There are 20 multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points, and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. If the student needs at least 40 points to pass the test, the probability the student passes is closest to

Step-by-step explanation:

Let's say the position of the fire is point C.

Bearings are measured from the north-south line.  So ∠BAC = 55°, and ∠ABC = 60°.

Since angles of a triangle add up to 180°, ∠ACB = 65°.

Using law of sine:

190 / sin 65° = a / sin 60° = b / sin 55°

Solving:

a = 181.6

b = 171.7

Station A is 181.6 miles from the fire and station B is 171.7 miles from the fire.

Answer:

50% chance

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

There are 3 coins, and each coin has 2 possible outcomes.  So there are a total of 6 possible outcomes.

Of these 6 outcomes, 3 are heads.  Of these 3, only 1 has tails on the opposite face.

So the probability is 1/3.

We can also show this using conditional probability:

P(A|B) = P(A∩B) / P(B)  

Probability that A occurs, given that B has occurred = Probability that both A and B occur / Probability that B occurs

Here, A = tails on opposite face and B = heads.

P(A|B) = (1/6) / (3/6)

P(A|B) = 1/3

Answer:

The length is 78 feet and the width is 30 feet.

Step-by-step explanation:

The perimeter of a rectangle can be calculated with this formula:

[tex]P=2l+2w[/tex]

Where "l" is the length and "w" is the width.

Since we know that the perimeter of the playing field is 216 feet and its length is 48 feet longer than the width ([tex]l=w+48[/tex]), we can substitute them into the formula and solve for "w":

[tex]216=2(w+48)+2w\\\\216=2w+96+2w\\\\216-96=4w\\\\\frac{120}{4}=w\\\\w=30\ ft[/tex]

Finally, substitute the width into [tex]l=w+48[/tex] to find the length. This is:

[tex]l=30+48\\\\l=78\ ft[/tex]

Final answer:

To find the dimensions of the playing field, we identify the width as w feet and the length as w + 48 feet. By using the perimeter formula and solving the resulting equation, we determine that the width is 30 feet and the length is 78 feet.

Explanation:

The student is asking to find the dimensions of a rectangle given its perimeter and the relationship between its length and width. The perimeter of the rectangle is known to be 216 feet, and the length is specified to be 48 feet longer than the width.

Let's call the width w feet. Then, the length would be w + 48 feet. Since the perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width, we can set up the following equation:

2(w + w + 48) = 216

Solving this equation, we find:

4w = 120

Therefore, the width of the playing field is 30 feet. To find the length, add 48 feet to the width:

Length = w + 48 = 30 + 48 = 78 feet.

The dimensions of the playing field are 30 feet in width and 78 feet in length.

The cost to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017 is:

                   4.45 cents

Electric power costs 17.8 cents per kWh in Los Angeles in July 2017.

Now we are asked to find the cost to run  a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017.

We know that: 1 w=0.001 kW

This means that:

   1500 W= 1.500 kW

Also, it is used for 10 minutes

i.e. 1/6 hours

Hence, the electric power used to run the hair dryer is: 1.500×(1/6)

i.e. Electric power to used by hair dryer is: 0.25 kWh

Cost of 1 kwh is: 17.8 cents

This means that cost of 0.25 kwh is: 17.8×0.25

                                                        =  4.45 cents

Hence, the answer is:

                      4.45 cents

Answer:

A) 4/33 hour

Step-by-step explanation:

This is a distance = rate * time problem

We are given the distance and the rate, now we need to solve for the time:

[tex]\frac{4}{7}=4\frac{5}{7}t[/tex]

Let's change that mixed fraction into an improper one:

[tex]\frac{4}{7}=\frac{33}{7}t[/tex]

Now to solve for t we can multiply the 33/7  by its recirocal:

[tex](\frac{7}{33})\frac{4}{7}=\frac{33}{7}(\frac{7}{33})t[/tex]

Multiplying a fraction by its reciprocal = 1, so that leaves only a t on the right:

[tex](\frac{7}{33})\frac{4}{7}=t[/tex]

The 7's cancel out on the left and that leaves you with

[tex]t=\frac{4}{33}hr[/tex]

Answer:

The price is $3.36 per infinity stone

Step-by-step explanation:

we know that

Five infinity stones cost $16.80

so

To find the price of each infinity stone (unit rate) divide the total cost by five

[tex]\frac{16.80}{5} =3.36\frac{\$}{infinity\ stone}[/tex]

Answer:

a) x = 7

b) x = 2

Step-by-step explanation:

* Lets revise some facts in the circle

- If two secant segments are drawn to a circle from a point outside the

 circle, the product of the length of one secant segment and its

 external part is equal to the product of the length of the other secant

 segment and its external part.

# Example:

- If AC is a secant intersects the circle at points A and and B

- If DC is another secant intersects the circle at points D and E

- The two secants intersect each other out the circle at point C

∴ AC × CB = DC × CE , where AC is the secant and CB is its external

  part and DC is the secant and CE is its external part

* Lets solve the problem

a) There are two secants intersect each other at point outside the circle

∵ The first secant is x + 5

∵ Its external part is 5

∵ the second secant is 4 + 6 = 10

∵ Its external part is 6

∴ (x + 5) × 5 = 10 × 6 ⇒ simplify

∴ 5x + 25 = 60 ⇒ subtract 25 from both sides

∴ 5x = 35 ⇒ divide both sides by 5

∴ x = 7

* x = 7

b) There are two secants intersect each other at point outside the circle

∵ The first secant is 5 + 3 = 8

∵ Its external part is 3

∵ the second secant is x + 4

∵ Its external part is 4

∴ 8 × 3 = (x + 4) × 4 ⇒ simplify

∴ 24 = 4x + 16 ⇒ subtract 16 from both sides

∴ 8 = 4x ⇒ divide both sides by 4

∴ 2 = x

* x = 2

Answer:

Step-by-step explanation:

It’s nothing

The probability that the team will win exactly 7 matches over the course of one season is:

                         0.1977

We know that the probability of k successes out of n successes is given by the binomial distribution as:

[tex]P(X=k)=n_C_kp^k(1-p)^{n-k}[/tex]

where p is the probability of success .

Here we are asked to find the probability that the team will win exactly 7 matches over the course of one season.

Since, there are 8 matches over the course of season.

This means n=8

and k=7

and p=0.70

(Since, 0.70 probability of winning a match )

Hence, we get:

[tex]P(X=7)=8_C_7\times (0.70)^7\times (1-0.70)^{8-7}\\\\i.e.\\\\P(X=7)=8\times (0.70)^7\times 0.30\\\\i.e.\\\\P(X=7)=0.1977[/tex]

         Hence, the answer is:

                  0.1977

Final answer:

The probability that a collegiate video-game competition team with a 0.70 chance of winning will win exactly 7 out of 8 matches is approximately 25.41%.

Explanation:

The question asks to calculate the probability that a collegiate video-game competition team, which has a 0.70 probability of winning a match, wins exactly 7 out of 8 matches in a season. This scenario can be modeled using the binomial distribution formula, which is given by P(X = k) = (n C k) * p^k * (1 - p)^(n - k), where 'n' is the total number of trials (matches), 'k' is the number of successful outcomes (wins), and 'p' is the probability of a single success.

To find the probability of winning exactly 7 matches, we set n = 8, k = 7, and p = 0.70. Thus, the calculation becomes P(X = 7) = (8 C 7) * (0.70)⁷ * (0.30)¹. Calculating further, we have P(X = 7) = 8 * (0.70)⁷ * (0.30) = 0.254121. Therefore, the probability that the team will win exactly 7 matches over the course of one season is approximately 25.41%.

let's recall that a rational whose numerator and denominator are of the same degree, has a horizontal asymptote at the fraction provided by the leading term's coefficients.

so we can simply pick any two polynomials, make them the same degree and give their leading term 2 and 9 respectively.

hmmmm say for the numerator x⁴ - 3x³.... and the denominator hmm say x⁴ + 7x, so then let's give them 2 and 9 respective... so

[tex]\bf \cfrac{\stackrel{\stackrel{\textit{leading term}}{\downarrow }}{2x^4}-3x^3}{\underset{\underset{\textit{leading term}}{\uparrow }}{9x^4}+7x}\implies \stackrel{\textit{horizontal asymptote}}{y=\cfrac{2}{9}}[/tex]

Answer:

Step-by-step explanation:

Let d represent the number of dimes. Then the number of quarters is 2d-3 and the total value of the coins is ...

  0.10d + 0.25(2d-3) = 7.05

  0.60d -0.75 = 7.05 . . . . . . . simplify

  d = (7.05 +0.75)/0.60 = 13 . . . . add 0.75, divide by 0.60

  2d-3 = 2·13 -3 = 23

Brandon has 23 quarters and 13 dimes.

Answer:

481/600

Step-by-step explanation:

Since the delay is exactly 10 min, or 600 seconds, the delay must be more than 480. Taking this, the probability of it not being 480 seconds or less becomes 481/600. (Since you can't have 480)

The probability is 481/600

Since the delay is exactly 10 min, or 600 seconds, the delay must be more than 480. Taking this, the probability of it not being 480 seconds or less becomes 481/600. (Since you can't have 480)

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Learn more about Problem-solving here: brainly.com/question/13818690

#SPJ2

Answer:

[tex]y =( x +9 )\times 4[/tex]

simplified

[tex]y = 4x + 48[/tex]

Step-by-step explanation:

first know that the result would be y or f(x), because it's the function applied to x that makes it y. so its starts with either y= or, f(x)=

increasing by a number is multiplying, the word and is used for addition so

+9 ×4 will be in the equation

used PEMDAS, distribution, and combining like terms to simplify

Answer:

a_n=-\frac{1}{4 a_{n-1}

Step-by-step explanation:

The recursive formula for the geometric sequence is given by:

a_n = a_{n-1} \cdot r

where,

r is the common ratio terms

-16, 4, -1, ...

This is a geometric sequence.

Here,  and

Since,

ans so on .....

Substitute the given values we have;

⇒

Therefore, the recursive formula for the following geometric sequence is,

Answer:

[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]

Step-by-step explanation:

Formulate the recursive formula for the following geometric sequence.

{-16, 4, -1, ...}

Here the common difference of two terms are not same.

LEts find the common ratio. To find common ratio, divide the second term by first term

[tex]\frac{4}{-16} =\frac{-1}{4}[/tex]

[tex]\frac{-1}{4} =\frac{-1}{4}[/tex]

So common ratio is -1/4

Recursive formula is

[tex]A_n= A_{n-1} (r)[/tex]

'r' is the common ratio.

Recursive formula becomes

[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]

Step-by-step explanation:

First, use trig to find the height of the slide.

The slide forms a right triangle.  We know the hypotenuse is 8.80 ft, and the angle opposite of the height is 25.0°.  So using sine:

sin 25.0°  = h / 8.80

h = 3.72 ft

Converting to meters:

h = 3.72 ft × (1 m / 3.28 ft)

h = 1.13 m

Potential gravitational energy is:

PE = mgh

where m is the mass, g is the acceleration due to gravity, and h is the relative height.

At the bottom of the slide, h = 0:

PE = (63.0 kg) (9.8 m/s²) (0 m)

PE = 0 J

At the top of the slide, h = 1.13 m:

PE = (63.0 kg) (9.8 m/s²) (1.13 m)

PE =  700 J

The change is the final potential energy minus the initial potential energy.

ΔPE = 0 J - 700 J

ΔPE = -700 J

Answer:

The average rate of change is [tex]\frac{18}{5}[/tex]

Step-by-step explanation:

Given function that shows the population of a culture of cells,

[tex]P(t)=\frac{90t}{t+1}------(1)[/tex]

Where, t represents the number of weeks.

Thus, the average rate of change in the population over the interval [0,24],

[tex]m=\frac{P(24)-P(0)}{24-0}[/tex]

From equation (1),

[tex]=\frac{\frac{90\times 24}{24+1}-\frac{90\times 0}{0+1}}{24}[/tex]

[tex]=\frac{\frac{2160}{25}-\frac{0+1}{0}}{24}[/tex]

[tex]=\frac{2160}{25\times 24}[/tex]

[tex]=\frac{2160}{600}[/tex]

[tex]=\frac{18}{5}[/tex]

Answer:

n = 22

Step-by-step explanation:

We will use the formula for the present value of an ordinary annuity :

[tex]P.V.=P(\frac{1-(1+r)^{-n}}{r})[/tex]

where P = periodic payment

          r = rate per period

          n = number of periods

Given P = PMT = $400, P.V. = $8,000, i = 0.01, and we have to find n.

Now we put the values in the formula

[tex]8000=400(\frac{1-(1+0.01)^{-n}}{0.01})[/tex]

After rearranging we have

[tex]\frac{8000\times 0.01}{400}=1-1.01^{-n}[/tex]

[tex]20\times 0.01=1-1.01^{-n}[/tex]

[tex]1.01^{-n}[/tex] = 1 - 0.2

[tex]1.01^{-n}[/tex] = 0.8

Taking log on both sides

-n log 1.01 = log 0.8

[tex]n=\frac{-log0.08}{log1.01}[/tex] = 22.4257

Therefore, n = 22

So there are total 22 payments

Answer:

The logarithmic function modeled by the given table:

f(x) = log₃x

Step-by-step explanation:

Given Table:

x     f(x)

9     2

27    3

81    4

We can see that x increases as powers of 3. And f(x) is the power.

We assume that f(x) = log₃x

Checking using the table:

for x = 9

f(x) = log₃9 = 2

for x = 27

f(x) = log₃27 = 3

for x = 81

f(x) = log₃81 = 4

Hence proved.  

Answer with explanation:

For, a 3 × 3, matrix

[tex]r_{1}=(3,-2,0)\\\\r_{2}=(0,1,1)\\\\r_{3}=(2,-1,0)[/tex]

which are entries of First, Second and Third Row Respectively.

So, if written in the form of Matrix (A)

 [tex]A=\left[\begin{array}{ccc}3&-2&0\\0&1&1\\2&-1&0\end{array}\right][/tex]

⇒Adjoint A= Transpose of Cofactor of A

[tex]a_{11}=1,a_{12}=2,a_{13}=-2\\\\a_{21}=0,a_{22}=0,a_{23}=-1\\\\a_{31}=-2,a_{32}=- 3,a_{33}=3\\\\Adj.A=\left[\begin{array}{ccc}1&0&-2\\2&0&-3\\-2&-1&3\end{array}\right][/tex]

⇒≡ |Adj.A|=1 ×(0-3) -2×(-2-0)

            = -3 +4

            =1     --------(1)

⇒For, a Matrix of Order, 3 × 3,

| Adj.A |=| A|²---------(2)

[tex]|2 A^{-2}|=2^3\times |A^{-2}|\\\\=2^3\times |A|^{-2}\\\\=\frac{8}{|A^{2}|}\\\\=\frac{8}{|Adj.A|}\\\\=\frac{8}{1}\\\\=8[/tex]

                                              --------------------------------------------(Using 1 and 2)

[tex]\rightarrow|2 A^{-2}|=8[/tex]

Answer:

Step-by-step explanation:

What level of math is this?

To determine if H is a subspace, we need to check three properties: the presence of the zero vector, closure under vector addition, and closure under scalar multiplication.

1. Does H contain the zero vector of V? The answer is no, because the zero vector (0,0) does not lie in the second or fourth quadrants.

2. Is H closed under addition? The answer is no. For example, the vectors (-1, 1) from the second quadrant and (-1, -1) from the fourth quadrant would sum to (-2, 0), which is not part of either quadrant.

3. Is H closed under scalar multiplication? The answer is no, as multiplying a vector in H by a negative scalar will place it in the opposite quadrant, which is outside H. For example, the scalar -1 and the vector (-1, 1) will yield the vector (1, -1), which is not in the second or fourth quadrants.

4. Is H a subspace of the vector space V? The answer is no, because it does not meet the required properties mentioned in parts 1-3.

Answer:

C

Step-by-step explanation:

The Pythagorean Theorem tells us that

a^2 + b^2 = c^2

a = b = s because a right angle and a 45 degree angle leaves only 45 degrees which means that both acute angles are 45 degrees

c = 2

2s^2 = 2^2         Divide by 2

s^2 = 4/2

s^2 = 2                Take the square root of both sides.

sqrt(s^2) = sqrt(2)              

s = sqrt(2)

Answer:

C: square root of 2.

Step-by-step explanation:

Ignore the picture that shows option D, jcherry99's description is correct.

Answer:

A.

[tex]y - 5 = -2(x-6)[/tex]

Negative reciprocal gives you the perpendicular slope so negative reciprocal of 1/2 is -2.

Then apply point-slope form.

B. The answer is x = 6.

The midpoint of JK is

[tex]\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{8+ 4}{2}, \frac{4 + 4}{2} \right) = \left(6,4\right)[/tex]

The line that goes through JK is just a horizontal line [tex]y = 4[/tex] because the y-coordinate does not change. So its perpendicular bisector is the vertical line that goes through the x-coordinate of the midpoint, that is, [tex]x = 6[/tex].

-10x - 3 = -10 - 3x

Bring -10x to the other side by adding it to both sides

(-10x + 10x) - 3 = -10 + (-3x + 10x)

0 - 3 = -10 + 7x

-3 = -10 + 7x

Bring -10 to the oposite side by adding 10 to both sides

-3 + 10 = (-10 + 10) + 7x

7 = 0 + 7x

7 = 7x

Isolate x by dividing 7 to both sides

7/7 = 7x/7

x = 1

Hope this helped!

~Just a girl in love with Shawn Mendes

-10x-3= -10-3x

-10x+10x-3= -10x+10x-3x

-3=-3x

divide by -4 for -3 and -3x

-3/-3= -3x/-3

1=x

x= 1

check answer by using substitution method

-10x-3= -10-3x

-10(1)-3=-10-3(1)

-13=- 13

Answer is x= 1

Answer: Our required linear equation would be [tex]x+48y=148[/tex]

Step-by-step explanation:

Since we have given that

Cost of deep fried bananas on a stick = $1.00

Number of sales reached = 100 per day

Cost of deep fried bananas on a stick becomes = $2.00

Number of sales reached = 52 per day.

Let x is the number of dollars each.

Let y be the number of vendors sale.

So, we need to form the linear equation:

As we know the formula for two point slope form:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-1=\dfrac{2-1}{52-100}(x-100)\\\\y-1=\dfrac{1}{-48}(x-100)\\\\-48(y-1)=(x-100)\\\\-48y+48=x-100\\\\-48y=x-100-48\\\\-48y=x-148\\\\x+48y=148[/tex]

Hence, our required linear equation would be [tex]x+48y=148[/tex]

Answer:

[tex]\large\boxed{\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\dfrac{1}{16}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ (a+b)(a-b)=a^2-b^2\\\\\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\left(\dfrac{1}{4}\right)^2=r^2-\dfrac{1^2}{4^2}=r^2-\dfrac{1}{16}[/tex]

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

[tex]\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\dfrac{1}{16}[/tex]

Answer: 90.5%

Step-by-step explanation:

Given: Mean : [tex]\mu = 1\text{ inch}[/tex]

Standard deviation : [tex]\sigma = 0.003\text{ inch}[/tex]

The formula to calculate z is given by :-

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

For x= 0.995

[tex]z=\dfrac{0.995-1}{0.003}=-1.66666666667\approx-1.67[/tex]

The P Value =[tex]P(z<-1.67)=0.0474597[/tex]

For x= 1.005

[tex]z=\dfrac{1.005-1}{0.003}=1.66666666667\approx1.67[/tex]

The P Value =[tex]P(z<1.67)= 0.9525403[/tex]

[tex]\text{Now, }P(0.995<X<1.005)=P(X<1.005)-P(X<0.995)\\\\=P(z<1.67)-P(z<-1.67)\\\\=0.9525403-0.0474597=0.9050806[/tex]

In percent ,

[tex]P(0.995<X<1.005)=0.9050806\times100=90.50806\%\approx90.5\%[/tex]

the probability that an elevator rail will meet the specifications is about 90.5%, which is 0.9525 - 0.0475.

The student is asking for the fraction of all elevator rails produced by Smalltown Elevator that will meet the given specifications, assuming that the diameter of an elevator rail follows a normal distribution with a mean of 1 inch and a standard deviation of 0.003 inches. To meet specifications, the diameter must be between 0.995 inches and 1.005 inches.

The z-score for the lower specification limit (0.995 inches) is calculated as: (0.995 - 1) / 0.003. This gives us a z-score of -1.67. The z-score for the upper specification limit (1.005 inches) is calculated as: (1.005 - 1) / 0.003. This gives us a z-score of 1.67.

Using the standard normal distribution table, we find that the cumulative probability for a z-score of 1.67 is approximately 0.9525, and for -1.67 is approximately 0.0475. Thus, the probability that an elevator rail will meet the specifications is about 90.5%, which is 0.9525 - 0.0475.

Answer:

Step-by-step explanation:

If you simply need to identify the inequality, it is

n + 5 ≥ 12

since "sum" means to add and "at least" is the inequality sign that is greater than or equal to.

If you are solving it, then the solution set will be

n ≥ 7

Answer:

5 + n ≥ 12.

Step-by-step explanation:

Given  :  sum of five and a number n is at least 12.

To find : Write expression .

Solution : We have given sum of five and a number n is at least 12.

According to given statement :

Sum of 5 and n

5 + n

At least 12 mean the number is 12 or greater than 12

So ,

5 + n ≥ 12.

Therefore, 5 + n ≥ 12.

Final answer:

The probability of getting exactly one topping on a hamburger, when up to 7 toppings are possible and each choice is unique, is 1 in 8 or 0.125.

Explanation:

When considering the probability of getting exactly one topping on a hamburger when the toppings could range from 0 to 7, and each topping is unique, we apply the concept of theoretical probability. The scenario implies there are 8 different events that could occur - getting no toppings to getting all 7 toppings. We are interested in the event where we get exactly one topping. Since each of these events - from getting 0 toppings to 7 toppings - is equally likely, the probability of getting exactly one topping is 1 in 8 or 0.125, when expressed as a decimal number rounded to four decimal places.

Answer:

3

Step-by-step explanation:

there are two solutions in the given system of two equations:

a=10; b=7 and a=7; b=10.

|a-b|=3.