A bag contains marbles of four different colors:
4 blue marbles
12 red marbles
8 green marbles
2 yellow marbles
(6) What is the probability of picking a blue marble at random out of the bag?

Answer:

0

Step-by-step explanation:

1) The statement of Lin is correct.

2) (a) When scale factor, k = 9, area of the new triangle = 8100 square inches

(b) When k = 3/4, area of the new triangle = 56.25 square inches.

Given that,

A triangle has area 100 square inches.

It's dilated by a factor of k = 0.25.

When the triangle is dilated by a scale factor of k, then, each of the base and height is dilated by the scale factor of k.

So new area of the triangle after the dilation with the original triangle having base = b and height = h is,

Area of new triangle = 1/2 (kb)(kh) = k² (1/2 bh) = k² × Area of original triangle

Here original area = 100 square inches.

k = 0.25

New area = (0.25)² 100 = 6.25 square inches

So the correct statement is that of Lin.

Mai may found the new area by just multiplying the scale factor with 100, instead of taking the square of the scale factor. That is why she got 25 square inches as the new area.

2) (a) When k = 9,

Area of the new triangle = 9² (100) = 8100 square inches

(b) When k = 3/4

Area of the new triangle = (3/4)² (100) = 56.25 square inches

Hence the areas are found.

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The growth rate for an exponential model can be found by calculating the rate at which the model is increasing over a certain period of time. This is typically represented as a percentage, which can be calculated by converting the growth rate from a decimal to a percentage. To do this, simply multiply the growth rate as a decimal by 100. For example, if the growth rate is 0.05, the percentage would be 5%.

To find the growth rate for an exponential model, you can use the formula:

Growth rate = (Ending value / Beginning value) ^ (1 / Number of periods) - 1

Once you have calculated the growth rate, you can convert it to a percentage by multiplying by 100 and rounding to two decimal places. For example, if the growth rate is 0.0723, the percentage would be 7.23%.

In the case of the question, it is unclear what the beginning value, ending value, and number of periods are for the exponential model in question. Without this information, it is not possible to calculate the growth rate. However, the formula and steps provided above can be used to calculate the growth rate for any exponential model, given the necessary information.

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Answer:

x = 2/3x + 5 1/2 = -10 = x = -93/4

Step-by-step explanation:

Answer:

option C

i have made it in above picture

It appears that Nolan has met the conditions for constructing a confidence interval for the mean birth weight in Somalia. However, he should also check the skewness and presence of outliers in the sample to ensure that the normal approximation is appropriate.

In other words, data with a lower bound are frequently skewed right, and data with an upper bound are typically biased left.

Start-up effects can also cause skewness.

To construct a confidence interval for the mean birth weight in Somalia, we need to ensure that the following conditions are met:

Random Sampling: Nolan used a simple random sample of 100 births, which meets the condition of random sampling.

Independence: Each birth weight in the sample should be independent of the other. This condition is met if the sample size is less than 10% of the total population of births in Somalia.

Sample size: In general, a sample size of at least 30 is recommended to use the normal distribution to approximate the sampling distribution of the sample mean. Since Nolan's sample size is 100, this condition is met.

Skewness and outliers: Nolan mentioned that the sample data was slightly skewed with a few outliers.

Therefore, all the required conditions are given above.

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Answer:

the data is a random sample from the population of interest.

the sampling distribution of x is approximately normal.

individual observations can be considered independent.

Step-by-step explanation:

The trigonometry used to solve for x in the right triangle is

A. tangent

In mathematics, the tangent is a trigonometric function that relates the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It is commonly abbreviated as tan.

The tangent function is defined for all real numbers except for certain values where the adjacent side is zero, resulting in division by zero. It takes an angle (measured in radians or degrees) as its input and returns the ratio of the length of the opposite side to the length of the adjacent side.

In a right triangle, if one of the acute angles is θ, then the tangent of θ (tan θ) is defined as:

tan θ = opposite side / adjacent side

tan 53 = x / 15

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Answer:77

Step-by-step explanation:

132 divided by 12(7+5) is 11

11*7=77 so theres 77 boys

The quadratic equation y = 6x²+ 19x -20 has the same standard form as Ax+By +C = 0.

what is quadratic equation ?

A quadratic polynomial in an independent condition is represented by the expression x ax²+bx+c=0. a 0. Since this equation is of second order, the Fundamental Theory of Algebra requires that it has at best one solution. There can be both simple and complex solutions.

A quadratic equation is just that—quadratic. This indicates that which has at least yet another word that has to be squared. One of the often cited solutions for differential calculus is "ax² + bx + c = 0." where X is an undefined parameter and a, b, and c are mathematical coefficients or constants.

y=(6x-5)(x+4)

y = 6x² - 5x + 24x - 20

y = 6x² + 19x -20

The quadratic equation y = 6x² + 19x -20 has the same standard form as Ax+By +C = 0.

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Answer:

120

Step-by-step explanation:

360

------

3

mark me on brainliest please follow me to

Step-by-step explanation:

the answer is (x, y) --->(x-8, y-1)

Answer:

9

Step-by-step explanation:

The equation for the perimeter is 2(L+B)

Since the perimeter is 68

Divide it by two

Subtract the quotient by 25 and

Yes!!! We got the answer

Answer:

E, A, F, A

Step-by-step explanation:

A,A

B,A

C,A

D,A

E,A

F,A

Answer:

Dear Johnson,

Answer to your query is provided below

The expression 3.14 x 10^3 is scientific notation for 3,140.

Step-by-step explanation:

The purpose of scientific notation is to write very large, or very small, numbers with ease.

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

a x 10^b

Follow the steps below to see how 3,140 is written in scientific notation.

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 3,140

New Number: 3.140

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 3 . 1 4 0

Decimal Count: 1 2 3

There are 3 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10^b

a = 3.14 (Please notice any zeroes on the end have been removed)

b = 3

Now the whole thing:

3.14 x 10^3

Step 4

Check your work:

10^3 = 1,000 x 3.14 = 3,140

Answer:

\( x = - 3 \frac{4}{15}\)

Step-by-step explanation:

\(2x - \frac{1}{3} + 3 = x - \frac{3}{5} \)

\( = > 2x - \frac{ 1 +9 }{3} = x - \frac{3}{5} \)

\( = > 2x + \frac{8}{3} = x - \frac{3}{5} \)

\( = > 2x - x = - \frac{3}{5} - \frac{8}{3} \)

\( = > x = - \frac{9 - 40}{15} \)

\( = > x = - \frac{49}{15} \)

\( = > x = - 3 \frac{4}{15} (ans)\)

Answer:

x = - \(\frac{49}{15}\)

Step-by-step explanation:

Given

2x - \(\frac{1}{3}\) + 3 = x - \(\frac{3}{5}\)

Multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions

30x - 5 + 45 = 15x - 9 , that is

30x + 40 = 15x - 9 ( subtract 15x from both sides )

15x + 40 = - 9 ( subtract 40 from both sides )

15x = - 49 ( divide both sides by 15 )

x = - \(\frac{49}{15}\)

Answer:

P≈28.28cm  = 28 cm

Step-by-step explanation:

Using the formulas

P=4a

d=√2a

Solving forP

P=2 √2d=2·√2·10≈28.28427cm

Answer:

7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Do you mean 7-12, or 7/(-12)?

7-12 = -5, so the absolute value of 7-12 is 5.

The absolute value of 7/(-12) is 7/12.

We have evidence to suggest that the standard deviation of the number of fish in a 20-gallon tank is different from twoat the 5% level.

To determine if the standard deviation is different from two at the 5% level, we can perform a hypothesis test. The null hypothesis is that the standard deviation is two, and the alternative hypothesis is that the standard deviation is different from two.

We can use a chi-square test statistic to test this hypothesis. The test statistic is calculated as:

χ² = (n - 1) * s² / σ²

where n is the sample size, s is the sample standard deviation, and σ is the hypothesized population standard deviation.

We can then compare this test statistic to the critical value from the chi-square distribution with n - 1 degrees of freedom at the 5% significance level.

Using the given data, we have:

n = 15

s = 1.256

σ = 2

Plugging these values into the formula, we get:

χ² = (15 - 1) * 1.256² / 2² = 42.891

Using a chi-square distribution table or a calculator, we find that the critical value with 14 degrees of freedom at the 5% level is 23.685.

Since our test statistic (42.891) is greater than the critical value (23.685), we reject the null hypothesis and conclude that the standard deviation is different from two at the 5% level.

Therefore, based on the data provided, we have evidence to suggest that the standard deviation of the number of fish in a 20-gallon tank is different from two.

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Negative leading coefficient. Therefore it is the downward paeabola.

Discriminant of -40 therefore the parabola does not touch x-axis

so the answer is 1.

Answer:

Total cost of the order is: $122

Step-by-step explanation:

Cost of 1 book = $13

Shipping cost of order = $5

If you buy 9  books, what is the cost of the order?

First calculate cost of 9 books

Cost of 1 book = $13

Cost of 9 books = $13*9

                          = $117

Now adding shipping cost to the cost of 9 books

Total cost of order = Cost of 9 books + Shipping Cost

                               = 117 + 5

                               = $122

So, Total cost of the order is: $122

The probability of NOT drawing a face card from a standard deck of 52 cards is 10 over 13.

First determine the total number of face cards and non-face cards in a standard deck of 52 cards.                                   In a standard deck, there are 12 face cards (3 face cards per suit: Jack, Queen, and King, and 4 suits: Hearts, Diamonds, Clubs, and Spades). This means there are 52 - 12 = 40 non-face cards.

Now, we'll calculate the probability of NOT drawing a face card:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability of NOT drawing a face card = (Number of non-face cards) / (Total number of cards)
Probability = 40 / 52

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (4):
Probability = (40/4) / (52/4)
Probability = 10 / 13

So, the probability of NOT drawing a face card from a standard deck of 52 cards is 10/13. Your answer: 10 over 13.

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The probability that you picked the fair coin given that the outcome of the toss was heads is 1/3.

There is a one in two chance of drawing the fair coin. The chances of flipping heads again are 1 in 2. As a result, there is a 1 in 4 chance that the coin will land on heads.

There is a one in two chance of drawing the trick coin. The probability of flipping heads is then 2 to 1. As a result, there is a 2 in 4 chance that the coin will land on heads.

When each is multiplied by four, the resulting integers are

fair: 1 and trick: 2

and overall results: 3. (fair and tails is not counted)

The likelihood of a fair coin is one in three.

The likelihood that the chosen coin will show heads and be the fair coin is 33.333%.

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If a boat is traveling upstream takes 45 minutes to travel 30 miles and on the return trip (with the current) takes 30 minutes, the speed displayed on the boat's speedometer is  50 mph.

Let the speed of the boat be x miles per hour and the speed of the current be y miles per hour. The boat is traveling upstream against the current. In this case, the effective speed of the boat is (x - y) miles per hour. The distance traveled is 30 miles.

Therefore, using the formula distance = speed x time, we have:

30 = (x - y) x (45/60)

Simplifying, we get:

30 = (3/4)(x - y)

x - y = 40(1)

On the return trip (with the current), the effective speed of the boat is (x + y) miles per hour. The distance traveled is still 30 miles. Therefore:

30 = (x + y) x (30/60)

Simplifying, we get:

30 = (1/2)(x + y)

x + y = 60(2)

Adding equations (1) and (2), we get:

2x = 100

x = 50 miles per hour

Therefore, the speed displayed on the boat's speedometer is 50 mph.

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Thus, the series converges for -4 < x < 2.In interval notation, the convergence sets are:

1)(-2, 2)

2)(-∞, ∞)

3)(-∞, ∞)

4)(-4, 2)

1) The power series ∑(n=0)∞ xn/(n+1)^(2n) converges for all x in (-1,1) by the ratio test.

2) The power series ∑(n=1)∞ (x-1)^n/n converges for x in the interval (0,2), with the endpoints excluded. To see this, we can use the ratio test and find that |(x-1)/(n+1)| → |x-1| as n → ∞. Thus, the series converges absolutely when |x-1| < 1, and diverges when |x-1| > 1. At x = 0, the series is the harmonic series which diverges, and at x = 2, the series becomes the alternating harmonic series which converges but not absolutely.

3) The power series ∑(n=1)∞ (x-n)^n/n! converges for all x in (-∞,∞). We can use the ratio test and find that |(x-n)/(n+1)| → 0 as n → ∞, and thus the series converges absolutely for all x.

4) The power series ∑(n=1)∞ (x+1)^n/3^n converges for x in the interval (-4,2) by the ratio test. When x = -4, the series becomes ∑(-1)^n/3^n which converges by the alternating series test. When x = 2, the series becomes ∑3^n which diverges.

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The series converges if |x+1|/3 < 1, i.e. if -4 < x < 2. The series converges at x=2 and diverges at x=-4, so the convergence set is (-4,2].

For the first power series, we use the ratio test:

lim |(x_{n+1}/(n+2)^{2(n+2)})/(x_n/(n+1)^{2n+2})| = lim |x_{n+1}|(n+1)^{2n+3}/|x_n|(n+2)^{2n+2}

= lim |x_{n+1}/x_n| ((n+1)/(n+2))^{2n+3} (n+1)/(n+2)

= lim |x_{n+1}/x_n| lim ((n+1)/(n+2))^{2n+3} lim (n+1)/(n+2)

= |x| lim (1/4)^n lim 1/2 = 0

Therefore, the series converges for all x.

For the second power series, we also use the ratio test:

lim |((x-1)^(n+1)/(n+1))/((x-1)^n/n)| = lim |x-1| (n+1)/n = |x-1|

Therefore, the series converges if |x-1| < 1 and diverges if |x-1| > 1. The series converges at x=0 and x=2, so the convergence set is [0,2].

For the third power series, we use the ratio test again:

lim |((x-(n+1))/(n+1)) ((x-n)/n!)| = lim |x-(n+1)|/|n+1| lim |x-n|/n! = 0

Therefore, the series converges for all x.

For the fourth power series, we use the root test:

lim sup |(x+1)/3|^n = |x+1|/3

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Answer:

28000 x 5 = 140000

Step-by-step explanation:

Have a great day!

Daniel's method is incorrect, as the interquartile range is given by the difference between the third quartile and the first quartile.

The interquartile range of a data-set is by the difference of the 75th percentile(Q3) by the 25th percentile(Q1) of the data-set.

The quartiles are described as follows:

From this, we get that the quartiles are related to the median of the set, that is, neither is given by the highest and by the lowest values, hence the interquartile range is given by the difference between the third quartile and the first quartile.

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By using the definition of continuity and exploiting the fact that f(0) = 1, we were able to prove the existence of an open interval (a, b) containing 0 such that for any real number r within this interval, the function value f(r) is greater than 0.

First, let's recall the definition of continuity at a point. A function f is continuous at a point c if, for any positive number ε, there exists a positive number δ such that whenever x is within δ of c, the value of f(x) will be within ε of f(c).

Now, since f is continuous at 0, we can say that for any positive ε, there exists a positive δ such that if |x - 0| < δ, then |f(x) - f(0)| < ε.

Since f(0) = 1, the above inequality simplifies to |f(x) - 1| < ε.

We want to find an open interval (a, b) containing 0 such that for any r within this interval, f(r) > 0. Let's consider ε = 1 as an arbitrary positive number.

From the definition of continuity at 0, we can find a positive δ such that if |x - 0| < δ, then |f(x) - 1| < 1. This implies -1 < f(x) - 1 < 1, which further simplifies to 0 < f(x) < 2.

Now, consider the interval (a, b) = (-δ, δ). Since δ is positive, it ensures that 0 is within this interval. Also, since f(x) is continuous on this interval, we can conclude that f(r) > 0 for all r within (-δ, δ).

To prove this, let's take any r within (-δ, δ). Since r is within this interval, we have -δ < r < δ, which implies |r - 0| < δ. By the definition of continuity at 0, we know that |f(r) - 1| < 1. Therefore, 0 < f(r) < 2, and we can conclude that f(r) > 0.

Hence, we have shown that there exists an open interval (a, b) containing 0 such that for all r within this interval, f(r) > 0.

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Answer:

Step-by-step explanation:

I'm assuming this is linear and that there is no special on a larger order of wings. To find the unit price of each piece, divide $28.80 by 16 to get that each piece cost $1.80 (that's a lot for a single chicken wing. That better be one BIG chicken...). To find the cost of 9 wings, multiply 9 by $1.80 to get $16.20

The rule of three is a way to solve problems of proportionality between three known values and one unknown. It establishes a relationship of linearity, proportionality, between the values involved.

Chicken Wings             Price

     16------------------------$28.80

      9-----------------------------x

First, multiply the number of wings purchased by the given price, divided by the number of wings purchased.

We solve

Answer: 9 wings would cost a total of $16.2

Answer:

(x + 9)(x - 7)

Step-by-step explanation:

We want to factorize \(x^2 + 2x - 63\)

We need to find two numbers such that their product is -63 and they add up to +2. The two numbers are +9 and -7:

\(x^2 + 9x - 7x - 63\\\\= x(x + 9) -7(x +9)\\\\ = (x +9)(x -7)\)

The complete factorization is (x + 9)(x - 7)

The factored form of the expression x² + 2x - 63 is (x + 9)(x - 7).

Given the expression in the question:

x² + 2x - 63

To determine the complete factorization of the quadratic expression x² + 2x - 63, we aim to break it down into its simplest factors.

This is achieved through factoring, a process of identifying the expressions that, when multiplied, result in the original quadratic expression.

x² + 2x - 63

Now, find a pair of integers whose sum equals 2,

and whose product equals -63.

We use integers 9 and -7.

Next, rewrite the quadratic expression using these factors:

(x + 9)(x - 7)

Therefore, the complete factorization of x² + 2x - 63 is (x + 9)(x - 7).

Option C) (x + 9)(x - 7) is the correct answer.

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