what is the y-coordinate of the vertex of the parabola?

f(x)= -x^2 - 2x +6

Final answer:

The probability of at least 16 adults requiring eyesight correction out of 17 is found by summing up individual probabilities of exactly 16 and exactly 17 adults in need, calculated using the binomial probability formula. A comparison of this probability to a typical significance threshold will determine if 16 is a significantly high number.

Explanation:

The probability that at least 16 out of 17 randomly selected adults need correction for their eyesight, given that 84% of adults need such correction, is calculated using the binomial probability formula. The binomial probability of exactly k successes in n trials, where p is the probability of success on a single trial, is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Here, we calculate the probability for exactly 16 adults and exactly 17 adults needing vision correction and then sum these to get at least 16:

Calculate P(X = 16), where n = 17, k = 16, and p = 0.84.

Calculate P(X = 17), where n = 17, k = 17, and p = 0.84.

Sum P(X = 16) and P(X = 17) for the total probability.

To answer if 16 is a significantly high number requiring correction, it is important to compare the probability with a threshold of significance, such as 0.05 commonly used in statistics. If the probability is less than this threshold, then 16 can be considered a significantly high number.

Answer:

4m²n

Step-by-step explanation:

The GCF is the factor by which all the terms among the given can be divided.

In the expression 8m²n³-24m²n²+4m³n,

The GCF between 8,24 and 4 is 4

The greatest common factor between m²,m² and m³ is m²

The greatest common factor between n³, n² and n is n

Thus multiplying the three we get:

4×m²×n

=4m²n

Answer: Option D

[tex]t_{max} =19\ s[/tex]

Step-by-step explanation:

Note that the projectile height as a function of time is given by the quadratic equation

[tex]h = -12t ^ 2 + 456t[/tex]

To find the maximum height of the projectile we must find the maximum value of the quadratic function.

By definition the maximum value of a quadratic equation of the form

[tex]at ^ 2 + bt + c[/tex] is located on the vertex of the parabola:

[tex]t_{max}= -\frac{b}{2a}[/tex]

Where [tex]a <0[/tex]

In this case the equation is: [tex]h = -12t ^ 2 + 456t[/tex]

Then

[tex]a=-12\\b=456\\c=0[/tex]

So:

[tex]t_{max} = -\frac{456}{2*(-12)}[/tex]

[tex]t_{max} =19\ s[/tex]

I think to solve this question, subtract the rate of feet per second disappearing from the distance of feet between the 2 cars.

100-85=15fps

The car is traveling at 15 feet per second.

Hope this helps!

Step-by-step explanation:

given a slope and a point that the line passes through you have 2 options

Option 1: Solve for the equation of the line so you can just use that to graph the line. In this scenario it would be y=(-5/2)x - (20/13)

Option 2: plot the given point and, based on the slope, plot the next point that it crosses. In this case the next point would be (5, 7). Then you can just draw a line using these 2 points.

Answer:

2400sq ft

Step-by-step explanation:

20×2 and 30×2

40×60

2400 sq ft

Answer:

Length = 40 feet

Width =30 feet

Step-by-step explanation:

It is given that a  rectangular patio measures 20 feet by 30 feet.

To find the area of first patio.

Area = length * breadth

 = 20 * 30 = 600 square feet

To find the value of x

It is given that new area will be the double the area of first patio.

Here area = 2 * 600 = 1200 square feet

Here length = 30 + x

width = 20 + x

Area = (30 +x)(20 + x) = 1200

x² + 50x + 600 =1200

x² + 50x - 600 = 0

By solving this quadratic equation we get,

x = 10 and x = -60

take positive value x = 10

To find the dimensions of new patio

New length = 30 + x = 30 + 10 = 40 feet

width= 20 + x = 20 + 10 = 30 feet

Answer:  The mean number of checks written per​ day  [tex]=0.3452[/tex]

Standard deviation[tex]=0.5875[/tex]

Variance  [tex]=0.3452[/tex]

Step-by-step explanation:

Given : The total number of checks wrote by person in a year = 126

Assume that the year is not a leap year.

Then  1 year = 365 days

Let the random variable x represent the number of checks he wrote in one​ day.

