Answer:
Step-by-step explanation:
Solving trig equations are just like solving "regular" equations. Let's get to it. First and foremost we are going to make a "u" substitution. You'll use that all the time in calculus, if you choose to go that route. Let
[tex]sin^2 \theta=u^2[/tex] and sinθ = u. Making the substitution, the equation becomes:
[tex]2u^2-u-1=0[/tex]
That looks like something that can be factored, right? If you throw it into the quadratic formula you get the factors:
(u - 1)(2u + 1) = 0
By the Zero Product Property, either u - 1 = 0 or 2u + 1 = 0, so we will solve those, but not until after we back-substitute!
Putting sinθ back in for u:
sinθ - 1 = 0 so
sinθ = 1 and in the other equation:
2sinθ + 1 = 0 so
2sinθ = -1 and
[tex]sin\theta=-\frac{1}{2}[/tex]
Get out the unit circle and look to where the sinθ has a value of 1. There's only one place in your interval, and it's at 90 degrees.
Now look to where the sinθ has a value of -1/2. There are 2 places within your interval, and those are at 210° and 330°. Now you're done!
Georgina has $5.60 in quarters and dimes. If Georgina has 14 more dimes than quarters, how many quarters does she have?
[I don't want the answer i just want someone to show me how the problem is set up because its confusing me...Thanks]
Answer:
She has 12 quarters.
Step-by-step explanation:
You have two unknowns, the number of quarters and the number of dimes. You need one equation per unknown, so you need two equations. One equation deals with the number of coins. The other equation deals with the values of the coins.
The first step is to choose variables. We can go with x and y, but I prefer to choose q and d, so I remember more easily what they represent.
Let q = number of quarters.
Let d = number of dimes.
Let's deal with the numbers of coins first.
"Georgina has 14 more dimes than quarters"
She has q number of quarters, but the number of dimes is 14 more than the number of quarters. d is 14 more than q. Our first equation is
d = q + 14
Now we deal with the values of the coins.
We don't know yet the actual numbers of dimes and quarters, so we use d and q to represent those numbers.
One dime is worth $0.10; d number of dimes is worth 0.1d.
A quarter is worth $0.25; q number of quarters is worth 0.25q.
The total value of the dimes and quarters is the sum of the values of the two sets of coins:
0.1d + 0.25q
We are told "Georgina has $5.60 in quarters and dimes."
This gives us our second equation.
0.1d + 0.25q = 5.6
Now we have a set of two equations in two variables:
d = q + 14
0.1d + 0.25q = 5.6
There are several methods for solving a system of equations. Since the first equation is already solved for a variable, d, we can use the substitution method.
We rewrite the second equation, but we substitute q + 14 for d in the second equation.
Second equation:
0.1d + 0.25q = 5.6
Substitute q + 14 for d:
0.1(q + 14) + 0.25q = 5.6
Distribute on the left side:
0.1q + 1.4 + 0.25q = 5.6
Combine like terms on the left side:
0.35q + 1.4 = 5.6
Subtract 1.4 from both sides:
0.35q = 4.2
Divide both sides by 0.35:
q = 12
There are 12 quarters.
(You are asked only the number of quarters, so you can stop here. I will continue to find also the number of dimes for 2 reasons. 1) You see how it's done, so it will help with other problems. 2) By finding the numbers of dimes and quarters, then we can check if our solution is correct, which I will do below at the end.)
Now we use the first equation, d = q + 14. We substitute 12 for q and solve for d.
d = q + 14
d = 12 + 14
d = 26
There are 26 dimes.
Check:
We check the numbers of coins:
26 - 12 = 14 The number of dimes is indeed 14 more than the number of quarters.
We check the values of the coins:
0.1(26) + 0.25(12) = 2.6 + 3 = 5.6 The value of the coins is indeed $5.60.
Our answer is correct.
Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years
Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years
The populations are normally distributed. Determine the:
Hypothesis in symbolic form?
Determine the value of the test statistic?
Find the critical value or value?
determine if you should reject null hypothesis or fail to reject?
write a conclusion addressing the original claim?
Answer:
Step-by-step explanation:
GIven that :
Company A
Sample size n₁ = 16 workers
Mean [tex]\mu[/tex]₁ = 5.2
Standard deviation [tex]\sigma[/tex]₁ = 1.1
Company B
Sample size n₂ = 21 workers
Mean [tex]\mu[/tex]₂ = 4.6
Standard deviation [tex]\mu[/tex]₂ = 4.6
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]H_o : \mu _1 = \mu_2[/tex]
[tex]H_1 : \mu _1 > \mu_2[/tex]
The value of the test statistics can be determined by using the formula:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
where;
[tex]\sigma p^2= \dfrac{(n_1 -1) \sigma_1^2+ (n_2-1)\sigma_2^2}{n_1+n_2-2}[/tex]
[tex]\sigma p^2= \dfrac{(16 -1) (1.1)^2+ (21-1)4.6^2}{16+21-2}[/tex]
[tex]\sigma p^2= \dfrac{(15) (1.21)+ (20)21.16}{35}[/tex]
[tex]\sigma p^2= \dfrac{18.15+ 423.2}{35}[/tex]
[tex]\sigma p^2= \dfrac{441.35}{35}[/tex]
[tex]\sigma p^2= 12.61[/tex]
Recall:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
[tex]t = \dfrac{5.2- 4.6}{\sqrt{12.61( \dfrac{1}{16}+\dfrac{1}{21})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61( \dfrac{37}{336})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61(0.110119)}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{1.38860059}}[/tex]
[tex]t = \dfrac{0.6}{1.178388981}[/tex]
t = 0.50917
degree of freedom df = ( n₁ + n₂ - 2 )
degree of freedom df = (16 + 21 - 2)
degree of freedom df = 35
Using Level of significance ∝ = 0.05, From t-calculator , given that t = 0.50917 and degree of freedom df = 35
p - value = 0.3069
The critical value [tex]t_{\alpha ,d.f}[/tex] = [tex]t_{0.05 , 35}[/tex] = 1.6895
Decision Rule: Reject the null hypothesis if the test statistics is greater than the critical value.
Conclusion: We do not reject the null hypothesis because, the test statistics is lesser than the critical value, therefore we conclude that there is no sufficient information that the claim that company a retains it workers longer than more than company b.
Peter is making green paint by mixing blue and yellow paint in a cuboid container, shown below. The container has width of 30cm and length of 40cm and is full. He mixes blue paint and yellow paint in the ratio 2: 3. Peter uses 8.4 litres of blue paint. Calculate the height of the container
Answer: height = 17.5cm
Step-by-step explanation: Peter mixes blue and yellow paint in the ratio 2:3, which means:
[tex]\frac{2}{3} = \frac{8.4}{x}[/tex]
[tex]x = \frac{8.4*3}{2}[/tex]
x = 12.6L
The container is full with the two paints, so total volume:
V = 12.6 + 8.4
V = 21L
Knowing that 1L = 1dm³ and sides of cuboid is measure in cm:
V = 21dm³ = 21000cm³
Volume of a cuboid is calculated as:
V = width*length*height
Height of the container is
height = [tex]\frac{V}{width*length}[/tex]
height = [tex]\frac{21000}{30*40}[/tex]
height = 17.5cm
The height of the container is 17.5cm.
1. Look at the numbers listed below. Which numbers are rational? Select all that apply.
9.1874639...
424, 489
121
5/3
A highway measuring 90 feet x 7 feet requires 1/2 a fluid ounce of cleaning situation per square root how much cleaning situation is required to clean the hallway
Answer:
1260 ounce of the fluid.
Step-by-step explanation:
Dimension of hallway = 90 feet × 7 feet
Area of the hallway = 90 × 7
= 630 square feet
Given that 1/2 (0.5) of a fluid ounce is required per square foot, the amount of cleaning situation to clean the hallway can be determined as;
= [tex]\frac{area of hallway}{cleaning situation per foot}[/tex]
= [tex]\frac{630}{0.5}[/tex]
= 1260 ounce
The amount of cleaning situation required to clean the hallway is 1260 ounce of the fluid.
what is 0.7619047619 as a fraction?
Answer:
7619047619
10000000000
Step-by-step explanation:
Yeah big numbers:
To write 0.7619047619 as a fraction you have to write 0.7619047619 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.7619047619 = 0.7619047619/1 =
7.619047619/10 = 76.19047619/100 =
761.9047619/1000 = 7619.047619/10000 =
76190.47619/100000 = 761904.7619/1000000 =
7619047.619/10000000 = 76190476.19/100000000 = 761904761.9/1000000000 = 7619047619/10000000000
Hope this helps, have a good day :)
(brainliest would be appreciated?)
Number of minutes 1 2 3 4 5 6 7 8 9 10
Number of trainees 2 3 5 10 15 30 25 15 10 5
1.) use the data to draw a bar chart
Answer: please find the attached file for the graph.
Step-by-step explanation:
Number of minutes 1 2 3 4 5 6 7 8 9 10Number of trainees 2 3 5 10 15 30 25 15 10 5
Given that data set above, the time in minutes will be on the x axis while the number of trainees will be in the y axis.
In bar chart, the bars will not touch each other.
Please find the attached file for the solution and figure
A movie theater sells only two types of tickets: adult tickets for $20 each and student tickets for $12 each. One weekend, the theater sold 2,000 tickets for a total of $35,072. How many more adult tickets than student tickets were sold that weekend?
A) 768 B) 770 C) 772 D) 774
Answer:
adults tickets=1384
kids:616 tickets
1384-616= 768 tickets
Step-by-step explanation:
let x be adult tickets and y kids
x+y=2000 ⇒x=2000-y
20x+12y=35072 solve by substitute for x=2000-y
20(2000-y)+12y=35072
40000-20y+12y=35072
-8y=35072-40000
-8y=-4928
y=-4928/-8
y=616
x=2000-616
x=1384 tickets
check:
20(1384)+12(616)=35072 ( correct)
Write a function rule for the table
х
f(x)
0
3
1
4
2
5
3
6
Answer:
f(x) = x +3
Step-by-step explanation:
The first differences for adjacent x-values are all 1, so this is a linear function. Because those differences are all 1, it is a linear function with a slope of 1. We observe that f(0) = 3, so that is the y-intercept.
__
The slope-intercept form of a linear function is ...
y = mx + b . . . . . where m is the slope (1) and b is the y-intercept (3).
A suitable function rule is ...
f(x) = x +3
Find the area of quadrilateral...
Answer:
Total area = 29.8 sq. units
Step-by-step explanation:
area of each triangle = sqrt(s * (s-a) * (s-b) * (s-c))
to get the value of s, use the semi-perimeter = s = perimeter / 2
Total area = area of triangle ABD + area of triangle ACD
semi-perimeter of ABD = (3.48 + 8.66 + 8.6) / 2 = 10.37
semi-perimeter of ABD = (3.54 + 8.84 + 8.6) / 2 = 10.49
area of triangle ABD = sqrt(10.37 * (10.37-3.48) * (10.37-8.66) * (10.37-8.6))
area of triangle ABD = 14.7 sq. units
area of triangle ACD = sqrt(10.49 * (10.49-3.54) * (10.49-8.84) * (10.49-8.6))
area of triangle ACD = 15.08
Total area = 14.7 + 15.1
Total area = 29.8 sq. units
0,2,4,0,2,3,2,8,6
What is the mean?
What is the median?!
What is the first quartile (Q1)?!
What is the third quartile (Q3)?
What is the minimum?
What is the maximum?
What is the interquartile range of the data?!
Answer:
LOOK BELOW
Step-by-step explanation:
Mean= add all of the numbers together and divide by total amount of
numbers
aka=3
Median= put all the numbers in order and find the number in the middle
aka=2.5
Minimum=0
Maximum=8
This data can only be found using a Box and Whisker Plot....
I can't really explain a box and whisker plot so you have to look that up to understand that.. SRY!!!
------------------------------------
First Quartile=1
Third Quartile=5
Interquartile Range=4
Answer:
Mean= add all of the numbers together and divide by total amount of
numbers
aka=3
Median= put all the numbers in order and find the number in the middle
aka=2.5
Minimum=0
Maximum=8
This data can only be found using a Box and Whisker Plot....
I can't really explain a box and whisker plot so you have to look that up to understand that.. SRY!!!
------------------------------------
First Quartile=1
Third Quartile=5
Interquartile Range=4
Step-by-step explanation:
Rebecca is saving money to purchase a laptop, which costs $1,099.51. She has already saved $354.20 and plans to continue
saving $50.60 per week. Which inequality could be used to find w, the number of weeks that Rebecca must save in order to
purchase the laptop?
OA $354.20 + $50.60w < $1,099.51
OB. $354.20w+ $50.60 $1,099.51
OC $354.20 + $50.60w< $1,099.51
OD. $354.20 + $50.60w $1,099.51
Answer:
354.20 + 50.60w ≥ 1099.51
Step-by-step explanation:
354.20 + 50.60w ≥ 1099.51
what is the solution to 2(3x+4)=20
Answer:
x=36
Step-by-step explanation:
Answer: X=2
Step-by-step explanation: you want to distribute the 2 to the 3x and 4. That will give you 6x+8 now you want to subtract 8 from both sides. That will give you 6x=12 and you divide both sides by 6 and your final answer should be X=2. :)
Find the measure of each side indicated. Round to the nearest tenth.
А) 8.2 В) 8.8
C) 7.1 D) 93
Answer:
[tex]\huge\boxed{x = 8.2}[/tex]
Step-by-step explanation:
Sin θ = opposite / hypotenuse
Where θ = 34 , opposite = 4.6 and hyp = x
Sin 34 = 4.6 / x
0.6 = 4.6 / x
x = 4.6 / 0.6
x = 8.2
Answer:
x = 8.2
Step-by-step explanation:
Since we have a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 34 = 4.6 /x
x sin 34 = 46
x = 4.6 /sin 34
x =8.22614159
To the nearest tenth
x = 8.2
Pls answer these McQ to be the brainliest
Step-by-step explanation:
1. c
2. a
3. c
4. c
5. d
6. b
7. a
8. b
9. c
HELP ASAP!!!! URGENT!!! LOOK AT SCREENSHOT! Identify all points and line segments in the picture below. This image has the potential for visual bias, so there is no alternative text. Select one: a. Points: A, B Line segments: bar(AB) b. Points: A, B, C, D Line segments: bar(AB) c. Points: A, B, C, D Line segments: bar(AB), bar(BC), bar(CD), bar(AD), bar(BD), bar(AC) d. Points: A, B, C, D Line segments: bar(AB), bar(AC), bar(BD)
Answer:
the answer is D
trigonometry help got one right need help with another
Answer:
B. [tex] \frac{HI}{GI} [/tex]
Step-by-step explanation:
The trigonometric ratio formula for tangent of any angle in a right triangle is given as:
tan(θ) = [tex] \frac{opposite}{adjacent} [/tex]
Note: it is the length of the side opposite to the θ, and the length of the side adjacent to θ.
Thus, in the right triangle given, ∆GHI,
θ = <G
The length of side the opposite <G = HI
The length of the side adjacent to <G = GI
Therefore, the equivalent of tan(<G) = [tex] \frac{HI}{GI} [/tex]
Please answer this question now
Answer:
30.9 cm²
Step-by-step explanation:
To find the surface area of this figure, we find the area of the base and the 3 identical sides.
The base is split into two identical right triangles. Let's find the area of one and multiply by two.
Half of 3: 1.5
[tex]1.5\cdot2.6=3.9\\3.9\div2=1.95[/tex]
There are two right triangles:
[tex]1.95\cdot2=3.9[/tex]
The area of one of the sides will be the same thing, except the height is 6.
[tex]1.5\cdot6=9\\9\div2=4.5\\4.5\cdot2=9[/tex]
There are 3 sides identical to this one:
[tex]9\cdot3=27[/tex].
Add 27 and 3.9:
[tex]27+3.9=30.9[/tex]
Hope this helped!
Answer:
30.9 square centimeters
Step-by-step explanation:
3 * 1/2(3)(6) + 1/2(3)(2.6) = 30.9
guess what... I need more help again...!!1
Answer:
Associative Property of Multiplication
Step-by-step explanation:
Definition:
Changing the grouping of the factors, but does not change the value of the product.
Example:
(2x4)x6 = 2x (4x6)
Hope this helps!:)
Solve for X
1.) 5(4)^x=320 solve for x
2.) 7 (1/3)^x=7/27 solve for x
Answer:
[tex]5(4)^x=320\\\frac{5(4)^x}{5}=\frac{320}{5}\\ 4^x=64\\x*(log(4) )=log(64)\\x=\frac{log(64)}{log(4)}\\ x=3[/tex]
Step-by-step explanation:
Let X denote the block rate of the host hotel for a particular conference, and let Y denote the lowest room rate available in the host hotel outside of the conference block. For a conference that requires a two-night hotel stay, which one of the following expressions represents the least amount of discount on the conference registration fee that, according to the article, would be sufficient to deter conference attendees from employing the ROB strategy in choosing accommodations?
A. X+Y2X+Y2
B. X−Y2X−Y2
C. X−YX−Y
D. X+YX+Y
E. 2(X−Y)
Answer:
C. X-Y X-Y
Step-by-step explanation:
The question asks to identify the least amount of discount on the conference registration. If the registration discount is at least half of the possible saving of ROB then all attendees will stay within the block. X is the block rate and Y is the non block rate. The saving for staying two nights outside the block is 2 (X-Y)
Jack got 76% of the questions correct on his math test.What is 76% written as a fraction in simplest form?
Answer:
19/25
Step-by-step explanation:
please answer Urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1 4/9 x 2 3/8
help please! Darren is finding the equation in the form y = m x + b for a trend line that passes through the points (2, 18) and (–3, 8). Which value should he use as b in his equation? a) –34 b) –19 c) 2 d) 14
Answer: d) 14
Step-by-step explanation:
Equation of a line passing through (a,b) and (c,d):
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Equation of a line passing through (2, 18) and (–3, 8):
[tex](y-18)=\dfrac{8-18}{-3-2}(x-2)\\\\\Rightarrow\ (y-18)=\dfrac{-10}{-5}(x-2)\\\\\Rightarrow\ (y-18)=2(x-2)\\\\\Rightarrow\ y-18=2x-4\\\\\Rightarrow\ y=2x-4+18\\\\\Rightarrow\ y=2x+14[/tex]
Comparing resulting equation [tex]y=2x+14[/tex] to [tex]y = m x + b[/tex], we get value of b= 14.
Hence, correct option is d) 14
Roberto is x years older than his only sister but 10 years ago he was twice her age. What are the current ages of the siblings?
Answer:
S = x + 10
R = 2x + 10
Step-by-step explanation:
If R is Roberto's age, and S is his sister's age, then:
R = S + x
R − 10 = 2 (S − 10)
Solve with substitution.
S + x − 10 = 2 (S − 10)
S + x − 10 = 2S − 20
S = x + 10
R = 2x + 10
Can you match the teachers comments to the definitions?
Answer:
Sorry
Correct
Close
Step-by-step explanation:
Answer:
Ivy's definition will go with third comment, Ethan's definition will go with the first comment, hence, Ebuka's definition will go with the second comment.
Step-by-step explanation:
Can someone help?
Identify the coefficients and degree of each item
Answer:
first term: degree=4, coefficient= -2
second term: degree=3, coefficient=1
third term: degree=1, coefficient= -8
fourth term: degree= 1, no coefficient
fifth term: degree=2, coefficient=5
Step-by-step explanation:
Answer:
Hey there!
First term, degree 4, coefficient -2.
Second term, degree 3, coefficient 1
Third term, degree 1, coefficient -8
Fourth term, degree 1, coefficient none
Fifth term, degree 2, coefficient 5
Hope this helps :)
The probability of rain and hail during a storm is 16%. The probability of only rain is 78%. What is the probability of hail given that there is already rain?
Answer:
The answer is 20.5% .
Step-by-step explanation:
This is the answer because it is already raining. since it is already raining we take the 16% and divide that by what has already occured to get 20.5%
Joey intends to roll a six-sided number cube 100 times. What probability model can he use to predict whether or not each roll will give a result that is divisible by 3?
Options :
A. Each roll has a 0.117 probability of being divisible by 3.
B. Each roll has a 0.333 probability of being divisible by 3.
C. Each roll has a 0.5 probability of being divisible by 3. D. Each roll has a 0.667 probability of being divisible by 3.
Answer: B. Each roll has a 0.333 probability of being divisible by 3.
Step-by-step explanation:
Sample space for a six-sided number cube :
1, 2, 3, 4, 5, 6
Number of outcomes divisible by 3:
(3, 6) = 2
Probability of an event = Number of required outcomes / total number of possible items
Probability (getting a number divisible by 3):
(Number of outcomes divisible by 3 / total outcomes in sample space)
Probability (getting a number divisible by 3):
2 / 6 = 1/3
= 0.333
SOLVE PLEASE if the radius of a cylinder is 2/3 the height and the height is 6, what is the area of the cylinder
Answer:
96π
Step-by-step explanation:
