0.85) - P(Z≤-0.65)

            = 0.5 + A( 0.85) - ( 0.5 - A(-0.65)

            = 0.5 + A( 0.85) -  0.5 +A(0.65)   ( ∵A(-0.65) = A(0.65)

           =   A(0.85) + A(0.65)

          = 0.3023 + 0.2422

         = 0.5445

Final answer:-

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = 0.5445

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:I think -1

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

cuz i already did

Answer: 30 degrees

Step-by-step explanation:

The Slope of the line that passes through the points (3,8) and (8,13) is

1.  

Equation =  slope(m)  = (y₂ - y₁) / (x₂ - x₁)

                                     = (13-8) / (8-3)

                                     = 5 / 5 = 1

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Let's check your solution by starting from the top:

Given the expression:

Let's simplify. We get,

Answer:

The mean number of books to a box is 11.

Step-by-step explanation:

Given - Garth is packing boxes with books. The list shows how many books are in each of 10 boxes.

6, 14, 6, 18, 9, 9, 12, 10, 11, 15

To find - Which statement is true about the number of books packed to a box?

Solution -

Mean of number of books is equal to

= (6+ 14+ 6+ 18+ 9+ 9+ 12+ 10+ 11+ 15)/10

= 110/10

= 11

∴ we get

The mean number of books to a box is 11.

For Median -

Firstly, arrange the data into increasing order

6, 6, 9, 9, 10, 11, 12, 14, 15, 18

Now, we know that,

If total data(n) is even then median is the average of value at (n/2)th place and [(n/2 + 1]th place

Here n = 10

So,

Median is average of 10 and 11

i.e. Median = (10+11)/2

                  = 21/2 = 10.5

So,

Median number of books to a box is 10.5

∴ we get

The correct option is - The mean number of books to a box is 11.

Answer:

The mean number of books to a box is 11.

Step-by-step explanation:

Using simple addition and multiplication, we concluded that the difference in height between sea gull and shark is 17m and distance between the heights of the sea gull and the shark is 29m.

Given,

Albatross is flying 87 m above the surface of the ocean

Sea gull is flying 6 m above sea level

shark is swimming 23 m below sea level

a) The difference in height between sea gull and shark is -

23m - 6m

= 17m

b) The distance between the heights of the sea gull and the shark is -

23m + 6m

= 29m

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Answer:

c

Step-by-step explanation:

For the given number 4 x 5³/₈. The whole part is 4 and the fraction part is 5³/₈. Both are added together to form a fraction of 43/8.

An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that.

For the given number 4 x 5³/₈.

The whole part is 4.

The fraction part is 5³/₈.

Solving the mixed fraction:

= 5³/₈.

= (5*8 + 3) /8

Both are added together to form a fraction:

= 43/8

The final number becomes:

= 4 x 5³/₈

= 4 x 43/8

= 43/2

Thus, the result of the final number obtained is 43/2.

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Answer:

\(Area = 1200m^2\)

\(Perimeter = 148m\)

Step-by-step explanation:

To find the area, just multiply the length by the width. In fact, we have a simple formula for this:

\(A(area) = lw\)

\(l(length) = 50\)

\(w(width)= 24\)

Now, we need to plug in our values:

\(A(area)= 50*24\)

Simplify:

\(A(area) = 1200\)

Therfore, the area of the rectangle is:

\(1200m^2\)

Now, lets move on to the perimeter(again, we have a simple formula!):

\(P(perimeter) = 2(l+w)\)

Plug in our values from before:

\(P(perimeter)= 2(50 + 24)\)

Simplify:

\(P(perimeter)= 2(74)\)

Multiply it out:

\(P(perimeter) = 148\)

Therfore, the perimeter of your rectangle is 148 m

Always remember to include the proper units and format your work well to minimize mistakes and leave less room for error.

~~~Harsha~~~

Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.

The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.

To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.

For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).

For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).

Since we want the final mixture to contain 7% butterfat, we can set up the following equation:

0.08x + 0.02y = 0.07(258)

Simplifying the equation, we have:

0.08x + 0.02y = 18.06

To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.

Substituting this value into the equation above, we get:

0.08x + 0.02(258 - x) = 18.06

Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.

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Answer:

Me: 60

Zayn and Attia: 6

Step-by-step explanation:

12 = 2 × 2 × 3

20 = 2 × 2 × 5

LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60

My number is 60.

Zayn's and Attia's numbers are 6.

Hello !

Answer :

Explanation :

\( \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } \)

\( \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } \)

\( ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}\)

Have a nice day ;)

Each decision variable must be non-negative in the optimal solution.

According to this restriction or constraint, x11, x12, x21, and x22 must all be bigger than zero. They cannot, therefore, be negative numbers. All the variables would have to be positive values if the limitation had been > (greater than). However, since it is (more than or equal to), the choice of 0 is acceptable.

The function \(f(x_{1} ,x_{2} ,....)=x_{1} ^{2},x_{2} ^{2} ......\) is always positive except at the origin where it is equal to zero. This means that the absolute minimum of this function must be a = 0 . Absolute maximum is when all of the variables are equal to zero except \(x_{1}\) which is equal to 1 (f evaluated at this point is equal to 1 do b=1). The function itself is then equal to 1. This is because when \(f(.....) = x_{1} ^{2} +x_{2} ^{2} .....\leq x_{1} ^{2} +2x_{2} ^{2}+3x_{3} ^{2} ....\leq 1\)

so it is at most equal to 1 and this happens exactly at the point

\((x_{1} ,x_{2} ,x_{3} .....) = (1,0,0...)\)

Therefore,

Each decision variable must be non-negative in the optimal solution.

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Therefore, using the multiplier formula, a $525,000,000 increase in RGDP would result in a total increase in spending of $2,625,000,000.

To use the multiplier formula, we need to know the marginal propensity to consume (MPC), which is the fraction of each additional dollar of income that is spent on consumption.

The multiplier formula is: Multiplier = 1 / (1 - MPC)

If we assume an MPC of 0.8 (meaning that for every additional dollar of income, 80 cents are spent on consumption), the multiplier would be:

Multiplier = 1 / (1 - 0.8) = 5

So, if the change in Real Gross Domestic Product (RGDP) is $525,000,000, the total increase in spending (including consumption, investment, government spending, and net exports) would be:

Total spending increase = Multiplier x RGDP change

Total spending increase = 5 x $525,000,000

Total spending increase = $2,625,000,000

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

Omg this so ez, 35

Step-by-step explanation:

105 divided by 3 duh, -_-

The probability of picking L and another A with replacement is: 2/49

Probability of picking A and then another A with replacement is:  1/49

We are given the letter DALLAS.

There are a total of 7 letters. Thus, the probability of picking L is:

2/7

Probability of picking A after that with replacement is: 1/7

Thus, probability of picking L and another A with replacement is:

(2/7) * (1/7) = 2/49

Probability of picking A and then another A with replacement is:

(1/7) * (1/7) = 1/49

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