Unit 6. 2) Please help. What is the probability that a student is absent given that today is Monday?

Enter your answer as a fraction in simplest form, formatted like this: 3/14

Answer:

10

Step-by-step explanation:

We cannot use the Pythagorean Theorem here because we only have one side length. However, we can use the fact that [tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

I decided to make the corner with the 60° as ∠A, the corner with the 30° as ∠B, and the corner with the right angle as ∠C. While then making side a as the unmarked side, side b as the side with 5, and the hypotenuse p as side c.

Since we do not need to solve for a in this equation to solve for p, we can simply use the sides and numbers we are given.

Manipulating two of our equations, preferably the equations with the variables b and c, we can get [tex]\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex] and solving for c, which is p in this case, will give us [tex]c=\frac{bsin(C)}{sin(B)}[/tex]

Plugging in the numbers we have gives us [tex]c=\frac{5sin(90)}{sin(30)}[/tex] = 10 mi

Answer:

Period = 8π

Phase shift = 2π/3

Amplitude = 1/2

Vertical shift = 2

Step-by-step explanation:

y = A sin((2π/T)θ − B) + C

where A is the amplitude,

T is the period,

B is the phase shift,

and C is the vertical shift.

y = ½ sin(¼θ − 2π/3) + 2

So A = 1/2, T = 8π, B = 2π/3, and C = 2.

Answer:

The original price of the food items was 24.

Answer:

Answer: I think c,e

Answer: The students were in school and were not allowed to text

The time-span from 10 AM to 3:59 PM is when 0 messages were sent in total. This is likely the duration of either the entire school day or much of it. So it's likely the school does not allow texting or does not allow phones to be in use.

Answer:

59/20

Step-by-step explanation:

good luck 8th grade k-12-ers!

Answer: The price of a fruit bowl at the cafe is $3

Step-by-step explanation:

$3 in the price of a Fruit bowl at the cafe.

According to the given In the question,

Let,

price of a Salad = Sl

price of a fruit bowl = Fb

Fb price of a sandwich = Sd

Sl + Fb+sd=$12         ..1

2 SI + 2 Sd = $14       ..2

Sl + 3Pb Fb = $14      ..3

from equation 2

Sl = 7 - Sd

from equation 3

7 - Sd + 3Fb = 14

Sd  = 3Fb - 7

from equation 1

14- 3Fb+Fb+ 2(3Fb-7)=12

14- 2 Pb +6Fb-14=12

4Fb = 12

Fb = 3

Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.

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Answer:

On the circle

Step-by-step explanation:

The distance between D and G is:

[tex]\sqrt{(-1-(-10))^2+(3-1)^2}=\sqrt{9^2+2^2}=\sqrt{81+5}=\sqrt{86}[/tex]

If point J is not exactly this far, then it is not on the circle.

[tex]\sqrt{(-1-(-3))^2+(12-3)^2}=\sqrt{2^2+9^2}=\sqrt{5+81}=\sqrt{86}[/tex]

Therefore, it is on the circle. Hope this helps!

Answer:

C

Step-by-step explanation:

Answer:

It is actually a

Step-by-step explanation:

Answer: it’s option c

Step-by-step explanation:

Simplified form of radical 8∛(a⁴b³c²)-14b∛(ac^(2)) is -6ab∛ac².

What is radical?

The symbol '√' that expresses a root of a number is known as radical and is read as x radical n or nth root of x. The horizontal line covering the number is called the vinculum and the number under it is called the radicand. The number n written before the radical is called the index or degree.

Given radical

8∛(a⁴b³c²)-14b∛(ac^(2))

Rewriting a⁴b³c² as (ab)³ ac²

8∛((ab)³ac²)-14b∛(ac²)

8ab∛ac² - 14b∛ac²

-6ab∛ac².

Hence, -6ab∛ac² is the simplified form of 8∛(a⁴b³c²)-14b∛(ac^(2)).

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Answer:

1 = 0

12x12 = 4

100=1

I think the last one is also 1

Step-by-step explanation:

Answer:

a) 0.55% probability that exactly 4 customers have the supermarket club card.

b) 0.01% probability that at most 2 customers have the supermarket club card.

c) 87.91% probability that at least 7 customers have the supermarket club card.

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they have the supermarket club card, or they do not. The probability of a customer having the supermarket club card is independent of other customers. So we use the binoial probability distribution 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 the following formula.

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

And p is the probability of X happening.

80 percent of customers have the supermarket club card.

This means that [tex]p = 0.8[/tex]

10 customers.

This means that [tex]n = 10[/tex]

a. Exactly 4 customers have the supermarket club card.

This is P(X = 4).

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

[tex]P(X = 4) = C_{10,8}.(0.8)^{4}.(0.2)^{6} = 0.0055[/tex]

0.55% probability that exactly 4 customers have the supermarket club card.

B. At most 2 customers have the supermarket club card.

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

[tex]P(X = 0) = C_{10,0}.(0.8)^{0}.(0.2)^{10} \cong 0[/tex]

[tex]P(X = 1) = C_{10,1}.(0.8)^{1}.(0.2)^{9} \cong 0[/tex]

[tex]P(X = 2) = C_{10,2}.(0.8)^{2}.(0.2)^{8} = 0.0001[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0.0001 = 0.0001[/tex]

0.01% probability that at most 2 customers have the supermarket club card.

C. At least 7 customers have the supermarket club card.

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

[tex]P(X = 7) = C_{10,7}.(0.8)^{7}.(0.2)^{3} = 0.2013[/tex]

[tex]P(X = 8) = C_{10,8}.(0.8)^{8}.(0.2)^{2} = 0.3020[/tex]

[tex]P(X = 9) = C_{10,9}.(0.8)^{9}.(0.2)^{1} = 0.2684[/tex]

[tex]P(X = 10) = C_{10,10}.(0.8)^{10}.(0.2)^{0} = 0.1074[/tex]

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2013 + 0.3020 + 0.2684 + 0.1074 = 0.8791[/tex]

87.91% probability that at least 7 customers have the supermarket club card.

Answer:

You should expect her to be wrong 32 times.

Step-by-step explanation:

For each forecast that she makes, there are only two possible outcomes. Either she is correct, or she is not. The probability of she being correct on a forecast is independent of other forecasts. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

0.8 chance of being correct.

So 1 - 0.8 = 0.2 change of being wrong, which means that [tex]p = 0.2[/tex]

160 forecasts:

This means that [tex]n = 160[/tex]

How many of these times would you expect she is wrong?

[tex]E(X) = np = 160*0.2 = 32[/tex]

You should expect her to be wrong 32 times.

Answer:

The area which would be painted grey will be "47.7812 ft²".

Step-by-step explanation:

The given values are:

Radius of circle, r = 5.4 feet

Value of pi, π = 3.14

As we know,

Area of Semicircle = [tex]\frac{\pi r^2}{2}[/tex]

On putting the values in the above formula, we get

                               = [tex]\frac{3.14\times (5.4)^{2}}{2}[/tex]

                               = [tex]\frac{3.14\times 29.26}{2}[/tex]

                               = [tex]\frac{91.5624}{2}[/tex]

                               = [tex]45.7812 \ ft^2[/tex]

Answer:

-0.5

Step-by-step explanation:

z-score = (x- mean)/SD

(145-155)/20 = -10/20 = -0.5

Answer:

Step-by-step explanation:

z=\frac{x-\mu}{\sigma}

z=

σ

x−μ

​

z-score formula

z=\frac{155-190}{20}

z=

20

155−190

​

Plug in values

z=\frac{-35}{20}

z=

20

−35

​

Subtract

z=-1.75

z=−1.75

Divide

\text{They scored 1.75 standard deviations below the mean.}

They scored 1.75 standard deviations below the mean.

Answer:

tan Z = 3/4

Step-by-step explanation:

[tex] \tan(Z) = \frac{21}{28} \\ \tan(Z) = \frac{3}{4} [/tex]

Answer:

(D)3 units

Step-by-step explanation:

To find the value of a, we use the Theorem of Intersecting Secants.

Applying this to the diagram, we have:

UV X TV = RV X SV

12 X a=(5+4)*4

12a=9*4

12a=36

Divide both sides by 12

a=3 units.

The correct option is D.

By applying the Theorem of Intersecting Secants, the length of TV (a) is equal to: D. 3 units.

The Theorem of Intersecting Secants states that the product of a secant and its external secant is equal to the product of the other secant and its external secant, when two (2) secants are drawn to a circle from an exterior (outside) point:

In order to determine the length of TV (a), we would apply the Theorem of Intersecting Secants as follows:

UV × TV = RV × SV

12 × TV = (5 + 4) × 4

12TV = 9 × 4

12TV = 36

TV = 36/12

TV = 3 units.

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Answer:

Step-by-step explanation:

First term is 3

common difference = 15/2 divided by 3 = 5/2

8th term = a * r^7

3 * (5/2)^7 = 1,831.0546875

To the nearest thousandth 1,831.055

Answer:

Step-by-step explanation:

Given the equation sec(x)cot(x)= -2 on the interval [0,2π]. In order to get the value of x, the following steps must be followed.

sec(x)cot(x)= -2

From trigonometry identity, sec(x)= 1/cos(x) and cot(x)= 1/tan(x) = cos(x)/sin(x)

subsituting this expressions in the given equation we have;

1/cos(x)*cos(x)/sin(x) = -2

1/sin(x) = -2

sin(x) = -1/2

[tex]x = sin^{-1}-1/2\\ x = -30^{0}[/tex]

Since sin is negative in the 3rd and 4th quadrant,

In the 3rd quadrant, x = 180+30 = 210°

In the 4th quadrant, x = 360-30 = 330°

Converting the values to radian;

since 180° =  πrad

210° = 210π/180 rad

210° = 7π/6 rad

Similarly, 330° = 330π/180 rad

330° = 11π/6 rad

The solutions are 7π/6 and 11π/6

Answer:

A=264

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given a rhombus ABCD

|AB|=|DC| (Opposite sides of a rhombus are equal)

|AB|=9s+29

|DC|=10s-16

Therefore:

9s+29=10s-16

Collect like terms

10s-9s=29+16

Recall: |AB|=9s+29

|AB|=9(45)+29=405+29=434 Units

Since all the sides of a rhombus are congruent

AB=AC=BD=CD

Therefore:

|BC|=434 Units

Answer:

s=45

ab=434

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

A. 8

Step-by-step explanation:

#platolivesmatter

Answer:

central tendency is the tendency for the values of a random variable 2 cluster round it's mean,mode amdedian

Step-by-step explanation:

it's also called center/location of the distribution

Answer:

360

Step-by-step explanation:

Formula

Sides -2 ×180

4-2=2×180=360

Answer:

The perimeter of the rectangle that contains the 3 squares is 24x + 36 units

Step-by-step explanation:

Here, we have a square with side length 2x + 3

The perimeter of this square would be calculated using the mathematical formula;

P = 4L

P = 4(2x + 3) = 8x + 12 units

Now, this particular rectangle is composed of three of these squares.

The expression which would represent the perimeter of the rectangle is equal to the sum of the perimeters of the 3 squares.

That would be 8x + 12 + 8x + 12 + 8x + 12 or simply 3(8x + 12) = 24x + 36

Answer:

B

Step-by-step explanation:

the mean goes up more than the median

Answer:

The reciprocal is 1/0.75. Using a calculator, the decimal form can be found by performing the operation: 1 divided by 0.75 ...

Answer:

The answer would have four decimal places and this is because when multiplying figures with decimals, the final result (the product) usually has the combination of decimal places of all values multiplied. Since 3.93 has TWO decimal places and 0.07 has TWO decimal places as well, the product of both numbers would have a combined total of FOUR decimal places.

So the correct answer is not 4, but rather the answer is 0.2751 (with FOUR decimal places)

Step-by-step explanation:

trust.

Answer: the roots are x = 20 and x = -8

Step-by-step explanation:

We have the function

y = (1/4)x^2 - 3x - 40

We want to find the roots, that are the points in where y(x) = 0

For a quadratic equation of the form:

y = a*x^2 + bx + c the roots are:

[tex]x = \frac{-b +-\sqrt{b^2 -4*a*c} }{2*a}[/tex]

in this case we have:

[tex]x = \frac{3 +-\sqrt{3^2 +4*(1/4)*40} }{2*(1/4)}= \frac{3 +-7}{(1/2)}[/tex]

So the two roots are:

x = 2*(3 + 7) = 20

x = 2*(3 - 7) = -8

Answer:

Graph.

f(x)=5(x−1)3−2

Step-by-step explanation: