Solve ( x – 3)( x + 2) > 0.
Solve ( x – 3)( x + 2) = 0. By the zero product property,
Make the boundary points. Here, the boundary points are open circles because the original inequality does not include equality (see Figure 1).
Select points from the different regions created (see Figure 2).
See whether the test points satisfy the original inequality.
Since x = –3 satisfies the original inequality, the region x < –2 is part of the solution. Since x = 0 does not satisfy the original inequality, the region –2 < x < 3 is not part of the solution. Since x = 4 satisfies the original inequality, the region x > 3 is part of the solution.
Represent the solution in graphic form and in solution set form. The graphic form is shown in Figure 3.
The solution set form is { x| x < –2 or x > 3}.
Figure 1. Boundary points.Figure 2. Three regions are created.Figure 3. Solution to ExampleSamir begins riding his bike at a rate of 6 mph. Twelve minutes later, Chris leaves from the same point and bikes along the same route at 9 mph. At any given time, t, the distance traveled can be calculated using the formula d = rt, where d represents distance and r represents rate. How long after Chris begins riding does he catch up to Samir?
Answer: After 24 minutes Chris begins riding so, he catch up to Samir.
Step-by-step explanation:
Since we have given that
Speed of Samir riding his bike = 6mph
Speed of Chris riding his bike = 9 mph
Time taken by Chris be x
Time taken by Samir be x+12
AS we have given that at any given time ,t, the distance traveled can be using the formula " d=rt "
where d means distance and r represents rate.
So, our equation becomes,
[tex]9x=6(x+12)\\\\9x=6x+72\\\\9x-6x=72\\\\3x=72\\\\x=\frac{72}{3}=24\ minutes[/tex]
As there is no need to change mph into miles per minutes as applying both will nullify the effect.
Hence, after 24 minutes Chris begins riding so, he catch up to Samir.
A fair coin is tossed 100,000 times. the number of heads is recorded. what is the probability that there are between 49,800 and 50,200 heads?
Using normal approximation: mean = 50,000, standard deviation = 500. Calculate Z-scores, find probabilities, and subtract. Result ≈ 0.3108.
To find the probability of getting between 49,800 and 50,200 heads when a fair coin is tossed 100,000 times, we can use the normal approximation to the binomial distribution since the number of trials is large.
The mean (μ) of a binomial distribution is given by n*p, where n is the number of trials and p is the probability of success (getting heads for a fair coin). In this case, n = 100,000 and p = 0.5, so μ = 100,000 * 0.5 = 50,000.
The standard deviation (σ) of a binomial distribution is given by sqrt(n*p*(1-p)). For this problem, σ = sqrt(100,000 * 0.5 * 0.5) = sqrt(25,000) = 500.
Now, we can use the normal distribution to approximate the probability of getting between 49,800 and 50,200 heads:
Z1 = (49,800 - μ) / σ = (49,800 - 50,000) / 500 = -0.4
Z2 = (50,200 - μ) / σ = (50,200 - 50,000) / 500 = 0.4
Now, we look up the corresponding probabilities for Z1 and Z2 in the standard normal distribution table (or use a calculator):
P(Z < -0.4) ≈ 0.3446
P(Z < 0.4) ≈ 0.6554
So, the probability of getting between 49,800 and 50,200 heads is approximately P(49,800 ≤ X ≤ 50,200) = P(-0.4 ≤ Z ≤ 0.4) = P(Z < 0.4) - P(Z < -0.4) ≈ 0.6554 - 0.3446 ≈ 0.3108.
Therefore, the probability is approximately 0.3108.
In England, mass is measured in units called stones. One pound equals 1/14 of a stone. A cat weighs 3/4 stone. How many pounds does the cat weigh?
Evaluate the expression 8√8.41 +1.8
The value of the expression is 25
What is an expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given is an expression, 8√8.41 +1.8
8√8.41 +1.8
= 8×2.9 + 1.8
= 23.2 + 1.8
= 25
Hence, the value of the expression is 25
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The approximate value of the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex] is 25.016.
To evaluate the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex], follow these steps:
1. First, approximate the square root of 8.41. The square root of 8.41 is approximately 2.902, because [tex]\( 2.902^2 \approx 8.41 \)[/tex].
2. Now, multiply this approximate square root by 8:
[tex]\[ 8 \times 2.902 \approx 23.216 \][/tex]
3. Finally, add 1.8 to this result:
[tex]\[ 23.216 + 1.8 \approx 25.016 \][/tex]
Therefore, the approximate value of the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex] is 25.016.
The answer is: 25.016.
Perform the indicated operation. 5 1/6 – 2 2/3
2 1/3
2 1/2
2 1/6
5 1/6 - 2 2/3
convert to improper fractions:
5 1/6 = 31/6
2 2/3 = 8/3
find common denominator:
8/3 = 16/6
31/6 - 16/6 = 15/6
15/6 = 2 3/6 = 2 1/2
Find the sum of (x+5)and(2x+3)
Answer:
3x + 8
Step-by-step explanation:
We have to find the sum of (x+5)and(2x+3).
Write it in sum form
x+5+2x+3
Group the like terms first.
(x+2x)+(5+3)
Combine the like terms
(1+2)x+8
= 3x +8
Therefore, the sum is 3x + 8
The sum of (x+5) and (2x+3) is calculated by adding the coefficients of like terms, which results in 3x + 8.
Explanation:To find the sum of (x+5) and (2x+3), you simply need to add the like terms. The first step is to add the terms that contain the variable x, and then add the constant terms.
Step 1: Add the x terms together: x + 2x = 3x.
Step 2: Add the constant terms together: 5 + 3 = 8.
Step 3: Combine the results from step 1 and step 2 to get the final sum: 3x + 8.
Therefore, the sum of (x+5) and (2x+3) is 3x + 8.
The difference of two supplementary angles is 32 degrees. what are the angles
Find a number such that one-half of the number is 2 less than two-thirds of the number
Two or more expressions with an Equal sign is called as Equation. The number is 16 in sentence one-half of the number is 2 less than two-thirds of the number
What is Equation?
Two or more expressions with an Equal sign is called as Equation.
We x be the unknown number which we have to find.
Given,
one-half of the number is 2 less than two-thirds of the number
Which is one-half of the number is x/2
2 less than two-thirds of the number is 2/3 x-2
So let us form a equation
x/2 = 2x/3-2
x/2=(2x-6)/3
Apply cross multiplication
3x=2(2x-6)
Use distributive law on RHS
3x=4x-16
16=4x-3x
16=x
Hence the number is 16 in sentence one-half of the number is 2 less than two-thirds of the number
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|+2|=4 Solve the equation step by step
Which is correct regarding the statement: “If x is an odd integer, then the median of x , x + 2, x + 6, and x + 10 is an odd number”
A.) the statement is sometimes true
B.) the statement is always false
C.) the statement is always true
D.) there is not enough information provided to answer the question
The sum of two consecutive odd integers is 244. what is the smaller integer? (1 point) 119 125 123 121
please help me thanks!!
Find all solutions to the equation 2sinθ-sqrt3=0 write your answer in radians in terms of π
Circle the letters of the parallel lines.
a. y = - 2/3 x +2
b. y = 2/3 x + 2
c. y =
Determine whether each variable is qualitative, continuous, or discrete. size is a ▼ variable. screen type is a ▼ variable. number of channels availablenumber of channels available is a ▼ qualitative discrete continuous variable.
Size is a continuous variable that can take on any value within a finite or infinite interval. Screen type is a qualitative variable that describes a characteristic of the data. Number of channels available is a discrete variable because it can only take on countable, distinct values.
Explanation:In statistics, variables can be classified into different types. Size would be a continuous variable because it can take on any value within a finite or infinite interval. For example, the size of a TV screen can be 32.1 inches, 32.2 inches, 32.25 inches, and so on. On the other hand, screen type would be a qualitative variable because it describes a quality or characteristic of the data, such as LED, LCD, or Plasma. Finally, number of channels available is a discrete variable because it can only take on countable, distinct values. For instance, you could have 200, 300, or 400 channels, but not 300.5 channels.
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I gave 3 packs of baseball cards to my friends. Each friend got 1/3 of a pack. How many friends got baseball cards
help. what's 400-20 + 40 divided by 2 + 210 = ?
Answer:
420
Step-by-step explanation:
400 - 20 = 380 + 40 = 420 ÷ 2 = 210 + 210 = 420.
Hey there!
400 - 20 + 40 ÷ 2 + 210
400 - 20 = 380
380 + 40 ÷ 2 + 210
40 ÷ 2 = 20
380 + 20 + 210
380 + 20 = 400
400 + 210 = 610
Answer: 610 ✅
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At the family reunion there were 15 more family members there this year than at the last family reunion. There were 46 people at this year’s family reunion. How many family members came to the last family reunion? Write a paragraph explaining what strategy or strategies could be used to solve this problem. Be sure to include a way in which a variable equation could be implemented:
31 people came last year, I know this because I removed 15 from 46 which equals to 31. This can be done in many ways either by subtraction or by finding the value of x. So, we all know that 31+x = 46 to find the value of x we have to add 15. So, 31+15 = 46 therefore the answer is 31 people came last year.
Hope this helps!
The measure of an angle is 1414 the measure of its complement. find the measure of each angle.
The angle is 14 times its complement, resulting in one angle being 84 degrees and its complement being 6 degrees, following the principle that complementary angles sum up to 90 degrees.
Explanation:The question mentions that the measure of an angle is 1414 times the measure of its complement. However, this seems to be a typo, and the correct interpretation might be that the angle is 14 times the measure of its complement. First, let's clarify that complementary angles sum up to 90 degrees. If we call the angle A and its complement C, then A = 14C. Knowing that A + C = 90, we can substitute the first equation into this to find C.
To find the measure of the angles, let's denote the measure of one angle as x and the measure of its complement as 90 - x (complementary angles add up to 90 degrees).
Given that x = 14 times the measure of its complement, we can set up the equation x = 14(90 - x) to solve for x. By solving this equation, we find that x = 70 degrees and 90 - x = 20 degrees. Therefore, the measure of the angle is 70 degrees and the measure of its complement is 20 degrees.
Therefore, A + C = 90 becomes 14C + C = 90, simplifying to 15C = 90. Solving for C gives C = 90 / 15, which equals 6 degrees. Subsequently, A, being 14 times C, is 14 * 6 = 84 degrees. Thus, the two angles are 84 degrees and 6 degrees.
Elizabeth brought a box of donuts to share. there are two-dozen (24) donuts in the box, all identical in size, shape, and color. threethree are jelly-filled, 55 are lemon-filled, and 1616 are custard-filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting a custardcustard-filled donut followed by a jellyjelly-filled donut.
Drawn
two arrays that represent 12
An array can be utilized to represent the multiplication of two numbers in Mathematics. In this representation, the number 12 can be depicted by a 3x4 or 2x6 arrays. There can be various arrays to represent a number such as 12.
Explanation:In mathematics, specifically in multiplication, arrays are often used to represent and visualize the multiplication of two numbers. The number 12 can be represented by an array in multiple ways, here we will use two ways:
A 3 rows by 4 columns array, which represents the equation 3 times 4 equals 12. You have 3 rows and 4 columns, so when you count every spot where a row and column intersect, you get 12.A 2 rows by 6 columns array, which represents the equation 2 times 6 equals 12. You have 2 rows and 6 columns, if you count every intersection, you get 12.
Remember, for any number, there can be multiple arrays that represent it. For the number 12, for instance, other arrays such as 1 row by 12 columns (1x12) or 12 rows by 1 column (12x1) are possible as well.
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Solve 1/r =1/r1+1/r2 for R
The solution of an equation 1/r =1/r1+1/r2 for R is r = r1 r2/(r1 + r2).
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We have been given a equation as
1/r = 1/r1 + 1/r2
Let r1 = x and r2 = y for an instance, then solve for equivalent r.
Therefore,
1/r = 1/x + 1/y
Solving further;
1/r = (y + x)/xy
Or
r = xy/(x +y)
Now substitute the real values of x and y, we get;
r = xy/(x +y)
r = r1 r2/(r1 + r2)
Hence, The solution of an equation 1/r =1/r1+1/r2 for R is r = r1 r2/(r1 + r2).
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A light on a computer comes for 26700 microseconds is 10-6 seconds.
Workout the length of time ,in seconds,that the light is on.
A) in standard form,
B)as a decimal
A) In standard form, the length of time the light is on is [tex]2.67 \times 10^{-2} \text{ seconds}[/tex]
B) As a decimal, the length of time the light is on is [tex]0.0267 \text{ seconds}[/tex]
Step 1: Understanding the conversion
1 microsecond ([tex]\mu s[/tex]) is equal to [tex]10^{-6}[/tex] seconds.Therefore, 26700 microseconds is equal to [tex]26700 \times 10^{-6}[/tex] seconds.Step 2: Converting microseconds to seconds
First, let's calculate the time in seconds as a decimal:
[tex]26700 \times 10^{-6} = 0.0267[/tex]
Step 3: Converting seconds to standard form
Standard form (also known as scientific notation) expresses numbers as a product of a number between 1 and 10 and a power of 10.
Here, [tex]0.0267[/tex] can be written as:
[tex]2.67 \times 10^{-2}[/tex]
If g(x) = 3x is graphed on a coordinate plane, what is the y-intercept of the graph?
A. 0
B. 1
C. 2
D. 3
The y - intercept of the line is 0.
We have f(x) = 3x
We have to find the y - intercept of this function f(x).
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to question, we have -
f(x) = 3x
or
f(x) = 3x + 0
Comparing it with the general equation of a straight line, we get -
y = f(x)
m = 3
c = 0
Here, c is the y - intercept of the line f(x) = 3x.
Hence, the y - intercept of the line is 0.
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A manufacturer of bicycles has 4802 wheels, 2299 frames, and 2249 handlebars. (a) how many bicycles can be manufactured using these parts?
The length of rectangle is 6 feet greater than the width. the perimeter is 40 ft. find the dimensions of the rectangle.
If the length of a rectangle is 6 ft greater than the width and the perimeter is 40 ft , then the dimensions of the rectangle will be 6ft x 7ft.
What is the Area of Rectangle?
The area of the rectangle is length times of width.
Let the Length and Width of the rectangle be 'L' and 'B' , then the dimensions of the rectangle will be L x B
Given data , we have L = 6 + B
The perimeter of the rectangle = 40 ft
= 2 x ( L + B ) = 40 ft
= 2 x ( 6 + B + B ) = 40 ft
= ( 6 + 2B ) = 20 ft
Substract both sides by 6
2B = 14 ft
Divide both sides by 2
B = 7 ft
Now , Length of the rectangle will be L = 6 + 7 = 13 ft
Hence, the dimensions of the rectangle is Length x Width = 13 ft x 7 ft
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Humans can hear sounds with frequencies up to 20,000 Hz, while dolphins can hear sounds as high as 150,000 Hz. Write these numbers in scientific notation.
Humans can hear up to 20,000 Hz, written as 2.0 x 10⁴ Hz in scientific notation, while dolphins can hear up to 150,000 Hz, written as 1.5 x 10⁵ Hz.
Humans can hear sounds with frequencies up to 20,000 Hz, while dolphins can hear sounds as high as 150,000 Hz. These numbers can be written in scientific notation as follows:
20,000 Hz = 2.0 x 10⁴ Hz
150,000 Hz = 1.5 x 10⁵ Hz
Writing these frequencies in scientific notation helps simplify and understand large numbers easily.
I need help on number 97 please
since gecko is 1/ the length of an iguana,
that would mean iguanas are twice as long as geckos
so 4*2 = 8 inches for iguanas
Anybody know this one?
What radius of a circle is required to inscribe an equilateral triangle with an area of 15.588 in2 and an altitude of 5.196 in? (round to nearest tenth)
Area of triangle = 1/2 base x height
15.588 = 1/2 * base x 5.196
15.588 = base x 2.598
base = 15.588 / 2.598 = 6
equi center of triangle = 1/3*5.196 = 1.732
radius of circle = Sqrt(1.732^2 + 3^2) =
sqrt (2.999824 +9) =
sqrt(11.999824) = 3.464
rounded to nearest tenth = 3.5 inches
The radius of the circle required to inscribe an equilateral triangle with the given dimensions is; radius = 3.5 inches
Usually, when we inscribe an equilateral triangle in a circle, the distance from the centroid of that triangle to one of the vertices is;
Centroid distance to vertex = ²/₃h
Where h is the altitude of the triangle.
We are given altitude = 5.196 in
Thus;
Centroid distance to vertex = ²/₃(5.196)
⇒ 3.464 inches
Approximating to the nearest tenth gives;
Centroid distance to vertex = 3.5 inches
Now, the distance from centroid to vertex of the inscribed equilateral triangle is also the radius of the circle.
Thus; radius = 3.5 inches
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