Complete the regression equation below.
F(x)=

Answer: The probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students from among ten students of which four are not of legal age is 0.288 or 28.8%.

Step-by-step explanation:

he probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated using the binomial probability formula.

The binomial probability formula is: P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where:

x = the number of successful outcomes (in this case, the number of minors refused service)

n = the total number of trials (in this case, the number of IDs checked)

p = the probability of a successful outcome in a single trial (in this case, the probability that a randomly chosen student is a minor)

In this case:

x = 3 (the number of minors refused service)

n = 5 (the number of IDs checked)

p = 4/10 (the probability that a randomly chosen student is a minor)

So, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated as:

P(3) = (5 choose 3) * (4/10)^3 * (6/10)^2 = (10/3) * (0.16) * (0.36) = 0.288

Therefore, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students is 0.288 or 28.8%.

It's worth noting that this problem assumes that the waitress randomly chooses the 5 students, if the waitress doesn't pick them randomly the result may be different.

Answer:

y = 5/4x - 8

Step-by-step explanation:

first you convert the equation to y = mx + b

then you add the the -8 into the x and the 2 into the y and solve for b

b = -8 and since it is parallel same slope.

hope this helps :)

Answer:

5

Step-by-step explanation:

We will use the Pythagorean theorem to solve this problem. We know [tex]a^{2} + b^{2} = c^{2}[/tex]. (a, in this case, will be c) Now, we can substitute in our numbers, giving us:

[tex]a^{2} + 12^{2} = 13^{2}[/tex]

Simplifying:

[tex]a^{2} + 144 = 169[/tex]

Subtract 144 from both sides gives us:

[tex]a^{2} = 25[/tex]

Square rooting both sides gives us:

[tex]a = 5[/tex]

So, the missing measurement (c) is 5.

Hope this helped!

The percentage of  mass of Cs in the sample is 25%

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage, indicates hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

To calculate the percentage of  Cs in the sample

100/400 x 100

=25%

To calculate the percentage of cesium (Cs) in the sample

300/400 x 100

=75%

Hence, 25% is the percentage of  Cs in the sample

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Answer:

You can buy 17 oranges for rupee 24.

Step-by-step explanation:

3 dozen = 3 x 12 = 39 oranges

54 ÷ 39 = 1.38461538462

1 orange = rupee 1.38

1.38461538462 x 17 = 23.5384615385

17 oranges = rupee 23.54

If you add the cost of 1 more orange it would cost more than rupee 24 so you can only buy 17 oranges for rupee 24.

Hope this helps :)

Answer:

yes b is a right answer hope it will help you and please make me brainlist

The value of x, if x is a real number and the expression, [tex]\frac{x + 2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex] is a purely imaginary number is x = -2. The correct option is option b.

b. -2

An imaginary number is a number which is obtained by finding the square root of a negative number.

The specified expression is; [tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex]

Multiplying the numerator and the denominator by the complex conjugate of the denominator, (1 - i), we get;

[tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}\times \frac{1 - \mathbf{i}}{1 - \mathbf{i}} =\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2}[/tex]

[tex]\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2} = \frac{x + (2 - x)\cdot \mathbf{i} + 2}{1 - (-1)} =\frac{x + (2 - x)\cdot \mathbf{i} + 2}{2}[/tex]

Where x is real, for the number to be purely an imaginary number, we get;

[tex]\dfrac{x + (2 - x)\cdot \mathbf{i} + 2}{2} = \dfrac{x +2+ (2 - x)\cdot \mathbf{i} }{2} = \dfrac{0+ (2 - x)\cdot \mathbf{i} }{2}[/tex]

[tex]\frac{0+ (2 - x)\cdot \mathbf{i} }{2} = \frac{(2 - x)\cdot \mathbf{i} }{2} = \frac{(2-x)}{2} \cdot \mathbf{i}[/tex]

Therefore, for the number to be a purely imaginary number, then; x + 2 in the numerator following the multiplication of the numerator and the denominator by the complex conjugate of 1 + i, which is 1 - i, should be 0, and we get;

x + 2 = 0

x = 0 - 2 = -2

x = -2

The value of x such that the expression (x + 2·i)/(1 + i) is a purely imaginary number is; x = -2

The correct option is; b. -2

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Answer:

x = 4

Step-by-step explanation:

We can look at the hypotenuse of both the triangles to find the factor that we multiply by. (In similar triangles, corresponding sides are always in the same ratio)

Big triangle:little triangle

25:5

5:1

So, we have to multiply the corresponding side of the little triangle by 5 to get an equivalent value.

Solve for x:

3x+8 = 4(5) [ratio!!]

3x+8 = 20

(subtract 8 from both sides)

3x = 12

(divide both sides by 3)

x = 4

Thus, we have our answer!

Answer:

Step-by-step explanation:

640 - 10x^2 = (4x-10)(160 + 4x)

The factors of 640-10x^2 are (4x-10) and (160 + 4x).

Answer:

30cm

Step-by-step explanation:

it will be the root of 900cm²

=30cm

statement CBA ≅ TWR is true.

The theorem that states that two triangle is congruent when there three corresponding sides are equal and all three corresponding angles are also equal.

given, triangle ABC and Triangle RWT both are right-angled.

we examined that three corresponding sides of ABC is equal to the corresponding sides of RWT and same for the three corresponding angles.

we measured, right angle A = right angle R

base length AB = base length RW

hypotenuse BC = hypotenuse WT

Side length AC = side length RT

angle C = angle T

angle B = angle W

as per the properties of congruence theorem ABC and RWT are congruent.

hence the statement CBA ≅ TWR is true.

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Adrian must multiply his money by 1.03 to find his total balance in a year in one step.

The following calculation must be done in order to determine what Adrian should multiply his current balance by in order to find his total balance in a year in one step, assuming that no money will be added to or subtracted from the investment. Adrian invests money in an account that offers simple interest of 3% per year.

Current balance = X

Interest = 3% = 3/100 = 0.03

Interest + principal = 1.03

1.03X = Total balance in a year

Therefore, Adrian must multiply his money by 1.03 to find his total balance in a year in one step.

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Answer:

11 days

Step-by-step explanation:

It will last: 10/1 : 9/10 = 10/1 x 10/9 = 100/9 = 11,111... days

Answer: 11.1 days

Step-by-step explanation:

Everyday, Sandy uses 9/10 of a bag of cups.

Use unitary method.

9/10 bag - 1 day

10 bag - 10/(9/10) = 100/9 ≈ 11.1 days

Pls mark as brainliest. I really need for no apparent reason. Cheers

Answer:

no

Step-by-step explanation:

An identity is an equality that is always true. An equation is an equality that is (only necessarily) conditionally true.

That is to say that for any real value inputted into a variable in an identity, an equality will result, whereas only certain values for a variable in an equation will necessarily result in an equality.

If the given equation is an identity, it should result in an equality no matter what the input for k is. So, to prove that it isn't an identity, we simply have to find one value for k that results in an inequality. To do so, we can simply plug in 0 for k and simplify.

[tex]k - 4 = 4 + k[/tex]

[tex]0 - 4 \stackrel{?}{=} 4 + 0[/tex]

[tex]-4 \ne 4[/tex]

We have found one value for k that results in an inequality. Thus, this equation is not an identity.

Answer:

The answer is, 5² + 12² = AC²

This is the Pythagorean theorem which states that sum of the squares of the two sides of a right angled triangle is equal to the square of the hypotenuse.

base² + height² = hypotenuse² or in this case, 5² + 12² = AC²

Pls mark as brainliest. I really need for no apparent reason. Cheers

The perimeter of the parallelogram is greater than the perimeter of the square.

What is a perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is obtained by adding up the length of all the sides and edges of the shape. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

Now, let's assume a geometric system of a square and a parallelogram having the same base and equivalent side of the square " a ".

Therefore, the respective two parallel sides of the Parallelogram will also be equal to " a ".

Now, let's rotate the one of the parallel lines with angle Φ clockwise then, the side lengths which aren't equal and parallel to the first set will get increased and it's incremental rate will be responsible for the increase in perimeter of the figures aslike , perimeter is the sum of the sides of the figure.

Now let's rotate alternate side length at maximum at angle θ , aslike it should touch the square at diagonally opposite angles ,

Now, let's calculate perimeters of both the figures -

Square of side length " a " = a + a + a + a = 4a

Parallelogram of two base side length " a " and two parallel set lines of length √2a

= a + a + √2a + √2a

= 2a + 2√2a

= 2a [ 1 + √2 ]

Hence, the acquired perimeter of Parallelogram is greater than that of square

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The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = AC / sin B

In triangle ABC, ∠A = 25°, ∠C = 55° and AB = 60. Then the third angle is given as,

∠A + ∠B + ∠C = 180°

25° + ∠B + 55° = 180°

∠B = 100°

Then the length of BC is given as,

60 / sin 55° = BC / sin 25°

BC = 30.955

BC ≈ 31

Then the length of AC is given as,

60 / sin 55° = AC / sin 100°

AC = 72.134

AC ≈ 72

The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.

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5 raised to the fourth power (written as 5^4) is equal to 5 multiplied by itself 4 times. Mathematically, it can be written as:

5^4 = 5 * 5 * 5 * 5 = 625

So, the value of 5 to the fourth power is 625.

I hope this helps :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5^4}[/tex]

[tex]\mathsf{= 5 \times 5 \times 5 \times 5}[/tex]

[tex]\mathsf{= 25 \times 25}[/tex]

[tex]\mathsf{= 625}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{625}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

[tex]A=lw=\frac{1}{3} \cdot \frac{2}{3}=\frac{2}{9}[/tex]

Answer: To find how long it takes Kyle to reach school, we can use the formula:

Time = Distance / Speed

Given that Kyle's parents travel at a constant speed of 40 km/h and the distance from their house to school is 60 km, we can substitute these values into the formula:

Time = Distance / Speed = 60 km / 40 km/h

To convert the answer from hours to minutes we have to multiply the result by 60.

Time = (60 km / 40 km/h) * 60 = 1.5 * 60 = 90 minutes

So it takes Kyle 90 minutes to reach school from their house if their speed is constant at 40 km/h and the distance they are traveling is 60 km.

Step-by-step explanation:

Answer: 80

Step-by-step explanation:

280-47=233 people who like cats or dogs

153+138=291 people who like cats, dogs, or both

291-233=58 people who like both

People who like cats = 138-58=80

The required dilated coordinates of the quadrilateral is given as,
D'  {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G'  (-2, 2).

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
Initial corrdiantes

D = (-6, 3)
G = (-3, 3)
E = (-4, -3)
F = (5, -2)

Dilated coordinates of a quadrilateral with by scale factor of 2/3 is given as,
D' = (-6 × 2 / 3, 3 × 2 / 3)

D' = {-4, 2}

Similarly,

G = (-2, 2)
E = (-8/3, -2)
F = (10/3, -4/3)

Thus, the required dilated coordinates of the quadrilateral is given as,
D'  {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G'  (-2, 2).

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1.600 amps of current flow through resistor r3 are measured.

A resistor is a passive, two-terminal electrical component used in circuits to apply electrical resistance.

Resistors are employed in electronic circuits for a variety of purposes, including reducing current flow, adjusting signal levels, dividing voltages, biassing active devices, and terminating transmission lines.

The parameters are determined by the query:

total current = 2 amperes

Total resistance = 80 ohms

Total current = voltage * Resistance

Total current = 2* 80

= 160V.

Consequently, the current passing through resistor R3 will be

V= IR (Ohms law)

where I (current)= V/R

current = 160/ 100

Current flowing through R3 =1.600  amperes.

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Answer: 1/2 PI actually ez not gonna lie

Step-by-step explanation: We know that pi times radius squared times 45/360 equals 1/2 pi. PI*radius^2*0.125 = 1/2PI. Solve algebra to get r^2 = 4 or radius = 2. We need the diameter to find circumference. D = 2*r or D = 4. D * PI * 45/360 = answer. We get 4 * PI * 0.125 = 1/2 PI

Answer:

5/12

Step-by-step explanation:

Use associative property of addition:

2/5 + 5/12 + (-2/5) = (2/5 + (-2/5)) + 5/12  ==> switch 5/12 and -2/5

(2/5 + (-2/5)) + 5/12 =    ==> simplify

(2/5 - 2/5) + 5/12 =

0 + 5/12 = 5/12

The total number of oranges that the trader bought is 31

A trader bought some oranges at the price of #50 each

He finds that Six of these oranges are rotten

He sells the remaining at #80

He makes a profit of #450

Therefore the number of oranges that the trader bought is

Let y represent the number of oranges that the trader bought

At a price of #50= 50x

6 oranges were rotten= x-6

Profit = 450

450= 80(x-6)-50x

450= 80x-480-50x

450= 80x-50x-480

450= 30x-480

450+480= 30x

930= 30x

x= 930/30

x= 31

Hence the trader bought 31 oranges

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The total height of the building would be nh + 30.

Option (B) is correct.

What is a simplification in mathematics?

In mathematics, simplification refers to the process of making an expression or equation simpler or easier to understand or work with. This can involve combining like terms, removing unnecessary terms or factors, or rearranging the order of the terms.

The building's total height in feet is represented by the sum of the height of each floor plus the height of the spire.

So if the height of each floor is h, and there are n floors in the building and the building's spire is 30 feet, the total height of the building is:

= n * h + 30

=nh + 30

This is because the height of each floor is h, and there are n floors, so the total height of the floors is n * h. Adding the height of the spire, 30 feet, to the total height of the floors gives nh + 30.

Hence, the total height of the building would be nh + 30.

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Staff at the learning center can teach whole groups of students who need extra help or focus on working one-on-one with a specific child. They work on improving knowledge of academic subjects like biology as well as skills like reading comprehension.

Learning centre instructors work in programmes that assist at-risk students in strengthening their academic skills. Learning centre instructors can work for a private or public learning centre. Learning centre instructors work with students to teach them valuable skills and academic subjects no matter where they work.

Learning centre instructors can teach large groups of students who require extra assistance or work one-on-one with a specific child. They work on improving academic knowledge, such as biology, as well as skills, such as reading comprehension.

They are in charge of creating the overall curriculum and training programme. Learning centre instructors must also have excellent classroom management skills as well as patience in order to work with students who are experiencing difficulties.

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Step-by-step explanation:

For 60 muffins sold there are 3 boxes, because there are 20 muffins per box.

For 600 muffins sold there are 30 boxes, because there are 20 muffins per box.

For 6000 muffins sold there are 300 boxes, because there are 20 muffins per box.

Because 2×3=6