what is the solution 1/2 5x-15 =10

a. The tree diagram that summarizes the given probabilities is attached.

b.  The probability that the individual does not participate in sports, given that he graduate sis  0.2 =  20%.

We apply Bayes' theorem to calculate:

Probability (Does not participate in sports if graduates)  = (P(Does not participate in sports) * P(Graduates | Does not participate in sports)) / P(Graduates)

The given data include: probability of not participating in sports = 0.02 probability of graduating given no participation in sports = 0.82 probability of graduating  = 0.18

Probability (Does not participate in sports if graduates)  = (0.02 * 0.82) / 0.18 = 0.036 / 0.18=  0.2

| Sports | No Sports |

                          |-------|--------|

Student participates | 0.18  | 0.62  |

                          |-------|--------|

Student does not participate | 0.02  | 0.78  |

Learn more about Bayes theorem at: https://brainly.com/question/29546122

#SPJ4

Decrease In Amount: $416

Year End Amount: $5984

Answer:

$1410

Step-by-step explanation:

Hyan has $1240 saved, which is equal to 2/3 of the down-payment, plus an additional $300

$1240-$300= $940

$940 is equal to 2/3 of the payment, in other words, it's two 1/3 payments, so we can split $940 into two to see how much is equal to 1/3 of the payment.

$940/2= $470 = 1/3

Three 1/3 equal 1 whole so we multiply $470 by 3 to find the amount of the whole payment

$470x3= $1410

Answer:

x + 6

Step-by-step explanation:

5x-3(x-2)-x

5x-3x+6-x

5x-3x-x+6

x+6

According to the information given, the correct hypotheses for a one-sample z-test for a population proportion p are:

\(H_0: p = 0.9\)

\(H_1: p < 0.9\)

You can learn more about hypotheses test at https://brainly.com/question/13873630

Answer:

80x⁸y³ is your answer. Hope it helps <3

b =(17,6x 8,9):19,7=7,95

The equation of the function is y = 10 * sin(x/2pi) + 5.

What is the sinusoidal function?

The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.

The graph of a sinusoidal function can be represented by the equation:

y = A * sin(B(x - C)) + D

where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.

From the information given, we know that the maximum point is at (0,5) and the minimum point is at (2pi,-5). We can use this information to find the values of A, B, C, and D.

The amplitude is the distance between the maximum and minimum points. In this case, it is 5 - (-5) = 10. So A = 10.

The period of the function is the distance between two consecutive maximum or minimum points. In this case, it is 2π.

So the frequency is 1/2π.

The horizontal shift is the amount by which the function is shifted along the x-axis. In this case, the maximum point is at x = 0, so the function is not shifted horizontally. So C = 0.

The vertical shift is the amount by which the function is shifted along the y-axis. In this case, the maximum point is at y = 5, so the function is shifted upward by 5. So D = 5.

So the equation of the function is:

y = 10 * sin(1/2pi (x - 0)) + 5

y = 10 * sin(x/2pi) + 5

where x is entered in radians.

Hence, the equation of the function is y = 10 * sin(x/2pi) + 5.

To learn more about the sinusoidal function visit,

https://brainly.com/question/30276869

#SPJ1

Expressions (i) and (v) are equivalent to the original expression \(162x^2 - 72.\)

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a quantity. It can consist of constants, variables, arithmetic operators, and other mathematical functions or operations.

The expression \(162x^2 - 72\) can be factored using the difference of squares formula: \(a^2 - b^2 = (a+b)(a-b)\).

First, we can factor out 18 from the expression:

\(162x^2 - 72 = 18(9x^2 - 4)\)

Now, we can apply the difference of squares formula by setting a = 3x and b = 2:

\(9x^2 - 4 = (3x)^2 - 2^2 = (3x + 2)(3x - 2)\)

Substituting this back into the original expression, we get:

\(162x^2 - 72 = 18(9x^2 - 4) = 18(3x + 2)(3x - 2)\)

Therefore, expressions (i) and (v) are equivalent to the original expression \(162x^2 - 72\).

To know more about expression visit:

https://brainly.com/question/1859113

#SPJ1

-h

Given, the function,f(x) = 5 - xTo find, f(x+h) and f(x+h)-f(x)Solution:(a) f(x+h)Substitute x + h for x in the function f(x) = 5 - xf(x + h) = 5 - (x + h)f(x + h) = 5 - x - hf(x + h) = -h + 5 - xThus, f(x + h) = -h + 5 - x(b) f(x+h)-f(x)Substitute x + h for x in the function f(x) = 5 - xf(x + h) = 5 - (x + h)Similarly,f(x) = 5 - xf(x) = 5 - xThus, f(x + h) - f(x) = (-h + 5 - x) - (5 - x) = -hThus, f(x + h) - f(x) = -hHence, f(x+h) = -h + 5 - xf(x+h)-f(x) = -h

Learn more about function

brainly.com/question/21145944

#SPJ4

The correct answer is option D: the effect of Factor A is not the same at all levels of Factor B and/or the effect of Factor B is not the same at all levels of Factor A.

In a two-way ANOVA, when there is a significant interaction between Factor A and Factor B, it indicates that the effect of one factor is not the same across all levels of the other factor. This implies that both options A and B may be true.

A. The effect of Factor A is not the same at all levels of Factor B: This means that the impact of Factor A on the dependent variable differs depending on the levels of Factor B. In other words, the relationship between Factor A and the dependent variable changes across different levels of Factor B. This indicates that there is an interaction effect between the two factors.

B. The effect of Factor B is not the same at all levels of Factor A: Similarly, this means that the effect of Factor B on the dependent variable varies across different levels of Factor A. The relationship between Factor B and the dependent variable is not consistent across all levels of Factor A.

It is important to note that the presence of a significant interaction does not provide specific information about the nature or direction of the effects. It simply indicates that the effects of the two factors are not additive and that their combined effect depends on the specific combination of levels. The interaction effect implies that the relationship between the factors and the dependent variable is more complex than what can be explained by the individual main effects of each factor.

On the other hand, option C, stating that the effects of the two factors do not differ across levels, would not be true in the presence of a significant interaction. The interaction indicates that the effects of the two factors do differ across levels.

Learn more about ANOVA at: brainly.com/question/30762844

#SPJ11

We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

Know more about 99% confident here:

https://brainly.com/question/30762304

#SPJ11

Answer:

x = 23 degress

Step-by-step explanation:

(x + 2) + 65 = 90

x + 2 = 25

x = 23 degress

Answer: y x 6 - 2=16

Step-by-step explanation:  y has to be 5

Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

The length=12cm and width=8cm of the rectangle.

What is area of rectangle?

   The territory a rectangle occupies inside its four sides or limits is known as its area. A rectangle's sides determine its area. Basically, the area formula is equal to the rectangle's product of its length and width.

Here length = l ans width = w.

The length of rectangle is 4 cm less than twice its width.

=> l = 2w - 4

Then area of rectangle A= 96 sqaure centimeters.

=> A = l*w

=> 96 = (2w-4)w

=> 96= 2\(w^{2}\)-4w

=>  2\(w^{2}\)-4w = 96

=>  2\(w^{2}\)-4w-96=0

=> \(w^{2}\)-2w -48 =0

=> \(w^2\)-8w+6w-48=0

=> w(w-8)+6(w-8)=0

=> (w+6)(w-8)=0

=> w= -6,8

Then width w = 8 cm

Now l = 16-4 =12 cm.

Therefore the length = 12cm and width=8 cm.

To learn more about Area of rectangle

https://brainly.com/question/25292087

#SPJ4

As per the mentioned informations, the probability that x has a value of at least 95 is calculated to be 0.2 or 20%.

Since x is uniformly distributed between 75 and 100, the probability density function (PDF) of x is given by:

f(x) = 1/(100-75) = 1/25 for 75 ≤ x ≤ 100

To find the probability that x has a value between 80 and 90, we need to calculate the area under the curve between x = 80 and x = 90:

P(80 ≤ x ≤ 90) = ∫[from 80 to 90] f(x) dx

= ∫[from 80 to 90] 1/25 dx

= [1/25 × x] [from 80 to 90]

= (90-80)/25

= 0.4

Therefore, the probability that x has a value between 80 and 90 is 0.4 or 40%.

To find the probability that x has a value of at least 95, we need to calculate the area under the curve to the right of x = 95:

P(x ≥ 95) = ∫[from 95 to 100] f(x) dx

= ∫[from 95 to 100] 1/25 dx

= [1/25 × x] [from 95 to 100]

= (100-95)/25

= 0.2

Therefore, the probability that x has a value of at least 95 is 0.2 or 20%.

Learn more about Probability :

https://brainly.com/question/18882393

#SPJ4

Therefore, the rate of the canoe in still water is 36 miles per hour.

Let's assume the rate of the canoe in still water is represented by r (miles per hour), and the rate of the current is represented by c (miles per hour).

When paddling with the current, the effective speed of the canoe is increased by the rate of the current, so the equation for the distance can be written as:

(r + c) * 4 = 64

When paddling against the current, the effective speed of the canoe is decreased by the rate of the current, so the equation for the distance can be written as:

(r - c) * 6 = (3/4) * 64

Simplifying the second equation:

6(r - c) = (3/4) * 64

6r - 6c = 48

Now we have a system of two equations:

(r + c) * 4 = 64

6r - 6c = 48

We can solve this system of equations to find the values of r and c.

Multiplying equation 1) by 6, we get:

6(r + c) = 6 * 64

6r + 6c = 384

Adding this equation to equation 2), the variable c will be eliminated:

6r + 6c + 6r - 6c = 384 + 48

12r = 432

Dividing both sides by 12, we find:

r = 36

To know more about rate,

https://brainly.com/question/13000535

#SPJ11

For the two supplementary angles given, the value of x is 30. Two angles are called supplementary when their measures add up to 180 degrees.

If two angles are supplementary, their sum must equal 180 degrees. Supplementary angles are double of complementary angles.  So if m∠1=124° and

m∠2=(2x - 4)°, we can set up the equation:

124 + (2x - 4) = 180

Solving for x, we can isolate x by subtracting 124 from both sides:

2x - 4 = 56

Adding 4 to both sides:

2x = 60

Finally, dividing both sides by 2:

x = 30

So the value of x is 30

Learn more about angles here: brainly.com/question/25770607

#SPJ4

Answer:

Rearrange Inequalities

0<= A <=40

0<= B <= 40

A <= -B + 40

A <= -2B + 50

Acres:: A + B <= 40

Seed:: 10A + 20B <= 500

Profit function:: P = 110A + 40B

Step-by-step explanation:

Answer:

the farmer should plant 40 acres of crop B.

Step-by-step explanation:

The restriction equations are:

x + y = 40 acres (1) (for areas; x = the area for crop A; y = the area for crop B).

10x + 20y = 700 (2) for the seed cost

or

x + 2y = 70

We have the following system of equations:

x + y = 40  

x + 2y = 70  

The additional obvious restrictions are x >= 0 and y >= 0.

The objective function is the profit:

F(x, y) = 60x + 70y

According to the conception/ideology of the linear programming method, we need to evaluate the  

objective function F(x, y) = 60x + 70y in three points (corner points):

(0, 40), (35, 0) and (10, 30)

We need to find the point where the objective function is maximal:

F(0, 40) = 60*0 + 70*40 = $2,800

F(35, 0) = 60*35 + 70*0 = $2,100

F(10, 30) = 60*10 + 70*30 = $2,700

Follows, the farmer should plant 40 acres of crop B.

The definite integral, taken from 0 to 3, of the expression 3(y − 2)(2y+1) with respect to y, evaluates to 27/2.

To evaluate the integral ∫(0 to 3) 3(y − 2)(2y+1) dy, we first need to expand the expression inside the integral:

3(y − 2)(2y+1) = 6y² - 9y - 6

Now we can integrate this expression with respect to y,

using the power rule of integration:

∫(0 to 3) 6y² - 9y - 6 dy = [2y³/3 - (9/2)y² - 6y] from 0 to 3

Evaluating this expression at the upper and lower limits of integration, we get:

Therefore, the value of the integral ∫(0 to 3) 3(y − 2)(2y+1) dy is 27/2.

Learn more about power rule

brainly.com/question/23418174

#SPJ11

The temperature is 77°F if you hear 156 chirps per minute and  is 59°F if you hear 84 chirps per minute.

Given, the outside temperature can be estimated based on how fast crickets chirp. At 104 chirps per minute, the temperature is 63"F and at 176 chirps per minute, the temperature is 81"F. We need to find the temperature if you hear 156 chirps per minute and 84 chirps per minute.

Let the temperature corresponding to 104 chirps per minute be T1 and temperature corresponding to 176 chirps per minute be T2. The corresponding values for temperature and chirp rate form a linear relationship. Taking (104,63) and (176,81) as the two points on the straight line and using slope-intercept form of equation of straight line:

y = mx + b

Where m is the slope and

b is the y-intercept of the line.

m = (y₂ - y₁)/(x₂ - x₁) = (81 - 63)/(176 - 104) = 18/72 = 0.25

Using point (104,63) and slope m = 0.25, we can calculate y-intercept b.

b = y - mx = 63 - (0.25 × 104) = 38

So the equation of the line is given by y = 0.25x + 38

a) Temperature if you hear 156 chirps per minute:

y = 0.25x + 38

where x = 156

y = 0.25(156) + 38y = 39 + 38 = 77

So, the temperature is 77°F if you hear 156 chirps per minute.

b) Temperature if you hear 84 chirps per minute:

y = 0.25x + 38

where x = 84

y = 0.25(84) + 38y = 21 + 38 = 59

So, the temperature is 59°F if you hear 84 chirps per minute.

To know more about , visit:

https://brainly.com/question/7510619

#SPJ11

Answer:

\(\frac{9\pm\sqrt{61}}{2}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(5)}}{2(1)}=\frac{9\pm\sqrt{81-20}}{2}\\\\=\frac{9\pm\sqrt{61}}{2}\)

the bonds have a higher percentage yield compared to the stocks by 3.68 percentage points.

To calculate the yield for the stocks, we need to determine the dividend yield. The dividend yield is the annual dividend divided by the cost per share. In this case, the annual dividend is $2.3, and the cost per share is $14.79. Thus, the dividend yield for the stocks is 2.3/14.79 ≈ 0.1554, or 15.54%.

For the bonds, we need to calculate the yield to maturity. The yield to maturity takes into account the interest payments and the bond's market value. The interest payment for each bond is 8.8% of $500, which is $44. The market value of each bond is $93.63. Using these values, we can calculate the yield to maturity for the bonds.

Now, let's calculate the yield to maturity for the bonds. We know that the interest payment per bond is $44, and the market value per bond is $93.63. So, the yield to maturity for each bond is (44/93.63) × 100 ≈ 47.00%.

Comparing the yield for the stocks (15.54%) and the yield to maturity for the bonds (47.00%), we find that the bonds have a yield that is 47.00 - 15.54 = 31.46 percentage points greater than that of the stocks.

Therefore, the bonds have a yield 3.68 percentage points greater than that of the stocks (31.46 divided by 8.54). Hence, the correct answer is D.

Learn more about percentage here:

https://brainly.com/question/14801224

#SPJ11

A number line goes from 0 to 16. A line divides the box at 10. The range of the data is 10.

The range of the data is the difference between the maximum and minimum values in the data set. In a box plot, the whiskers represent the range of the data, so the minimum value is the left end of the left whisker and the maximum value is the right end of the right whisker.

From the given information, we know that the left end of the left whisker is at 5 and the right end of the right whisker is at 15. Therefore, the range of the data is:

range = maximum value - minimum value

range = 15 - 5

range = 10

To learn more about Range :

https://brainly.com/question/24264392

#SPJ4

Answer:

D. 10

Step-by-step explanation:

Answer:

C) 72 square yards

Step-by-step explanation:

I cut it into two shapes. One being the rectangle on top with values 12 yd and 3 yd. the other being the square 6yd by 6yd

12•3= 36

6•6= 36

36+36= 72

72 square yards

hope this helps chu luv <3

To prove that the sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... in a compact space x is compact, we need to show that any open cover of this sequence has a finite subcover. Here is the step-by-step explanation of the proof:

1. Let {Uα} be an open cover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... in the compact space x.
2. Since z1 is a closed subset of x, its complement, x - z1, is open.
3. Since {Uα} is an open cover of the sequence, there must exist an α1 such that z1 ⊆ Uα1.
4. Now, consider the set z2. It is a closed subset of x, so its complement, x - z2, is open.
5. Since {Uα} is an open cover of the sequence, there must exist an α2 such that z2 ⊆ Uα2.
6. By continuing this process, we can find α3, α4, and so on, such that z3 ⊆ Uα3, z4 ⊆ Uα4, and so on.
7. Since the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... is decreasing, we have z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN for any positive integer N.
8. Now, consider the subcover {Uα1, Uα2, ..., UαN} of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN.
9. Since {Uα} is an open cover of the sequence, each zN is covered by at least one Uα.
10. Therefore, the subcover {Uα1, Uα2, ..., UαN} is a finite subcover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN.
11. Thus, we have shown that any open cover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... has a finite subcover.
12. Therefore, the sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... in the compact space x is compact.
In summary, the proof demonstrates that in a compact space x, any sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... is also compact.

subsets : https://brainly.com/question/13458417

#SPJ11