In a library 3 out of 4 books are nonfiction. of the nonfiction books. 40% are biographies. The Library has a total of 840 books.

x>-9 is the solution of the inequality 5x + 30 > - 15

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 5x+30>-15

Five times of x plus thirty greater than minus fifteen.

Subtract 30 on both sides

5x>-45

Divide both sides by 5

x>-9

Hence, x>-9 is the solution of the inequality 5x + 30 > - 15

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Answer:

-10v([tex]v^{2}[/tex] - 5v - 4)

Step-by-step explanation:

First, we have to find the GCF

The GCF is: -10v

We factor the GCF outside, and what is left we put in the ( )

-10v([tex]v^{2}[/tex] - 5v - 4)

The number of grapes for 14 strawberries is 10

From the question, we have the following parameters that can be used in our computation:

She adds 5 grapes for every 2 strawberries.

So, we have the ratio to be

Grapes : Strawberries = 5 : 2

Multiply the ratio by 7

So, we have the following representation

Grapes : Strawberries = 10 : 14

This means that 10 grapes are required for 14 strawberries

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The experimental probability of picking a spade is 0.15 (first option)

Probability is used to determine how likely it is that a random event would happen. The odds that the event would happen has a probability value that lies between 0 and 1.

Experimental probability is based on the result of an experiment that has been carried out multiples times.

Experimental probability of picking a spade = number of times a spade was drawn / number of times the experiment was repeated

3/20 = 0.15

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The original fraction is 3/12.

The original fraction is 5/12. This can be determined by solving the equation provided. The equation states that the denominator of a fraction is 9 more than the numerator and that if the numerator is decreased by 3 and the denominator is increased by 3, the value of the fraction is 1/4. To solve, we can set up an equation, where x is the numerator and (x+9) is the denominator.

Let the original fraction be x/y

According to the given information,

y = x + 9

After making the changes,

x - 3 = 1

and

y + 3 = 4

Now, substituting the value of y from the first equation in the second equation,

x - 3 = 1

and

x + 6 = 4

Solving the above equations,

x = 3

and

y = 12

Therefore, the original fraction is 3/12.

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Answer:

A. 11.025

Step-by-step explanation:

1 Kilogram equals exactly 2.20462 pounds.

2.20462 multiplied by 5 is 11.025

The slope of the perpendicular line is the inverse reciprocal of the line on which the line is perpendicular.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x can be used to express the change in the y coordinate with regard to the change in the x coordinate.

The slope of two parallel lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other. The relationship between the slope of perpendicular lines can be represented by the formula m1 if the slopes of the two perpendicular lines are m1, m2.

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A, B, and D are some advantages of online surveys.

The advantages of online surveys are:

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The probability of having a blue in the spin is given as; 17/200.

Probability can be calculated as the ratio of the number of favorable outcomes to the number of possible outcomes in a given scenario. It is usually expressed as a decimal or a fraction between 0 and 1.

We know that in this case we are going to look at the table to see the number of times that we land a blue.

If the total number of the outcomes is 200 and the number of the expected outcomes is 17. We would have the probability as P(blue) = 17/200.

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m is usually slope

lets analyze this problem

its a linear line, meaning a straight line

i see that y, the output, increases by 4 every time x goes up 2

slope, or m, is equal to the rise/run

rise is 4, run is 2

4/2 = 2

m = 2

this means that for every x, y goes up 2

or, for every 2 x, y goes up 4

hope this helps :)

The lateral surface area of the cylinder is given by the equation

S = 1,583.36 cm²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the surface area of the cylinder be represented as S

Now , the diameter of the cylinder d = 18 cm

So , the radius of the cylinder r = 18/2 = 9 cm

The height of the cylinder h = 28 cm

And , the lateral surface area of cylinder = 2πrh

Substituting the values in the equation , we get

The lateral surface area of cylinder = 2 ( 3.14 ) ( 9 ) ( 28 )

On simplifying the equation , we get

The lateral surface area of cylinder = 504π cm²

The lateral surface area of cylinder = 1,583.36 cm²

Hence , the lateral surface area is 1,583.36 cm²

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Answer:

3x - 6

Step-by-step explanation:

Let's call the number of coins Karen has "x".

According to the information given, Bill has 6 coins fewer than two times the number of coins Karen has, so we can write the following expression for the number of coins Bill has:

Bill: 2x - 6

To find the total number of coins Karen and Bill have, we simply add the number of coins each person has:

Karen + Bill: x + (2x - 6) = 3x - 6

So the total number of coins Karen and Bill have is 3x - 6.

Answer:  the total amount of coins Bill and Karen have can be found with the following equation: 3x-6

Step-by-step explanation:

Karen has x coins

Bill's coins are twice the x, so 2x, and he has 6 fewer than that.

The equation becomes x+2x-6 which can be simplified to 3x-6.

Based on the data provided, the probability that one student studied for exactly one hour is 0.22.

When it comes to calculating the probability, we need to identify the frequency of a specific outcome (the probability a student studied for one hour) and compare it to the total outcome (total of students) as follows:

Total of students who studied for one hour: 8

Total of students: 1+8+2+5+9+7+3 = 35

Total of students who studied for one hour / total students

8/35 = 0.228 which can be rounded as 0.23 or 23% if expressed as a percentage.

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The slant height of the right cone is 24.2 units, rounded to the nearest tenth.

A right triangle's hypotenuse, or side opposite the right angle, has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean Theorem can be used to determine the slant height of a right cone. The circular base's radius is equal to its diameter times half, or 6/2 = 3 units.

The volume of the cone can be found using the formula:

V = (π/3)r²h

Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:

72π = (π/3)r²h

72π = (π/3)3²h

72π = (π/3)9h

72π = 3πh

24 = h

Using the Pythagorean Theorem, we can find the slant height as follows:

c² = a² + b²

Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:

c² = 24² + 3²

c² = 576 + 9

c² = 585

c = 24.2

Hence, the slant height of the right cone is 24.2 units, rounded to the nearest tenth.

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Check the picture below.

The value of x rounded to the nearest tenth is 10.2 units, this is found using trigonometric functions.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

The triangle is a right-angles triangle and the given angle is 22 degrees.

Taking the cosine function, we have:

cos A = adjacent side/ hypotenuse

cos (22) = x / 11

0.927 = x/11

x = 10.2

Hence, the value of x rounded to the nearest tenth is 10.2 units, this is found using trigonometric functions.

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Answer:

Larger number will be 33

Smaller number will be 24

Step-by-step explanation:

So the easiest way to go about this is to divide the each of numbers by two

57/2 = 28.5

9/2 = 4.5

so now we have two 28.5's we will add 4.5 to one and subtract 4.5 from one

28.5 + 4.5 = 33

28.5 - 4.5 = 24

Proof:

33 + 24 = 57

33 - 24 = 9

Answer:

Smaller number = 24, Larger number = 33

Step-by-step explanation:

x + (x+9) = 57 Set up equation x is the smallest number and (x+9) is he larger number

2x+9 = 57

2x = 48

x = 24

Smaller number = 24, Larger number = 33

The high temperature is a linear function of the number of days after the new year.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

Three points on the graph are given as follows:

(1, -3), (3,1) and (10,15).

The slopes, calculated as the change in y divided by the change in x, for each of the intervals is given as follows:

Due to the constant slopes, the relationship is in fact a linear function.

The problem asks if the high temperature in this city a linear function of the number of days after the new year.

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The probability that the three friends are seated next to each other is 1/420

The total number of ways to seat the 7 people is 7! To find the number of ways to seat the three friends next to each other, we need to consider the number of ways to seat the other 4 people around them. So the number of favorable outcomes is 4!

The probability that the three friends are next to each other is then given by the ratio of the number of favorable outcomes to the total number of outcomes: (4!)/(7!) = 4!/5040 = 1/420.

So the probability that the three friends are seated next to each other is 1/420.

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Answer:

56.27⁰

Step-by-step explanation:

a/sinA =b/sinB

35/sin 50⁰ = 38/sin B

cross multiply

35sinB = 38sin50⁰

sin B=29.1096/35

sinB=0.8317 find the inverse sine

angle BCA= 56.27⁰

Answer:

-10

Step-by-step explanation:

-8 + n/2 = -13

n/2 = -13 + 8

n/2 = -5

n = -5 * 2

n = -10

Hope it helps!

Answer:A quadrilateral is a polygon having four sides, four angles, and four vertices. The word 'quadrilateral' is derived from the Latin words 'quadri,' which means four, and 'latus', which means side. The above image is an example of a quadrilateral. AB, BC, CD, and DA are the four sides of the quadrilateral ABCD.

hope this helps alot<3

a) If two points on a line are A(-5,7) and B(-2,1), the rise -6, the run is of 3, and then the slope is of -2.

b) If two points on a line are A(10,-3) and B(12,9), the rise 12, the run is of 2, and then the slope is of 6.

c) If two points on a line are A(4,6) and B(8,-8), the rise -14, the run is of 4, and then the slope is of -3.5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

As the slope represents the rate of change of the output relative to the input, it is calculated as the change in the output y divided by the change in the input x, that is, the rise divided by the run.

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Answer:

Y- intercept= (0, -1)

Slope = 2/3

Step-by-step explanation:

Finding the Y-Intercept is pretty much finding the Y value when X is 0

Looking at this table, when x = 0, y is -1. Which means your y intercept is (0, -1)

To find slope, you take two points (x,y) and apply it to the slope formula. We'll do the bottom 4 since those are all nice looking numbers

[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]

plugging it in...

[tex]slope = \frac{3 - 1}{6 - 3} [/tex]

3-1 = 2 and 6-3 = 3

Keep that in fraction form

[tex]slope = \frac{2}{3} [/tex]

The probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354

Denote S= Event that a purchase bought a basic camera, then P(S)=0.32

Denote D= Event that a purchase bought a deluxe camera, then

S and D are mutually exclusive.

P(D)=1-P(S)=0.68

P(W/S)=0.4

P(W/D)=4.9

We need to calculate the probability that a randomly selected purchaser who bought an extended warranty has a basic model. By notations, this is equivalent to finding P(S/W).

P(S/W)=P(W/S)*P(S)/P(W)

Since S and D are disjoint and P(S)+P(D)=1,

P(W)=P(W∩S)+P(W∩D)

P(W)=[0.4*0.32]+[4.9*0.68]

=3.61

Hence, our required probability is: P(S/W)=P(W/S)*P(S)/P(W)

[tex]=\frac{0.4*0.32}{3.61}\\=0.0354[/tex]

Hence, the probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354

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Only one student is expected receive an A for the exam.

The 68-95-99.7 rule states that for a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean is 70 and the standard deviation is 10, so the range of scores that would be considered an "A" would be between 90 and 100.

We can calculate the number of standard deviations from the mean that the range 90 to 100 covers and use the 68-95-99.7 rule to estimate the percentage of students who would receive an "A".

For a score of 90, the number of standard deviations from the mean is (90 - 70) / 10 = 2.

For a score of 100, the number of standard deviations from the mean is (100 - 70) / 10 = 3.

So, the range of scores between 50 and 90 covers two standard deviations from the mean and between 40 and 100 covers three standard deviations from the mean. According to the 68-95-99.7 rule, 99.7% of the data falls within three standard deviations of the mean and 95% of the data falls within two standard deviations of the mean, so we would expect about (99.7% - 95%)/2 = 2.35% of the students to receive an "A".

With 50 students, we would expect approximately 50 * 0.0235 = 1.175 ≈ ` student to receive an "A". We can round up to the nearest whole number to get an estimate of 50 students.

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a) When x = 4, the function y = 4 has the greater numeric value.

b) The two equations have the same value for x = 6.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

From graph, when x = 0, y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by two, y increases by one, hence the slope m is given as follows:

m = 1/2

m = 0.5.

Meaning that the function is given as follows:

y = 0.5x + 1.

When x = 4, the value is given as follows:

y = 0.5(4) + 1

y = 3 < 4.

The two functions will have the same value when:

0.5x + 1 = 4

0.5x = 3

x = 3/0.5

x = 6.

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The probability that the average height of Canadians is less than 157 cm is 0.337.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score. A value that is one standard deviation from the mean would have a Z-score of 1.0. Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean.

Given that the standard deviation = 7cm and the mean = 160cm.

The z -score is given as:

z = x - mean / SD

z = 157 - 160/ 7

z = -3/7

z = - 0. 428

z = 0.337

P (X < 157) = P (z < -0.428)

P(X < 157) = 0.337

Hence, the probability that the average height of Canadians is less than 157 cm is 0.337.

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The formula a(7) * 1.01 represents an exponential growth model, where a(7) is the area covered by mold at week 7, and 1.01 represents a growth rate of 1% per week.

The exponential growth model is represented by the formula a(7) * 1.01, where a(7) is the area covered by mould at week 7, and 1.01 indicates a weekly growth rate of 1%.

By multiplying the area at week 7 by 1.01, we can approximate the area covered by mold at week 8.

However, it's important to note that this model assumes that the growth rate remains constant and does not account for any limiting factors such as availability of food or changes in environmental conditions.

Additionally, this model may not accurately represent the actual growth of mold, as mold growth can be complex and affected by many variables.

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The table can be completed including the Elapsed Time and Average Speed, with the assumption that the length of the entire track is 1 meters as follows;

[tex]{}[/tex]                       Time (Initial)(s)   (Final)(s)    Elapsed(s)    Average Speed (m/s

1st 1/4 of the Track  [tex]{}[/tex]  0.74           2.07        1.33               0.19

2nd 1/4 of the Track  1.40 [tex]{}[/tex]          1.09         0.31               0.81

3rd 1/4 of the Track[tex]{}[/tex]   1.60           0.95        0.65             0.38

Final 1/4 of the Track [tex]{}[/tex]1.88           0.81          1.07             0.23

Average speed is the ratio of the distance an object travels to the duration the object takes to travel.

The data in the table can be completed by plugging in the values in the following equations.

Elapsed Time = Time (Final) - Time (initial)

Average Speed = Distance traveled in the time interval/(Elapsed Time)

The values of the 1st 1/4 of the track, indicates that we get;

Elapsed Time = 2.07 - 0.74 = 1.33

The elapsed time is 1.33 seconds

Average Speed = (1/4)/1.33 = 25/133 ≈ 0.19

The Average Speed is about 0.19 m/s

The values for the 2nd 1/4 of the Track, we get;

Elapsed Time = 1.40 - 1.09 = 0.31

Elapsed Time = 0.31 s

Average Speed = (1/4)/(0.31)  = 25/31 ≈ 0.81

The Average Speed for the 2nd 1/4 is about 0.81 m/s

The 3rd 1/4 of the Track indicates;

Elapsed Time = 1.60 - 0.95 = 0.65

The Elapsed Time = 0.65 s

Average Speed = (1/4)/0.65 = 5/13 ≈ 0,38

The Average Speed ≈ 0.38 m/s

The Final 1/4 of the Track indicates;

Elapsed Time = 1.88 - 0.81 = 1.07

The Elapsed Time is 1.07 s

The Average Speed = (1/4)/1.07 = 25/107 ≈ 0.23

The Average Speed for the Final 1/4 of the Track is about 0.23 m/s

The table can be completed with the above calculated values

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