Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period. This is calculated using:
[tex]T = \frac{2\pi}{w}[/tex]
Where:
[tex]w =\frac{3\pi}{8}[/tex]
So, we have:
[tex]T = \frac{2\pi}{\frac{3\pi}{8}}[/tex]
[tex]T = \frac{2}{\frac{3}{8}}[/tex]
[tex]T = \frac{2*8}{3}[/tex]
[tex]T = \frac{16}{3}[/tex]
Solving (b): The maximum and the minimum height
To do this, we have:
[tex]-1 \le \sin(\theta) \le 1[/tex]
Which means:
[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]
So, the minimum is:
[tex]\sin(\frac{3\pi}{8}) =- 1[/tex]
And the maximum is:
[tex]\sin(\frac{3\pi}{8}) =1[/tex]
Recall that the height is:
[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]
So, the maximum and the minimum of are:
[tex]h_{min} =12 * -1 + 42[/tex]
[tex]h_{min} =30[/tex]
and
[tex]h_{max} =12*1+42[/tex]
[tex]h_{max} =54[/tex]
What is the value of 6 / x + 2x squared when x = 3
Answer:
8
Step-by-step explanation:
The equation will become 6/3+2(3)
-->6/3=2
-->Because of Order of Operation we will multiply the 2 and 3 before adding so 2(3) = 6
--> 6+2=8
Answer:
x=6
Step-by-step explanation:
when its squared you multiply by 2
6. Roll a pair of dice. What is the probability that a total of 12 will be face up?
Answer:
The Probability would be 2.78%
Step-by-step explanation: Hope this helps :)
Choose the correct vertex of the function f(x) = x2 - X + 2.
Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
f(x) = x² - X + 2.
Quadratic equation with [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]
[tex]x_{v} = -\frac{(-1)}{2} = \frac{1}{2}[/tex]
[tex]y_{v} = -\frac{-7}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line
Answer:
The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation the equation of the straight line will be.
Step-by-step explanation:
i need help pls it’s timedd!!!!
Answer:
5.
Step-by-step explanation:
If you were to rotate the triangle, you can apply Pythagoras Theorem.
Therefore,
a^2 = 12^2 - 13^2 (Note: a^2 = a squared)
a^2 = 144 - 169
a^2 = -25.
a = 5.
Not sure why its negative though im pretty sure its the right answer.
in BCD triangle :
DC^2 = BC^2 + BD^2
13^2 = 12^2 + BD^2
169 = 144 + BD^2
BD^2 = 169 - 144
BD^2 = 25
BD = 5
_______________________
In the other hand we have :
BD^2 = AB × BC
5^2 = AB × 12
AB = 25/12
________________________
Also we have :
AD^2 = AB × AC
AD^2 = 25/12 × ( 25/12 + 12 )
AD^2 = 25/12 × ( 25/12 + 144/12 )
AD^2 = 25/12 × 169/12
AD^2 = 25 × 169 / 12 × 12
AD^2 = 5 × 5 × 13 × 13 / 12 × 12
AD = 5 × 13 / 12
AD = 65 / 12
AD = 5.42
Thus the correct answer is option C
Question 11 of 45
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
12
6 R
X 2 z
O A. Similarity cannot be determined,
B. SSS theorem
O C. AA postulate
D. SAS theorem
Answer:
You are only given a Side, an Angle, and then a side. So that is what I would choose. It can't be AA because you weren't given two angles. It can't be SSS because you weren't given 3 sides.
Step-by-step explanation:
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Option B is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
Similar triangles are triangles that have the same shape but may have different sizes.
Two triangles are similar if their corresponding angles are equal, and their corresponding sides are proportional.
When two triangles are similar, they have the same shape, but one may be larger or smaller than the other.
Now,
ΔPQR and ΔXYZ
PQ/XY = 12/4 = 3
PR/XZ = 6/2 = 3
Since the two sides are proportional,
QR/YZ will be proportional.
Now,
PQ/XY = PR/XZ = QR/YZ
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Thus,
ΔPQR and ΔXYZ are similar due to the SSS theorem.
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Can someone help me with this question please.
Answer:
40
Step-by-step explanation:
As the lawn size increases by 4 the weight increases by 8
Find x. Round to the nearest tenth: 29° 500ft
X=[?]ft
9514 1404 393
Answer:
437.3 ft
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(29°) = x/(500 ft)
x = (500 ft)cos(29°)
x ≈ 437.3 ft
anyone help me, let's prove
Answer:
In my opinion the limit is equal to 1 not 0, sorry.
Step-by-step explanation: 6 25 13 43
lim n ⇒∞ ((2n - 1)/2n)
lim n ⇒∞ (2n/2n) - 1)/2n) 2n/2n = 1 1/∞ = 0
= 1 - 0
= 1
when I graphed the function I also got 1
Helppppo plsssssssssss I need helppp with thissss
Answer:
82 is what r equals
Step-by-step explanation:
So, lets go over what we know:
D equals rt, or r * t:
D=r*t
The table shows:
t=2 - d=164
t=3 - d=246
These are the only 2 values we need to look at.
