Answer:
T = [tex]\frac{2}{x}[/tex]
Step-by-step explanation:
Since we are only given the total number of hours that the project will take and nothing else, we can simply divide the 2 hours by the total number of hours in order to create an expression for the percent that will be completed in that time which in this expression would be represented by the variable T.
T = [tex]\frac{2}{x}[/tex]
We can then use this equation by plugging in a value for x in order to calculate the percent of the project that will be completed in 2 hours.
Find the solutions in the interval [0, 2π). (Enter your answers as a comma-separated list.)sec θ − tan θ = cos θ
Answer:
π/2Step-by-step explanation:
Given the expression;
secθ − tan θ = cosθ
We are to find the solution in the interval [0, 2π).This is as shown;
From trigonometry identity;
secθ = 1/cosθ
tanθ = sinθ/cosθ
Substitute into the formula;
secθ − tan θ = cosθ
1/cosθ-sinθ/cosθ = cosθ
Multiply through by cosθ
1 - sinθ = cos²θ
1-sinθ = (1-sin²θ)
1-sin²θ-1+sinθ =0
-sin²θ+sinθ = 0
sin²θ = sinθ
sinθ = 1
θ = arcsin 1
θ = 90
θ = π/2
Hence the solution is π/2
The equation is an illustration of trigonometry ratios and identities
The solution in the interval [0, 2π) is [tex]\mathbf{\theta = \frac{\pi}{2}}[/tex]
The equation is given as:
[tex]\mathbf{sec\theta - tan \theta = cos\theta}[/tex]
In trigonometry identity, we have:
[tex]\mathbf{sec\theta = \frac{1}{cos\theta}}[/tex]
and
[tex]\mathbf{tan\theta = \frac{sin\theta}{cosθ}}[/tex]
So the equation becomes
[tex]\mathbf{\frac{1}{cos\theta} -\frac{sin\theta}{cos\theta} = cos\theta}[/tex]
Multiply through by cosθ
[tex]\mathbf{1 - sin\theta = cos\²\theta}[/tex]
In trigonometry,
[tex]\mathbf{cos\²\theta = 1 - sin^2\theta }[/tex]
So, we have:
[tex]\mathbf{1-sin\theta = 1-sin\²\theta}[/tex]
Subtract 1 from both sides
[tex]\mathbf{sin\theta = sin\²\theta}[/tex]
Divide both sides by [tex]\mathbf{sin\theta}[/tex]
[tex]\mathbf{1 = sin\theta}[/tex]
Rewrite as:
[tex]\mathbf{sin\theta = 1}[/tex]
Take arc sin of both sides
[tex]\mathbf{\theta = sin^{-1}(1)}[/tex]
This gives
[tex]\mathbf{\theta = \frac{\pi}{2}}[/tex]
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
the area of the trapezoid is 176 cm^2. The height is 16 cm and the length of one of the parallel sides is 9 cm. Find the length of the second parallel side
Answer:
44,55,77
Ratio is 11/1
Step-by-step explanation:
176=4x+5x+7x
176=16x
11=x
44,55,77
Step-by-step explanation:
PLS HELP!!
What is x
Answer:
2
Step-by-step explanation:
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day,
311 people entered the park, and the admission fees collected totaled 804.00 dollars. How many
children and how many adults were admitted?
Your answer is
number of children equals_____
number of adults equals_____
Answer:
There are 104 kids and 162 adults
Step-by-step explanation:
104x1.5=156 Dollars from the kids
162x4=648 dollars from adults
648+156=804
Can I get brainiest now?
Rosa spent $11.52 on 8 candy necklaces for each of her two friends. How much did each necklace cost?
Answer:
£1.44
Step-by-step explanation:
11.52/8=1.44
:)
Answer:
I think the answer is $1.44 each necklaces
Step-by-step explanation:
We know the total amount is $11.52 and there were 8 candy necklaces, so you divide 11.52 by 8 and that gives you 1.44
Indicate whether the lines are parallel, perpendicular, or neither. Justify your answer. y=52x-3 and 2y= -5x
-4 2x+8y= -24and 48y = -12x-144
2x-7y= -56and 7x+2y=8
A band expects to put 16 songs on their next CD. The band writes and records 12.5% more songs than they expect to put on the CD. During the editing process,50 % of the songs are removed. How many songs will there be on the final CD?
