b. Express the mass of 21,000 molecules of oxygen in scientific notation.
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(Type your answer using the appropriate number of significant digits. Type you

From cosecant identity the expression cos(x)+sin(x)/ sin(x) =1+cot(x) was verified.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) ,  cos  (x) and tan  (x) , where:

sin (x) = [tex]\frac{opposite\ leg}{hypotenuse}[/tex]

cos(x)=[tex]\frac{adjacent\ leg}{hypotenuse}[/tex]

tan (x) = [tex]\frac{\frac{opposite\ leg}{hypotenuse} }{\frac{adjacent\ leg}{hypotenuse} } = \frac{opposite\ leg}{adjacent\ leg}[/tex]

The question gives the following identity:  [tex]\frac{cos (x)+sin(x)}{sin(x)}[/tex]

First, you should rewrite the identity using the cosecant  identity -                          csc(x)= 1/sin(x) . Then,

(cos(x)+sin(x)) * csc(x)

After that, you should expand the previous expression.

cos(x)*csc(x) + sin(x)  * csc(x)

cos(x)*1/sin(x) + sin(x)  * 1/sin(x)

cos(x)/sin(x) + sin(x)/sin(x)

cot(x) + 1

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Lisa's car gets 31 miles per gallon.

Thus in 22 gallons she can drive,

22x31=682 miles.

Lisa can drive 682 miles.

The actual distance between the golf vein and the farthest gold dust strike is; 79 miles.

It follows from the task content that the actual distance between both locations is to be determined.

It follows from the distance formula in coordinates geometry that;

D = √{(x2 - x1)² + (y2 - y1)²}

Therefore, the distance between the gold vein and the farthest gold dust strike is;

D = √{(-9 -(-9))² + (71 - (-8))²}

D = √79²

D = 79.

Ultimately, the distance on the graph is 79 units and since each unit on the.graoh represents 1 mile, the actual distance between the gold vein and the farthest gold dust strike is; 79 miles.

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Part D: There are more than 200,000 people in this city is the correct option

The population of the city in which Devon lives <=240000

Data interpretation: The process of examining data through some predetermined processes in order to give it some meaning and reach a pertinent conclusion is known as data interpretation. It entails using the outcomes of the data analysis to draw conclusions about the relationships that were looked at.

Part a:

According to this part, more than 300,000 people live in this city, which may be possible but we cannot be sure about it.

Part b:

According to this part more than 250,000 people live in the city, which may or may not be possible as we are sure only about 240,000 people

Part c:

According to this part, more than 245,000 people live in this city, which is again a may or may not be possible situation given the fact

Part d:

According to this part, more than 200,000 people live in the city. We are sure about this because it is estimated that 240,000 people live in the city. Hence this is the correct option

Although a part of your question is missing, you might refer to this full question: Devon lives in a city with an estimated population of 240,000 people. Which statement about this population is true?

A) There are more than 300,000 people in this city.

B) There are more than 250,000 people in this city.

C) There are more than 245,000 people in this city.

D) There are more than 200,000 people in this city

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Answer:

These points are mine :)))

Step-by-step explanation:

EXPLANATION

Let's see the facts:

Heights of 8th grade boys ---------------> Normally distributed

Mean= 50 inches

Standard deviation= 4 inches

d) Probability that boy shorter than 56 inches:

x=56

P(x<56)

We know that z-score=

Replacing terms:

P-value from Z-table =

P(x<56) = 0.93319

Answer: The probability that an 8th grade boy will be shorter than 56 inches is 0.93319*100= 93.3%.

c) Percentage of 8th grade boys that are between 56 and and 60 inches tall is:

P-value from Z-table =

P(x<60) = 0.93319

P-value from Z-table =

P(x<60) = 0.99379

Then, subtracting both probabilities.

P(56

Answer: the percentage of 8th grade boys that are between 56 and 60 inches tall is 0.0606*100 = 6.06%.

a) We have that,

According to the Empirical Rule, we can assevere that 50+- 3σ = 50+- 3*4 ---->

50 + 12 = 62 inches

50 - 12 = 38 inches

About 99.7% of 8th grade boys height will fall between 38 inches and 62 inches.

Answer: Approximately 99.7% of the heights fall between 38 inches and 62 inches.

b) According to the Empirical Rule, we can assevere that around 68% of the data will fall within one standard deviation of the mean. As we already know, the standard deviation σ is a natural yardstick for any measurements that follow a normal distribution.

So, 50 +- σ = 50 +- 4 ---->

50 + σ = 50 + 4 = 54

50 - σ = 50 - 4 = 46

Answer: About 68% of 8th grade boys height will fall between 46 inches and 54 inches.

The solution of the equation for t is t = i/pr

The equation is given as

i = prt

Divide both sides of the equation by p

So, we have the following equation

i/p = prt/p

Divide both sides of the equation by r

So, we have the following equation

i/pr = prt/pr

Evaluate the quotients

i/pr = t

Rewrite as

t = i/pr

By the above computation, we changed the subject of the formula in i = prt from i to t.

This implies that solving for t is a concept of subject of formula

Hence, the solution is t = i/pr

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7+14m

Explanation

Step 1

Let

m represents Marbel's age

Then,

the product of 14 and Mabel's age=

now, Seven more than the product of 14 and Mabel's age

then

Answer:

4

Step-by-step explanation:

put in equation form

7x - 12 = 16

solve for x

7x = 28

x = 4

Given:

Here the system of eqution is given as

Required:

Solve using the substitution method

Explanaton:

First put

in

we get

now isolate x

now put the value of x first equation

Final answer:

Solution of given system of equation by using elimination is

Solution:

Given:

The dinner bill = $21.00

The tip = 15% of the bill

Hence,

Therefore, the tip will be $3.15

Multiply the numbers and combine exponents with the same base.

We have to estimate how much he expects to make investing $4200 if he should make $12 for every $100.

We can apply the rule of three as:

Answer: he expects to make $504.

x³ is N²/15. The index form of a number is that digit written as an exponential expression or an unmarried number presented to another number.

A number's index form is that number written as an exponential expression or as a single number raised to another number. The exponent, or index, of an exponential expression indicates how many times the base must be multiplied by itself to evaluate the expression.

This fact can be used to write a number in index form. An index number is a number that has been multiplied by a power. The power, also known as the index, indicates how many times the number must be multiplied by itself. For example, 25 means multiplying 2 by itself five times

= 222222 = 32. There are several important index number rules:

ya × yb = y.

Therefore,

[tex]$x^3=\frac{N^2}{15}[/tex]

For [tex]$x^3=f(a)$[/tex] the solutions are

[tex]$x=\sqrt[3]{f(a)}, \sqrt[3]{f(a)} \frac{-1-\sqrt{3} i}{2}, \sqrt[3]{f(a)} \frac{-1+\sqrt{3} i}{2}$$$[/tex]

[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2},[/tex][tex]$x=\sqrt[3]{\frac{N^2}{15}} \frac{-1-\sqrt{3} i}{2}$$[/tex]

Simplify

[tex]$\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2}: \quad-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]

[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}-\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]

[tex]$x^3=\frac{N^2}{15}[/tex]

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ANSWER:

B. Similar - SAS

EXPLANATION:

Given:

Recall that the SAS Similarity Rule states that if two sides of one triangle are proportional to two corresponding sides of another triangle and the included angle in both triangles are congruent, then the two triangles are said to be similar.

Looking at triangles ABC and DEF, we can see that, we can see that;

Since the two corresponding sides of both triangles are in equal proportion and the included angle in both triangles are congruent, then triangles ABC and DEF are similar by the SAS Similarity Rule

In order to find the solution to this equation graphically, let's use each side of the equation as a function, and then graph both functions in the same coordinate plane:

Graphing y1 in red and y2 in blue, we have:

The intersection point between the graphs is located at (-0.26, 0.77), therefore the solution to the equation is:

The height of the ball at a horizontal distance of R meters from Kaori is H(R)=4H.

Kaori taking a free throw is a guarantee. H(d) simulates the basketball's height (in meters) at d meters of horizontal separation from Kaori.

It is said that H(R) = 4H.

In this case, H(R) displays the height of a basketball instead of H(d). Therefore, it is evident that a basketball's height is 4H since H(R)=4H at d = R.

The horizontal distance from Kaori is R because d is the horizontal distance from Kaori.

Thus the height of the ball is 4H meters at a horizontal distance of R meters from Kaori, according to the expression H(R)=4H.

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We must write the ratio 7 to 15 and reduce it to the lowest term if possible.

The ratio is:

Because 15 is not divisible by 7, we conclude that the ratio is already in its lowest form.

The system of inequalities is 1.25x + 2y >= 375 and x + y <= 500, while the smallest number of chocolate covered almonds is 400

We make use of the following representations:

x = chocolate bars

y = chocolate covered almond

Using the above as a guide, and the given parameters;

We have:

1.25x + 2y >= 375 -- the amount raised

x + y <= 500 --- number of bars sold

From the question, we have

x = 100

Substitute x = 100 in x + y <= 500

100 + y <= 500

Evaluate

y <= 400

So, the least amount to sell is 400

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The given parallelogram is a rhombus when x = 9 units

The parallelogram is a four sided plane with opposite sides parallel. So the opposite angles are equal. A parallelogram that has all angles are right angles is called rectangle.

The rhombus is a four sided plane with all of whose sides have the same length.

The sides are given,

9x-8 and 5x+28

In rhombus all the sides are equal

Then the equation will be

9x-8 = 5x+28

Rearrange the terms and solve it

9x-5x = 28+8

4x = 36

x = 36/4

x = 9

Hence, the given parallelogram is a rhombus when x = 9 units

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Given:

Find: Area of the figure.

Sol:

The area of Triangle ABH is:

Area

In triangle is:

Base = (9-3)

Height = 8

So Area of ABH is:

Area of rectangle BDFH so,

Width = 8

Step 1:

Write the equation

Step 2:

Express the equation in exponential form

Final answer

x = 4

The distance between the points (−3, −5) and (−3, −7) is 2 units.

The distance formula gives the shortest distance between two points in a two-dimensional plane.

The distance formula is a useful tool for calculating the distance between two points.

Therefore,

d = √(x₂ - x₁)²+(y₂ - y₁)²

Let's find the distance between the points (−3, −5) and (−3, −7).

Hence,

x₁ = -3

x₂ = -3

y₁ = -5

y₂ = -7

d = √(-3 + 3)² + (-7 + 5)²

d = √(-2)²

d = √4

d = 2

Therefore, the distance between the point is 2 units.

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He spent $14.44 more on groceries this week than last week

From the question, the given parameters are

Amount spent last week = $58.34

Amount spent this week = $72.78

The additional amount that was spent at the grocery store this week is calculated by subtracting the amount spent this week from the amount spent last week

This is represented as

Additional amount = Amount spent this week - Amount spent last week

Substitute the known values in the above equation

So, we have

Additional amount = 72.78 - 58.34

Evaluate the difference

Additional amount = 14.44

Hence, an additional of $14.44 was this week

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x³+2x²+4x+8=0

Rearrange

x³ + 4x + 2x²+ 8 = 0

x ( x² + 4 ) + 2( x² + 4) = 0

(x + 2) ( x² + 4) = 0

The factors are;

(x + 2) (x² + 4)

(x²+ 4) can further be simplified to give (x- 2i) (x + 2i)

Answer:

175,760,000

Step-by-step explanation:

This is the counting principle.

There are 7 positions. Multiply the number of possible characters in each position.

_ × _ × _ × _ × _ × _ × _

The numbers are from 0 to 9, so there are 10 of them.

There are 26 letters in the English alphabet.

10 × 10 × 26 × 26 × 26 × 10 × 10

Answer: 175,760,000

STEP - BY - STEP EXPLANATION

Whatto find?

• 90% confidence interval for the population proportion.

• 95% confidence interval for the ppulation proportion.

Given:

n= 800

p=0.66

q=1- p= 1- 0.66 =0.34

a) Given a 90% confidence interval,

α =1- 0.90= 0.10

b)

Given 95% confidence interal.

1- 0.95 =0.

ANSWER

a) (0.6276, 0.6324)

The contrapositive of the statement is:

Jose isn't going for a bike ride if and only if he doesn't woke up early.

What is contrapositive?

A conditional statement's hypothesis and conclusion are switched, and both are then rejected, in a contrapositive. For instance, "if not B then not A" is the opposite of "if A then B." A conditional statement's contrapositive combines the inverse and converse.

The given statement is,

Jose wakes up early if and only if he is going for a bike ride.

We divide the statement into two parts.

1. Jose wakes up early.

2. He is going for a bike ride.

The negative of the statements are,

Jose doesn't wakes up early and he isn't going for a bike ride.

Therefore, the contrapositive of the statement is,

Jose isn't going for a bike ride if and only if he doesn't woke up early.

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Solution:

Scott paid;

$13.24 for 3.41-pound bag of shrimp

This means,

$18.99 for 4.96-pound bag of shrimp

This means,

Therefore, the bag that is a better buy based on the unit price is the 4.96-pound because of the unit price which is lesser than the unit price for the 3.41-pound bag.

Thus, the 4.96-pound is a better buy.

Is his answer reasonable: No, Emtiaz's answer is not reasonable because he assumed that the rate of descent was proportional.

The average rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Next, we would determine the rate at which the skydiver falls per seconds:

Rate = time/distance

Rate = 100/0.8

Rate = 125

Also, an equation which models the height (h) of the skydiver at a 0.8 seconds is given by:

h = 125t

At 3.1 seconds, we have:

Rate = time/distance

Rate = 500/3.1

Rate = 161.3

At 1.5 seconds, we have:

Rate = time/distance

Rate = 187.5/1.5

Rate = 125

Therefore, the average rate of change at each time interval is not equal and as such Emtiaz's answer is not reasonable because the rate increases as the time increases.

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