Subtract. Write your answer in simplest form.

7/10 - 3/10

Answer:

D

Step-by-step explanation:

Answer:

2 Triangles can be made with the given measurements

Step-by-step explanation:

Start by solving for side b

b = 9/sin33 = appr 16.5

9<15<16.5 there are two possible triangles

sin33/15 = sinB/16.5 = sinB=(16.5sin33)/15

B=36.9, 180-36.9=143.1 Next determine if the angles are correct

36.9+33=69.9 143.1+33=176.1 Both of these are less than 180, two triangles can be drawn.

Answer:

0.4 Pints

Step-by-step explanation:

The probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm is 0.01715.

A normal distribution is a probability distribution that has been symmetrical around this mean, with most observations clustering around the central peak and probabilities tapering off evenly in both directions.

Now, according to the question,

The formula for normal distribution is;

z = (x - μ)/(σ/√s)

x is the sample size (= 96)

μ = standard mean (= 92)

σ = standard deviation (= 10)

s = random sample (= 28)

Substituting all the values in the equation;

z = (96 - 92)/(10/√28)

z = 2.117

Now, calculate the probability;

P(X > 96) = 1 - P(X ≤ 96)

               = 1 - P(X ≤ 2.117)

               = 1 - 0.98285

P(X > 96) =  0.01715

Therefore, the probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm is 0.01715.

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The complete question is-

The reading speed of a second grade students in a large city is approximately normal with a mean of 92 words per minute and a standard deviation of 10 wpm. What is the probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm?

Answer:

3

Step-by-step explanation:

55% of 20 is 11 so she originally got 11 shots in. 56% of 20 + 5 = 25 is 14 so after the 5 extra shots she got 14 in. The answer is 14 - 11 = 3.

Answer:

hungry as can be sorry needed the points

The iterated integral evaluates to zero when converted to polar coordinates.

The iterated integral can be converted to polar coordinates using the following equation:

0 0 4x2y dx dy = 2π ∫0 a r dr dθ

This can be further simplified by integrating with respect to r:

2π∫0 a (a2−r2) dr

The integral can now be evaluated by calculating the definite integral between 0 and a:

2π [a3/3 - r3/3] |0 a

The evaluated integral is then simplified to:

2π[a3/3 - a3/3]

Finally, the evaluated integral is multiplied by 2π to give the final result:

2π(0)

Therefore, the answer is 0.

The iterated integral can be converted to polar coordinates using the equation

0 0 4x2y dx dy = 2π ∫0 a r dr dθ.

This can then be further simplified by integrating with respect to r, resulting in

2π∫0 a (a2−r2) dr.

The integral can be evaluated by calculating the definite integral between 0 and a, which is

2π [a3/3 - r3/3] |0 a.

This evaluated integral is simplified to

2π[a3/3 - a3/3]

and is then multiplied by 2π to give the final result; 2π(0). Therefore, the answer is 0.

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Answer:

18 miles

Step-by-step explanation:

162 ÷ 3 × ⅓ = 18 miles

Hope this helps =)

The probability that exactly 1 of the chosen Californians were born outside the US when 4 Californians are chosen randomly where 27% of California residents were born outside the united states is 0.42.

This is a case of Binomial distribution where there is 0.27 probability a resident of California were born outside US and 0.73 probability they were born inside the US.

In this case of Binomial distribution, the total number of successful trial(n) is the number of Californian residents chosen that is n = 4. Probability that exactly 1 of the chosen resident is

P = 4C1 × (0.27)¹ × (0.73)⁽⁴⁻¹⁾

= 4!/ ((4-1)! × 1!) × 0.27 × 0.73³

= 4 × 0.27 × 0.389017

= 0.42013836

≈ 0.42

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Answer:

A timeframe of 8 years is when there were 45 raccoons in the area.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Equality Properties

Standard Form:
\(\displaystyle ax^2 + bx + c = 0\)

Quadratic Formula:
\(\displaystyle x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Step-by-step explanation:

Step 1: Define

Identify given.

