Step-by-step explanation:
a polynomial of degree n (that means the highest exponent of x is n) must have n zeroes.
in our case that means 3 zeroes.
the best way to find them is to have the factorial form of the polynomial : to see how several terms are multiplied to give us the polynomial.
the first f(x) gives us exactly that (the second f(x) is just the form with all the multiplications done) :
f(x) = x(x + 6)(x - 2)
when is the product of factors 0 ?
only when at least one factor is 0.
so, let's see,
when is x 0 ? well, x = 0.
when is (x + 6) = 0 ? x = -6.
when is (x - 2) = 0 ? x = 2.
so, the 3 zeroes are
x = -6
x = 0
x = 2
Given that is a standard normal random variable, compute the following probabilities. Round your answers to 4 decimal places.
a.
b.
c.
d.
e.
f.
The probabilities, using the normal distribution, are given as follows:
a. P(0 < x < 0.5) = 0.1915.
b. P(-1.42 < x < 0) = 0.4222.
c. P(x > 0.46) = 0.3228.
d. P(x > -0.5) = 0.6915.
e. P(x < 2.05) = 0.9798.
f. P(x < -0.70) = 0.2420.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.For a standard normal random variable, the mean and the standard deviation are given as follows:
[tex]\mu = 0, \sigma = 1[/tex]
Hence each value of x is it's own z-score.
For item a, the probability is the p-value of Z = 0.5 subtracted by the p-value of Z = 0, hence:
P(0 < x < 0.5) = 0.6915 - 0.5 = 0.1915.
For item b, the probability is the p-value of Z = 0 subtracted by the p-value of Z = -1.42, hence:
P(-1.42 < x < 0) = 0.5 - 0.0778 = 0.4222.
For item c, the probability is one subtracted by the p-value of Z = 0.46, hence:
P(x > 0.46) = 1 - 0.6772 = 0.3228.
For item d, the probability is one subtracted by the p-value of Z = -0.5, hence:
P(x > -0.5) = 1 - 0.3085 = 0.6915.
For item e, the probability is the p-value of Z = 2.05, hence:
P(x < 2.05) = 0.9798.
For item f, the probability is the p-value of Z = -0.70, hence:
P(x < -0.70) = 0.2420.
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256361225 prime factorization
Prime factors from the factors of the given numbers are as follow :
a. 256 = { 2 }
b. 361 = { 19 ]
c. 225 = { 3, 5 }
As given in the question,
Given numbers are as follow:
a. 256 b. 361 c. 225
Prime numbers are those numbers which has only two factors 1 and number itself.
Simplify given numbers to get the prime factors from the factors of the followings are as follow:
a. 256 = 16 × 16
= 2⁴ × 2⁴
= 2⁸
Prime factor of 256 = { 2 }
b. 361 = 19 × 19
19 itself is prime number.
Prime factor of 361 = { 19 }
c. 225
225 = 15 × 15
= ( 3 × 5 )²
Prime factors are { 3, 5 }
Therefore, prime factors from the factors of the given numbers are as follow :
a. 256 = { 2 }
b. 361 = { 19 ]
c. 225 = { 3, 5 }
The complete question is :
Find the prime factorization of the following:
a. 256 b. 361 c. 225
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M is the midpoint of LN. What is LM? Also what is LN?
Using the given information, the length of LM is and the length of LN is 12
Calculating lengthFrom the question, we are to determine the length of LM and LN.
From the given information,
M is the midpoint of LN
Therefore,
LM = MN
Also,
From the given information,
LM = 3x
MN = 2x + 2
Thus,
3x = 2x + 2
Solving for x
3x = 2x + 2
3x - 2x = 2
x = 2
Then,
Substitute the value of x in the equation
LM = 3x
LM = 3(2)
LM = 6
Also,
LN = LM + MN
LN = 3x + 2x + 2
LN = 5x + 2
Substitute the value of x
LN = 5(2) + 2
LN = 10 + 2
LN = 12
Hence, the value of LM is 6 and the value of LN is 12
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Consider two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.
The Two Consecutive integers are 7 and 8.
What is an integer?
A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8
Let the first Integer be x
Since the two numbers are consecutive
therefore the second number will be x+1
Now given:
square of the second integer added to 6 times the first is equal to 106.
( x+1 )²+6x=106
Expand ( x+1 )² using [tex](a+b)^2=a^2+2ab+b^2[/tex]
x²+2x+1+6x=106
x²+8x+1-106=0
x²+8x-105=0
Factor the expression
(x-7)(x+15)=0
x-7=0, x+15=0
x=7, x=-15
Now we get 2 values of x which is 7 and -15.
Since it is given that number is a positive Integer hence the number will be 7.
and the other number would 7 + 1 = 8.
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Each student in Mr. Jones's class has two standard number cubes. Each student records the number of rolls it takes until he or she rolls doubles. The results are shown on the dot plot. Based on the results, what is the probability of needing exactly 6 rolls to get doubles?
Answer:1/5
Step-by-step explanation:
it correct
Answer:
Step-by-step explanation:
Second part to the answer is 3/20
¿Como se escribe siete millones setecientos cuarenta mil novecientos treinta y dos?
Help please. Need it soon as possible
Answer:
Step-by-step explanation:
1=205
2=63
3=45
4=5
The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 15600.
(a) Find a function that models the population t years after 2000 ( t=0 for 2000).
Hint: Use an exponential function with base e.
Your answer is P(t)=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)
a. The function that models the population t years after 2000 is
Pf = 15600(1.04)^t
b. The estimate of the fox population in the year 2008 is 21349.67.
Given,
A fox population in a certain region has a continuous growth rate of 4% per year.
It is estimated that the population in the year 2000 was 15600.
we are asked to determine a function that models the popualtion t years after 2000 (t = 0 for 2000)
Pf = Pi(1 + r)^t where Pf is the final population, Pi is the initial population, r is the annual growth rate in decimal (not %), and t is the time in years.
a. Pf = 15600(1.04)^t
b. Pf = 15600(1.04)⁸ = 24497.386
= 21349.67
hence we get the required answers.
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How many subsets does the set S, seasons of the year, have? S={ Summer, Spring, Fall, Winter }.
The number of subsets that the set S , seasons of the year is 16 .
In the question ,
it is given that
the Set S have elements as the seasons of the year , that is
Set S [tex]=[/tex] { Summer , Spring , Fall , Winter }
So , the number of elements that are present in the set S = 4 ,
we know that the number of subsets of the set having n elements is = 2ⁿ .
So , the number of subsets of the set S having 4 elements is = 2⁴ = 16
Therefore , The number of subsets that the set S , seasons of the year is 16 .
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Need soon pls! Super easy
Answer:
choose 2nd option
Step-by-step explanation:
The length of the fifth rectangular slate is 16 inches. If its length and width are each decreased by 2 inches, the area will be 56 square inches less than the original area. What is the width of the original rectangular slate?
The width of the original rectangular slate is 14 inches.
What is the width?A rectangle is an object that has four sides. The opposite sides are of equal length. A rectangle has two diagonals that are of equal length that bisect each other at right angles.
The area of a rectangle = length x width
Area of the new rectangular slate = (16 - 2) x (w - 2) = (16 x w) - 56
Area of the new rectangular slate = 14 x (w - 2) = 16w - 56
Area of the new rectangular slate = 14w - 28 = 16w - 56
In order to determine the value of w, take the following steps:
Combine similar terms together: 56 - 28 = 16w - 14w
Add similar terms together: 28 = 2w
Divide both sides of the equation by 2 : w = 28 / 2
w = 14
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Help with another slope and intercept ?
Answer:
Slope = 1/3
Y-intercept = 0
Step-by-step explanation:
Hello!
Slope - Intercept Form: y = mx + b
m = slopeb = y-interceptThe slope is the coefficient before the x-variable. Which means that the slope would be 1/3.
The y-intercept is the constant term after the x-term. In this case, there is no term, so the y-intercept is 0.
Answer:
Slope: 1/3
y-intercept: 0
Step-by-step explanation:
y=mx+b
the coefficient (m) of x is always the slope, so therefore the slope is 1/3
the y-intercept (b) is not here in this equation, so the y-intercept is 0
Which expression is equivalent to 5m - (2m - 8) + 12 + 6m?
A 9m + 4
B.9m + 20
C.13m + 4
D. 13m + 20
Answer:
b) 9m + 20
Step-by-step explanation:
Given expression,
→ 5m - (2m - 8) + 12 + 6m
Simplifying the expression,
→ 5m - (2m - 8) + 12 + 6m
→ 5m - 2m + 8 + 12 + 6m
→ (5m - 2m + 6m) + (8 + 12)
→ 9m + 20
Hence, answer is 9m + 20.
Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave.
The speed of the wave is 2 m/s.
Given,
Time taken by wave to travel back and forth=25 seconds
Length of the pool = 25 meters
As given, the wave travels the length of pool and returns back then,
distance covered by wave is twice the length of pool i.e. [tex]2*25=50[/tex] meters
To find speed of the wave, use formula
[tex]Speed=\frac{Distance covered }{time taken}\\\\Speed=\frac{50}{25} \\\\Speed=2 m/s[/tex]
Thus, the speed of the wave is 2 meter/sec.
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2. Which choice best describes this function? *
exponential growth
O exponential decay
O quadratic growth
O quadratic decay
Lines CD and DE are tangent to circle A, as shown below: Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 125 degrees. Point B lies on circle A. If arc CE is 125°, what is the measure of ∠CDE? 55° 62.5° 117.5° 125°
The measure of angle CDE ( ∠CDE) is 55°. The correct option is the first option 55°
Calculating the measure of the angle formed by two tangentsFrom the question, we are to determine the measure of angle CDE.
From one of the circle theorems, we have that
"The measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs"
Thus,
m ∠CDE = 1/2(measure of arc CBE - measure of arc CE)
From the given information,
Measure of arc CE = 125°
Then,
Measure of arc CBE = 360° - 125°
Measure of arc CBE = 235°
Therefore,
m ∠CDE = 1/2(235° - 125°)
m ∠CDE = 1/2(110°)
m ∠CDE = 55°
Hence, the measure of ∠CDE is 55°
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Answer:
Guys this answer is wrong
Step-by-step explanation:
when you are coming from the center point of the circle it mirrors the arc wich is 125 degrees
But when we are trying to figure out the angle which is CDE its always half of the arc of the circle
So you would do 125/2
wich gives you 62.5
therefore your answer is 62.5
No hate to the other guy but plsssss make sure you read the question before answering
(2a^2 +a + 3) divided by (a - 1)
The value of the equation (2a^2 +a + 3) divided by (a - 1) is 2a + 3.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the equation is illustrated as:
(2a² +a - 3) divided by (a - 1). This will be
(2a² +a - 3) / (a - 1)
It should be noted that (2a² +a + 3) will be:
(2a² +a + 3)
= 2a² - 2a + 3a - 3
= 2a(a - 1) + 3(a - 1)
= (2a + 3)(a - 1)
This will be:
= (2a + 3)(a - 1) / (a - 1)
= 2a + 3
The value is 2a + 3.
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Complete question
(2a^2 +a - 3) divided by (a - 1)
The volume of 10 drops of a liquid is 0.001 fluid ounces.
What is the volume of 10,000 drops?
Answer:
10
Step-by-step explanation:
You take 10,000 and divide it by 10 leaving 1,000. Then, you multiply 1,000 by 0.001 resulting in 10.
Find another point on a line that includes the points (-5, 4) and (4, 1).
The other points (7.3, 2.2) are on a line that includes points (-5, 4) and (4, 1).
What is the equation of a line?
The equation of a line is written as axe + by + c = 0, which is its conventional form. In this equation, the variables x and y are the constant term, while the coefficients a and b are the coefficients. It is a first-order equation with the variables x and y.
Slope using the formula:
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
We have two points, (-5, 4) and (4, 1).
m = (1 - 4) ÷ (4 - (-5))
m = −1/3
m = -0.3
Line Equations with Slope : y - y1 = m(x - x1)
Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point-slope form.
Let's use a point from the original example above (4, 1). and the slope we calculated as -0.3. Put those values in the point-slope format to get an equation of that line in the point-slope form:
y - 1 = -0.3(x - 4)
y = -0.3x + 2.2
Using the equation y = -0.3x + 2.2, set x=0 to find the y-intercept.
y = -0.3(0) + 2.2
y = 2.2
The y-intercept is 2.2
Using the equation y = -0.3x + 2.2, set y=0 to find the x-intercept.
0 = 3x - 6
0 = -0.3x + 2.2
0.3x = 2.2
x = 7.3
The x-intercept is 7.3.
Hence, the other points (7.3, 2.2) are on a line that includes the points (-5, 4) and (4, 1).
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What is the measure of m?
28
m =
[?]√
m
7
3
The value of m is equal to 7√5 using the Pythagoras' theorem.
What is are Right Angled Triangle?
According to the definition of a right triangle, if one of the triangle's angles is a right angle (90°), the triangle is referred to as a right-angled triangle or just a right triangle. Triangle ABC is a right triangle in the example image, and its components are the base, altitude, and hypotenuse. Here, the base is represented by AB, the altitude by AC, and the hypotenuse by BC. The largest side and side opposite to the right angle of a right triangle, the hypotenuse, is the side that needs to be considered.
The sum of any two sides of a triangle's three sides is always more than the sum of its third side, making it a regular polygon. A triangle only possesses this quality.
In the figure
From Pythagoras' theorem, we have, h² = p²+b²
Now we can write 3 equations from the figure i.e
m²=7²+n²
m²=35²-x²
x²=n²+28²
So we have m²=35²-n²-28²
⇒m²=35²-28²-m²+7²
⇒2m²=35²-28²+7²
⇒2m²= 490
⇒m²= 490/2
⇒m= 7√5
Hence, the value of m in the figure is 7√5
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An electrician requires 250 energy saving light bulbs. He comes across four suppliers of these light bulbs.
ELECTRA sells the light bulbs at R 123.00 each, with a R 350.00 delivery fee. ZZZ LIGHTING sells the light bulbs at R
140.00 with a 13% discount on the final amount, but with a
R 260.00 delivery fee. SPARX sells the light bulbs at R 255.00 each with a buy one, get one free offer and no delivery fee.
Finally, BRIGHTEX sells the light bulbs at R 190.00 each
with a third off the final amount, and a delivery fee of R 100.00. Which supplier offers the best deal for the electrician?
Supplier which gives the best deal of selling light bulbs for the electrician is ZZZ LIGHTING with the total selling amount of
$ 30676.2.
As given in the question,
Different suppliers sells energy saving light bulbs with different deals,
Number of bulbs required by an electrician = 250
Different deals of selling amount are as follow:
1. ELECTRA :
123 (250) + 350
=$31100
2. ZZZ LIGHTING :
140(250) + 260
= $35260
13% discount on final amount
= 13% of 35260
= 4583.8
Total amount to pay = 35260 - 4583.8
= $30676.2
3. SPARX :
Offer of Buy one get one and no delivery fee
Total amount to be pay for 125 light bulbs.
255 (125)
= $31875
4. BRIGHTEX :
190(250) + 100
= $47600
With a third off on the final amount
(1/3) of 47600
= $15866.666..
= $15867 (approximately)
Final payment = 47600 - 15867
= $31733
$31875 > $31733 > $31100 > $30676.2
Therefore, supplier which gives the best deal of selling light bulbs for the electrician is ZZZ LIGHTING with the total selling amount of
$ 30676.2.
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A group of friends wants to go to the amusement park. They have $114.75 to spend on
parking and admission. Parking is $8.75, and tickets cost $26.50 per person,
including tax. Which equation or tape diagram could be used to represent the context
if a represents the number of people who chan go to the amusement park
The equation if a=4 represents the number of people who can go to the park is 8.75 + 26.50a = C.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
a formula that expresses the connection between two expressions on each side of a sign.
Typically, it has a single variable and an equal sign.
Like this: 2x - 4 = 2.
In the above example, the variable x exists.
So, the equation represents the number of people who can go to the park:
The total budget is $114.75.
Parking costs $8.75.
The cost of a ticket per person is $26.50.
So form the equation:
Let, a be the number of people and C be the total cost.
8.75 + 26.50a = C
Now, let a be 4.
8.75 + 26.50a = C
8.75 + 26.50(4) = C
8.75 + 106 = C
114.75 = C
Therefore, the equation if a=4 represents the number of people who can go to the park is 8.75 + 26.50a = C.
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Please help! How do u get this?
The component form of the vector that translates C to D is <7, -3>
How to determine the component form of the vector?A translation is a movement in a straight line.
In order to determine the component form of the vector that translates C to D, we have to subtract the coordinate values of point C from the coordinate values of the image C:
(x, y) = D - C
The movement from C to D on the x-axis is 7 units to the right (positive 7) while movement on the y-axis is 3 units down (negative -3). Thus:
(x, y) = (7, -3)
In vector form, <x, y> = <7, -3>
Therefore, the vector that translates C to D is <7, -3>
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Use the number line below, where RS
I need help with this please
Answer:
y = 6RS = 39ST = 38Step-by-step explanation:
You have segment RT of length 77 with point S on it dividing it into segments RS=6y+3 and ST=5y+8. You want to know the value of y and the lengths of segments RS and ST.
Segment sum theoremThe segment sum theorem tells you the whole is the sum of the parts:
RS +ST = RT
(6y +3) +(5y +8) = 77 . . . . . use given values
Solution11y +11 = 77 . . . . . . . . . . . . collect terms
y +1 = 7 . . . . . . . . . . . . . . . divide by 11
y = 6 . . . . . . . . . . . . . . . . . subtract 1
The lengths of the parts are ...
RS = 6y +3 = 6(6) +3 = 39
ST = 5y +8 = 5(6) +8 = 38
Which variables would the scatter plot at the right be most likely to represent?
p1
Question 2 options:
The number of people at a concert and the total concession sales
The number of guests at a hotel and the total water consumption
The number of siblings a person has and the person's GPA
The total number of miles driven and the total gallons of gas used
The scatter plot shows the number of days since several people filled their cars with gas and the gallons of gas in their tank. Which is the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up?
Question 1 options:
10 gallons
13 gallons
23 gallons
17 gallons
1) The scatter plot at the right most likely represents the number of siblings a person has and the person’s GPA.
2) The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is; 17 gallons
How to Interpret a Scatter Plot Diagram?1) Scatter plots are defined as the graphs that present the particular relationship between two variables in a data-set.
A scatter plot is also defined as a chart type that is usually used to observe and visually display the relationship between variables.
From the given scatter plot, we can say that the scatter plot at the right would most likely be used to represent the number of siblings a person has and the person’s GPA.
2) From the given scatter plot, we can see that the x-axis shows the number of days left since filling up while the y-axis represents the gallons of gas.
Now, we want to find out the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up. We will trace 3 on the x-axis and the corresponding value on the y-axis would be approximately 17 gallons.
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3/1 divided by 3/4 in simplest form
Answer:
4
Step-by-step explanation:
3/1=3
hence 3/(3/4 )= 3 x4/3=4
Answer:
4
Step-by-step explanation:
keep switch flip
3/1 * 4/3 = 12/3 = 4
From the chart, estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040?
The estimates for the number of transistors per IC, using an exponential function, are given as follows:
2012: 4,194,304,000.2040: 6.87 x 10¹³.What is the format of an exponential function?The format of an exponential function is presented as follows:
[tex]y = ab^\frac{x}{n}[/tex]
In which the parameters of the function are listed as follows:
a is the initial value of the function.b is the rate of change of the function.n is the period relative to the rate of change.Moore's Law states that the number of transistors per IC doubles every two years, hence the values of parameters b and n both have values of two, hence:
b = 2, n = 2.
The number of transistors per IC in the reference year of 1972 was of 4000, hence the initial value is of:
a = 4000.
Then the exponential function is:
[tex]y = 4000(2)^{\frac{x}{2}}[/tex]
2012 is 2012 - 1972 = 40 years after 1972, hence the estimate is given as follows:
[tex]y = 4000(2)^{\frac{40}{2}} = 4,194,304,000[/tex]
2040 is 68 years after 1972, hence hence the estimate is given as follows:
[tex]y = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}[/tex]
Missing InformationThe chart is given by the image at the end of the answer.
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Find 18 and 90 using GCF prime factorization
At Keller's Bike Rentals, it costs $16 to rent a bike for 4 hours. How many hours of bike use does a customer get per dollar?
The customer will rent 4 bikes per dollar
How to calculate the number bikes per dollar?Keller's bike deal with renting of bikes
At the Keller's bike rentals it costs $16 to rent a bike for 4 hours
Therefore the number of bikes per dollar can be calculated as follows
16= 4
x= 1
Cross multiply
4x= 16
x= 16/4
x= 4
Hence it costs a customer 1 dollar to get 4 bikes
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100% - 26% as a percentage and decimal
Answer: 1- 26%
Step-by-step explanation:
just divide 100 by 100 and remove the % sign :)