what was your favorite year of high school?

Answer:

A and D are correct. This is a parallelogram, which is a quadrilateral. B is not correct because not all the sides are congruent. C is not correct. E and F are not correct because this parallelogram does not have any right angles.

The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4.

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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A salesman earns $490 as commission on his sales.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a salesman earns 7% commission on all the merchandise that he sells.

Last month he sold $7000 worth of merchandise.

Now, the commission is 7% of 7000

7/100 ×7000

= 0.07×7000

= $490

Therefore, a salesman earns $490.

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1% is the probability that the sample mean for a sample of size 35 will be at least 26.

To calculate the probability, we need to use the central limit theorem, which states that the sampling distribution of the sample mean is approximately normal, with mean μ and standard deviation σ/√n, where μ is the population mean, σ is the population standard deviation, and n is the sample size.

Since we do not have the population mean and standard deviation, we will assume that they are unknown and use the sample mean and standard deviation instead. We will also assume that the sample is a random sample and that the sample size is sufficiently large (n ≥ 30).

We can use the z-score formula to calculate the probability as follows:

z = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we want to find the probability that the sample mean is at least 26, so we can rewrite the formula as:

z = (26 - X) / (s / √35)

where s is the sample standard deviation.

We can then use the z-table to find the probability that corresponds to the calculated z-score. The portion of the z-table provided gives the probability for the area under the curve to the left of the z-score.

Using a calculator, we can calculate the z-score as follows:

z = (26 - X) / (s / √35) = (26 - X) / (4.2 / √35)

Assuming a significance level of α = 0.05 (corresponding to a confidence level of 95%), we can find the z-score that corresponds to the area to the left of α/2 = 0.025 in the z-table, which is approximately 1.96.

Therefore, we can rewrite the formula as:

1.96 = (26 - X) / (4.2 / √35)

Solving for X, we get:

X = 26 - 1.96 * (4.2 / √35)

X ≈ 24.59

So, the probability of obtaining a sample mean of at least 26 is equivalent to the probability of obtaining a z-score of:

z = (26 - 24.59) / (4.2 / √35) ≈ 0.98

Using the z-table, we can find that the probability corresponding to a z-score of 0.98 is approximately 0.8365 or 83.65%.

Rounding to the nearest percent, we get the answer B. 1%.

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Correct question:

What is the probability that the sample mean for a sample of size 35 will be at least 26?

A. 0.01%

B. 1%

C. 5%

D. 10%

Answer:84

Step-by-step explanation:

Answer:

84 hamburgers were sold

The balance sheet attached shows the Total Assets to be $55.968M  and Total Liabilities and Capital to be $252M respectively.

1. Assets:

  a. Cash in Reserves:

The required reserves are 5.4% of checkable deposits.

Therefore, the required reserves amount to 5.4% of $92 million, which is:

(0.054 * $92 million) = $4.968 million.

This amount is considered a liability for the bank, but it is held as an asset in the form of cash reserves.

  b. Loans: The bank made a $28 million commercial loan and a $23 million mortgage loan. Therefore, the total loans amount to:

total loan =  $28 million + $23 million

                 = $51 million.

2. Liabilities:

  a. Checkable Deposits:

The bank received $92 million in checkable deposits.

  b. Required Reserves:

As mentioned above, the required reserves amount to $4.968 million.

3. Capital:

  The bank started with $155 million in capital.

Based on the above information, the bank's balance sheet would look as attached.

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Answer:

Two points that satisfy include (-2,5) (0,0) (2,-5) (I know this is more than 2, but in case the (0,0) origin isn't allowed.

Step-by-step explanation:

This is 5x+2y=0

Screenie is the 5x+2y=0 btw

Hope this helps!

The scale factor of figure B to figure A is 1/2.

To find the scale factor of figure B to figure A, we need to determine how much the corresponding sides of the two figures have been multiplied or divided by.

Looking at the figures, we can see that the corresponding sides of figure B are half the length of the corresponding sides of figure A. For example, the length of side AB in figure A is twice the length of side AB' in figure B, and the length of side BC in figure A is twice the length of side B'C' in figure B.

Since the corresponding sides of figure B are half the length of the corresponding sides of figure A, the scale factor of figure B to figure A is 1:2 or 1/2.

Therefore, the scale factor of figure B to figure A is 1/2.

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Answer:

13 weeks they both have $ 225

Step-by-step explanation:

Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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Answer:

D. 6

Explanation:

The general equation for a circle centered at the origin (0,0) is:

Given the equation of the circle:

Thus, the radius of the given circle is 6.

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

1/3 foot longer

Step-by-step explanation:

2/3-1/3=1/3

Answer:

I don't think you can solve this because they don't say the price per pound of fruit or nuts

Answers:

4 liters of the 18% acid

8 liters of the 45% acid

========================================================

Explanation:

Let's call the bottles A and B

x = amount, in liters, of bottle A used

12-x = amount, in liters, of bottle B used

Bottle A has 0.18x liters of pure acid

Bottle B has 0.45(12-x) liters of pure acid

These amounts must add to 0.36*12 = 4.32 liters of pure acid since we want 12 liters of a 36% solution.

So,

0.18x + 0.45(12-x) = 4.32

0.18x + 0.45(12)+0.45(-x) = 4.32

0.18x + 5.4-0.45x = 4.32

-0.27x + 5.4 = 4.32

-0.27x = 4.32 - 5.4

-0.27x = -1.08

x = (-1.08)/(-0.27)

x = 4 liters which is the amount of bottle A needed

12-x = 12-4 = 8 liters is the amount of bottle B needed

--------------------

Check:

Using 4 liters of bottle A means we contribute 4*0.18 = 0.72 liters of pure acid from this bottle alone.

Using 8 liters from bottle B adds another 8*0.45 = 3.6 liters of pure acid

Then, 0.72+3.6 = 4.32 which matches with the 4.32 mentioned earlier. Therefore, the answer is fully confirmed.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

Step-by-step explanation:

$100x0.5x1=$5

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer:

First = 1000

Second = 10,000

Step-by-step explanation:

Given the following :

Amount invested = $11,000

A portion earns 2 1/2 % interest per year

The rest earns a rate of 2% per year

Total Interst earned after a year = $255

Amount invested at each rate

Let amount invested at 2 1/2% = a

Amount invested at 2% = 11,000 - a

Simple interest = principal * rate * time

First investment :

a * 5/2% * 1

Second :

(11000 - a) * 2%

Firat investment + second = $225

a * 0.025 + (11000 - a) * 0.02 = 225

0.025a + 220 - 0.02a = 225

0.005a = 225 - 220

0.005a = 5

a = 5 / 0.005

a = 1000

Amount in first investment = 1000

Second investment = 11000 - 1000 = 10,000

Answer:

35

Step-by-step explanation:

75% of 40 is 30

40+30=70

70/2=35

Mathpapa

Step-by-step explanation:

The link above should give you the answer. If the link that you click on does not work, then you can look up mathpapa on your computer and type this math equation in. I am terrible at math, but I figured I could give you my mathematical calculator. I hope that helps you!

There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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If Given f(x) = 1/2 (3 - x) ^ 2 , the value of f(15) is 72.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

The given function is:

f(x) = 1/2 (3 - x)²

To find the value of f(15), we need to substitute 15 for x in the function:

f(15) = 1/2 (3 - 15)²

Here, we subtract 15 from 3 to get -12 in the parentheses, and then we square it to get 144. We can simplify the expression further by multiplying 144 by 1/2, which gives us 72:

f(15) = 1/2 (144)

f(15) = 72

Therefore, the value of f(15) is 72.