\(\displaystyle \begin{aligned}y & = 0.4x^2 + 2x + 2 \\y & = 45 \ \text{raccoons} \\\end{aligned}\)

Step 2: Find Specific Year

We are trying to find the year when there were 45 raccoons present in the area. From first glance, we see we probably can't factor the quadratic expression, so let's set up to use the Quadratic Formula:

Now that we have our variables from Standard Form, we can use the Quadratic Formula to find which years when there were 45 raccoons present in the area:

Since time cannot be negative, we can isolate the other root to obtain our final answer:

\(\displaystyle\begin{aligned}x & = 8.16536 \ \text{years} \\& \approx \boxed{ 8 \ \text{years} } \\\end{aligned}\)

∴ we have found the approximate amount of years to be 8 years when there were 45 raccoons in the area.

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Topic: Algebra I

Answer:

x=12

Step-by-step explanation:

Step 1: Subtract 7 from both sides.

Step 2: Multiply both sides by 4.

and you get x=12

Answer:

12

Step-by-step explanation:

first move the 7 to the right of your equation, which then becomes 10-7= 3. then divide 3 by 1/4 and x= 12

plug in 12 back into x to make sure it is correct

The percentage increase in x​ is 44 %.

According to the definition of proportion, when two ratios are equivalent, they are in proportion. The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as,

a : b :: c : d = a/b = c/d

There are two other proportional formulas based on direct or indirect variation. If two quantities x and y are in direct proportion, then y = kx and when two quantities x and y are in indirect proportion, then y = k/x, where k is the constant of proportionality.

We are given that x is proportional to ​y where y > 0 and y is increased by 44%.

We have to find the percentage increase in x.​

x is proportional to ​y

=> x = k ​× y

Let say y = 10n

=> x =  k ​× 10n

=> x = 10kn

Now, y = 10n and y is increased by 44%.

=> y = 10n   + (44/100)10n

= 14.4n

=> x =  k ×​14.4n

=> x = 14.4kn

x changed from 10kn to 14.4kn

Increase = 14.4kn - 10kn = 4.4kn

% increase = (4.4kn/10kn) * 100  = 44 %

percentage increase in x​ = 44 %

Thus, the percentage increase in x​ is 44 %.

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The time you haven't spent building the crane is half an hour or 0.5 hour.

Assuming that you build cranes continuously for 1 hour then you make 40 cranes and you make 100 cranes in 3 hours.

Inference involves drawing logical conclusions based on stated evidence or assumptions.

It is said that you can make 40 cranes in 1 hour without rest. The time  to work 100 cranes continuously is:

time = number of cranes / number of cranes in one hour

time = 100 cranes / 40 cranes in one hour

ime = 2.5 hours

So if you make 100 cranes in a 3-hour period, then you have spent 3-2.5 = 0.5 hours not making cranes.

So you don't waste time building cranes when you build 40 cranes in 1 hour and 100 cranes in 3 hours in 0.5 hours.

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Answer:

c

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

\(7 + (15 - 5) \times (10 - 6) \times \frac{1}{2} + 5 \times 10 = 84\)

Answer:

The answer is 84 inches Squared!

Step-by-step explanation:

Here is the explanation to the answer:-

All you have to do is divide the whole figure into some parts!

Here is what I have divided the figure into.

The triangle area is 1/2 * L*H

The measurements are 1/2 * 4*3 = 6in Squared.

                         ( The Next Shape To The Triangle)

 Rectangle area is L*B

The Measurements are 4*7 = 28inches Squared.

                          (The next shape to the rectangle)

Rectangle area is L*B

Measurements are 5*4 = 20inches squared.  

                                    (Above Shape of the rectangle)

Area of rectangle is L*B

Measurements are 6*5 = 30 Inches Squared.

    Now, add all the areas of the figure:-

6 + 28 + 20 + 30 = 84 Inches Squared.

Thanks, and hope this helps.

