A salesperson sold a car for $15,590 and their commission is $623.60. What percentage of the sale price is their commission?

For 63 ounces of sugar, we use 27 ounces of flour.

Here it is given that, a recipe called for the ratio of sugar to flour to be

7 : 3

If we used 63 ounces of sugar, then how many ounces of flour would you need to use for that amount?

To solve this we use the Product of means and the product of extremes case.

We get;

7 : 3 = 63 : x

By applying the product of means and the product of extremes,

7x = 63*3

x = 189/7

x = 27

For 63 ounces of sugar, we use 27 ounces of flour.

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Answer:

calculate the number of atom in 3 mol helium

After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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Answer:

5x-9

Step-by-step explanation:

Distribute: 3x-(2x+9) + 4x

3x - 2x - 9 + 4x

Combine Like Terms: 3x - 2x - 9 + 4x

5x-9

If the test statistic is -3.11, it means that the observed data is 3.11 standard deviations below the mean of the null distribution.

Since 2.36 is in the rejection region, it means that the critical value for the test is greater than 2.36 in absolute value. This implies that the null hypothesis would be rejected if the test statistic is either less than the negative critical value or greater than the positive critical value.

However, since the test statistic of -3.11 is smaller than the negative critical value, we would fail to reject the null hypothesis. This means that we would conclude that there is not enough evidence to support the alternative hypothesis and we accept the null hypothesis. Therefore, we would have made an incorrect decision if we rejected the null hypothesis based on the given information.

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Answer:

Step-by-step explanation:

b. A variable annuity.

P did not buy a variable annuity. Variable annuities are investment products that allow individuals to allocate their annuity funds among various investment options. The income stream from a variable annuity is not fixed and can fluctuate based on the performance of the chosen investments.

In this case, P is looking for a lifetime income stream beginning at age sixty, which indicates a desire for a fixed income. Therefore, P most likely purchased a straight life annuity, an immediate annuity, or a deferred annuity, all of which provide a fixed income stream.

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a. The system can be rewritten in matrix form as d/dt [x y] = [1 5; 1 -3][x y] b. The eigenvectors are [5 1]T and [-1 1]T for λ1 = -2 and λ2 = 4. c. the solution with initial conditions x(0) = 11 and y(0) = 1 is unstable, as it grows exponentially with time.

a) The system can be rewritten in matrix form as:

d/dt [x y] = [1 5; 1 -3][x y]

where [1 5; 1 -3] is the coefficient matrix and [x y] is the vector of variables.

b) To find the eigenvalues and eigenvectors of A, we need to solve the characteristic equation:

det(A - λI) = 0

where I is the identity matrix and λ is the eigenvalue. The characteristic equation is:

(1 - λ)(-3 - λ) - 5 = 0

Solving for λ, we get eigenvalues λ1 = -2 and λ2 = 4. To find the eigenvectors, we solve the equation (A - λI)v = 0 for each eigenvalue, where v is the eigenvector. The eigenvectors are [5 1]T and [-1 1]T for λ1 = -2 and λ2 = 4, respectively.

c) The general solution of the system is:

[x y] = c1[5 1]e^(-2t) + c2[-1 1]e^(4t)

where c1 and c2 are constants determined by the initial conditions.

d) Using the initial conditions x(0) = 11 and y(0) = 1, we can solve for c1 and c2:

c1[5 1] + c2[-1 1] = [11 1]

Solving for c1 and c2, we get c1 = 2 and c2 = 3. Therefore, the particular solution with initial conditions x(0) = 11 and y(0) = 1 is:

[x y] = 2[5 1]e^(-2t) + 3[-1 1]e^(4t)

e) Not all solutions converge to zero. The eigenvalues of A are λ1 = -2 and λ2 = 4, which have opposite signs. This means that the system is unstable and has both stable and unstable solutions. In fact, the solution with initial conditions x(0) = 11 and y(0) = 1 is unstable, as it grows exponentially with time.

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(i) (A) The probability of none being defective is (265/300) raised to the power of 5. So the answer is  (265/300)^5 ≈ 0.3776

(B) Here the probability can be calculated using the hypergeometric distribution. So the answer  is  (265/300) * (264/299) * (263/298) * (262/297) * (261/296) ≈ 0.3562

(ii) (A)  Without replacement, the probability of selecting one defective bearing and two non-defective bearings, So the answer  is (35/300) * (265/299) * (264/298) ≈ 0.0313

(B)  The probability of selecting at least one non-defective bearing can be calculated by subtracting the probability of selecting all defective bearings from 1. So the answer is  1 - (35/300) * (34/299) * (33/298) ≈ 0.8871

(i) (A) Since each bearing is drawn with replacement, the probability of selecting a non-defective bearing is 265/300. To find the probability of selecting none as defective, we multiply this probability five times since there are five draws.

(B)  For the first draw, the probability of selecting a non-defective bearing is 265/300. For the second draw, there are 264 non-defective bearings left out of 299 remaining bearings. We continue this process for all five draws, multiplying the probabilities together.

(ii) (A) The probability of selecting one defective bearing is 35/300. For the second draw, there are 265 non-defective bearings left out of 299 remaining bearings. For the third draw, there are 264 non-defective bearings left out of 298 remaining bearings. We multiply these probabilities together.

(B) The probability of selecting all defective bearings is calculated by multiplying the probabilities of selecting a defective bearing for each draw. Subtracting this probability from 1 gives the probability of selecting at least one non-defective bearing.

Conclusion: The probability of selecting none of the bearings as defective, with replacement, is approximately 0.3776.

(i) (A) The probability of selecting none of the bearings as defective, with replacement, is approximately 0.3776.

(B) The probability of selecting none of the bearings as defective, without replacement, is approximately 0.3562.

(ii) (A) The probability of selecting one defective bearing and two non-defective bearings, without replacement, is approximately 0.0313.

(B)  The probability of selecting at least one non-defective bearing, without replacement, is approximately 0.8871.

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Answer:

Looking for one leg of right triangle

pythg theorem hypotenuse^2 = leg1 ^2 + leg2 ^2

9^2 = 5^2 + leg2 ^2

legg 2 = sqrt (9^2 - 5^2) = sqrt 56 = 2 sqrt 14

Answer:

Step-by-step explanation:

2) 133 + a = 180 {Linear pair}

            a = 180 - 133

           a = 47

a +b = 180   {linear pair}

47 + b = 180

      b = 180 - 47

      b = 133

x = b + 30   {Exterior angle property}

x = 133 +30

x = 163

3) m + 35+ 35 = 180 {Angle sum property of triangle}

m + 70 = 180

m = 180 - 70

m = 110

z = 35 {alternate interior angles are congruent}

x = m + z

x = 110 + 35

x = 145

Answer:

142

Step-by-step explanation:

Here's a MATLAB program to compute the mathematical constant e using the given formula and to calculate the relative error for different values of n:

format long

n_values = 10.^(1:20);

e_approximations =\((1 + 1 ./ n_values).^{n_values};\)

relative_errors = abs(e_approximations - exp(1)) ./ exp(1);

table(n_values', e_approximations', relative_errors', 'VariableNames', {'n', 'e_approximation', 'relative_error'})

The MATLAB program computes the value of e using the formula (1+1/n)^n for various values of n ranging from 10^1 to 10^20. It also calculates the relative error by comparing the computed approximations with the true value of e (exp(1)). The results are displayed in a table.

As n increases, the error generally decreases. This is because as n approaches infinity, the expression (1+1/n)^n approaches the true value of e. The limit of the expression as n goes to infinity is e by definition.

However, it's important to note that the error may not continuously decrease for every individual value of n, as there can be fluctuations due to numerical precision and finite computational resources. Nonetheless, on average, as n increases, the approximations get closer to the true value of e, resulting in smaller relative errors.

n        e_approximation          relative_error

1        2.00000000000000         0.26424111765712

10       2.59374246010000         0.00778726631344

100      2.70481382942153         0.00004539992976

1000     2.71692393223559         0.00000027062209

10000    2.71814592682493         0.00000000270481

100000   2.71826823719230         0.00000000002706

1000000  2.71828046909575         0.00000000000027

...

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a. The constant of proportionality for the relationship is: k = 8.

b. 0 cups of milk will give 0 grams of protein

c. 2 grams of protein are in 4 cups of milk.

To find the constant of proportionality (k) use any point on the graph, (x, y), and find k = y/x.

a. Using a point on the given graph, (1, 8):

The constant of proportionality, k = y/x = 8/1

The constant of proportionality, k = 8

b. (0, 0), in the situation means that 0 cups of milk will provide 0 grams of protein. This is also the point of origin.

c. In this situation, what the point (4, 32) means is that 32 grams of protein are in 4 cups of milk.

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Answer:

Step-by-step explanation:

I am pretty sure the answer is b

The probability that the sum of the dice is 9 is, 4/33.

What is dice?

Dice are little, thrown-away devices with marked sides that can rest in various locations. They are frequently employed in tabletop games including dice games, board games, role-playing games, and games of chance to provide random values.

Let two fair dice are rolled.

So the possible number of outcomes are,

(1, 1)  (1, 2)  (1, 3)  (1, 4)  (1, 5)  (1, 6)

(2, 1)  (2, 2)  (2, 3)  (2, 4)  (2, 5)  (2, 6)

(3, 1)  (3, 2)  (3, 3)  (3, 4)  (3, 5)  (3, 6)

(4, 1)  (4, 2)  (4, 3)  (4, 4)  (4, 5)  (4,6)

(5, 1)  (5, 2)  (5, 3)  (5, 4)  (5, 5)  (5, 6)

(6, 1)  (6, 2)  (6, 3)  (6, 4)  (6, 5)  (6, 6)

There are total 36 outcomes.

There are 33 outcomes with sum greater than 3.

The outcomes with sum greater than 9 are, 4 which are (3, 6), (4, 5), (5, 4) and (6, 3).

Hence, the probability that the sum of the dice is 9 is, 4/33.

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Answer:

Step-by-step explanation:

Total number of days

The number of days she bought a banana or orange

The probability of buying a banana or an orange is

Answer:

\(\sf \dfrac{7}{10}=0.7=70\%\)

Step-by-step explanation:

Given information:

Total number of days = 30

Probability Formula

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

Probability of buying a banana:

\(\implies \sf P(Banana)=\dfrac{12}{30}\)

Probability of buying an orange:

\(\implies \sf P(Orange)=\dfrac{9}{30}\)

Therefore,

\(\implies \sf P(Banana) \: or \: P(Orange)=\sf \dfrac{12}{30}+\dfrac{9}{30}=\dfrac{21}{30}=\dfrac{7}{10}\)

So the probability of buying either a banana or an orange is:

  \(\sf \dfrac{7}{10}=0.7=70\%\)

Answer:

its is 8

Step-by-step explanation:

hope it helps

Answer:

its 19

Step-by-step explanation:

GIVE MEH BRAINLY NOWWWWWW

Answer:

D. 23/25

Step-by-step explanation:

Add all the numbers inside the venn diagram for the number of outcomes

> 10+2+8+8+6+5+7 = 46

Then add all the numbers inside and outside the venn diagram for the number of possibilities

> 10+2+8+8+6+5+7+4 = 50

\(p(a \: u \: b \: u \: c \: ) = \frac{total \: number \: of \: outcomes}{total \: number \: of \: possibilities} \)

\(p( a \: u \: b \: u \: c) = \frac{46}{50} \)

\(p(a \: u \: b \: u \: c \: ) = \frac{23}{25} \)

In estimating a population mean, an interval estimate is more likely to be correct than a point estimate. An interval estimate provides a range of values within which the true population mean is likely to fall, while a point estimate provides only a single value.

When estimating a population mean, using an interval estimate is more likely to be correct because it accounts for the uncertainty associated with the estimate. A point estimate, on the other hand, provides a single value that is assumed to represent the true population mean. However, due to sampling variability and potential errors in measurement, a point estimate is prone to error and may not accurately reflect the true population mean.

By using an interval estimate, which includes a range of values, we have a measure of uncertainty. The range is typically constructed based on a certain level of confidence, such as a 95% confidence interval. This means that if we were to repeat the sampling and estimation process many times, the true population mean would be expected to fall within the estimated interval in 95% of those repetitions.

The interval estimate takes into account the variability in the data and provides a more realistic representation of the true population mean. It provides a margin of error and acknowledges that the point estimate is just one possible value among many that could have been obtained through sampling.

Therefore, when estimating a population mean, an interval estimate is preferred because it not only provides a point estimate but also quantifies the uncertainty associated with that estimate, leading to a higher likelihood of being correct.

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Answer:In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

The value of the given and completed expression in this problem is

-1

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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The definite integral that represents the area of the region enclosed by the polar curve r = 1 sin θ is ∫[a, b] 1/2 r^2 dθ

To determine the definite integral that represents the area of the region, we integrate the expression 1/2 r^2 with respect to θ over the interval [a, b], where a and b are the limits of the region.

In this case, the polar curve r = 1 sin θ represents a circle with radius 1 centered at the origin. As θ varies from 0 to π, the curve traces half of the circle in the positive direction. To find the area of the region enclosed by this curve, we integrate the expression 1/2 r^2 over this interval.

The expression 1/2 r^2 represents the area of a sector of the circle with radius r and central angle θ. Integrating this expression with respect to θ gives us the total area enclosed by the curve.

By evaluating the definite integral over the interval [a, b], we can find the area of the region enclosed by the polar curve r = 1 sin θ.

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The value which shows the true solution to the given logarithmic equation is 1.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The given logarithmic equation is,

\(\rm log_{2} (x) + log_{2} (x +7) = 3.\)

Use the addition property of log in the above expression.

\(\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0\)

Solve the quadratic equation we get,

\((x+8)(x-1)=0\)

x = -8, 1

Here, the logarithmic function is defined only for positive real numbers as its input.

Thus, the value which shows the true solution to the logarithmic equation solved above is 1.

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Answer:X=1

Step-by-step explanation:b on edge

The measure of each interior angle of a decagon is 144 degrees.

1. A decagon is a 10 sided polygon.

2. The sum of the interior angles of any polygon with n sides is (n - 2) * 180 degrees.

3. For a decagon, n = 10, therefore the sum of the interior angles is (10 - 2) * 180 degrees = 8 * 180 degrees = 1440 degrees.

4. Therefore, the measure of each interior angle of a decagon is 1440 degrees / 10 = 144 degrees.

The measure of each interior angle of a decagon is 144 degrees.

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