Answers
The discrimination of a function determines what type of answers you will get.
If the discriminant is greater than 0(positive) than you will get 2 real numbers(2 x-intercepts).
If the discriminant is 0 than you will get 1 real number(1 x-intercept).
If the discriminant is less than 0(negative) than you will get no real numbers(0 x-intercept) and 2 imaginary/complex numbers.
Related Questions
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 12521252 and standard deviation 129129 chips. (a) What is the probability that a randomly selected bag contains between 10001000 and 15001500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 10251025 chocolate chips? (c) What proportion of bags contains more than 11751175 chocolate chips? (d) What is the percentile rank of a bag that contains 10501050 chocolate chips?
Answers
Answer:
A) 0.947; B) 0.0392; C) 0.7257; D) 6th
Step-by-step explanation:
For part A,
We find the z-score for both of these values and subtract them; this will give us the area under the curve between the scores, which is the same as the probability between them.
[tex]z=\frac{X-\mu}{\sigma}\\\\z=\frac{1000-1252}{129}\text{ and } z=\frac{1500-1252}{129}\\\\z=\frac{-252}{129}\text{ and } z=\frac{248}{129}\\\\z=-1.95\text{ and }z=1.92[/tex]
Using a z-table, we see that the area to the right of z = -1.95 is 0.0256. The area to the right of z = 1.92 is 0.9726. This means the area between them is
0.9726 - 0.0256 = 0.947.
For part B,
To find the probability that fewer than 1025 chips are in the bag, we find the z-score:
[tex]z=\frac{X-\mu}{\sigma}=\frac{1025-1252}{129}=\frac{-227}{129}\\\\=-1.76[/tex]
Looking this number up in the z-table, we find the area under the curve to the left of, or less than, this is 0.0392.
For part C,
Once we find the z-score for the value 1175, the z-table chart will give us the area under the curve less than this. To find the proportion greater than this, we subtract from 1:
[tex]z=\frac{X-\mu}{\sigma}=\frac{1175-1252}{129}=\frac{-77}{129}=-0.60[/tex]
In the z-table, we see that the area under the curve less than this is 0.2743. This means that the area greater than this is 1-0.2743 = 0.7257.
For part D,
We again find the area under the curve less than this. This tells us the proportion of values that will be less than this; this will tell us the percentile value for this.
[tex]z=\frac{1050-1252}{129}=\frac{-202}{129}=-1.57[/tex]
In the z-table, we see the area to the right of this is 0.0582. This means that 5.82% of values are less than this; this means the value is the 5.82 percentile, which rounds to the 6th percentile.
These questions are solved by converting the specified number of chips to a Z-score and using it to find the corresponding probability in a standard normal distribution table. The various calculated probabilities provide the answers to the different parts of the question.
Explanation:In order to answer these questions, we need to convert the number of chips to a Z-score, which is a measure of how many standard deviations an element is from the mean, and then find the corresponding probability from a standard normal distribution table.
(a) To calculate the probability of a bag containing between 1000 - 1500 chips, you subtract the mean from each and divide by the standard deviation to get Z-scores. Then one can find the corresponding probabilities in a Z-table and subtracting the smaller probability from the larger. This will give you the probability of number of chips falling between those two amounts.
(b) Similarly, to compute the probability of a bag containing fewer than 1025 chips, find the Z-score for 1025 and look it up in the Z-table. The probability that corresponds to that Z-score is the likelihood of having fewer than 1025 chips.
(c) For the the proportion of bags that contains more than 1175 chips, first compute the Z-score for 1175. The corresponding probability in the Z-table gives the proportion for those with numbers equal or less than 1175. To get the proportion for bags with more than 1175 chips, you need to subtract that value from 1 (since the total probability is always 1).
(d) Finally, for the percentile rank, it's again the same process. You find the Z-score for 1050, look up its corresponding probability and multiply it by 100 to convert it into percentile rank.
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(8CQ) Find the sum of the geometric series.
20-10+5-5/2+...
Answers
Answer:
b. [tex]\frac{40}{3}[/tex]
Step-by-step explanation:
The given geometric series is;
[tex]20-10+5-\frac{5}{2}+...[/tex]
The first term of this series is
[tex]a_1=20[/tex]
The common ratio is
[tex]r=\frac{-10}{20}=-\frac{1}{2}[/tex]
The sum to infinity of this series is
[tex]S_{\infty}=\frac{a_1}{1-r}[/tex]
Substitute the given values to obtain;
[tex]S_{\infty}=\frac{20}{1--\frac{1}{2}}[/tex]
This implies that;
[tex]S_{\infty}=\frac{20}{\frac{3}{2}}[/tex]
[tex]S_{\infty}=\frac{40}{3}[/tex]
Answer:
B edge
Step-by-step explanation:
The rule for a pattern is add 6. The first term is 5. Write the first five terms in a pattern
Answers
Just start with 5 and add 6 every time.
If there are 8520 bacteria present after 15minutes find K and round to the nearest thousandth (picture below)
Answers
Answer:
Choice A
Step-by-step explanation:
The scenario presented relates to exponential growth models; the population of bacteria is growing at an exponential rate given by the equation;
[tex]B=1000e^{kt}[/tex]
In this case B represents the population of the bacteria, t the time in minutes, k the growth constant and 1000 represents the initial population at time 0.
After 15 minutes, the population of bacteria grows to 8520. This implies that B is 8520 while t is 15. We substitute this values into the given equation and solve for k, the growth constant;
[tex]8520=1000e^{15k}[/tex]
Divide both sides by 1000;
[tex]8.52=e^{15k}[/tex]
The next step is to introduce natural logs on both sides of the equation;
[tex]ln8.52=ln(e^{15k})\\ln8.52=15k\\k=\frac{ln8.52}{15}=0.143[/tex]
Select the property of equality used to arrive at the conclusion.
If x = 3, then x^2 = 3x
a. the multiplication property of equality
b. the division property of equality
c. the addition property of equality
d. the subtraction property of equality
Answers
Answer:
A
Step-by-step explanation:
The statement "If x = 3, then x^2 = 3x" was formed by multiplying x = 3 by x on both sides. Thus x = 3 becomes x*x=3*x. This simplifies to x^2 = 3x. This property is the multiplication property of equality.
The multiplication property of equality is used to arrive at the conclusion from 'x = 3' to 'x^2 = 3x'. This property allows you to multiply both sides of an equation by the same non-zero number, maintaining equality.
Explanation:The property of equality used to reach the conclusion from 'x = 3' to 'x^2 = 3x' is the multiplication property of equality. This property states that if you multiply both sides of an equation by the same non-zero number, the equation will still be equal. Here, 'x' is being replaced by '3' in 'x^2', leading to '3x'. Therefore, the multiplication property of equality is applied.
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A store which formerly sold peppers at 3 pounds for $2.00 changed the price to 2 pounds for $1.50. If x is the percent increase in the price per pound x=
A)25%
B)20%
C)16 2/3%
D)12 1/2%
Answers
Answer:
D 12½%
Step-by-step explanation:
∆=1.5/2-2/3
=4.5/6-4/6
=0.5/6
∆=0.083 $/lb
X=∆/(original price)•100
=0.083/(2/3)•100
=0.1245•100
X=12.45%
A family has two cars. During one particular week, the first car consumed 40 gallons of gas and the second consumed 35 gallons of gas. The two cars drove a combined total of 2125 miles, and the sum of their fuel efficiencies was 55 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Answers
Answer:
Car 1 : 40 gallons
Car 2 : 15 gallons
Step-by-step explanation:
F = Car 1 Fuel Efficiency
S = Car 2 Fuel Efficiency
F + S = 55
40F + 35S = 2125
Using the first equation...
S = 55 - F
Then substitute into the second equation.
40F + 35(55 - F) = 2125
Simplify
40F + 1925 - 35F = 2125
5F + 1925 = 2125
5F = 200
F = 40
Then plug it back into S = 55 - F
S = 15
Plug it back into F + S = 55 to check.
Hope this helps.
Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.
Let car 1 fuel efficiency = x
Let car 2 fuel efficiency = y.
Based on the information given,
x+ y = 55 ...... i
40x + 35y = 2125 ...... ii
Therefore, y = 55 - x ..... iii
Put equation iii into ii
40x + 35(55 - x) = 2125
40x + 1925 - 35x = 2125
Collect like terms
40x - 35x = 2125 - 1925
5x = 200
x = 200/5
x = 40
Since x + y = 55.
y = 55 - 40 = 15
Therefore, Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.
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Find the probabilities of the events described and arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability of occurrence.
the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles
the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples
the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens
the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls
Answers
2.)the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles.
3.)the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples.
4.)the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls
(1 being lowest)
Answer: The probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.
i.e. 0.2<0.42<0.7<0.87
Step-by-step explanation:
Since we have given that
1) the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles
Probability would be [tex]\dfrac{\text{Red Marble}}{Total\ marble}}=\dfrac{5}{12}=0.42[/tex]
2) the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples
Probability would be [tex]\dfrac{Peach}{Total}=\dfrac{7}{10}=0.7[/tex]
3) the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens
Probability would be [tex]\dfrac{Green}{Total}=\dfrac{4}{20}=\dfrac{1}{5}=0.2[/tex]
4) the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls
Probability would be [tex]\dfrac{Golf\ ball}{Total}=\dfrac{13}{15}=0.87[/tex]
We need to arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability occurrence:
So, 0.2<0.42<0.7<0.87
Hence, it becomes
the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.
Consider two events such that P(A)=1/4, P(B)=2/5, and P(A∩B)=1/10. Are events A and B independent events?
Yes, they are independent because P(A)×P(B)=P(A∩B)
No, they are dependent because P(A)×P(B)=P(A∩B)
No, they are dependent because P(A)×P(B)≠P(A∩B)
Yes, they are independent because P(A)×P(B)≠P(A∩B)
Answers
Events A and B are independent events because the product of their probabilities (P(A)P(B)) equals the probability of the intersection of both events (P(A∩B)).
To determine if events A and B are independent events, we need to check if the product of their probabilities equals the probability of their intersection. According to the formula for independent events:
P(A AND B) = P(A)P(B)
Given:
P(A) = 1/4
P(B) = 2/5
P(A∩B) = 1/10
Let's calculate the product of P(A) and P(B):
P(A)P(B) = (1/4) × (2/5) = 1/10
Since P(A∩B) also equals 1/10, which is the same as the product of P(A) and P(B), it is therefore true that:
P(A AND B) = P(A)P(B)
This implies that events A and B are indeed independent because their combined probability equals the product of their probabilities.
Find x in this right triangle.
Answers
Answer:
x = 12
Solve for x:
Using Pythagorean Theorem
a^2 + b^2 = c^2
a = 9
c = 15
b = x
9^2 + x^2 = 15^2
81 + x^2 = 225
x^2 = 144 | sqrt
x = 12
Please Help! I'm having a lot of trouble with this question!!!
Kayla wants to find the distance, AB, across a creek. She starts at point B and walks along the edge of the river 62 ft and marks point C. Then she walks 93 ft further and marks point D. She turns 90° and walks until her final location and marks point E. Point E, point A, and point C are collinear.
(a) Can Kayla conclude that ∆ABC and ∆EDC are similar? Why or why not?
(b) Suppose (DE) ̅=125 ft. Calculate the distance of (AB) ̅ to the nearest tenth of a foot. Show your work. Don’t forget to label your answer.
Answers
Answer:
a ∆ABC and ∆EDC are similar
b. AB = 83.3 ft
Step-by-step explanation:
a. We need to determine if ∆ABC and ∆EDC are similar.
We know B = D = 90
We know C = C because they are vertical angles and vertical angles are equal
Therefore A = E because they are triangles, and if 2 angles in a triangle are equal the third angles must be equal.
∆ABC and ∆EDC are similar
b. We know that because they are similar triangles
AB BC
------ = ---------
ED DC
Substituting in
AB 62
------ = ---------
125 93
Using cross products
93 AB = 62*125
93 AB = 7750
Divide by 93
AB = 7750/93
AB = 83.3333333333(repeating)
Rounding to the nearest tenth ft
AB = 83.3 ft
Dario has 1 foot of gum. It is cut into 4 equal pieces, or quarters. Dario wants to share these 4 pieces equally among himself and 4 friends (5 people in total). Write and solve the equation for sharing the 1/4 piece of gum equally with 5 people. Please explain and show the work pls help I want to get 100% on this answer pls!
Answers
Answer:
Each person will have the amount of 4/20 ft piece of gum equivalent to 1/5 ft
Step-by-step explanation:
we know that
For sharing the 1/4 piece of gum equally with 5 people, first divide each piece of 1/4 by 5
so
[tex]\frac{(1/4)}{5}=\frac{1}{20}\ ft[/tex]
At this moment we have 20 pieces and each one is 1/20 ft
The number of pieces that corresponds to each person is 20 divided by 5.
so
[tex]20/5=4[/tex]
[tex]4*\frac{1}{20}=\frac{4}{20}\ ft[/tex]
each person will have the amount of 4/20 ft piece of gum
simplify
[tex]\frac{4}{20}=\frac{1}{5}\ ft[/tex]
Answer:
each person gets 4/20 pieces
Step-by-step explanation:
(1/4)/5
10=16(x-2)^2+10
show work
Answers
Answer:
x=2
Step-by-step explanation:
10=16(x-2)^2+10
Subtract 10 from each side
10-10=16(x-2)^2+10-10
0 =16(x-2)^2
Divide by 16
0/16 = 16/16 (x-2)^2
0 = (x-2)^2
Take the square root of each side
sqrt(0) = sqrt( (x-2)^2)
0 = x-2
Add 2 to each side
0+2 = x-2+2
2 =x
[tex]Cancel \ 10 \ on \ both \ sides.\\\\0 = 16(x - 2)^2\\\\\\Divide \ both \ sides \ by \ 16.\\0 = (x - 2)\\\\\\Now take the square root of both sides.\\\\0 = x - 2\\\\\\Add 2 to both sides.\\\\2 = x\\\\Switch sides.\\\\\fbox{x = 2}[/tex]
To the nearest hundredth, what is the value of x?
Question 2 options:
36.08
41.51
47.81
72.88
Answers
➷ cos41 = x/55
x = cos41 x 55
x = 41.50902
The correct option would be 41.51
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
41.51
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{55}[/tex]
Multiply both sides by 55
55 × cos41° = x
⇒ x = 41.51 ( to the nearest hundredth )
There are 5 brown horses and 4 tan horses in a barn. Sonia will randomly select two horses to ride with her friend. What is the probability that the first horse selected is tan and the second horse selected is brown?
Answers
The first one is 4/9 and the second one is 5/9
Final answer:
The probability that the first horse selected is tan and the second horse selected is brown, out of a total of 5 brown horses and 4 tan horses, is 5/18.
Explanation:
The question asks for the probability that the first horse selected is tan, and the second horse selected is brown when there are 5 brown horses and 4 tan horses in a barn. To find this probability, we will multiply the probability of each event happening in sequence.
First, the probability of selecting a tan horse out of the total 9 horses (5 brown + 4 tan) is 4/9. Once a tan horse is selected, there are now 8 horses left, 5 of which are brown. Therefore, the probability of then selecting a brown horse is 5/8.
To find the total probability of both events occurring in sequence (first selecting a tan horse, then a brown horse), we multiply the two probabilities together: 4/9 * 5/8 = 20/72, which simplifies to 5/18.
I will mark brainliest
Answers
Answer:
On the surface of the sea
Step-by-step explanation:
Six feet below sea level is marked as -6
Go up 6 feet
-6+6 =0 feet below sea level
That would mean we are at 0, which would be sea level
We would be on the surface of the sea
Plsss Urgent !! A container at the petting zoo holds 8138.88 cubic centimeters of grain. Visitors can fill paper cones with grain from the container. The cones have a radius of 4 centimeters and a height of 9 centimeters. How many times can you fill a cone with the grain that is stored in the container? Use 3.14 to approximate the value of Pi.
Answers
Answer:
54 times you can fill a cone with the grain that is stored in the container
Step-by-step explanation:
step 1
Find the volume of the paper cone
The volume of the cone is
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]r=4\ cm[/tex]
[tex]h=9\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=\frac{1}{3}(3.14)(4)^{2} (9)=150.72\ cm^{3}[/tex]
step 2
Divide the total volume of the container by the volume of one paper cone
[tex]\frac{8,138.88}{150.72}=54[/tex]
Answer:
Its 54
Step-by-step explanation:
Look at the function f(x)=x^2-2. Which of the following describes the domain and range of the function and its inverse?
Answers
Answer:
A
Step-by-step explanation:
The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.
This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.
An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.
Answer:
A.
Step-by-step explanation:
I just got 100% on the quiz.
The mean number of words per minute (WPM) read by sixth graders is 81 with a standard deviation of 17 WPM. If 130 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 77.21 WPM? Round your answer to four decimal places.
Answers
Answer:
The probability that the sample mean would be greater than 77.21 WPM = 0.9945
Step-by-step explanation:
Mean number of Words per Minute = u = 81
Standard Deviation = s = 17
sample size = n = 130
Target value = x = 77.21
we can find the probability by converting x to z-score.
The formula for z-score = [tex]\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
using given values, z-score = [tex]\frac{77.21-81}{\frac{17}{\sqrt{130} } }[/tex]
=> -2.54
using the z table, we can find the find the probability of -2.54, that is 0.9945.
Therefore, the probability that the sample mean would be greater than 77.21 WPM = 0.9945
The probability that the sample mean would be greater than 77.21 WPM is approximately [tex]\(0.9945\)[/tex] (rounded to four decimal places).
To find the probability that the sample mean is greater than 77.21 WPM, we need to use the Central Limit Theorem.
Here's the step-by-step process:
1. Identify the given information:
Population mean [tex](\(\mu\))[/tex]: 81 WPM
Population standard deviation [tex](\(\sigma\))[/tex]: 17 WPM
Sample size [tex](\(n\))[/tex]: 130
Sample mean [tex](\(\bar{x}\))[/tex]: 77.21 WPM
2. Calculate the standard error of the mean (SEM):
[tex]\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{17}{\sqrt{130}} \approx \frac{17}{11.4018} \approx 1.4910 \][/tex]
3. Find the Z-score for the sample mean:
[tex]\[ Z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{77.21 - 81}{1.4910} \approx \frac{-3.79}{1.4910} \approx -2.543 \][/tex]
4. Use the Z-score to find the probability:
We look up the Z-score of -2.543 in the standard normal distribution table.
[tex]\[ P(Z < -2.543) \approx 0.0055 \][/tex]
This is the probability that the sample mean is less than 77.21 WPM. Since we need the probability that the sample mean is greater than 77.21 WPM, we subtract this value from 1.
[tex]\[ P(\bar{x} > 77.21) = 1 - P(Z < -2.543) = 1 - 0.0055 = 0.9945 \][/tex]
Toshi has to work at the car wash for 3 hours. So far, he has worked 1 3/4 hours. How many more hours will it be before he can leave work?
Answers
Final answer:
Toshi has 1 1/4 hours left before he can leave work, which is found by subtracting the time he has already worked (1 3/4 hours) from his total shift (3 hours).
Explanation:
The student asked how many more hours Toshi has to work before he can leave the car wash, given that he has to work a total of 3 hours and has already worked 1 3/4 hours. To find this out, we subtract the time already worked from the total work time required:
Convert 1 3/4 hours to an improper fraction: 1 3/4 = 7/4 hours.
Convert 3 hours to 4/4 hours increments to have a common denominator: 3 hours = 12/4 hours.
Subtract the time worked from the total time: 12/4 - 7/4 = 5/4 hours.
Convert the answer back to mixed numbers: 5/4 hours = 1 1/4 hours.
Therefore, Toshi has 1 1/4 hours left before he can leave work.
Jen started her homework at 3:45 and she worked for 2 hours and 37 minutes, What time did she finish her homework?
Answers
GUYS PLS HELP URGENT
Answers
Answer:
[tex]\boxed{0.2}[/tex]
Step-by-step explanation:
Put -2 where x is in the function and do the arithmetic. Any number of calculators will compute this for you.
x ≈ 0.23781036584 ≈ 0.2
_____
Comment on the above result
The number above came from the Google calculator (2nd attachment). Surprisingly, it is rounded incorrectly in the last displayed digit. To 20 significant digits, the value is ...
0.23781036584658190876
It appears the Google calculator didn't carry enough digits to get the answer correct in the last displayed decimal place.
Answer:
your answer would be 0.2
Step-by-step explanation:
Write a number with one decimal place that is bigger than 6 4/5 but smaller than 7
Answers
Answer: 6.85
Step-by-step explanation: 4 divided by 5 equals .8, so you need to write any number that is greater than 6.8, but less than 7. Other options would be 6.86, 6.9 or 6.95.
URGENT
Let x1 = 6, y1 = 8, and y2 = 2. Let y vary inversely as x. Find x2.
A x2 = 1.5
B x2 = 24
C x2 = 2.67
D x2 = 46
Answers
i think the answer is B
The value of x2 is 24.
What is inversely varying?Two variables are inversely varying if one variable value increases then other variable value decreases. We can represent this relation with an equation
y ∝ 1/x
⇒ y=k/x
where k is a constant.
According to asked problem y is varying inversely with x.
given, x1=6
y1=8
putting these values in the above equation,
8=k/6
⇒k=48
Now we have the value of k.
So the inversely varying equation will become,
y=48/x
By putting the value y2=2
2=48/x
⇒x=48/2
⇒x=24
The value of x2 is 24.
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Plz help!
The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.
What is the equation of the new function g(x) ?
Enter your answer in the box.
g(x)= ____
Answers
Answer:
g(x) = 2sin(x) + 3
Step-by-step explanation:
f(x) = sin(x)
transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.
so
g(x) = 2sin(x) + 3
If there are 42 boys and 56 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Answers
The simplest direct ratio of boys to girls in the room is 3:4, which means for every 3 boys, there are 4 girls. This is determined by finding the greatest common divisor of the two quantities. Other possible ratios such as 6:8, 9:12, 12:16, and 15:20 are multiples of this base ratio.
Explanation:The question is asking for us to form all the possible ratios of boys to girls in the given situation. We are given that there are 42 boys and 56 girls. The simplest ratio of boys to girls can be determined by finding the greatest common divisor (GCD) of both numbers and then dividing both numbers by it. The GCD of 42 and 56 is 14, so if we divide both numbers by the GCD, we get the ratio of 3:4. This implies that for every 3 boys, there are 4 girls. However, other possible ratios could use multiple of these numbers. Therefore, the possible ratios of boys to girls in this scenario also include 6:8, 9:12, 12:16, 15:20, and so on.
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PLS HELP SQDANCEFAN!!!!!!! Given: circle k(O), the measure of arcs PL=80°, PY=150°
Find: m∠YPL
Thx :)))
Answers
Answer:
∠P = 65°
Step-by-step explanation:
The measure of arcs LP and PY are given as 80° and 150°, so their sum is 230°. Arc LY completes the circle of 360°, so is 130°. Inscribed angle P is half that measure, so ...
∠P = 130°/2 = 65°.
Which of the following represents a geometric series (remember what a series is as opposed to a sequence)?
3 + 9 + 15 + ...
3 + 9 + 27 + ...
3, 9, 27, ...
3, 9, 15, ...
Answers
The first answer is correct
Answer:
3 + 9 + 27 + ...
Step-by-step explanation:
3 + 9 + 15 + ... is not a geometric series because it has no common ratio.
[tex]\frac{15}{9}\ne \frac{9}{3}[/tex]
3 + 9 + 27 + ... is a geometric series because there is a common ratio;
[tex]r=\frac{27}{9}=\frac{9}{3}=3[/tex]
3, 9, 27, ... is a geometric sequence and not a series. The sum of all the terms in a geometric sequence forms a geometric series.
3, 9, 15, ... is a not a geometric series.
If the ratio of the edges of two cubes is 3:2, what is the ratio of the volume of the larger cube to the volume of the smaller one?
Answers
Answer:
81 : 8
Step-by-step explanation:
Cube 1 has side lengths of 3, so it's volume is 3³ = 81
Cube 2 has side lengths of 2, so it's volume is 2³ = 8
So the ration of volume of the larger cube to the smaller cube is 81 : 8
Triangle with a height of 25 feet and base of 12 feet. What is the area of the triangle?
Answers
Answer:
150 ft
Step-by-step explanation:
triangle area formula= (b*h)/2
25 time 12 is 300. divide 300 by 2 and get 150.
Answer:
A = 150 ft^2
Step-by-step explanation:
The area of a triangle is found by using
A = 1/2 b*h where b is the base and h is the height
A = 1/2 (12)*25
A = 6*25
A = 150 ft^2