Then , the mean number of checks wrote by person each days id=s given by :-

[tex]\lambda=\dfrac{126}{365}\approx0.3452[/tex]

Since , the distribution is Poisson distribution , then the variance must equal to the mean value i.e. [tex]\sigma^2=\lambda=0.3452[/tex]

Standard deviation : [tex]\sigma=\sqrt{0.3452}=0.5875372328\approx0.5875[/tex]

Answer:

8418

Step-by-step explanation:

1 + 2 + ... + n is (n^2 + n)/2

46 + 47 + ... + 137

is the same as

1 + 2 + ... + 137 - (1 + 2 + ... + 45)

or

(137^2 + 137)/2 - (45^2 + 45)/2

= 8418

It would take 200 years (by definition of half-life). 50 is 1/2 of 100.

Answer:

[tex]\large\boxed{\text{if}\ m\geq0,\ \text{then}\ \sqrt{m^6}=m^3}\\\\\boxed{\text{if}\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3}[/tex]

Step-by-step explanation:

[tex]\sqrt{m^6}=\sqrt{m^{3\cdot2}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(m^3)^2}\qquad\text{use}\ \sqrt{a^2}=|a|\\\\=|m^3|\\\\\text{if}\ m\geq0,\ \text{then}\ \sqrt{m^6}=m^3\\\\\text{if}\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3[/tex]

Answer:M^3 is the square root of m6

Step-by-step explanation:

good luck!!!

Answer:  George receive 44 % of his full dose .

Step-by-step explanation:

Given : The amount for full dose : 25  grams

The amount received by George = 11 grams

Now, the percent of his full dose received by George :-

[tex]\dfrac{\text{Dose taken by George}}{\text{Full dose}}\times100[/tex]

[tex]=\dfrac{11}{25}\times100=44\%[/tex]

Hence, George receive 44 % of his full dose .

Answer:

  $195.50

Step-by-step explanation:

  0.17% × $115,000 = $195.50

Jill's account will be charged $195.50 in expense fees.

Answer:

Jill will have to pay $195.5 in fees this year.

Step-by-step explanation:

This question may be solved by a simple rule of three.

This fund has an expense ratio of 0.17 percent. This means that for each investment in this fund, there is a fee of 17% percent of the value.

$115,000 is 100%, that is, decimal 1. How much is 0.17%, that is, 0.0017 of this value. So

1 - $115,000

0.0017 - $x

[tex]x = 115000*0.0017 = 195.5[/tex]

Jill will have to pay $195.5 in fees this year.

1.

a. 30

b. 44

c. 36

d. 40

2. I don't really remember how to do these but if you cant make the denominator smaller then I belive it's

a. 24

b. 20

c. 4

d. 5

3.

a. =

b. not =

c. not =

d. not =

4. Gary

5.

a. 5/6

b. 5/12

c. 19/45

d. 13/14

e. 7/11

f. 1/2

6.

a. 2/3

b. 8/9

c. 3/10

d. 9/11

e. 3/4

f. 1/5

7.

a. 36/40

b.

c.

8.

a. yes

b. no

c. no

d. no

9. no

10. yes

11.

a. 40

b. 48

c. 77

d. 48

12. 4,620

c. 27⁄90

d. 63⁄77

e. 24⁄32

f. 73⁄365

7.What is the next fraction in each of the following patterns?

a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .?

b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .?

c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .?

8.In each pair, tell if the fractions are equal by using cross multiplication.

a. 5⁄30 and 1⁄6

b. 4⁄12 and 21⁄60

c. 17⁄34 and 41⁄82

d. 6⁄9 and 25⁄36

1.

a. 30

b. 44

c. 36

d. 40

2.

a. 24

b. 20

c. 4

d. 5

3.

a. =

b. not =

c. not =

d. not =

4. Gary

5.

a. 5/6

b. 5/12

c. 19/45

d. 13/14

e. 7/11

f. 1/2

6.

a. 2/3

b. 8/9

c. 3/10

d. 9/11

e. 3/4

f. 1/5

7.

a. 36/40

b.

c.

8.

a. yes

b. no

c. no

d. no

9. no

10. yes

11.

a. 40

b. 48

c. 77

d. 48

12. 4,620

Step-by-step explanation:

Step-by-step answer:

Given:

alarm clocks that fail at 15.7% on any day.

Solution

Probability of failure of a single clock = 15.7% = 0.157

(a)

probability of failure of a single clock on any given day (final exam or not)

= 15.7%  (given)

(b)

probability of failure of two independent alarm clocks on the SAME day

= 0.157^2

= 0.024649  (from independence of events)

(c)

probability of failure of three independent alarm clocks on the SAME day

= 0.157^3

= 0.00387  (from independence of events)

(d)

Since the probability of failure has been reduced from 0.157 to 0.00387, we can conclude that yes, even though malfunction of all three clocks is not impossible, it is unlikely at a probability of 0.00387 (less than 1 %)

Using the binomial distribution, it is found that:

a) 15.7% probability that the​ student's alarm clock will not work on the morning of an important final​ exam.

b) 0.0246 = 2.46% probability that they both fail on the morning of an important final​ exam.

c) 0.0039 = 0.39% probability of not being awakened if the student uses three independent alarm​ clocks.

d)

(C) ​Yes, because total malfunction would not be​ impossible, but it would be unlikely.

---------------------------

For each alarm clock, there are only two possible outcomes. Either it works, or it does not. The probability of an alarm working is independent of any other alarm, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of a success on a single trial.

---------------------------

Item a:

---------------------------

Item b:

The probability of both falling is the probability that none works, thus P(X = 0).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.843)^{0}.(0.157)^{2} = 0.0246[/tex]

0.0246 = 2.46% probability that they both fail on the morning of an important final​ exam.

---------------------------

Item c:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.843)^{0}.(0.157)^{3} = 0.0039[/tex]

0.0039 = 0.39% probability of not being awakened if the student uses three independent alarm​ clocks.

---------------------------

Item d:

(C) ​Yes, because total malfunction would not be​ impossible, but it would be unlikely.

A similar problem is given at https://brainly.com/question/23576286

The length of the ramp required can be determined by using conservation

of energy principle.

The length of the ramp should be approximately 154.97 meters.

Reasons:

Given parameters are;

The angle of inclination of the ramp, θ = 6.0°

Coefficient of friction, μ = 0.30

Mass of the truck, m = 15,000 kg

Speed of the truck, v = 35 m/s

Required;

The length of the ramp to stop the truck

Solution:

From the law of conservation of energy, we have;

Kinetic energy = Work done against friction + Potential energy gained by the truck at height

K.E. = [tex]W_f[/tex] + P.E.

Kinetic energy of the truck, K.E. = [tex]\frac{1}{2} \cdot m \cdot v^2[/tex]

Therefore;

K.E. = [tex]\frac{1}{2} \times 15,000 \times 35^2 = 9,187,500[/tex]

The kinetic energy of the truck, K.E. = 9,187,500 J

Friction force,[tex]F_f[/tex] = m·g·cos(θ)·μ

Therefore;

[tex]F_f[/tex] = 15,000 × 9.81 × cos(6) × 0.30 = 43,903.169071

Friction force,[tex]F_f[/tex] = 43,903.169071 N

Work done against friction = [tex]F_f[/tex] × d

Therefore;

Work done against friction, [tex]W_f[/tex] = 43,903.169071·d

Potential energy gained, P.E. = m·g·h

The height, h = d × sin(6.0°)

∴ P.E. = 15,000 × 9.81 × d × sin(6.0°) = 147150 × d × sin(6.0°)

Which gives;

9,187,500 J = 43,903.169071·d + 147150 × d × sin(6.0°)

[tex]d = \dfrac{9187500}{43,903.169071 + 147150 \times sin(6.0^{\circ})} \approx 154.97[/tex]

The length of the ramp, d ≈ 154.97 m.

Learn more here:

https://brainly.com/question/20166060

Answer: .11

Step-by-step explanation:

Let F be the event that the first truck is available and S be the event that the second truck is available.

The probability of neither truck being available is expressed as P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex]) , where P([tex]F^{C}[/tex]) is the probability that the event F doesn't happen and P([tex]S^{C}[/tex]) is the probability that the event S doesn't happen.

P([tex]F^{C}[/tex])= 1-P(F) = 1-0.73 = 0.27

P([tex]S^{C}[/tex])=1-P(S) = 1-0.59 = 0.41

Since  [tex]F^{C}[/tex] and [tex]S^{C}[/tex] aren't mutually exclusive events, then:

P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex]) = P([tex]F^{C}[/tex]) + P([tex]S^{C}[/tex]) - P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex])

Isolating the probability that interests us:

P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex])= P([tex]F^{C}[/tex]) + P([tex]S^{C}[/tex])- P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex])

Where P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex]) = 1 - 0.43 = 0.57

Finally:

P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex]) = 0.27+ 0.41 - 0.57 = 0.11

Step-by-step explanation:

[tex] \sqrt{25} = \pm \: 5 \\ \\ \sqrt{100} = \pm \: 10 \\ \\ \sqrt{36} = \pm \: 6 \\ \\ \sqrt{84} = \pm \: 9.165\\ \\ \sqrt{4} = \pm \: 2 \\ \\ [/tex]

Answer:

$804,680.814 ( approx )

Step-by-step explanation:

The amount formula in compound interest is,

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where, P is the principal amount,

r is the annual rate of interest,

n is the compounding periods in a year,

t is the time in years,

Given, P =  $ 400,000,

r = 3.5 %=0.035,

n = 12,    ( 1 year = 12 months )

t = 20 years,

Thus, the amount would be,

[tex]A=400000(1+\frac{0.035}{12})^{240}[/tex]

[tex]=400000(\frac{12.035}{12})^{240}[/tex]

[tex]=\$ 804680.813963[/tex]

[tex]\approx \$ 804680.814[/tex]

The amount owed on the mortgage on January 1, 2030, would be approximately [tex]\$765,320.99.[/tex]

To solve this problem, we need to calculate the compound interest on the mortgage over a period of 20 years (from January 1, 2010, to January 1, 2030). The formula for compound interest is given by:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

where:

-  A is the amount of money accumulated after n years, including interest.

-  P is the principal amount (the initial amount of money).

- r  is the annual interest rate (decimal).

-  n is the number of times that interest is compounded per year.

-  t is the time the money is invested for, in years.

Given:

- [tex]\( P = \$400,000 \)[/tex]

-[tex]\( r = 3.5\% = 0.035 \)[/tex] (as a decimal)

-  n = 12  (since the interest is compounded monthly)

-  t = 20  years

Plugging these values into the compound interest formula, we get:

[tex]\[ A = 400,000 \left(1 + \frac{0.035}{12}\right)^{12 \times 20} \][/tex]

[tex]\[ A = 400,000 \left(1 + \frac{0.035}{12}\right)^{240} \][/tex]

[tex]\[ A = 400,000 \left(1 + 0.002916667\right)^{240} \][/tex]

[tex]\[ A = 400,000 \left(1.002916667\right)^{240} \][/tex]

Now, we calculate the value inside the parentheses:

[tex]\[ 1.002916667^{240} \ = 1.913209802 \][/tex]

Finally, we multiply this by the principal amount to find out how much would be owed:

[tex]\[ A \ = 400,000 \times 1.913209802 \][/tex]

[tex]\[ A \ = \$765,320.99 \][/tex]

Answer:

Step-by-step explanation:

The slope of the graph at x=0 is related to the value of b. It is also proportional to the value of a, which is the same for all but curve B. The red curve R has the largest slope at x=0, (much larger than 3/4 the slope of curve B), so curve R has the greatest value of b.

Similarly, the smallest value of b will correspond to the curve with the smallest (most negative) slope. That would be curve K. Curve K has the smallest value of b.

Answer:

  344 ft²

Step-by-step explanation:

The area of the square is (40 ft)² = 1600 ft².

The area of the four circles is ...

  4×(πr²) = 4×3.14×(10 ft)² = 1256 ft²

Then the area that is not covered by the circles is ...

  1600 ft² -1256 ft² = 344 ft²

The area not sprinkled is 344 ft².

Answer:

First city: $5,500

Second city: $5,000

Step-by-step explanation:

Let's define x as the hotel price in the first city and y the hotel price in the second city.  We can start with this equation:

y = x - 500 (The hotel before tax in the 2nd city was $500 lower than in the 1st.)

Then we can say

0.065x + 0.045y = 582.50  (the sum of the tax amounts were $582.50)

We place the value of y from the first equation in the second equation:

0.065x + 0.045 (x - 500) = 582.50

0.065x + 0.045x - 22.50 = 582.50 (simplifying and adding 22.5 on each side)...

0.11x = 605

x = 5,500

The cost of the first hotel was $5,500

Thus, the cost of the second hotel was $5,000 (x - 500)

Not entirely sure what the question is supposed to say, so here's my best guess.

First, find the partial fraction decomposition of

[tex]\dfrac{x-9}{x^2-3x-18}[/tex]

This is equal to

[tex]\dfrac{x-9}{(x-6)(x+3)}=\dfrac a{x-6}+\dfrac b{x+3}[/tex]

Multiply both sides by [tex](x-6)(x+3)[/tex], so that

[tex]x-9=a(x+3)+b(x-6)[/tex]

Notice that if [tex]x=6[/tex], the term involving [tex]b[/tex] vanishes, so that

[tex]6-9=a(6+3)\implies a=-\dfrac13[/tex]

Then if [tex]x=-3[/tex], the term with [tex]a[/tex] vanishes and we get

[tex]-3-9=b(-3-6)\implies b=\dfrac43[/tex]

So we have

[tex]\dfrac{x-9}{x^2-3x-18}=-\dfrac1{3(x-6)}+\dfrac4{3(x+3)}[/tex]

I think the final answer is supposed to be [tex]a+b[/tex], so you end up with 1.

Answer:   -0.36

Step-by-step explanation:

Given: Mean : [tex]\mu=10\text{ minutes}[/tex]

Standard deviation : [tex]\sigma=5\text{ minutes}[/tex]

We know that the formula to calculate the z-score is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x=8.2 minutes, we have

[tex]z=\dfrac{8.2-10}{5}=0.36[/tex]

Hence, the z-score for this amount of advertising time = -0.36

Final answer:

The z-score for the observed amount of advertising time (8.2 minutes) compared to the radio station's average of 10 minutes with a standard deviation of 5 minutes is -0.36, when rounded to two decimal places.

Explanation:

To calculate the z-score for the amount of advertising time observed on the radio station (8.2 minutes), we use the formula: Z = (X - μ) / σ, where X is the value to calculate the z-score for, μ is the mean of the data, and σ is the standard deviation. Plugging in the given values: X = 8.2 minutes (amount of advertising time observed), μ = 10 minutes (average advertising time), σ = 5 minutes (standard deviation).

So, the z-score is calculated as follows:

Z = (8.2 - 10) / 5 = -1.8 / 5 = -0.36.

Thus, the z-score of the amount of advertising time (8.2 minutes) is -0.36, rounded to two decimal places.

[tex]|\Omega|=14^2=196\\|A|=2\cdot8=16\\\\P(A)=\dfrac{16}{196}=\dfrac{4}{49}\approx8.2\%[/tex]

Answer:

b) An empirically testable statement that is an unproven supposition developed in order to explain phenomena.

Step-by-step explanation:

b) An empirically testable statement that is an unproven supposition developed in order to explain phenomena.

A hypothesis is an unproven supposition.This may be derived from previous research or theory and is developed prior to data collection.

Note:

Variance is the average squared deviations about the mean of a distribution of values.

Step-by-step explanation:

Given:

Mean = 33700

Median = 34600

Mode = 35600

The mean is the average, the median is the middle number, and the mode is the most common number.

a)

First, we need to find the new mean (average) if one of the employees gets a 3500 raise.  The average is the total salary divided by number of employees:

(5 × 33700 + 3500) / 5 = 34400

b)

The mode is the most common number in a set.  Since there are only five employees, and the mode is different than the median, then the two highest earners must have the same salary.  The salaries from smallest to largest is therefore:

?, ?, 34600, 35600, 35600

When the median gets the 3500 raise, the set becomes:

?, ?, 35600, 35600, 38100

So the new median is 35600.

c)

The most common number is still 35600.  So the mode hasn't changed: 35600.

Answer:

0.23

Step-by-step explanation:

A standard deck has 4 suits (spade, club, diamond, and heart), and each suit has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king).

We want to know the probability of drawing an ace, a 2, or a 3.  There are four aces, four 2's, and four 3's in a deck (one for each suit).  That's a total of 12 cards.  So the probability is:

12 / 52 ≈ 0.23

Using the probability concept, it is found that there is a 0.2308 = 23.08% probability of selecting a number less than 4.

--------------------------

Thus, the probability of selecting a number less than 4 is:

[tex]p = \frac{D}{T} = \frac{12}{52} = 0.2308[/tex]

0.2308 = 23.08%

A similar problem is given at https://brainly.com/question/13484439

Answer:

The solutions are x = -9 , x = -5

Step-by-step explanation:

* Lets find the vertex of the parabola

- In the quadratic equation y = ax² + bx + c, the vertex of the parabola

 is (h , k), where h = -b/2a and k = f(h)

∵ The equation is y = x² + 14x + 45

∴ a = 1 , b = 14 , c = 45

∵ h = -b/2a

∴ h = -14/2(1) = -14/2 = -7

∴ The x-coordinate of the vertex of the parabola is -7

- Lets find k

∵ k = f(h)

∵ h = -7

- Substitute x by -7 in the equation

∴ k = (-7)² + 14(-7) + 45 = 49 - 98 + 45 = -4

∴ The y-coordinate of the vertex point is -4

∴ The vertex of the parabola is (-7 , -4)

- Plot the point on the graph and then find two points before it and

 another two points after it

- Let x = -9 , -8 and -6 , -5

∵ x = -9

∴ y = (-9)² + 14(-9) + 45 = 81 - 126 + 45 = 0

- Plot the point (-9 , 0)

∵ x = -8

∴ y = (-8)² + 14(-8) + 45 = 64 - 112 + 45 = -3

- Plot the point (-8 , -3)

∵ x = -6

∴ y = (-6)² + 14(-6) + 45 = 36 - 84 + 45 = -3

- Plot the point (-6 , -3)

∵ x = -5

∴ y = (-5)² + 14(-5) + 45 = 25 - 70 + 45 = 0

- Plot the point (-5 , 0)

* To solve the equation x² + 14x + 45 = 0 means find the value of

  x when y = 0

- The solution of the equation x² + 14x + 45 = 0 are the x-coordinates

 of the intersection points of the parabola with the x-axis

∵ The parabola intersects the x-axis at points (-9 , 0) and (-5 , 0)

∴ The solutions of the equation are x = -9 and x = -5

* The solutions are x = -9 , x = -5

Ok, the student needs 40 points and each question is worth 5, so 40/5 = 8 questions are needed.

Each question has 4 possibilities, 1 is right, so the chances to guess it correctly is one in 4, or 1/4, or 25%.

[tex]\frac{8}{20} = \frac{2}{5}[/tex]

To know the probability to pass the exam we can do:

[tex]\frac{25}{100}*\frac{2}{5} = 10%[/tex]

Answer: 0.102 or  10.2%.

Step-by-step explanation:

Given : Number of multiple-choice questions = 20

Number of options in any question=4

Each question is worth 5 points and only one response per question is correct.

Probability of getting a correct answer =  [tex]\dfrac{1}{4}=0.25[/tex]

If the student needs at least 40 points to pass the test, that mean he needs at-least [tex]\dfrac{40}{5}=8[/tex] questions correct.

Let x denotes the number of correct questions .

By using binomial distribution , we find

[tex]P(x\geq8)=1-P(x<8)\\\\ =1-P(x\leq7)\\\\=1-0.898\ \ \text{[By using binomial table for n= 20 , p=0.25 and x=7]}\\\\=0.102[/tex]

[Binomial table gives the probability [tex]P(X\leq x)=\sum_{x=0}^c^nC_xp^x(1-p)^{n-x}[/tex] ]

Hence, the probability the student passes is closest to 0.102 or 10.2%.

Answer:

12.85 cm

Step-by-step explanation:

Area ratio of 49:36 means a side length ration of 7:6.

7/6 = 15/x

7x = 90

x = 90/7

= 12.85

Answer: 12.85 cm

Step-by-step explanation: