Answer: X = -5
Step-by-step explanation:
1) Multiply both sides by 6, which is 4x - 3 = 2 + 5x
2) Move the terms, 4x - 5x = 2 + 3
3) Combine like terms, -x = 5
4) Multiply both sides by -1, x = -5
A card is chosen from a standard deck of cards. The drawer is looking for clubs and face cards.
Club not a club
Face card 3 9
Not a face card 10 13
Find P(Club | Not a Face Card).
Question 13 options:
52/13
3/13
1/4
10/13
Answer:
[tex](C)\dfrac{1}{4}[/tex]
Step-by-step explanation:
In a standard deck,
Total Number of cards=52Number of face cards=12Number of Clubs =13The table below gives the distribution of the cards.
[tex]\left|\begin{array}{c|c|c|c}&$Club&$Not a club\\----&----&---&----\\$Face card&3&9&12\\$Not a face card&10&30&40\\----&----&---&----\\$Total&13&39&52\end{array}\right|[/tex]
[tex]P($Club$ | $Not a Face Card)$=\dfrac{10}{40}\\ =\dfrac{1}{4}[/tex]
The correct option is C.
The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20.Does the frequency distribution appear to be roughly a normaldistribution?data0.3800.220.06000.2100.530.18000.02000.24000.01001.280.2400.190.53000.240Daily Rainfall(in inches)Frequency0.00 dash 0.190.00-0.19nothing0.20 dash 0.390.20- 0.39nothing0.40 dash 0.590.40-0.59nothing0.60 dash 0.790.60-0.79nothingDaily Rainfall(in inches)Frequency0.80 dash 0.990.80-0.99nothing1.00 dash 1.191.00-1.19nothing1.20 dash 1.391.20-1.39nothingDoes the frequency distribution appear to be roughly a normaldistribution?A. No, although the distribution is approximately symmetric, the frequencies do not start low, increase to some maximum frequency, then decrease.B. No, although the frequencies start low, increase to somemaximum, then decrease, the distribution is not symmetric.C. No, the distribution is not symmetric and the frequencies do not start off low.D. Yes, all of the requirements are met.
Answer:
C. No, the distribution is not symmetric and the frequencies do not start off low.
Step-by-step explanation:
Hello!
You have the data of daily rainfall for one month (inches)
To arrange a data set in a frequency table you have to determine the number of class intervals you want to make, then you calculate their widths as: "total observations"/"desired number of intervals". Once you have the class width, you can determine the limits of the intervals. For the first interval, you select the minimum value of the sample and add the width to obtain the upper limit. Then you have to use that limit as the lower limit of the next interval and add the width to obtain the next limit. And so on until the last one.
In this example you have a given class width of 0.20 and the lower limit for the first interval is 0.00.
Once you have all intervals determined, you have to arrange the data set from least to greatest and count how many observations correspond to each interval.
The symbol [;) in the intervals indicates that the interval is "closed" on the lower limit and "open" on the upper limit. Meaning, if you have for example the observation "0.20" and the intervals [0.00; 0.20) and [0.20; 0.40), the first interval has a limit equal to 0.20 but is open, meaning that the observation does not belong to it, it belongs to the next interval.
(See table in attachment)
Does the frequency distribution appear to be roughly a normal distribution?
A. No, although the distribution is approximately symmetric, the frequencies do not start low, increase to some maximum frequency, then decrease.
B. No, although the frequencies start low, increase to some maximum, then decrease, the distribution is not symmetric.
C. No, the distribution is not symmetric and the frequencies do not start off low.
D. Yes, all the requirements are met.
As you can see not all defined intervals have at least one observed frequency, most of the observations belong to the first and second one. And there is value, 1.28 inches, that shifts the distribution to the right making it strongly skewed. This distribution is far away from being normally distributed.
Hope it helps!
Gabriel started to calculate the area of the triangle. His work is shown.
A =
1
2
bh
=
1
2
(
1
2
) (
3
4
)
Answer:
Like for black lives
Step-by-step explanation:
black lives matter yeahhhhhh
Classify the triangle based on its angles and sides
Answer:
Options (c) and (f)
Step-by-step explanation:
In the given triangle,
Measure of one angle is 90°.
Therefore, it's a right angle triangle.
Since two angles of the given triangle are equal, opposite sides of this triangle will be equal.
Therefore, the given right triangle is an isosceles triangle.
Options (c) and (f) will be the answer.
You entered a room, of 34 people. A shooter then enters killing 30. How many people are left in the room?
Answer: 5 people
Step-by-step explanation: I was the killer... lol
Here is a quote from a Gallup report: "According to a 2018 Gallup poll, 5% of U.S. adults consider themselves to be vegetarian. Nonwhite Americans (9%) are three times as likely as white Americans (3%) to describe themselves as vegetarian." This statement is based on a random sample of 1033 American adults interviewed in July 2018, in which 270 respondents identified as "nonwhite" and 742 as "white."
The cited value 5% is part of the:___________.
A. Experimental,
B. Conditional,
C. Observational,
D. Anecdotal,
E. Marginal
distribution of the
A. Ethnicity, given diet choice,
B. Diet choice, given ethnicity,
C. Ethnicity,
D. Diet
The cited value 9% is part of the:________.
A. conditional
B. observational
C. anecdotal
D. marginal
E. experimental
distribution of:__________
1. diet choice, given ethnicity
2. ethnicity, given diet choice
3. ethnicity, diet choice.
Which math symbol represents the cited value 5%?
Answer:
Options C, D
Options E, 1
Step-by-step explanation:
The cited value 5% is part of the observational distribution of the diet
The cited value 9% is part of the experimental distribution of diet choice, given ethnicity
The math symbol that represent the 5% is P- the population proportion.
Please answer this correctly
Answer:
12.49 ft²
Step-by-step explanation:
The straight parts of P are both r,
So 2r + 2πr / 4 = 14.28
r (2 + π/2) = 14.28
r = 14.28 / 3.57 = 4
the area will be πr²/4 ≈ 12.56 ft²
Answer: 12.56 ft²
Step-by-step explanation:
Perimeter of a circle is known as the circumference.
C = 2π·r where r is the radius.
Perimeter of the curve of the quarter circle + both sides
[tex]Perimeter=\dfrac{1}{4}Circumference+2\ sides\\\\\\P = \dfrac{1}{4}2\pi \cdot r+2r\\\\\\14.28=\dfrac{\pi\cdot r}{2}+2r\\\\\\28.56=\pi \cdot r+4r\\\\\\28.56=r(\pi +4)\\\\\\\dfrac{28.56}{\pi +4}=r[/tex]
A = π·r²
[tex]\dfrac{1}{4}A=\dfrac{1}{4}\pi \cdot r^2\\\\\\.\quad =\dfrac{1}{4}\pi \bigg(\dfrac{28.56}{\pi +4}\bigg)^2\\\\\\.\quad =\dfrac{1}{4}(3.14)\bigg(\dfrac{28.56}{7.14}\bigg)^2\\\\\\.\quad = \large\boxed{12.56}[/tex]
Find the missing value
A) 14
B) 12
C) 10
D) 13
Answer:
12
Step-by-step explanation:
One part is 1 so 13 minus 1 is 12
What is the square root of a triangle
Answer:
30 60 90
Step-by-step explanation:
A ball thrown into the air from a roof 15 feet above the ground with an initial vertical velocity of 30 ft/sec can be modeled by the equation: . How long will the ball be in the air? What is it’s maximum height?
Answer:
Total time of flight= 6.3 s
Total Max height= 60.87ft
Step-by-step explanation:
Height above ground = 15ft
Velocity=30ft/sec
Angle = 90°
Max height traveled= U²Sin²tita/2g
Max height traveled= ( 30²*1²)/(2*9.81)
Max height traveled= 900/19.62
Max height traveled= 45.87 ft
Total Max height= 15+45.87= 60.87ft
Time travel to Max height
=( usin90)/g
Time travel to initial position
= (30*sin90)/9.81
= 3.1 s
Time to travel to the ground from Max height
H = 1/2gt²
60.87= 1/2 * 9.81*t²
(60.87*2)/9.81= t²
3.5 = t
Total time of flight = 3.5+3.1
Total time of flight= 6.3 s
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
Answer:
a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less
b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours
c) 0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours
d) 86 should have a battery life of at least 9 hours.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
The probability of being higher than x is:
[tex]P(X > x) = \frac{b - x}{b-a}[/tex]
The probability of being between c and d is:
[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]
Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
This means that [tex]a = 8.5, b = 12[/tex]
a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286[/tex]
0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.
b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?
[tex]P(X > x) = \frac{b - x}{b-a}[/tex]
[tex]P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857[/tex]
0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours
c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?
[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]
[tex]P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714[/tex]
0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.
d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
Proportion of iPad Minis with a battery life of at least 9 hours.
[tex]P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571[/tex]
Out of 100:
0.8571*100 = 85.71
To the nearest whole number
86 should have a battery life of at least 9 hours.
What are the advantages of a closed question? A. Closed questions allow the respondent to go in-depth with their answers. B. It is possible to automate the collection of results for closed questions. C. Closed questions allow for new solutions to be introduced. D. It is easy to quantify and compare the results of surveys with closed questions.
Answer:
closed questions are questions with fixed answer options
A. Closed questions allow the respondent to go in-depth with their answers.
no, it is relevant to open questionsB. It is possible to automate the collection of results for closed questions.
yesC. Closed questions allow for new solutions to be introduced.
no, it allows to collect statistical data but not good for new solutions, it better works with open questions when new ideas, solutions may appearD. It is easy to quantify and compare the results of surveys with closed questions.
yesIn a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient skewness is - 0.38
What is the appropriate value of the third quartile
Answer:
56.45
Step-by-step explanation:
Coefficient skewness=(Third quartile+ first quartile)-n*Median/Third quartile-first quartile
Third quartile is the unknown?
First quartile is 30.8
n is the number of steps taken from first quartile to reach third quartile which is 2 steps.
coefficient skewness is -0.38
let p represent third quartile
-0.38=(p+30.8)-2(48.5)/p-30.8
by cross multiplication
-0.38(p-30.8)=(p+30.8)-97
-0.38p+ 11.704 =p+30.8-97
-0.38p-p=30.8-97-11.704
-1.38p=-77.904
p=-77.904 /-1.38= 56.45
Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and the length of side S T is 16. The length of side T U is 8 and the length of U V is 6. Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem? StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
Answer:
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
Step-by-step explanation:
The expression below means RS/VU = ST/UT
See the attachment for better explanation.
Answer:
A
Step-by-step explanation:
I took the test
A can of pumpkin pie mix contains a mean of 30 ounces and a standard deviation of 2 ounces. The contents of the cans are normally distributed.. Supposed four can of pumpkin pie mix are randomly selected What is the probalility that the average content of cans in sample is between 28.0 ounces and 31.5
Answer:
[tex]P(28<X<31.5)=P(\frac{28-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{31.5-\mu}{\sigma})=P(\frac{28-30}{2}<Z<\frac{31.5-30}{2})=P(-1<z<0.75)[/tex]
We can find this probability with this difference
[tex]P(-1<z<0.75)=P(z<0.75)-P(z<-1)[/tex]
If we use the normal standard distribution or excel we got:
[tex]P(-1<z<0.75)=P(z<0.75)-P(z<-1)=0.773-0.159=0.614[/tex]
Step-by-step explanation:
Let X the random variable that represent the weights for a can of pumpkin pie, and for this case we know the distribution for X is given by:
[tex]X \sim N(30,2)[/tex]
Where [tex]\mu=30[/tex] and [tex]\sigma=2[/tex]
We are interested on this probability
[tex]P(28<X<31.5)[/tex]
We can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(28<X<31.5)=P(\frac{28-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{31.5-\mu}{\sigma})=P(\frac{28-30}{2}<Z<\frac{31.5-30}{2})=P(-1<z<0.75)[/tex]
We can find this probability with this difference
[tex]P(-1<z<0.75)=P(z<0.75)-P(z<-1)[/tex]
If we use the normal standard distribution or excel we got:
[tex]P(-1<z<0.75)=P(z<0.75)-P(z<-1)=0.773-0.159=0.614[/tex]
The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes. Assume a person has waited for at least 4 minutes to be served. What is the probability that the person will need to wait at least 9 minutes total
Answer:
43.46% probability that the person will need to wait at least 9 minutes total
Step-by-step explanation:
To solve this question, we need to understand conditional probability and the exponential distribution.
Conditional probability:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Expontial distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In this question:
Event A: Waited at least 4 minutes.
Event B: Waiting at least 9 minutes.
The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes.
This means that [tex]m = 6, \mu = \frac{1}{6}[/tex]
Probability of waiting at least 4 minutes.
[tex]P(A) = P(X \geq 4) = P(X > 4)[/tex]
[tex]P(A) = P(X > 4) = e^{-\frac{4}{6}} = 0.5134[/tex]
Intersection:
The intersection between a waiting time of at least 4 minutes and a waiting time of at list 9 minutes is a waiting time of 9 minutes. So
[tex]P(A \cap B) = P(X > 9) = e^{-\frac{9}{6}} = 0.2231[/tex]
What is the probability that the person will need to wait at least 9 minutes total
[tex]P(B|A) = \frac{0.2231}{0.5134} = 0.4346[/tex]
43.46% probability that the person will need to wait at least 9 minutes total
An athlete eats 85 grams of protein per day while training. How much is this in milligrams ?
Which equation represents this number sentence?
Two less than one-fourth of a number is 10.
Answer:
1/4n-2=10
Step-by-step explanation:
What’s the correct answer for this?
Answer:
x = 7
Step-by-step explanation:
<ACF = 90° (since AB is the diameter and it is perpendicular to EF)
But <ACF = 2(7x-4)
So
2(7x-4) = 90
14x-8 = 90
14x = 90+8
14x = 98
Dividing both sides by 14
x = 7
7-9. A deli sliced 13.7 kilograms of
roast beef one week and 22.53
kilograms the next. How many total
kilograms of roast beef did the deli
slice in the two weeks?
Answer:
36.23 kilograms of roasted beef
Step-by-step explanation:
If deli sliced 13.7 kilograms (kg) of roasted beef one week
He sliced 22.53 kilograms (kg) the next week
Total sliced kilograms of roasted beef=13.7 kg + 22.53 kg
=36.23 kg
The deli sliced a total of 36.23 kilograms of roasted beef in the two weeks.
These box plots show daily low temperatures for a sample of days in two different towns.
Town A. 10,15,20,30, and 55
Town B. 5,20,30,40, and 55
*The question is incomplete. Attached below is the diagram of the box plots being referred to followed by the complete question and options.
Answer:
D. The median for town A, 20 degrees, is less than the median of town B, 30 degrees
Step-by-step Explanation:
From the given diagram of the box plots showing the daily low temperatures for town A and B, the median of town A and B is shown on the box plots by the line that divides the box. Therefore, the median of town A is where the line that divides the box is. Median for town A is 20⁰. Same applies for town B. Town B median is 30⁰.
Therefore, option D is the most appropriate comparison of the centers. Median of town A is less than median of town B.
From 1985 to 2003, the total attendance A (in thousands) at NCAA women’s basketball games can be modeled by =−1.95^3 +70.1x^2 −188+2150 where x is the number of years since 1985.
a. What is the initial value of this function (the attendance in 1985)?
b. Find the attendance for the year 1998.
Answer:
21507269Step-by-step explanation:
We assume your intended attendance equation is ...
A = -1.95x^3 +70.1x^2 -188x +2150
a. For x=0 (corresponding to 1985), the first three terms are 0, so we have ...
A = 2150 . . . . the initial value of the function
__
b. For x=13 (corresponding to 1985) we have ...
A = ((-1.95(13) +70.1)(13) -188)(13) +2150 = (44.75(13) -188)(13) +2150
= 393.75(13) +2150 = 7268.75
Attendance in the year 1998 is modeled to be about 7269.
The range of which function includes -4?
A y=-x-5
B y=√x+5
C y=√x+5
D y=-{X-5
Range of the given function y=-x-5 includes -4
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
For the given function,
y = -x-5
Wen we put x = -1
we get y = -4
Also,
The range of this function is (-∞, ∞)
Hence,
The function y = -x-5 includes the -4.
To learn more about function visit:
https://brainly.com/question/8892191
#SPJ7
Before soccer practice, Laura warms up by jogging around the outside of the entire soccer field. The field measures 80 meters by 120 meters.
If Laura wants to know how many meters she jogged in all, which measurement should she find?
Choose 1 answer:
area
length
perimeter
Answer:
perimeter
Step-by-step explanation:
She would choose perimeter
Because perimeter is the outside of a object and she ran the outside of the soccer field so ya mark be as brainliest plssss
These two figures are the image and pre-image of a
dilation.
Find the value of x.
4 m
6 m
8 m
9 m
Answer:
D.) 9m
Step-by-step explanation:
Answer:
its d
Step-by-step explanation:
i just did the question
Matthew can jog 3 and ⅖ miles in ⅞ of an hour. Find his average speed in miles per hour.
Answer:
3 [tex]\frac{31}{35}[/tex] mph ≈ 3.8857 mph
Step-by-step explanation:
Speed = distance/time
1) Plug the numbers in.
Speed = 3 ⅖ / ⅞
2) Convert the numbers to decimals.
Speed = 3.4 / 0.875
3) Solve.
Speed ≈ 3.8857 mph = [tex]\frac{136}{35}[/tex] mph = 3 [tex]\frac{31}{35}[/tex] mph
ANOTHER WAY TO SOLVE
Speed = distance/time
1) Plug the numbers in.
Speed = 3 ⅖ / ⅞
2) Convert into improper fractions
Speed = [tex]\frac{17}{5}[/tex] / [tex]\frac{7}{8}[/tex]
3) Multiply by the reciprocal
Speed = [tex]\frac{17}{5}[/tex] × [tex]\frac{8}{7}[/tex] = [tex]\frac{136}{35}[/tex] mph = 3 [tex]\frac{31}{35}[/tex] mph
Solve the following quadratic equation using the quadratic formula. Separate multiple answers with a comma if necessary.
[tex]−yx^{2} +4y−6=0[/tex]
Answer:
[tex] y^2 -4y +6=0[/tex]
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where [tex] a = 1, b= -4 ,c =6[/tex]
And replacing we got:
[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]
And solving we got:
[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]
Where [tex] i =\sqrt{-1}[/tex]
And the possible solutions are:
[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]
Step-by-step explanation:
For this case we use the equation given by the image and we have:
[tex] -y^2 +4y -6=0[/tex]
We can rewrite the last expression like this if we multiply both sides of the equation by -1.
[tex] y^2 -4y +6=0[/tex]
Now we can use the quadratic formula given by:
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where [tex] a = 1, b= -4 ,c =6[/tex]
And replacing we got:
[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]
And solving we got:
[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]
Where [tex] i =\sqrt{-1}[/tex]
And the possible solutions are:
[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]
Given tan θ = 2 and sin θ < 0. Find cos(θ +pi/4)
Answer:
√10 / 10
Step-by-step explanation:
tan θ > 0 and sin θ < 0, so θ is in quadrant III. That means cos θ < 0.
cos(θ + π/4)
Use angle sum formula.
cos θ cos(π/4) − sin θ sin(π/4)
½√2 cos θ − ½√2 sin θ
Factor.
½√2 cos θ (1 − tan θ)
½√2 cos θ (1 − 2)
-½√2 cos θ
Write in terms of secant.
-½√2 / sec θ
Use Pythagorean identity (remember that cos θ < 0).
-½√2 / -√(1 + tan²θ)
-½√2 / -√(1 + 2²)
½√2 / √5
√10 / 10
Determine the total number of roots of each polynomial function using the factored form.
f (x) = (x + 5)^3(x - 9)(x + 1)
Answer:
5
Step-by-step explanation:
When the factors are linear, as here, the total number of roots is the sum of the exponents of the factors:
3 + 1 + 1 = 5 . . . . sum of factor exponents
f(x) has 5 roots.
Express as a ratio: the speed of 1 km/min to
the speed of 10 m/s.
Answer:
10 : 6
Step-by-step explanation:
1km / min = 1000m / 60 sec = 100/6 m/s
Ratio :
100/6 : 10
10/6 : 1
10 : 6