We know that D= r*t, and we can just plug in the values found in the table for t and d to solve for r. So:
164= r * 2
Divide both sides by 2 to iscolate r:
82=r
So it seems like r is equal to 82, however this might be exponential or inaccurate, so lets double check witht the nexty values on the table:
246=r*3
Divide by 3 to iscolate the r:
82=r
So we know that r must equal 82.
Hope this helps!
please help with the steps thx
Answer:
amount financed: 47800
monthly payment: 454.97
FC: 6796.40
558390.76
198390.76
Step-by-step explanation:
1.)
the amount financed is the cost- amount paid today
61800-14000=47800
effective rate: .027/12=
assuming it's an annuity immediate...
x=payment
[tex]47800=x\frac{1-(1+.00225)^{-(10*12)}}{.00225}\\47800=105.0617517x\\x=454.97[/tex]
going to assume that the last part is asking for the interest
to find the interest do financed amount-total paid
454.97*10*12-47800=6796.4
2.)
Find the effective rate
.056/4=.014
assuming annuity immediate
[tex]6000\frac{(1+.014)^{15*4}-1}{.014}=558390.7595[/tex]
interest earned:
558390.7595-6000*60=198390.76
giải phương trình vi phân: y" - 5y' + 6y = 6x + 7
Неоднородное ДУ второго порядка. Детали в аттаче.
I don’t get this at all
Answer:
0.21
Step-by-step explanation:
There's 21 kids with a cell phone and no tablet
so 21/100 = 0.21
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random and finds the mean number of runs scored is 7.4 with a sample standard deviation of 2.88.
Required:
Is it likely that his team's scores is different than the national average?
Answer:
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Step-by-step explanation:
The National average number of runs scored by a LL team is
μ = 5.7
Sample Information:
size sample n = 5
sample average x = 7.4
sample standard deviation s = 2.88
Is required to investigate if that sample average is statistically different from the National average
We will do a test with 95 % of confidence Interval that means
significance level α = 5 % or α = 0.05.
The sample size is 5 then even when we assume normal distribution the sample size indicates that we need to use t-student distribution. Furthermore, as the question is if the sample average is different from the national the test will be a two-tail test.
Then α = 0.05 α/2 = 0.025
df = n - 1 df = 5 - 1 df = 4
Then from t-student table we get t(c) = 2.132
Hypothesis test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x ≠ μ
To calculate t (s)
t(s) = ( x - μ ) / s/√n
t(s) = ( 7.4 - 5.7 )* 2.24 / 2.88
t(s) = 1.7* 2.24 / 2.88
t(s) = 1.32
Comparing t(s) and t(c)
1.32 < 2.132
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
what are functions in math
Nếu cắt mặt cầu bởi một mặt phẳng chiếu đứng thì hình chiếu bằng của giao tuyến là:
Answer:
Im sorry I can't understand you
There are 750 identical plastic chips numbered 1 through 750 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Answer:
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
There are 750 identical plastic chips numbered 1 through 750 in a box
This means that [tex]a = 1, b = 750[/tex]
What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?
[tex]P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358[/tex]
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Can I get some help with this question? I have attempted several times and failed.
9514 1404 393
Answer:
B. relative maximum of 8.25 at x=2.5
Step-by-step explanation:
A quadratic of the form ax²+bx+c has an absolute extreme at x=-b/(2a). For your quadratic, that is ...
x = -5/(2(-1)) = 5/2
The value of the extreme is ...
f(5/2) = (-5/2 +5)(5/2) +2 = 25/4 +2 = 33/4 = 8.25
The negative leading coefficient tells you the graph opens downward, so the extreme is a maximum.
The function has a relative maximum of 8.25 at x = 2.5.
__
A graphing calculator can show this easily.
Q2 find the degree of the polynomial
x4(4x+1)
Step-by-step explanation:
x⁴(4x+1)
4x⁵+x⁴
degree is 5
A square-based tent covers an area of 64 square feet. What is the length of one side of the tent?
Answer:
8 feet
Step-by-step explanation:
A square's area can be expressed as l², with l representing one side of the tent. Therefore, as our area is 64, we can say that 64 = l². Taking the square root of both sides, we get that √64 = l, and l = 8 feet
Yam
190
Groundnuts
90
Vegetables
30. What is the ratio of the land used
for groundnuts to the land for
vegetables
Answer:
3:1
Step-by-step explanation:
90:30 simplified is 3:1
I need help please I dont understand
PLEASE HELP
If the absolute value represents the distance from zero, can we have a negative distance?
Answer:
No, you cannot have a negative distance.
Step-by-step explanation:
No, you cannot have a negative distance.
Let's say you were asked for the absolute value of -4. How many units is -4 away from 0? The answer would be 4. There is no negative distance from 0.
Hope this helps, please mark brainliest! :)
Find the length of side x
Answer:
Step-by-step explanation:
tan(30) = x/1
sqrt(3) / 3 = x/1
x= sqrt(3) / 2
Alla and Balla together drink 750 milliliters (ml) of water. If Alla drinks 50% more than
Balla, how much does Alla drink?
Answer:
Step-by-step explanation:
A + B = 750
A = 1.5 B
~~~~~~~~~~~~~~
750-B = 1.5 B
750 = 1.5 B + B
750 = B(1.5 +1)
750 = B (2.5)
B = 300
A = 450
Alix is 10 years older than tamia. Alanna is twice as old as tamia. If the sum of their ages is 74, how old is alanna
Answer:
Alanna is 32 years old
Step-by-step explanation:
Hi there!
We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.
Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x
Alix is 10 years older than Tamia, so Alix must be x+10 years old
Alanna is twice as old as Tamia, so she must be 2x years old
We're also given that Alix+Alanna+Tamia=74
When we substitute it with the expressions we have, it becomes:
x+x+10+2x=74
now combine like terms
4x+10=74
subtract 10 from both sides
4x=64
divide both sides by 4
x=16
We found the value of x (Tamia's age)
However, the problem asks for Alanna's age, which we have set as 2x
So Alanna is 2*16, or 32 years old
Hope this helps! :)
Answer:
32 years
Step-by-step explanation:
that is the procedure above
The Madison Cosmetics Company has developed a new women's facial cleanser that they believe is superior to those currently on the market in the $5 - $10 range. They wish to test the cleanser against the two current best-sellers.
A. Identify a potential problem with using a completely randomized experimental design to test the cleanser. Explain.
B. The company executives decide to design and carry out a block design experiment to test the new cleanser against its competition. Choose an appropriate blocking scheme for the experiment and justify your choice.
C. Should the company put a control group into the experiment? Why or why not?
D. Could the experiment be a double-blind experiment? Explain.
Answer:
a. there could be a problem of high error
b. randomized block design can remove the issue of heterogeneity
c. yes they should
d, yes it could
Step-by-step explanation:
a. if their is a lack of homogeneity among the sample population, then the results that would be obtained are going to be with increased experimental error.
b. given the number of treatment, the randomized block design technique can be done. This would then remove the issue of heterogeneity. It also gives more information and the results from the test are easier. Even in the presence of missing data, the missing plot technique can be employed.
c. when a control group is used, it makes easier the examination of the market research in a more effective way.
d. Yes it could be a double blind one. This would help to take away the problem of bias.
At a price of per ticket, a musical theater group can fill every seat in the theater, which has a capacity of . For every additional dollar charged, the number of people buying tickets decreases by . What ticket price maximizes revenue? Revenue is maximized when the price is
Answer:
The appropriate answer is "$12".
Step-by-step explanation:
As per the question,
Price per ticket,
= [tex]4+k[/tex]
Number of people,
= [tex]1800-90k[/tex]
Now,
The revenue (R) will be:
= [tex]Price \ per \ ticket\times Number \ of \ people[/tex]
By putting the values, we get
= [tex](4+k) (1800-9k)[/tex]
= [tex]-90k^2+1440k+7200[/tex]
or,
⇒ [tex]R'=1440-180k=0[/tex]
⇒ [tex]180k=1440[/tex]
⇒ [tex]k=\frac{1440}{180}[/tex]
[tex]=8[/tex]
hence,
The ticket price will be:
= [tex]4+k[/tex]
= [tex]4+8[/tex]
= [tex]12[/tex] ($)
ASSESSMENT:
Act as the person in the problem Do the activity. Record your
findings then answer
1. A farmer placed 250 mangoes in a crate, these are 150 ripe and 100 unripe
mangoes, his wife randomly selected 80 mangoes, she got 50 ripe mangoes
and 20 unripe mangoes, find the experimental probability of the mangoes she
selected.
2. A table tennis player has 40 orange table tennis balls, 30 white and 20 yellow
table tennis balls. After selecting 18 balls, he found out that he got 6 white
table tennis balls. Find out the experimental probability of getting white table
tennis table tennis balls.
please answer this
Answer:
in 1st his wife selected 80 mangoes 50 ripe and 20 unripe how it can be
Step-by-step explanation:
50+20=70 not 80
please share the correct question than I may help you
A graph is shown below:
A graph is shown. The values on the x axis are 0, 4, 8, 12, 16, and 20. The values on the y axis are 0, 16, 32, 48, 64, and 80. Points are shown on ordered pairs 0, 64 and 4, 48 and 8, 32 and 12, 16 and 16, 0. These points are connected by a line.
What is the equation of the line in slope-intercept form?
Answer:
b
Step-by-step explanation:
The equation of the line in slope-intercept form is y= 4x+0
What is slope intercept?The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
slope m,
= y2-y1/x2-x1
= 16-0/4-0
=16/4
=4
m=4
So, the equation will be , y= 4x+0
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