Can someone help I don’t know the answer
The length of a rectangle is 12x and the width is 4+x which of the following equations would find the area of the rectangle
A 12x+(4+x)
B 2(12x)+2(4+x
C12x(4+x)
Answer: The answer is C.
Step-by-step explanation:
Remember that the formula for the area of a rectangle is [tex]lw[/tex]. This gives you 12x as the length and 4+x as the width. You just need to multiply those two number together, and you get 12x(4+x) which is C.
When a pentagonal spinner is spun, it lands on one of 1, 2, 3, 4, or 5. If this spinner is spun
twice, what is the probability of it landing on even numbers on both the occasions?
A) 4/25
B) 6/25
C) 1/5
D) 9/25
Please help me
Answer:
1/5
Step-by-step explanation:
S
T
80°
70
Find the measure of RST.
A)
20
B)
30°
40°
D)
60°
Answer:
D
Step-by-step explanation:
If its right let me know I think this is right
How do you graph the solution of this inequality b< 6
Answer:
The graph of the solution to inequality is shown in the attached figure.
Step-by-step explanation:
Considering the inequality
[tex]b< 6[/tex]
As this inequality could simply further
so
[tex]b<6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:b<6\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:6\right)\end{bmatrix}[/tex]
As the interval notation indicates that b is less than 6, hence 6 will not be included on the graph.
Therefore, the graph of the solution to inequality is shown in the attached figure.
A digital clock displays military time in hh:mm format. Find the probability that the number made up of the first two digits on the clock is less than 25.
Answer:
0
Step-by-step explanation:
there is a maximum of 24 hours in a day and the highest we can have is 23:59.. it's impossible for it to be the 25th hour in a day
What is the equation of the line that is parallel to the
given line and passes through the given point?
O y=-2
O x= -2
Oy=-4
O x= -4
Answer:
y= -4
Step-by-step explanation:
Edge 2020 :)
A store has been selling 200 DVD burners sold per week at 400 each. A market survey indicates that for each $ 20 rebate offered to buyers, the number of units sold will increase by 40 a week. Find the demand function and the revenue function. How large a rebate should the store offer to maximize its revenue
Answer:
The answer is "50".
Step-by-step explanation:
Let,
[tex]\to p(200) = 400[/tex]
If we assume the $20 reduction would raise the number of items sold to $40 so the increment is (x - 200) if x is the number of units sold.
[tex]\to (\frac{1}{40}) \times 20 = 0.5[/tex]
[tex]\to D(x) = 400 - 0.5 \times ( x - 200 ) \\\\ \ and \\ \to R(x) = x \times (D(x) \\\\[/tex]
[tex]= x \times [ 400 - 0.5\times ( x - 200 )]\\\\ = x\times[400 - 0.5x - 100]\\\\= x\times [300 - 0.5 x]\\\\= 300x - 0.5 x^2[/tex]
[tex]R(x)= 300x- \frac{1}{2} x^2\\\\R'(x)=300-x\\[/tex]
if R'(x)=0
x=300
if 0 < x < 300 and R(x) > 0 then R(x) for maximum x is = 300
[tex]D(300) = 400 - 0.5\times ( x - 200 )\\\\[/tex]
[tex]= 400 - 0.5\times ( 300- 200 )\\\\ = 400 - 150+ 100\\\\ = 500 - 150 \\\\=350[/tex]
The rebate must be : 400 - 350 = 50
A baseball team practices 4 times a week. Each practice lasts for 115 minutes. The team practiced for 12 weeks during the season.
Part A
How many hours did the team practice during the entire season?
*HINT: Remember that there are 60 minutes in one hour.
Answer:
Your answer would be 92 Hours
Step-by-step explanation:
4 x 115 = 460
460 x 12 = 5,520
5,520 ÷ 60 = 92
Therefore your answer would be 92
HELP ME OUT HERE PLEASEE I WILL MAKE BRAINLIST TO THE PERSON WHO DID EXPLANATION.
Answer:
5 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]2\frac{4}{5}[/tex] + [tex]3\frac{7}{10}[/tex] = [tex]2\frac{8}{10}[/tex] + [tex]3\frac{7}{10}[/tex] = [tex]5\frac{15}{10}[/tex] = [tex]6\frac{1}{2}[/tex]
12 - [tex]6\frac{1}{2}[/tex] = (12 - 6) - [tex]\frac{1}{2}[/tex] = 6 - [tex]\frac{1}{2}[/tex] = 5 [tex]\frac{1}{2}[/tex]
A family wants to make a %20 down payment on a house that cost 200,000 what is the amount of the down payment
Answer:
40
Step-by-step explanation:
Valerie bought a coat at a winter half-price sale. A sales tax of $6.24 was added to the sale price, bringing the cost of the coat to $84.24. Which of the following equations would give the original price ( p ) of the coat?
Answer:
84.24 - 6.24 = p
Step-by-step explanation:
Sorry if it’s blurry it’s hard to take pictures of a computer screen lol im not very good at this subject in math so all help is appreciated :D
Answer:
If they are similar triangles then the ratio AE:BE equals the ratio DE:BCThe ratio AE:BE can be written as the fraction [tex]AE:BE=\frac{AE}{BE}= \frac{9cm}{BE}[/tex] The ratio DE:BC can be written as the fraction [tex]DE:BE=\frac{DE}{BE}=\frac{6cm}{16cm} =\frac{3}{8}[/tex] [tex]AE:BE=DE:BC\\\frac{9cm}{BE}=\frac{3}{8} \\BE*3=8*9cm\\BE*3=72cm\\BE=24cm[/tex]PLEASE HELP ME WITH THIS QUESTION ASAP
Answer:
y=5x+(-19)
Step-by-step explanation:
Refer to the picture that given
In 2010, the average price of a movie ticket was $7.89. Since then, the price has increased by an average of $0.15 per year. Write a linear equation to represent the cost C of a movie ticket y years after 2010.
Answer:
C=0.15y+7.89
Step-by-step explanation:
The linear equation represents the cost C of a movie ticket y is C=0.15y+7.89. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What is meant by linear equation?A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We define a linear equation. Equations of degree 1 are linear equations. It is the straight line's equation. A linear equation with parameters a and b equal to zero has the conventional form ax+by+c = 0.
When two linear expressions are equal, there is a linear equation in one variable. Or, to put it another way, a graph would be one method of solving this equation.
Given ,
Average price of movie ticket =$7.89
Increased average tickets =$0.15
So Simplifying the equation is
C=0.15y+7.89
Therefore The linear equation represents the cost C of a movie ticket y is C=0.15y+7.89.
To learn more about Linear equation refer to:
https://brainly.com/question/2030026
#SPJ2
Heights were measured for a random sample of 10 plants grown while being treated with a particular nutrient. The sample mean and sample standard deviation of those height measurements were 46 centimeters and 7 centimeters, respectively. Assume that the population of heights of treated plants is normally distributed with mean μ. Based on the sample, can it be concluded that μ is different from 45 centimeters? Use the 0.05 level of significance.
Answer:
The calculated value t = 0.452< 2.2621 at 0.05 level of significance
null hypothesis is accepted
Based on the sample, can it be concluded that μ is not different from 45 centimeters
Step-by-step explanation:
Step( i ):-
Heights were measured for a random sample of 10 plants
Size of the sample 'n' = 10
Mean of the sample (x⁻ ) = 46 centimeters
Standard deviation of the sample (s) = 7 centimeters
Mean of the Population ( μ ) = 45
Step(ii):-
Null Hypothesis :H₀:( μ ) = 45
Alternative Hypothesis : H₁: μ ) ≠ 45
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{46-45}{\frac{7}{\sqrt{10} } }[/tex]
t = 0.452
Degrees of freedom
γ = n-1 = 10 -1 = 9
t₀.₀₅ = 2.2621
The calculated value t = 0.452< 2.2621 at 0.05 level of significance
null hypothesis is accepted
Based on the sample, can it be concluded that μ is not different from 45 centimeters
Describe the shape of the distribution.
O A. It is uniform.
B. It is bimodal.
O C. It is symmetric.
D. It is skewed.
Answer:
The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity. (Distributions that are skewed have more points plotted on one side of the graph than on the other.) PEAKS: Graphs often display peaks, or local maximums.
Answer: It is Skewed
Step-by-step explanation: More positive space than negative. So it is positively skewed.
Yesterday it took 40 minutes to drive to school. Today is took 32 minutes to drive to
school. What is the amount of percent decrease?
Answer:
20%
Step-by-step explanation:
To find the percent decrease, we do old number subtracted from the new numbers over old.
We do
40 - 32 = 8
Then we put the 8 over the old and get
8/40
In percentage form it would be 20%
A 20-inch-long piece of rope is approximately 0.5 meters long.
What is the length, in inches, of a rope that is 2.5 meters long, rounded to the nearest tenth? Enter the answer in the box.
inches
Answer:
100 inches
Step-by-step explanation:
Given
20 inch ≈ 0.5 m
Required
Determine the equivalent of 2.5m in inches
The question illustrated conversion between units of same measurements.
And we have that:.
20 in ≈ 0.5 m
Which can be rewritten as:
0.5 m ≈ 20 in
To solve further, we multiply both sides by 5
0.5 m * 5 = 20 in * 5
2.5 m ≈ 100 in
Hence, we can conclude that the 2.5m rope is approximately 100 inches long
The 2.5m rope is approximately 100 inches long
We have to given that,
20 inch ≈ 0.5 m
And, To Determine the equivalent of 2.5m in inches.
Since, It is illustrated conversion between units of same measurements.
And we have that;
20 in ≈ 0.5 m
Which can be rewritten as:
0.5 m ≈ 20 in
we multiply both sides by 5
0.5 m x 5 = 20 in x 5
2.5 m ≈ 100 in
Hence, we can conclude that the 2.5m rope is approximately 100 inches long.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ6
27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 47 college students are randomly selected, find the probability that
a. Exactly 13 of them major in STEM.
b. At most 12 of them major in STEM.
c. At least 9 of them major in STEM.
d. Between 8 and 15 (including 8 and 15) of them major in STEM.
Answer:
0.12995
0.47508
0.0841
0.738
Step-by-step explanation:
Given that:
Percentage of STEM (p) = 27% = 0.27
Sample size (n) = 47
Using Normal approximation :
Mean (m) = n*p = 47 * 0.27 = 12.69
Standard deviation (s) = √(n*p*q)
q = 1 - p = 1 - 0.27 = 0.73
Standard deviation (s) = √(47*0.27*0.73) = 3.04
a. Exactly 13 of them major in STEM.
P(12.5 < x < 13.5)
USing the z formula :
(x - m) / s
(12.5 - 12.69) / 3.04 < x (13.5 - 12.69) / 3.04
-0.0625 < z < 0.2664
Using the z probability calculator:
P(Z < - 0.0625) = 0.47508
P(Z < 0.2664) = 0.60503
0.60503 - 0.47508
= 0.12995
b. At most 12 of them major in STEM.
P(X ≤ 12.5)
Zscore = (x - m) / s
Zscore = (12.5 - 12.69) / 3.04
Zscore = −0.0625
P(Z ≤ - 0.0625) = 0.47508
c. At least 9 of them major in STEM.
P(X ≥ 8.5)
Zscore = (x - m) / s
Zscore = (8.5 - 12.69) / 3.04
Zscore = −1.378
P(Z ≤ - 1.378) = 0.0841
d. Between 8 and 15 (including 8 and 15) of them major in STEM.
(8.5 - 12.69) / 3.04 < x (15.5 - 12.69) / 3.04
-1.378 ≤ z ≤ 0.924
Using the z probability calculator:
P(Z ≤ 0.924) = 0.82226
P(Z ≤ - 1.378) = 0.084102
0.82226 - 0.084102
= 0.738
Reduce to simplest form. - 3/5 + 1/3
Answer: -4/15
Step-by-step explanation: To add these two fractions together,
we start by finding their Least Common Denominator (LCD).
Since our denominators of 5 and 3 have no factors in common,
our least common denominator is 5 · 3 or 15.
In order to get a denominator of 15 in each fraction,
we multiply top and bottom of the first fraction by 3
and top and bottom of the second fraction by 5.
That gives us -9/15 + 5/15 which simplifies to -4/15.
As your last step, make sure that the fraction
that you end up with doesn't reduce.
In this case, -4/15 does not reduce but watch out for this last step.
Lauren has a balance of $60 in your checking account. She spends $80 a day for 3 days vacationing at the beach. What is Laurens new balance in her checking account after her vacation?
Based on Lauren's spending patterns and the balance in her account, her new balance must be an overdraft of $180.
Lauren Balance after Vacation
Her balance after the vacation can be found as:
= Balance before vacation - ( Amount spent)
= 60 - ( 80 x 3)
= 60 - 240
= -$180
In conclusion, she will have a bank overdraft of $180.
Find out more about bank overdrafts at https://brainly.com/question/8283687.
If you use 2 cups of sugar for every 3 cups of lemon juice how many cups of sugar do you need for 9 cups of juice
Answer:
6 cups of lemon juice
Step-by-step explanation: