Find x



1,) -54


2.) 48

3,) 52

4.) 54

Final answer:

To determine the angle of elevation of the sun, calculate the inverse tangent (arctan) of the height of the tower (106 feet) divided by the length of its shadow (141 feet). The angle of elevation is approximately 37 degrees to the nearest degree.

Explanation:

To find the angle of elevation of the sun given that a 106 feet tall tower casts a shadow of 141 feet long, we can use trigonometry. Specifically, the tangent of the angle, which is the ratio of the opposite side (the height of the tower) to the adjacent side (the length of the shadow).

We use the formula:

tangent of angle = opposite / adjacent

Tan(angle) = 106 / 141

Now we need to calculate the inverse tangent (arctan) of this ratio to find the angle in degrees:

Angle = arctan(106/141)

After performing this calculation with a calculator or using a trigonometric table, we find that the angle to the nearest degree is approximately 37 degrees.

Question is Incomplete,Complete question is given below;

At a college, the cost of tuition increased by 10%. Let b be the former cost of tuition. Use the expression b + 0.10b for the new cost of tuition.

a)  Write an equivalent expression by combining like terms.

b)  What does your equivalent expression tell you about how to find the new cost of tuition?

Answer:

a. The equivalent expression is [tex]1.1b[/tex].

b. The new cost of tuition is 1.1 times the former cost of tuition.

Step-by-step explanation:

Given:

Former cost of tuition = [tex]b[/tex]

the cost of tuition increased by 10%.

New cost of tuition = [tex]b+0.10b[/tex]

Solving for part a.

we need to find the equivalent expression by combining the like terms we get;

Now Combining the like terms we get;

new cost of tuition = [tex]b(1+0.1) = 1.1b[/tex]

Hence The equivalent expression is [tex]1.1b[/tex].

Solving for part b.

we need to to say about equivalent expression about how to find the new cost of tuition.

Solution:

new cost of tuition = [tex]1.1b[/tex]

So we can say that.

The new cost of tuition is 1.1 times the former cost of tuition.

Answer:

Step-by-step explanation:

1) since the sixth term is 3 and the fifth term 24, the common ratio would be 3/24 = 1/8

The formula for finding the nth term of a geometric sequence is

Tn = ar^(n - 1)

If t6 = 3,r = 1/8, then

3 = a × 1/8^(6 - 1) = a × (1/8)^5

a = 3/(0.125)^5 = 98304

The first term is 98304.

Second term is 98304 × 1/8 = 12288

Third term is 12288 × 1/8 = 1536

Third term is 1536 × 1/8 = 192

2) t1 = 4

t2 = - 3t(2- 1) = - 3t1 = - 3 × 4 = - 12

t3 = - 3t(3- 1) = - 3t2 = - 3 × - 12 = 36

t4 = - 3t(4- 1) = - 3t3 = - 3 × 36 = - 108

3) let the numbers be t2,t3 and t4

The sequence becomes

1/2, t2,t3, t4,8

The formula for finding the nth term of a geometric sequence is

Tn = ar^(n - 1)

8 = 1/2 × r^(5 - 1)

8 = 1/2 × r^4

16 = r^4

2^4 = r^4

r = 2

t2 = 1/2 × 2 = 1

t3 = 1 × 2 = 2

t4 = 2 × 2 = 4

Answer:

(a) At 5% significance level, reject H0

At 1% significance level, reject H0

(b) At 5% significance level, fail to reject H0

At 1% significance level, fail to reject H0

Step-by-step explanation:

(a) The test is a one tailed test

At 5% significance level, the critical value is 1.645

Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 1.645

At 1% significance level, the critical value is 2.326

Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 2.326

(b) The test is a two tailed test

At 5% significance level, the critical value is 1.96. The region of no rejection of H0 lies between -1.96 and 1.96

Conclusion: Fail to reject H0 because the test statistic -1.78 falls within -1.96 and 1.96

At 1% significance level, the critical value is 2.576. The region of no rejection of H0 lies between -2.576 and 2.576

Conclusion: Fail to reject H0 because the test statistic falls within -2.576 and 2.576

The conclusion that can be made from an hypothesis test depends on

the significance level and p-value.

Response:

(a) The conclusion at 5% is there is statistical evidence to suggest that p < 0.65

At 1% level; fail to reject H₀: p = 0.65, there is statistical evidence to suggest that p = 0.65

(b) With Hₐ ≠ 0.65, the conclusion at the 5% significance level is that there is sufficient statistical evidence that p = 0.65

At the 1% level, fail to reject H₀: p = 0.65,

The null hypothesis, H₀: p = 0.65

The alternative hypothesis, Hₐ: p < 0.65

The z-score is z = -1.78, which gives;

The p-value = 0.0375

(a) The significance level is 5%

Which gives, α = 0.05

Given that the p-value is less than the significant level, we have that

there is sufficient evidence against the null hypothesis, given that the

probability that the null hypothesis is correct is less than the significant

level of 5%.

Therefore, reject H₀, p = 0.65

However, at 1% significant level, α = 0.01, and the p-value, p = 0.0375 is

larger than the significance level.

(b) Hₐ: p ≠ 0.65

We have;

[tex]\alpha = \dfrac{5 \%}{2} = 2.5 \% = \mathbf{0.025}[/tex]

Which gives;

The p-value (0.0375) is larger than the significant level, therefore, we

fail to reject the null hypothesis.

At the 1% level of significance, we have;

[tex]\alpha = \dfrac{1 \%}{2} = 0.5 \% = 0.005[/tex]

Which gives;

The p-value at z = -1.78 (p = 0.0375) is larger than the significant level

Therefore;

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Answer:

The answer to your question is below

Step-by-step explanation:

a) The intervals in which the graph is decreasing are the right section of the first parabola, the left section of the second parabola and also the right section of the third parabola.

               (9, 11) U (14.5, 17) U (21, 27)

b) There are only two intervals in which the graph is increasing

                (1, 9) U (17, 21)

c) During the time the graph is increasing, Andre is getting away from his origin.

Answer:

There are 7 dogs.

Step-by-step explanation:

7 (dogs) x 7 (biscuits) = 49

3 (cats) x 6 (biscuits) = 18

49 + 18 = 67

Answer:

Zeke will catch up with Niko at 16 yards from the start line, y = 16 yards.

Zeke will catch up Niko after 8 seconds, x = 8 seconds.

Step-by-step explanation:

i) distance to be run = 30 yards

ii) Niko has a head start of 12 yards.

iii) speed of Zeke = 2 yards / second

iv) speed of Niko = 1 yard every 2 seconds  = 0.5 yard / second

v) x represents the number of seconds they have been racing.

vi) y represents the distance from the start line.

vii) the time at which Zeke catches up with Niko will be given by

     [tex]x = \frac{y - 12}{0.5} = \frac{y}{2}[/tex]

    Therefore 2y - 24 = 0.5y     [tex]\Rightarrow[/tex]  1.5 y = 24    [tex]\therefore[/tex] y = 24 / 1.5  = 16 yards

Therefore x  = 16 /2  = 8 seconds

The equations that represent Niko's and Zeke's distance from the start line are [tex]y = 12 + \frac 12 x[/tex] and [tex]y = 2 x[/tex], respectively.

The given parameters are:

[tex]Total = 30[/tex] --- the total distance

Niko is 12 yards ahead, and runs at 1 yard per 2 seconds. So, Niko's equation is

[tex]N i k o = 12 + \frac 12 x[/tex]

Zeke runs 2 yards per seconds. So, Zeke's equation is

[tex]Zeke = 2 x[/tex]

Hence, Niko's and Zeke's distance from the start line are [tex]y = 12 + \frac 12 x[/tex] and [tex]y = 2 x[/tex], respectively.

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Answer:

[tex]11b+9c+7v\leq 1256[/tex]

Step-by-step explanation:

Let 'b' plates of beef, 'c' plates of chicken, and 'v' plates of vegetarian dishes are purchased for the party.

Given:

Cost of 1 plate of beef dish = $11

Cost of 1 plate of chicken dish = $9

Cost of 1 plate of vegetarian dish = $7

Total money available to spend = $1256

So, as per question:

Total money spent on purchasing the dishes must be less than or equal to the total money available by the Math club.

Total cost of all the dishes is equal to the sum of the costs of 'b' plates of beef, 'c' plates of chicken, and 'v' plates of vegetarian dishes.

Therefore, total cost of all the dishes is given as:

Total cost = [tex]11b+9c+7v[/tex]

Now, the inequality for the given situation is:

Total cost on dishes ≤ Total money available to spend

⇒ [tex]11b+9c+7v\leq 1256[/tex]

Hence, the inequality is [tex]11b+9c+7v\leq 1256[/tex]

Each chef at "sushi emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On tuesday, each customer ate 2 regular rolls & 3 vegetarian rolls. by the end of the day, 4 regular rolls & 1 vegetarian roll remained uneating. how many chefs were on tuesday ? and how many customers were they ?

There were 2 chefs and 13 customers on tuesday

Let x be the number of chefs at Sushi Emperor and y be the number of customers on Tuesday.

From given,

Each chef prepares 15 regular rolls and 20 vegetarian rolls daily

If each chef prepares 15 regular rolls, then x chefs prepare 15x regular rolls

If each customer ate 2 regular rolls, then y customers ate 2y regular rolls

By the end of the day, 4 regular roll remained un eating

Therefore,

15x - 2y = 4 --------- eqn 1

If each chef prepares 20 vegetarian rolls, then x chefs prepare 20x vegetarian rolls

If each customer ate 3 vegetarian rolls, then y customers ate 3y vegetarian rolls

By the end of the day, 1 vegetarian roll remained uneating

Therefore,

20x - 3y = 1 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 3

45x - 6y = 12 ------- eqn 3

Multiply eqn 2 by 2

40x - 6y = 2 ------- eqn 4

Subtract eqn 4 from eqn 3

45x - 6y = 12

40x - 6y = 2

( - ) --------------

5x = 10

x = 2

Substitute x = 2 in eqn 1

20(2) - 3y = 1

40 - 3y = 1

3y = 39

y = 13

Thus there were 2 chefs and 13 customers

Answer:

61.12 units²

Step-by-step explanation:

(½ × pi × r²) + (½ × b × h)

½ [(3.14 × 4²) + (8 ×9)]

½(122.24)

61.12 units²

Answer:

61.13 units squared

Step-by-step explanation:

This figure is composed of a semicircle and a triangle. Let's find these areas separately:

1) SEMICIRCLE:

The area of a semicircle is: [tex]A=\frac{\pi r^2}{2}[/tex] , where r is the radius (which is the distance from the center to a point on the circle). In this case, the radius of the circle is 4. So, we have:

[tex]A=\frac{\pi *4^2}{2} =\frac{16\pi }{2} =8\pi[/tex] ≈ 25.13 units squared

2) TRIANGLE:

The area of a triangle is: [tex]A=\frac{bh}{2}[/tex] , where b is the base and h is the height. Here, the base is 8 (b = 8) and the height is 9 (h = 9). So, we have:

[tex]A=\frac{8*9}{2} =\frac{72}{2} =36[/tex] units squared

Finally, we add these two areas together:

25.13 + 36 = 61.13 units squared.

Hope this helps!

To solve the programming task, you would create a loop to read integers, use a counter to track consecutive duplicates and print the count after a negative number is entered to end the input.

The student's question involves writing a piece of code that reads a sequence of non-negative integers, ends the input with a negative integer, and reports the number of consecutive duplicate values entered before the negative integer is encountered. This is a programming task that typically involves a loop and a counter.

To address this question, you would write a loop that continues to accept input until a negative number is entered. Inside the loop, you would use a counter to keep track of the number of consecutive duplicates. Here is a pseudocode example:

Initialize the previous Value to None (or some value that won't occur in the sequence).

Initialize the count Of Duplicates to 0.

Start a loop that reads integers until a negative number is encountered.

Inside the loop, compare the current number to the previous Value.

If they are the same, increment the count Of Duplicates by 1.

Set the previous Value to the current number before the next iteration.

Outside the loop, print count Of Duplicates.

The counter pattern is a fundamental concept in programming that is used to tally occurrences within iteration structures like loops.

Answer:

Correct answer choices are [tex]27x^{2}[/tex] and [tex]657 cm^{2}[/tex]

Step-by-step explanation:

We are able to arrive at these answers through basic equation used to calculate area of an triangle and monomial laws

Answer: the equations are

b + d = 8

6x + 5y = 43

Step-by-step explanation:

Let b represent the number of hours that Julia babysits.

Let d represent the number of hours she walks dogs.

Julia worked for a total of 8 hours babysitting and walking the dogs.. This means that

b + d = 8

Julia earns $6 an hour babysitting and earns $5 an hour walking dogs. She earned a total of $43 after working a total of 8 hours at her two jobs. This means that

6x + 5y = 43

Answer: the salesperson earns $54 as commission.

Step-by-step explanation:

A furniture salesperson earns 4.5% commission on every piece of furniture sold. The salesperson sells a sofa for $1000. This means that the commission that he earned from the sale of the sofa is

4.5/100 × 1000 = 0.045 × 1000 = $45

The salesperson also sold a chair for $200. This means that the commission that he earned from the sale of the chair is

4.5/100 × 200 = 0.045 × 200 = $9

The total commission that the salesperson earns is

45 + 9 = $54

Step-by-step explanation:

average rate of change of function is given by :

[tex]f= (f(a+h)-f(a))/h[/tex]

where

[tex]f(x)=3x[/tex]

and a= 7

so inserting values is formula for h=1

[tex]f=(f(7+1)-f(7))/1[/tex]

[tex]f= f(8)-f(7)= 3(8)-3(7)=24-21=3[/tex]

now for h= 0.1

[tex]f=(f(7+0.1)-f(7))/0.1=(f(7.1)-f(7))/0.1=(3(7.1)-3(7))/0.1[/tex]

[tex]f=3[/tex]

similarly average rate of change of given function is same for all given step sizes.

Final answer:

The question involved calculating the average rate of change of the function f(x) = 3x over various intervals, showing that the rate of change is constant and equals 3 for all given values of h.

Explanation:

The question asks to calculate the average rate of change of the function f(x) = 3x over the intervals [a, a + h] for values of h = 1, 0.1, 0.01, 0.001, and 0.0001, where a = 7.

The average rate of change is calculated using the formula [tex]\frac{f(a+h) - f(a)}{h}[/tex]

For each value of h, we substitute a and h into the function and use the formula to find the average rate of change.

For h = 1, the average rate of change is 3.

For h = 0.1, the average rate of change is also 3.

For h = 0.01, the average rate of change remains 3.

For h = 0.001, the average rate is again 3.

Similarly, for h = 0.0001, the average rate of change is 3.

Using technology for values of h smaller than 0.1 is recommended due to the precision required in calculations. However, for this particular function, the rate of change is constant across these intervals, simplifying the process.

Answer: it will take 0.23 hours for the first car to catch the second one.

Step-by-step explanation:

Let t represent the time it will take for the first car to catch the second one.

The initial distance between the cars was 30 miles. This means that by the time both cars meet, they would have covered a total distance of 30 miles.

Distance = speed × time

The first car was going 70 miles per hour.

Distance covered by the first car after t hours is

70 × t = 70t

The second was going 60 miles per hour. Distance covered by the second car after t hours is

60 × t = 60t

Since the total distance covered is 30 miles, then

70t + 60t = 30

130t = 30

t = 30/130 = 0.23 hours

Answer:

[D] 11.25

Step-by-step explanation:

Broker/dealers must trade with customers based on the current bid and ask.

10.50 Bid for customers selling

11.25 Ask for customers buying

Answer:

Home away should record the contribution to a Net assets with donor restriction

Step-by-step explanation

A Net asset with donor restriction is the part of net assets of a not- for - profit making organisation  that is subject to donor-imposed restrictions.  

The stipulation that the fund of $15,000 should be used to buy beds automatically makes it to be classified as a Net assets with donor restriction  item.

Answer:

Y=2000x+175,000

Step-by-step explanation:

y=mx+b so your M will be your 2000 and your x is gonna be years, and your b is gonna be 175,000

Answer:

The probability of selecting a non-defective part provided by supplier A is 0.807.

Step-by-step explanation:

Let A = a part is supplied by supplier A, B = a part is supplied by supplier B and D = a part is defective.

Given:

P (D|A) = 0.05, P(D|B) = 0.09

A supplies four times as many parts as B, i.e. n (A) = 4 and n (B) = 1.

Then the probability of event A and B is:

[tex]P(A)=\frac{n(A)}{n(A)+N(B)}= \frac{4}{4+1}=0.80\\P(B)\frac{n(B)}{n(A)+N(B)}= \frac{1}{4+1}=0.20[/tex]

Compute the probability of selecting a defective product:

[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)\\=(0.05\times0.80)+(0.09\times0.20)\\=0.058[/tex]

The probability of selecting a non-defective part provided by supplier A is:

[tex]P(A|D')=\frac{P(D'|A)P(A)}{P(D')} = \frac{(1-P(D|A))P(A)}{1-P(D)}\\=\frac{(1-0.05)\times0.80}{(1-0.058)}\\ =0.80679\\\approx0.807[/tex]

Thus, the probability of selecting a non-defective part provided by supplier A is 0.807.

The required probability of selecting a non-defective part provided by supplier A is 0.807.

Let,

A part is supplied by supplier A,

B part is supplied by supplier B,

And D = a part is defective.

Given:

P ([tex]\frac{D}{A}[/tex]) =5% = 0.05,

P([tex]\frac{D}{B}[/tex]) = 9% =  0.09

A supplies four times as many parts as B, .

Then, n (A) = 4 and n (B) = 1.

The probability of event A and B is:

Probability of event P(A) = [tex]\frac{n (A)}{n (A) + n(B)}[/tex] = [tex]\frac{4}{4+1}[/tex]

                                 P(A) = [tex]\frac{4}{5}[/tex]

And Probability of Event P(B) = [tex]\frac{n (B )}{n (A) + n(B)} = \frac{1}{4+1}[/tex]

                                        P(B) = [tex]\frac{1}{5}[/tex]

Then , the probability of selecting a defective product:

P(D) = [tex]P(\frac{D}{A}) P(A) + P(\frac{D}{B}) P(B)[/tex]

P(D) = 0.50×0.80 + 0.09×0.20

P(D) = 0.058

The probability of selecting a non-defective part provided by supplier A is

[tex]P(\frac{A}{D'} )= \frac{P(D'(A)) . P(A)}{P(D')} \\\\[/tex]

          = [tex]\frac{1- P(D(A)). P(A)}{1-P(A)} \\\\\frac{(1-0.05) . 0.80}{1- 0.05} \\\\[/tex]

          = 0.807

Hence, the probability of selecting a non-defective part provided by supplier A is 0.807.

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Answer:

A cross-section that is perpendicular to the base of a cube.

A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.

Step-by-step explanation:

We have to select from options that the two-dimensional cross section are squares.

The correct options are :

A cross-section that is perpendicular to the base of a cube.

A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.  

In both the cases the length and the width of the section are equal. (Answer)

Among the given options, only the cross-section that is perpendicular to the base of a cube is guaranteed to be a square. The other options will generally result in different shapes, such as triangles or circles.

The question asks which two-dimensional cross sections are squares. To find the answer, we must consider the shape of the object and the orientation of the cross section.

At first glance, only the cross-section perpendicular to the base of a cube is a square. However, depending on specific conditions not typically met by the listed shapes, other cross-sections can appear square-shaped. Therefore, generally, the answer is a cross-section that is perpendicular to the base of a cube will be square.

Answer:

14 gums.

Step-by-step explanation:

Given: Jacob bought 13 pack of gum

           He already had 5 piece of gum.

           He shared gum with six of his friends.

           Each one of them received 27 pieces of gum.

Lets assume the number of gums in each pack be "x".

Total number of gum= [tex]number\ of\ gum\ in\ each\ pack\times number\ of\ pack + 5[/tex]

Also gum has been shared among jacob and his 6 friends, which is 7 person.

∴ Share of each person= [tex]\frac{Total\ number\ of\ gums}{number\ of\ person}[/tex]

Now, forming equation to find number of gums in each pack.

⇒ [tex]\frac{13\times x+5}{7} = 27[/tex]

Multiplying both side by 7

⇒ [tex]13x+5= 189[/tex]

Subtracting both side by 5

⇒ [tex]13x= 189-5[/tex]

⇒[tex]13x= 184[/tex]

Dividing both side by 13

⇒ [tex]x= \frac{184}{13}[/tex]

∴[tex]x= 14.15 \approx 14\ gum[/tex]

Hence, each pack have 14 gums.

Answer:

not a function - it does not pass the vertical line test.

Step-by-step explanation:

Final answer:

It will take Daniel approximately 0.26 hours, or 15.6 minutes, to catch up with Frank.

Explanation:

To find how long it will take Daniel to catch up with Frank, we can use the formula time = distance / speed. Since Frank started out first, we can calculate his distance using the formula distance = speed * time. Let's assume it takes Daniel t hours to catch up with Frank. The time it takes Frank to travel 13 miles is 13 miles / 45 mph = 0.289 hours. Therefore, when Daniel starts, Frank has already traveled a distance of 0.289 hours * 45 mph = 13 miles. To catch up with Frank, Daniel needs to travel the same distance in t hours at a speed of 50 mph. So, 13 miles = 50 mph * t hours. Dividing both sides by 50 mph gives us t = 13 miles / 50 mph = 0.26 hours. Therefore, it will take Daniel approximately 0.26 hours, or 15.6 minutes, to catch up with Frank.

Answer:

Option (2) is correct graph.

Step-by-step explanation:

Given:

The function to graph is given as:

[tex]f(x)=4(\frac{1}{2})^x[/tex]

Now, the above function is an exponential function of the form [tex]f(x)=ka^x[/tex]

Where, 'k' and 'a' are constants.

The range of an exponential function is always greater than 0.

The domain is all real numbers.

Now, for graphing it, we need to find some points on it and its end behaviour.

Now, for x = 0, the function value is given as:

[tex]f(0)=4(\frac{1}{2})^0=4[/tex]

So, (0, 4) is a point on the graph.

Now, for x = 1, the function value is given as:

[tex]f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2[/tex]

So, (1, 2) is another point on the graph.

Now, for x = 2, the function value is given as:

[tex]f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1[/tex]

So, (2, 1) is another point on the graph.

Now, as 'x' tends to ∞, the function value tends to:

[tex]f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0[/tex]

So, as

[tex]x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty[/tex]

Now, from among all the options, only option (2) fulfills all the conditions given above.

So, option (2) is correct graph.

Answer:

option 2

Step-by-step explanation:

Answer:

The value of x that gives the maximum transmission is 1/√e ≅0.607

Step-by-step explanation:

Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.

[tex]f'(x) = k*((x^2)'*ln(1/x) + x^2*(ln(1/x)')) = k*(2x\,ln(1/x)+x^2*(\frac{1}{1/x}*(-\frac{1}{x^2})))\\= k * (2x \, ln(1/x)-x)[/tex]

We need to equalize f' to 0

Thus, the value of x that gives the maximum transmission is 1/√e.

The rate of transmission in a telegraph cable is given by the equation: rate of transmission = x^2 ln(1/x), where x is the ratio of the radius of the core to the thickness of the insulation.

The rate of transmission in a telegraph cable is given by the equation: rate of transmission = x2 ln(1/x), where x is the ratio of the radius of the core to the thickness of the insulation.

This equation shows that the rate of transmission is directly proportional to the square of x and logarithmically inversely proportional to x.

For example, if x is 0.5, the rate of transmission is (0.5)2 ln(1/0.5) = 0.25 ln(2).

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Answer:

25.15 ponds is the weight of two year old baby corresponds to 10th percentile.      

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 29 pounds

Standard Deviation, σ = 3 pounds

We are given that the distribution of weight of two year old babies is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.10

P(X < x)  

[tex]P( X < x) = P( z < \displaystyle\frac{x - 29}{3})=0.10[/tex]  

Calculation the value from standard normal z table, we have,  

[tex]P(z < -1.282) = 0.10[/tex]

[tex]\displaystyle\dfrac{x - 29}{3} = -1.282\\x = 25.154 \approx 25.15[/tex]

Thus, 25.15 ponds is the weight of two year old baby corresponds to 10th percentile.

Option A: -24 is the coefficient of i

Explanation:

The expression is [tex](6-2 i)^{2}[/tex]

To determine the coefficient of i, first we shall find the square of the binomial for the expression [tex](6-2 i)^{2}[/tex]

The formula to find the square of the binomial for this expression is given by

[tex](a-b)^{2}=a^{2}-2 a b+b^{2}[/tex]

where [tex]a=6[/tex] and [tex]b=2i[/tex]

Substituting this value and expanding, we get,

[tex](6-2 i)^{2}=6^{2} -2(6)(2i)+(2i)^{2}[/tex]

Simplifying the terms, we have,

[tex](6-2 i)^{2}=36-24i-4[/tex]

Thus, from the above expression the coefficient of i is determined as -24.

Hence, Option A is the correct answer.

Answer: B.  [tex]\dfrac{28}{55}[/tex] .

Step-by-step explanation:

Given : Number of blue disks =4

Number of green disks = 8

Total disks = 12

Total number of combinations of drawing any 3 disks from 12 = [tex]^{12}C_3[/tex]

Number of combinations of drawing 1 blue and 2 green disks = [tex]^{4}C_1\times^{8}C_2[/tex]

Now , the probability that 1 of the disks selected is blue, and 2 of the disks selected are green will be :

[tex]\dfrac{^{4}C_1\times^{8}C_2}{^{12}C_3}\\\\=\dfrac{4\times\dfrac{8!}{2!6!}}{\dfrac{12!}{3!9!}}\\\\=\dfrac{4\times28}{220}\\\\=\dfrac{28}{55}[/tex]

Hence, the correct answer is B.  [tex]\dfrac{28}{55}[/tex] .

Final answer:

The question is a mathematical problem where we find that Devon has 70 points after setting up and solving an algebraic equation based on the conditions given.

Explanation:

The student's question revolves around a Mathematical problem concerning the points scored by two players, Erin and Devon, in a game. Erin has 42 points, and the question provides a condition that if Devon had 14 more points, he would have double the points Erin has. This scenario can be translated into an algebraic equation to solve for the number of points Devon currently has.

Let's denote the current number of points Devon has as D. According to the problem, if Devon had 14 more points, his total would be D + 14. We are also told that this hypothetical total would be double the points Erin has, which is 42. Therefore, we can write the equation as:

D + 14 = 2 × 42

By solving this equation, we can find out how many points Devon has:

Devon currently has 70 points.

Erin has 42 points. Devon has 70 points. If he had 14 more, he'd have double Erin's points.

let's break it down step by step:

Given:

- Erin has 42 points.

- If Devon had 14 more points, he'd have double the points Erin has.

Let's denote Devon's points as [tex]\( D \).[/tex]

According to the given information, if Devon had 14 more points, he'd have double the points Erin has. So, mathematically, we can represent Devon's points as [tex]\( 2 \times 42 \)[/tex] when we add those 14 points.

So, we can write the equation:

[tex]\[ D + 14 = 2 \times 42 \][/tex]

Now, let's solve for [tex]\( D \):[/tex]

[tex]\[ D + 14 = 84 \][/tex]

Subtract 14 from both sides of the equation:

[tex]\[ D = 84 - 14 \]\[ D = 70 \][/tex]

So, Devon currently has 70 points.