Question 9 Use the Law of Cosines to find the missing angle. Find mA to the nearest tenth of a degree. с 22 17 B O 33.9⁰ O 57.7° O 46.3° O 85.7⁰ 30 A

There is a 0.044% probability of having exactly 8 boys in a sample of 10 births.

Simply put, the probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2 (a head or tail).

P(heads) = 1/2 is what we write.

So, X is the proportion of boys among n particular births. Let p represent the likelihood of having a boy at a certain birth.

Here n=10.

Additionally, because male and female births are equally likely, there is a 50% chance of having a boy or a girl.

P(Boy) = P(girl) = 0.5

p = 0.5

Based on the information provided, there will be a defined number of trials (n) of 10, with a constant chance of success (p).

Furthermore, every trial stands alone from the others.

So, with n=10 and p=0.5, X follows a binomial distribution.

The following is the probability function of the binomial distribution for the k number of successes, where x = k.

\(\mathrm{P}(\mathrm{X}=\mathrm{k})=(10 C k) 0.5^k(1-0.5)^{10-k}\)

Finding the likelihood of 8 boys in n=10 births is necessary.

P(X=8) = (10C8)0.5⁸(1-0.5)¹⁰⁻⁸

= 45 × 0.0039 × 0.25

P(X = 8) = 0.0438

Therefore, there is a 0.044% probability of having exactly 8 boys in a sample of 10 births.

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Answer:

x = 25%

Step-by-step explanation:

At the first sale of 25% off, the handbag price dropped from $400 to $300. This is because (400 x 0.25 = 100) and (400 - 100 = 300) Therefore, the selling price of the handbag after one sale was $300.

At the second sale of 25% off, the handbag price dropped from $300 to $225. This is because (300 x 0.25 = 75) and (300 - 75 = 225). Therefore, the selling price of the handbag after two sales is $225.

The value of x remained the same for both sales. x = 25% or 0.25

Step-by-step explanation:

(-37)-(-38)

=(-37)+38

=1

Based on the type I error, if a hypothesis test leads to the probability of a type I error decreasing, then the a. probability of incorrectly accepting the null hypothesis decreases.

A type I error refers to when we are are engaged in a hypothesis test and end up rejecting the Null hypothesis even though it is true.

If we are in hypothesis tests and the probability of a type 1 error decreases, then it means that the probability of us correctly rejecting the null hypothesis when it is false increases.

It also means that the probability of us correctly accepting the null hypothesis when it is true increases as well.

This can further be said as the probability of us accepting the null hypothsis when it is false, decreases. There are therefore less chances of us incorrectly accepting the null hypothesis.

Options for this question include:

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Answer:

since , 9^x / 9^3 = 9^5

and since there is a law for exponents that says if the bases of the exponent are equal and divided by each other we subtract the exponents

, so 9^x-3 = 9^5

then x-3 =5 , therefore the final answer will be X= 8 .

Answer: 4x+20

Step-by-step explanation:

4x5=20

4x1x=4x

One example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.

Therefore, one example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.

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The correct question is given below:
A researcher is interested in the sleeping habits of students at the local state college. The average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a ____.

Answer:

domain: ( 3,6,6)

range : (b,a,d)

Answer:

The mass of the 30,000 molecules is 1.59\times 10^{-18}1.59×10

−18

Given that,

There are 30,000 molecules.

And, the mass of one molecule of oxygen i.e. 5.3\times 10^{-23}5.3×10

−23

gram.

Based on the above information, the calculation is as follows:

\begin{gathered}= 30,000 \times 5.3\times 10^{-23}\\\\= 3\times10^4 \times 5.3\times 10^{-23}\\\\= 15.9\times 10^{-23+4}\\\\= 15.9\times 10^{-19}\\\\= 1.59\times 10^{-19}\times 10\\\\= 1.59\times 10^{-18}\end{gathered}

=30,000×5.3×10

−23

=3×10

4

×5.3×10

−23

=15.9×10

−23+4

=15.9×10

−19

=1.59×10

−19

×10

=1.59×10

−18

Therefore we can conclude that the mass of the 30,000 molecules is 1.59\times 10^{-18}1.59×10

−18

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Answer:

see below

Step-by-step explanation:

second one

fourth one

Answer:

64

Step-by-step explanation:

23

41

____

 6 4

The circulatory system is responsible for carrying blood throughout the body, delivering oxygen, nutrients, and removing waste products. The heart is the organ that pushes blood through the body.

The circulatory system plays a crucial role in the human body by transporting blood, which is essential for the delivery of oxygen, nutrients, hormones, and other vital substances to different tissues and organs. It also helps remove waste products such as carbon dioxide and urea. Blood flows through a network of blood vessels that include arteries, veins, and capillaries.

The heart, located in the chest, acts as the central pump of the circulatory system. It contracts and relaxes rhythmically to push blood through the blood vessels. The heart consists of four chambers: two upper chambers called atria, and two lower chambers called ventricles. The atria receive blood returning to the heart, while the ventricles pump blood out of the heart and into the circulation.

With each heartbeat, blood is pumped from the heart into the arteries, which carry oxygen-rich blood away from the heart to the body's tissues. The arteries gradually branch into smaller blood vessels called arterioles, which further divide into tiny vessels known as capillaries. Capillaries allow for the exchange of oxygen, nutrients, and waste products between the blood and surrounding tissues. Oxygen-depleted blood returns to the heart through veins, which progressively merge into larger vessels. Finally, the blood is pumped from the heart to the lungs through the pulmonary artery to be oxygenated and then returns to the heart through the pulmonary vein. The circulatory system is responsible for the distribution of blood throughout the body, and the heart acts as the pump that propels blood through the blood vessels.

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Answer:

1. The value of the variable, y is 11

2. (B) QRS is congruent to segment (E) ΔWXY by the hypotenuse leg congruency criteria

Step-by-step explanation:

1. The lengths of the sides of the given triangles ABC are  AB = 14, BC = 27, AC = 19, and ∡A = 32°

The lengths of the sides of the given triangle FGH, FG = 14, GH = 19, FH = 2y + 5, ∡G = 32°

From the given parameters, we have;

Segment AB (AB = 14) is congruent to segment FG (FG = 14)

Segment AC (AC = 19) is congruent to segment GH (GH = 19)

Angle ∡A (∡A = 32°) is congruent to angle ∡G (∡G = 32°)

∴ ΔBAC is congruent to ΔFGH by the Side-Angle-Side rule of congruency

Therefore, segment BC is congruent to segment FH by Congruent Parts of Congruent Triangle are Congruent, CPCTC

Segment BC = Segment FH by definition of congruency

∴ 27 = 2·y + 5

2·y + 5 = 27

2·y = 27 - 5 = 22

y = 22/2 = 11

y = 11

The value of the variable, y = 11

2. For option A. the vertices of triangle ABC are A(-7, 4), B(-4, 1), C(-2, 5)

The length of the sides are;

The length of side AB = √((-4 - (-7))² + (1 - 4)²) = 3·√2

The length of side BC = √((-4 - (-2))² + (1 - 5)²) = √20

The length of side AC = √((-2 - (-7))² + (5 - 4)²) = √26

For option B. the vertices of triangle QRS are Q(3, -4), R(3, -1), S(7, -1)

The length of the sides are;

The length of side QR = √((3 - 3)² + ((-4) - (-1))²) = 3

The length of side RS = √((7 - 3)² + (-1 - (-1))²) = 4

The length of side QS = √((3 - 7)² + ((-4) - (-1))²) = 5

For option C. the vertices of triangle DEF are D(-2, 6), E(1, 3), F(3, 7)

The length of the sides are;

The length of side DE = √(((-2) - 1)² + (6 - 3)²) = 3·√2

The length of side EF = √((3 - 1)² + (7 - 3)²) = √20

The length of side DF = √((3 - (-2))² + (7 - 6)²) = √26

For option D. the vertices of triangle TUV are T(-6, -5), U(-6, 1), V(4, 1)

The length of the sides are;

The length of side TU = √(((-6) - (-6))² + ((-5) - 1)²) = 6

The length of side UV = √(((-6) - 4)² + (1 - 1)²) = 10

The length of side TV = √(((-6) - 4)² + ((-5) - 1)²) = 2·√34

For option E. the vertices of triangle WXY are W(-6, 4), X(-6, 1), Y(-2, 1)

The length of the sides are;

The length of side WX = √(((-6) - (-6))² + (4 - 1)²) = 3

The length of side XY = √(((-6) - (-2))² + (1 - 1)²) = 4

The length of side WY = √(((-6) - (-2))² + (4 - 1)²) = 5

Therefore;

Segment QR of ΔQRS is congruent to segment WX of ΔWXY

Segment RS of ΔQRS is congruent to segment XY of ΔWXY

Segment QS of ΔQRS is congruent to segment WY of ΔWXY

Whereby QS and WY are the hypotenuse side of ΔQRS and ΔWXY respectively, because QS = WY = 5 = √(\(\overline {QR} ^2\) + \(\overline {RS} ^2\)) = (√(3² + 4²)

and also RS = XY, by the definition of congruency, we have;

QRS is congruent to segment ΔWXY by the hypotenuse leg congruency criteria

In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

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Answer:

Step-by-step explanation:

The Pythagorean Theorem holds for both positions.

The first configuration is an 6-8-10 right triangle.

The second configuration using the Pythagorean Theorem:

10^2 = (8-2x)^2 + (6 + x)^2

100 = 64 - 32x + 4x^2 + 36 + 12x + x^2

100 = 100 - 20x + 5x^2

5x^2 - 20x = 0  

5x(x - 4) = 0

x = 4 feet (we throw out the x = 0 solution as extraneous)

Answer:

Step-by-step explanation:

The Pythagorean Theorem holds for both positions.

The first configuration is an 6-8-10 right triangle.

The second configuration using the Pythagorean Theorem:

10^2 = (8-2x)^2 + (6 + x)^2

100 = 64 - 32x + 4x^2 + 36 + 12x + x^2

100 = 100 - 20x + 5x^2

5x^2 - 20x = 0  

5x(x - 4) = 0

x = 4 feet (we throw out the x = 0 solution as extraneous)

Answer:

192

Step-by-step explanation:

16 × LCM = 3072

LCM = 3072 ÷ 16

LCM = 192

Or, if your money is earning a 5 percent interest rate, you'll double it in 14.4 years (72 divided by 5 equals 14.4). If your money is earning a measly 1 percent interest rate, it will take you—yep, you guessed it—a whopping 72 years to double it.

Answer:

Pretty sure its C?

Answer:

128 ft³

Step-by-step explanation:

given the scale factor of 2 similar solids is a : b , then

ratio of volumes = a³ : b³

here a : b = 3 : 4

then 3³ : b³ = 3³ : 4³ = 27 : 64

let x be volume of larger solid then by proportion

\(\frac{27}{54}\) = \(\frac{64}{x}\) ( cross- multiply )

27x = 3456 ( divide both sides by 27 )

x = 128

the volume of the larger solid is 128 ft³

Answer:

B

Step-by-step explanation:

i hope this helps a bit.

The linear equation is 3x + 5y = 75. Then the value of A, B, and C will be 3, 5, and 75 respectively.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation of a line is given as

y = mx + c

where m is the slope and c is the constant.

Then we have

y = (-3/5)x + c

The line is passing through (25, 0). Then we have

25 = c

Then we have

y = (-3/5)x + 25

On simplifying, we have

5y = -3x + 75

3x + 5y = 75

Then the value of A, B, and C will be 3, 5, and 75 respectively.

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Answer:

C. Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)

Step-by-step explanation:

The student first made a mistake in step 2. In order to check if the sum of the measures of the two remote interior angles of a triangle is equal to the measure of the exterior angle, it is necessary to use the property of alternate exterior angles. Alternate exterior angles are angles that are on opposite sides of the transversal and between the same parallel lines, so they are congruent. The measure of alternate exterior angles is always equal to 180 degree. Therefore, the correct statement in step 2 is that m∠o + m∠p = 180 degrees (alternate exterior angles)

Hope this helps

Answer:

c mystify

Step-by-step explanation:

mystify means

utterly bewilder or perplex (someone).

"maladies that have mystified and alarmed researchers for over a decade"

The probability of committing type 1 error best describes notion of significance level of hypothesis test.

What is probability?

Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 represents an impossible event, and 1 represents certain event. The probability of an event is calculated by dividing number of favorable outcomes by total number of possible outcomes. Probability is used in various fields, including statistics, economics, finance, and science. It is used to make predictions, assess risk, and make informed decisions. Probability theory helps to explain random phenomena, such as the outcomes of a coin toss or the probability of a disease occurring in a population.

Complete Question:

Which one of the following best describes the notion of the significance level of a hypothesis test?

i) the probability of committing a type 1 error

ii) the probability of committing a type 2 error

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Answer:

No

Step-by-step explanation:

The answer is B. In order to create a triangle you should be able to add the two shortest sides and get the final side so this is not going to equal a triangle at all.

The SI units for the quantities you mentioned are:

1. Length: The SI unit for length is the meter (m).

2. Mass: The SI unit for mass is the kilogram (kg).

3. Time: The SI unit for time is the second (s).

4. Electric current: The SI unit for electric current is the ampere (A).

5. Amount of substance: The SI unit for the amount of substance is the mole (mol).

6. Temperature: The SI unit for temperature is the kelvin (K).

7. Luminous intensity: The SI unit for luminous intensity is the candela (cd). An angstrom (symbol: Å) is a unit of length equal to 10^(-10) meters or 0.1 nanometers. It is often used to express the sizes of atoms and molecules.

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The difference quotient for the function f(x) = 2x^2 + 4 is [(f(x + h) - f(x)) / h] = (2(x + h)^2 + 4 - (2x^2 + 4)) / h.The solution involves applying algebraic principles and operations

In order to simplify this expression, we expand and simplify the terms within the brackets. First, we expand (x + h)^2 to x^2 + 2hx + h^2. Then we substitute these values into the expression, which becomes [(2(x^2 + 2hx + h^2) + 4 - (2x^2 + 4)) / h].

we simplify the expression further by distributing the 2 to the terms inside the brackets: [(2x^2 + 4hx + 2h^2 + 4 - 2x^2 - 4) / h].Combining like terms, we can cancel out the 2x^2 and the -4: [(4hx + 2h^2) / h].

Finally, we simplify the expression by factoring out h from the numerator: [h(4x + 2h) / h].Canceling out the h terms, we are left with the simplified difference quotient: 4x + 2h.Therefore, the difference quotient (f(x + h) - f(x)) / h for the function f(x) = 2x^2 + 4 simplifies to 4x + 2h.

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Answer:

hope this helps

Step-by-step explanation:

9+6(10-7x)

=9+60-42x

=69-42x