What is the magnitude (size) of 3.7?
O A. 0.37, because 13.71 = 0.37
O B. 3.7, because 13.71 = 3.7
O C. 3.7, because 13.71 = -3.7
O D.-3.7, because 13.71 = 3.7

Answer:

(100/500) *200 =40%

Step-by-step explanation:

52s is the maximum time that she can take on her last lap and still make the team.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).

The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

We need to find the maximum time (in seconds) that she can take on her last lap and still make the team

Let x be the maximum time (in seconds) that she can take on her last lap

60=(63+62+65+58+x)/5

300=63+62+65+58+x

300=248+x

Subtract 248 on both sides

300-248=x

x=52s

Hence, 52s is the maximum time that she can take on her last lap and still make the team.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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If two parallel lines are crossed by a transversal, the value of x is option (b) x = 70 degrees

When two parallel lines are intersected by a transversal, eight angles are formed. Two of these angles are vertical angles, which are opposite angles that share the same vertex and are formed by the intersection of two lines.

Vertical angles are always congruent, meaning they have the same measure. This is a geometric property that is true regardless of the angle's degree measurement.

In this problem, one of the vertical angles is given to be 70 degrees. Therefore, the other vertical angle must also have a measure of 70 degrees. This means that the value of x, which is the measure of one of the vertical angles, is also 70 degrees.

So, correct option is (b) x = 70 degrees.

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The given question is incomplete, the complete question is:

Two parallel lines are crossed by a transversal. What is the value of x? a) x = 40 b) x = 70 c) x = 110 d) x = 130.

Answer: The shorter side = 11.83 cm

Step-by-step explanation:

The diagonal of a rectangle creates a right triangle with its adjacent sides.

Given: The diagonal and the longer side of a rectangle make an angle of 43.2°. If the longer  side is 12.6cm.

According to trigonometry,

\(\tan x=\frac{\text{Side opposite to x}}{\text{Side adjacent to x}}\)

\(\tan 43.2^{\circ}=\frac{\text{Shorter side}}{12.6 }\\\\0.93906251=\frac{\text{Shorter side}}{12.6}\\\\ \text{Shorter side}=12.6\times 0.93906251\\\\=11.832187626\approx11.83\ cm\)

Hence, the shorter side = 11.83 cm

Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer: 1 and 3

Step-by-step explanation:

I got it right on edge 2021

Answer:

1 and 3

Step-by-step explanation:

Answer:

6t + 10t - 9t

(6 + 10 - 9 ) t

7t

Step-by-step explanation:

Answer:

7t

Step-by-step explanation:

Answer:

Step-by-step explanation:

Permutation has to do with arrangement. If r objevt selected from n pool of objects are to be arranged in a straight line, this can be done in nPr number of ways.

nPr = n!/(n-r)!

If 5 people are to be chosen and arranged in a straight line, if there are 6 people to choose from, this can be done in  6P5 numbe of ways.

6P5 = 6!/(6-5)!

6P5 = 6!/1!

6P5 = 6*5*4*3*2*1

6P5  = 720 different ways

Answer:

Know the properties of vertical angles.

Step-by-step explanation:

Vertical angles are equal to each other, so we must make them equal to each other in an equation:

6x+2=80

6x=78

x=13

Answer:

Asthenosphere

Step-by-step explanation:

Answer:

The model is \(V(t)=2239+249\sin(\frac{\pi}{2}t)\).

Step-by-step explanation:

Consider the given information.

The volume of air inside the lungs increases or decreases so for this we will use the basic sine function \(B(t)=d+a\sin[b(t+ \frac{c}{a})]\) as our parent function.

Let us assume that the phase shift is 0 it means \(\frac{c}{b}=0\).

The air that moves into and out of the lungs is about 498 mL.

It means the amplitude of the function will vary by 249(half of 498).

The reserve and residual volumes of air that remains in the lungs occupy about 1990 mL which is the minimum air in the lungs.

So, the max air will be: 1990+498 =2488 mL

And the average will be d=1990+249=2239 ml

The horizontal stretch will be  \(b=\frac{2\pi}{4}=\frac{\pi}{2}\) as we know that period of \(y=\sin t\) is \(2\pi\) and respiratory cycle for an average human takes about 4 seconds.

Hence, the model is \(V(t)=2239+249\sin(\frac{\pi}{2}t)\).

The standard deviation of the distribution is given as follows:

1.3.

Before obtaining the standard deviation, first we must obtain the expected value, which is given by the sum of each value multiplied by it's respective probability, hence:

E(X) = 1 x 0.18 + 2 x 0.2 + 3 x 0.26 + 4 x 0.21 + 5 x 0.15

E(X) = 2.95.

The standard deviation is then calculated as the square root of the sum of the difference squared between each observation and the mean, multiplied by their respective probabilities, hence:

S(X) = sqrt[(1-2.95)² x 0.18 + (2-2.95)² x 0.2 + (3-2.95)² x 0.26 + (4-2.95)² x 0.21 + (5-2.95)² x 0.15]

S(X) = 1.3.

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Answer:

-a^3 -3a^2

Step-by-step explanation:

(fg) (x) = x^2 (x-3)

= x^3 - 3x^2

(fg) (-a) = (-a)^3 -3 (-a)^2

= -a^3 -3a^2

Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

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The mean of the data in the frequency distribution that includes temperature would be 52. 17 degrees.

The mean of the temperatures when given the frequency distribution can be calculated by the formula :

= ( ∑ ( Frequency x Mean of range ) ) / Total frequency

The mean is

= ( ( ( 40 + 44 ) / 2 x 3 ) + ( ( 45 + 49 ) / 2 x 5 ) + ( ( 50 + 54 ) / 2 x 12 ) + ( ( 55 + 59 ) / 2 x  6 ) + ( ( 60 + 64 ) / 2 x 3 ) ) / ( 3 + 5 + 12 + 6 + 3 )

= 1, 513 / 29

= 52. 17 degrees

It computed mean is lower than the actual mean.

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Solve for x.

2x + 9 = 33

2x = 24

x = 12

A. x = 7.5

B. x = 12

C. x = 21

D. x = 84

Answer:

\(2x + 9 = 33 \\ 2x = 33 - 9 \\ 2x = 24 \\ x = \frac{24}{2} \\ x = 12\)

Answer:

4916 pesos

Step-by-step explanation:

What we can do is set up a proportion.

1/12.29=400/x

This works because both of these fractions are dollars/pesos.

There are other proportions we could set up too.

For example:

12.29/1=x/400

12.29/x=1/400

x/12.29=400/1

However, using our orignial proportion we can simplify it.

Cross multiply.

1*x=12.29*400

x=4916

He will get 4916 pesos for his trip.

The ordered pairs are (1,0), (2,6/5),(3,12/5)

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation as y = 6x/5 - 6/5

putting (1,0) in the equation we get 6×1/5-6/5=0

Similarly we can find the ordered pair as y = 6/5x - 6/5

Hence, The ordered pairs are (1,0), (2,6/5),(3,12/5)

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The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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The price of the notebooks after adding the sales tax is $9.01.

Given that, a case of the notebooks is having a price of $8.50 before taxes, the tax is 6%, we need to find the price of the notebooks after adding the tax,

Therefore,

The price after the tax = 8.50 + 6% of 8.50

= 8.50 + 0.06 × 8.50

= 8.50 + 0.51

= 9.01

Hence the price of the notebooks after adding the sales tax is $9.01.

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1) Since in the USA 8 x 10 ^9 messages are sent every month, that means that approximately 8 billion messages are sent.

2) We can Prime factorize it:

Note that on the right side we've picked only prime numbers. In this case, 2 and 5.

So we can rewrite 8 x 10^9 as prime factors.

3) Hence, the answer is:

Answer:

a

Step-by-step explanation:

Answer:

BC = 21 cm

Step-by-step explanation:

In similar triangles the corresponding sides are in same proportion.

Its given in the sum that AC = 12 cm; DF = 20 cm and EF = 35 cm.

      \(\sf \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}\\\\\\\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\\dfrac{12}{20}=\dfrac{BC}{35}\)

     \(\sf \dfrac{12}{20}*35=BC\\\\\\\dfrac{12}{4}*7=BC\\\\\\3*7=BC\\\\ \boxed{BC = 21 cm}\)

As a ladybug on the outer surface of the Klein bottle, there is no direct path to the inside. However, you can travel along a specific type of curve called a "cross-cap curve" to reach the inside. and using topology.

To do this, start by moving along the outer surface of the Klein bottle until you reach the point directly opposite to your starting position. Then, imagine folding the surface of the bottle in half along a line that runs through this point.

This folding will create a new surface that intersects with the original surface of the bottle along a cross-cap curve. Follow this curve until you reach the inside of the Klein bottle, where the special gentleman bug is waiting for you.

It's important to note that the Klein bottle is a non-orientable surface, which means that there is no "inside" or "outside" in the traditional sense. However, the concept of inside and outside can still be useful for navigation purposes.

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Answer:

Step-by-step explanation:

STEP 1: Show the array of values.

The array is {199, 16, 186, 115, 158, 135, 186, 14, 10}

STEP 2: Determine the number of elements/values.

Here, it is 9

STEP 3: Starting from zero, assign number tags to each value.

Since the values are 9 in number, the numerical tags will be 0, 1, 2, ..., 8

mv

STEP 3: Check if the sub-array is a base case.

This sub-array has at least 2 figures or values, hence is not a base case.

STEP 4:

Answer:

6 meters

Step-by-step explanation:

7x6=42