Answer:

30 miles

Step-by-step explanation:

300/10=30

30 miles is the answer

Answer:

22.3 x 1.8 = 40.14

Step-by-step explanation:

22.3

x  1.8  

________

1784

2230

________

40.14

Answer:

40.14

Step-by-step explanation:

22.3

× 1.8  ← Forget about the decimal places and multiply by the one's place.

1 7 8 4

2 2 3 0 ← Put a 0 to hold the one's place and multiply 223 by ten's place.

4 0 . 1 4 ← Add those 2 numbers and keep 2 decimal places.

Translations, reflections, and rotations produce a figure that is congruent to the original figure.

When we perform translations, reflections, and rotations on a figure, the resulting figure maintains the same size, shape, and orientation as the original figure. In other words, the transformed figure is congruent to the original figure.

Here's a brief explanation of each transformation:

1. Translations: A translation involves sliding a figure in a particular direction without changing its orientation or shape. Every point of the figure moves the same distance and direction. The resulting figure is congruent to the original because all corresponding sides and angles remain the same length and measure.

2. Reflections: A reflection involves flipping a figure over a line, called the line of reflection. Each point of the figure is mirrored across the line, creating a symmetrical image. The resulting figure is congruent to the original because the distance between corresponding points remains the same, and the angles formed between intersecting lines are preserved.

3. Rotations: A rotation involves turning a figure around a fixed point, known as the center of rotation. The figure is rotated by a specific angle in a clockwise or counter clockwise direction. The resulting figure is congruent to the original because all corresponding angles and side lengths remain unchanged.

In each of these transformations, the congruency of the resulting figure to the original figure is a fundamental property. Congruent figures have the same shape and size, even though they may be positioned differently in space. This property allows us to apply the concept of congruence in geometry to establish relationships, prove theorems, and solve geometric problems.

Therefore, when we perform translations, reflections, and rotations on a figure, we produce a transformed figure that is congruent to the original figure.

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Answer:

C) 12

Step-by-step explanation:

These type of questions is basically asking you to replace x with 2. f(x) is the same thing as y = but inside the f(x) is the value of x. So in this case, the numerical value of x is 2. All we need to do is replace x with it's numerical value, 2, and solve the equation.

\(y=7(2-2) + 4(2+1)\\y=7(0) + 4(3)\\y = 12\)

Answer:

[2,4]

Step-by-step explanation:

Answer:

1) 23, 3, 13

2) 7, 13, 18

3) 9, 6, 77

4) 39, 8, 46

5) 13, 1, 32

6) 45, 9, 54

7) 14, 45, 30

8) 25, 10, 39

Step-by-step explanation:

Left to Right

The balance in the savings account will grow at a rate of approximately $525.62 per year after 2 years.

When money is compounded semiannually, the interest is applied twice a year. In this case, the savings account offers a 5% interest rate per year, so the interest rate per compounding period would be half of that, or 2.5%. To calculate the growth rate after 2 years, we need to determine the compound interest earned during that period.

The formula to calculate compound interest is A = P(1 + r/n)^(nt), where:

A = the final amount (balance) in the account

P = the principal amount (initial investment)

r = the interest rate per compounding period (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is $10,000, the interest rate (r) is 2.5% (0.025 as a decimal), the number of compounding periods per year (n) is 2 (since interest is compounded semiannually), and the number of years (t) is 2.

Plugging these values into the formula, we get:

A = $10,000(1 + 0.025/2)^(2*2)

A ≈ $10,000(1.0125)^4

A ≈ $10,000(1.050625)

A ≈ $10,506.25

The growth in the balance over 2 years is approximately $506.25. To determine the growth rate in dollars per year, we divide this amount by 2 (since it's a 2-year period):

$506.25 / 2 ≈ $253.12

Therefore, the balance in the savings account is growing at a rate of approximately $253.12 per year after 2 years. Rounded to two decimal places, the answer is $253.12.

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The possible arrangement is 3960.

Permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.

Given that, Bart wants to plant 8 trees in a row along his fence.

Possible arrangement of 4 birches = 5 x 4 x 3 x 2 x 1 = 120

If 3 birches are next to each other, therefore, 6 possible arrangement are possible = A₄⁴ x A₅² = 480

Similarly,

If 2 birches are next to each other, therefore, 6 possible arrangement are possible = A₄⁴ x A₅² = 480

If 4 birches are not next to each other, therefore, possible arrangement are possible = A₄⁴ x A₅⁴ = 2880

Therefore, total arrangements = 120+480+480+2880 = 3960

Hence, the possible arrangement is 3960.

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Given:

A social security number contains nine digits.

As there are 10 digits from 0 to 9.

There are 9 positions and every position has 10 possibilities.

If repetition is allowed the number of ways are,

Answer: the number of ways are,

The answers are =

a) the expected number of power trios that Jack will find is 1/221.

b) the expected number of perfect power trios that Jack will find is 6/221.

To solve this problem, we can use the concept of linearity of expectation.

Let's break down the problem into smaller parts.

a) Expected Number of Power Trios:

We need to find the expected number of sets of 3 consecutive cards where all cards are either a Jack, Queen, or King.

Let's consider each position in the line of cards. For each position, the probability that it starts a power trio is 3/52, because there are 3 possible starting cards (J, Q, or K) out of 52 cards in total.

Now, for each position, the probability that the next two cards complete the power trio is 2/51 and 1/50, respectively.

This is because there are 2 possible cards that can be the second card (out of the remaining 51 cards), and only 1 possible card that can be the third card (out of the remaining 50 cards).

Therefore, the probability that a given position forms a power trio is (3/52) x (2/51) x (1/50).

Since there are 50 possible positions in the line where a power trio can start (positions 1 to 48 for the first two cards, and positions 2 to 49 for the second two cards, and so on), we can calculate the expected number of power trios as follows:

Expected number of power trios = (3/52) x (2/51) x (1/50) x 50 = 1/221.

So, the expected number of power trios that Jack will find is 1/221.

b) Expected Number of Perfect Power Trios:

We need to find the expected number of sets of 3 consecutive cards with exactly 1 Jack, 1 Queen, and 1 King in any order.

Similarly to part (a), the probability that a given position starts a perfect power trio is (3/52) x (2/51) x (1/50).

However, there are six possible orders in which the three cards can appear (J-Q-K, J-K-Q, Q-J-K, Q-K-J, K-J-Q, K-Q-J). Each of these orders has the same probability, so we multiply the probability by 6.

Therefore, the probability that a given position forms a perfect power trio is (3/52) x (2/51) x (1/50) x 6.

Using the same reasoning as in part (a), the expected number of perfect power trios is:

Expected number of perfect power trios = 6/221.

So, the expected number of perfect power trios that Jack will find is 6/221.

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The graph which represents the relationship between the year and the computers value is; Choice A.

According to the task content, it follows that the computer loses 1/3 of its value every year. Hence, it follows that the value of the computer each year is 2/3 of its previous value.

Hence, the relationship can best be modelled by an exponential function, a decay function to be more specific and can best be represented by Choice A.

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Answer:

10% out of 100%.

Or 4/40=1/10 which is 10%.

Shen has ridden her bike for 10% of the course

Answer:

0.118

Step-by-step explanation:

11.8 = 118/10

= 118/10 × 1/100

= 118× 1/10×100

= 118/1,000

= 0.118

The solution of the quadratic equation is x=5±√35 .

A quadratic equation is given by the equation which can be written in the form ax²+bx +c.

the given quadratic equation is :

x²-10x+25=35

Simplifying the equation we get:

or, x²-10x+25-35=0

or, x²-10x-10=0

Now we will solve the equation by completion squares method:

x²-10x-10=0

or, x²-2×x×5+5²-5²-10=0

or, (x-5)²=35

or, x-5=±√35

or, x= 5±√35

Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .

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