Solve for x in the diagram below.

The probability of the arrow landing on section a is 1/5 since there are 5 equal sections. The probability of the coin landing on heads is 1/2 since there are only 2 possible outcomes (heads or tails) for the coin.

To find the probability of both events happening, we need to multiply the probability of the arrow landing on section a by the probability of the coin landing on heads. This gives us (1/5) * (1/2) = 1/10. So the probability that the arrow will land on the section labeled a and the coin will land on heads is 1/10. In other words, there is a 1 in 10 chance of both events happening. It is important to note that each event is independent of each other, meaning the outcome of one does not affect the other. This is because the spinner and the coin are not connected or related in any way.

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Answer:

Never second guess yourself

Step-by-step explanation:

Joshua scored 65, 80, 85, and 100 on his math tests. 90 score Joshua has to earn on his fifth test to have a mean score of 85

       To calculate the mean score, add up all of the scores and divide by the total number of tests.

       To figure out what score Joshua needs to get on the fifth test, use the formula:

            Total score = mean score × total number of tests

            Total score = 85 × 5

            Total score = 425

  Joshua's total score on all five tests must be 425. He has already earned 330 points from his first four tests (65 + 80 + 85 + 100).

  Therefore, Joshua must earn 95 points on his fifth test (425 - 330 = 95) to achieve a mean score of 85.

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Answer:

20.65%

Step-by-step explanation:

\( \frac{19}{92} \\ \\ = \frac{19 \times 100}{92} \% \\ \\ = \frac{1900}{92} \% \\ \\ = 20.6521739 \%\\ \\ = 20.65\%\)

Answer: A) 1/2

Step-by-step explanation:

Answer:

If you flip a coin three times in the air, what is the probability that tails lands up all three times?

Step-by-step explanation:

1/2

Answer:

(0, 1)

Step-by-step explanation:

First, we need to make y the subject of the formula from both expressions

For 4x+8y=5

8y = 5- 4x

y = (5-4x)/5

Similarly for x-3y= -3

-3y = -3 - x

3y = x+3

y = (x+3)/3

Since both lines intersects, hence;

(5-4x)/5 = (x+3)/3

Cross multiply

5(x+3) = 3(5-4x)

5x + 15 = 15 - 12x

5x + 12x = 15 - 15

17x = 0

x = 0/17

x = 0

Sustitute x = 0 into any of the equations

Given that y = x+3/3

y = 0+3/3

y = 3/3

y = 1

This shows that the lines intesects at (0, 1)

Answer:

3/8 - 1/16 simplifies to 5/16.

Step-by-step explanation:

To subtract two fractions, we need to find a common denominator. In this case, the least common multiple of 8 and 16 is 16.

So, we need to rewrite 3/8 and 1/16 with a denominator of 16:

3/8 = 6/16

1/16 = 1/16

Now we can subtract:

6/16 - 1/16 = 5/16

AnswerAns

5/6

Step-by-step explanation

3/8 - 1/16 = (3×2 -1)÷16 = 5/16

The value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

According to the given question.

We have an equation

2x + 2/y = 4w + 2

Since, we have to find the value of x for the given equation

2x + 2/y = 4w + 2

Thereofore,

2x + 2/y = 4w + 2

⇒ 2(x + 1)/y = 2(2w + 1)    (taking 2 common from both the sides)

⇒ (x + 1)/y = 2w + 1

⇒ (x + 1) = y(2w + 1)         (multiplying both the sides by y)

⇒ x + 1 = 2yw + y

⇒ x = 2yw + y - 1         ( subtracting 1 both the sides)

Hence, the value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

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The distance from the base of the ladder to the house is given as follows:

32 feet.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The distance from the base of the ladder to the house is the hypotenuse of the right triangle formed, hence:

d² = 20² + 25²

d = sqrt(20² + 25²)

d = 32 feet.

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x = - b/(a - c)

Hi there !

ax + b = cx

ax - cx = - b

x(a - c) = - b

x = - b/(a - c)

Good luck !

Answer:

point form: (-3, 5)

equation form: x = -3, y = 5

In part (b) of the previous question, we found that the power series representation of the function $f(x)=\frac{x^2}{1+x^2}$ is:

 \(\lim_{n \to \infty} (-1)^{n} x^{2n}\)

To find the interval of convergence of this power series, we can use the ratio test. Let $a_n=(-1)^n x^{2n}$ be the general term of the series. Then, the ratio of consecutive terms is:

\(\left[\begin{array}{ccc}an+1/an\end{array}\right] = \left[\begin{array}{ccc}(-1)^{n+1} x^{2(n+1)} )/ (-1)^{n}x^{2n} \end{array}\right] = \left[\begin{array}{ccc}x^{2}\end{array}\right]\)

The series converges if the limit of the ratio as $n$ approaches infinity is less than 1, and diverges if the limit is greater than 1. Therefore, we have:

\(\lim_{n \to \infty} \left[\begin{array}{ccc}(a_{n}+1)/a_{n} \end{array}\right] = \left[\begin{array}{ccc}x^{2} \end{array}\right]\)

The series converges if $|x|^2<1$, and diverges if $|x|^2>1$. If $|x|^2=1$, the test is inconclusive and we need to use other convergence tests.

Therefore, the interval of convergence of the series is $-1<x<1$. To check the convergence at the endpoints $x=-1$ and $x=1$, we can use the alternating series test. At $x=-1$, the series becomes:

\(\lim_{n \to \infty} (-1)^{n}(-1)^{2n} = \lim_{n \to \infty} 1\)

which diverges. At $x=1$, the series becomes:

\(\lim_{n \to \infty} (-1)^{n}1^{2n} = \lim_{n \to \infty} (-1)^{n}\)

which also diverges. Therefore, the interval of convergence of the series is $-1<x<1$, and the series diverges at the endpoints.

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a)Approximately 1.76% of adults

b) about 35 people

c)About 12.9% of adults

d)Approximately 106.95

Solution:

a. Approximately 1.76% of adults in the USA have stage 2 high blood pressure, which is a systolic bp of 160 or higher.

b. If you sampled 2000 people, you would expect about 35 people to have a systolic bp greater than 160.

c. About 12.9% of adults in the US qualify for stage 1 high blood pressure, which is specified as systolic bp between 140 and 160.

d. If you are in the 30th percentile for blood pressure among US adults, your systolic bp is approximately 106.95, rounded to two decimal places.

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There are 128 number of bit string of length 7.

For the data given in question-

7-character string with two possible values for each (0 or 1).

a) For strings with an average length of 7 bits:

The 7-digit string contains two possibilities for each digit.

As, a bit is a 0 or a 1.

The 7-digit number is;

N = 2×2×2.... = 2^7 = 128

Thus, there are 128 number of bit string of length 7.

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The cost of the wall paper per square feet is 0.72 dollars.

The wall paper is rectangular in shape. The dimension of the wall paper is 42 feet by 25.5 feet.

The total cost of the wall paper is 771.12 dollars. Therefore, let's find the cost per square ft.

Hence,

area of the wall paper = 42 × 25.5

area of the wall paper = 1071 ft²

Therefore,

1071 ft² =  771.12 dollars

1 ft² = ?

Hence,

cost per square feet = 771.12  / 1071

cost per square feet = 0.72 dollors

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p(4)= 8

because

-2(x-5)2+4

-2(4-5)2+4

-8+10+2+4

2+2+4=8

The probability is approximately 0.9544 or 95.44%.

To solve this problem, we need to calculate the z-scores for both values of interest and use a standard normal distribution table or calculator to find the probability.

The z-score for a score of 70 is:

z = (70 - 80) / 5 = -2

The z-score for a score of 90 is:

z = (90 - 80) / 5 = 2

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected student scored between -2 and 2 on the standard normal distribution. This probability is approximately 0.9544.

However, we need to adjust this probability to account for the fact that the scores are not rounded. Since the distribution is continuous, we need to use the probability of the interval between 70 and 90, inclusive, which is:

P(70 ≤ X ≤ 90) = P(X ≤ 90) - P(X < 70)

where X is the random variable representing the exam score.

Using the z-scores we calculated earlier, we can find these probabilities as:

P(X ≤ 90) = P(Z ≤ 2) ≈ 0.9772

P(X < 70) = P(Z < -2) ≈ 0.0228

So, the probability of a randomly selected student scoring between 70 and 90 on the exam is:

P(70 ≤ X ≤ 90) = P(X ≤ 90) - P(X < 70) ≈ 0.9772 - 0.0228 = 0.9544

Therefore, the probability is approximately 0.9544 or 95.44%.

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The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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Using the properties of half-life we calculate the artifact was made in 6601 years ago.

Given that

   The percentage of the carbon-14 remaining

We have the percentage of the carbon-14 remaining :  

           w = 45%

  we can convert it into a decimal

        w  = 45/100 = 0.45

The half of carbon-14 is :

  T = 5730 year

According to radioactive decay equation :

       ln(w)  = - kt

    Rearranging the rate constant  in terms of half -  life  :

       k = ln(2)/T

  we obtain :

       ln(w)  = - ln(2)/T× t

  Finally solving for time :

    t  = - T ln(w) /ln(2)

    t = - (5730×ln(0.45))/ln(2)

    t = 6601 year

Therefore the age of the artifact about is

     t = 6601 year

Thus,  we get the age of the artifact  to be 6601 years.

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The graph of the equation x^2/49 + (y + 1)^2/4 = 1 is added as an attachment

The expression that represents the function in words is given as

StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1

Express the equation properly

So, we have

x^2/49 + (y + 1)^2/4 = 1

The above equation is an ellipse

Next, we plot the graph on a coordinate plane using a graphing tool

See attachment for the graph of the equation

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Answer: The hourly production rate is about 102.3 widgets per hour

Step-by-step explanation:

1.) divide 225 by 2.2, which gives you 102.2727

2.) round to the nearest tenth

Answer:

It should be 10%

Answer:

x = 1.2

Step-by-step explanation:

The final amount in the account after 16 years, compounded monthly at a 3.5% annual interest rate, is $6384.74.

We can use the formula for compound interest to calculate the final amount, A, in the account after 16 years:

\(A = P * (1 + r/n)^{(n*t)}\)

where P is the principal (initial amount) in the account, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $3650, r = 0.035 (since 3.5% is the annual interest rate as a decimal), n = 12 (since the interest is compounded monthly), and t = 16.

Substituting these values into the formula, we get:

A = $3650 * (1 + 0.035/12)^(12*16) ≈ $6384.74

Therefore, the final amount in the account after 16 years, compounded monthly at a 3.5% annual interest rate, is $6384.74.

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The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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Answer:

2(4) + 1(5) ÷ 5(4)

8 + 5/20

13/20

3(8) + 2(6) ÷ 6(8)

24 + 12 ÷ 48

36/48

3/4

1(3) + 2(7) ÷ 7(3)

3 + 14 ÷ 21

17/21

3(6) + 5(1) ÷ 5(6)

18 + 5/30

23/30

1(5) + 2(3) ÷ 3(5)

5 + 6/15

11/15

-TheUnknownScientist 72

The flux of the vector-field F = 1i + 1j + 2k across the surface S is 2. We find out the flux of the vector-field using Green's Theorem.

Flux form of Green's Theorem for the given vector-field

φ = ∫ F.n ds

= ∫∫ F. divG.dA

Here G is equivalent to the part of the plane = 2x+4y+z = 2.

and given F = 1i + 1j + 2k

divG = div(2x+4y+z = 2) = 2i + 4j + k

Flux = ∫(1i + 1j + 2k) (2i + 4j + k) dA

φ = ∫ (2 + 4 + 2)dA

= 8∫dA

A = 1/2 XY (on the given x-y plane)

2x+4y =2

at x = 0, y = 1/2

y = 0, x = 1

1/2 (1*1/2) = 1/4

Therefore flux = 8*1/4 = 2

φ = 2.

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Here, x value of 8 would be located on the left tail of the normal distribution curve, 3.67 standard deviations below the mean (μ=22.3) and with a very low value in terms of percentile or probability (0.015%).

To indicate where the given x value of 8 would be on the curve, we need to plot it on a normal distribution curve with a mean (μ) of 22.3 and a standard deviation (σ) of 3.9.
First, we need to convert the given x value of 8 into a z-score by using the formula:  z = (x - μ) / σ
Plugging in the values, we get: z = (8 - 22.3) / 3.9 = -3.67
This means that the value of 8 is located 3.67 standard deviations below the mean.
Next, we need to find this point on the normal distribution curve. We can use a z-score table or a graphing calculator to find the corresponding area under the curve.
If we use a z-score table, we can look up the area to the left of -3.67, which is 0.00015. This means that only 0.015% of the data falls below this point.
To plot this on the curve, we can locate the mean (μ) and mark it as the center of the curve. Then, we can count 3.67 standard deviations to the left of the mean and mark this as the point where the value of 8 would be located.

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