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Answer:

It's actually A, because the US population got doubled ever year

1. The correct exponential function for each graph is

a.  f(x) = 2ˣ is graph (III)     b. f(x) = 2⁻ˣ is graph (I)   c. f(x)= -2ˣ graph (II)  D. f(x) = -2⁻ˣ is graph (IV)

2. The evaluated exponential functions are;

a. f(1) = 1  b. f(-1) = 0.1  c. f(0) = 0.3

3. The exponential function for the graph  is f(x) = \(\frac{1}{2}^x\)

4. The model for the rate population is N(t) = 320 × \(2^{t}\) . After 8 years, the population will be 81,920.

5. The compounded interest after 2 years: 2628.17. After 3 years 2694.7. After 6 years 2904.57

6. The compounded interest after a) 3 years = 4221.81  b) 6 years = 5092.47  c) 9 years = 6142.69

7. At time t = 0, the mass is 13 kg. After 45 days, the mass is approximately 6.62 kg

1. For the exponential function,  

a. f(x) = 2ˣ has a coordinate (0,1).  f(1) = 2⁰ = 1 It matches (III)

b.  f(x) = 2⁻ˣ When x = -1, f(x) = 2,  x = 0, f(x) = 1, x = 1, f(x) = 0.5; x = 2, f(x) = 0.25. If you plot this coordinates, you will see the graph falls from left to right

c. f(x)= -2ˣ it should pass through  (0, -1),  x = -1, when f(x) = -0, x = 0, f(x) = -1, x = 1, f(x) = -2

d. f(x) = -2⁻ˣ will pass through the point (0, -1). When x = -1, f(x) = -2; x = 0, f(x) = -1; x = 1, f(x) = -0.5. The graph should rise from left to right.

2. If the exponential function is f(x) = 3ˣ⁻¹ then we evaluate

f(1) = 3¹⁻¹ = 3⁰ = 1

f(-1) = 3⁻¹⁻¹ = 3⁻² = 1/3² or 0.1

f(0) = 3⁰⁻¹ = 3⁻¹ = 1/3 or 0.3

3. For the graph whos exponential function should be in the form f(x) = aˣ, we can find the actual function by looking at the coordinated (-3, 8)

a⁻³ = 8

a = \(8^1/-3\)

a = 1/2

f(x) = (1/2)ˣ

4. The mouse population can be modeled as

N(t) = N₀ × (1 + \(r)^{t}\) ⇒ N(t) = 320 × \(2^{t}\)

After 8 years ⇒ N(8) = 320 × 2⁸

N(8) = 320 × 256

N(8) = 81920

5. We use the formula A = P(1 + \(r/n)^{nt}\)

$2500 invested at an annual interest rate of 2.5% compounded daily,

After 2 years (t = 2):                          After 3 years

A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ²⁾         A = A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ³⁾

A = 2628.17                                       A = 2694.7

After 6 years

A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ⁶⁾

A = 2904.57

6. For a  continuous compounded interest, we use the formula;

A = P × \(e^{rt}\)

the principal is $3500, the interest rate is 6.25%, or 0.0625 as a decimal.

a) After 3 years:                 After 6 years:             After 9 years

A = 3500 × \(e^{0.0625 * 3}\)          A = 3500 × \(e^{0.0625 * 6}\)     A = 3500× \(e^{0.0625 * 9}\)

A = 4221.81                       A = 5092.47                A = 6142.69

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The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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Answer:

1

Step-by-step explanation:

Answer:

69.314718056

Step-by-step explanation:

Answer:

The number of planes that land in a given time period follows a Poisson distribution with parameter lambda equal to the average rate of landing per unit time. In this case, lambda is equal to 0.1 planes per minute.

The probability that between 2 and 6 planes will land in 10 minutes is given by the cumulative distribution function of the Poisson distribution:

P(2 <= X <= 6) = P(X <= 6) - P(X <= 1)

Where X is the number of planes that land in 10 minutes.

Using the cumulative distribution function for the Poisson distribution, we have:

P(X <= 6) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)

P(X <= 1) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10)

Therefore,

P(2 <= X <= 6) = (1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)) - (1 - e^(-0.1 * 10) * (1 + 0.1 * 10))

The exact value of this probability can be calculated using a calculator or computer software.

Answer:

0.3

Step-by-step explanation: