Answer:
[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta} = \frac{1}{\sin\theta} = \csc\theta[/tex]
Step-by-step explanation:
We have the expression:
[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}[/tex]
And we want to write the expression in terms of sine and cosine and simplify.
Thus, let tanθ = sinθ / cosθ and secθ = 1 / cosθ. Substitute:
[tex]=\displaystyle \frac{\dfrac{\sin\theta}{\cos\theta}}{\dfrac{1}{\cos\theta}-\cos\theta}[/tex]
Multiply both layers by cosθ:
[tex]=\displaystyle \frac{\left(\dfrac{\sin\theta}{\cos\theta}\right)\cdot \cos\theta}{\left(\dfrac{1}{\cos\theta}-\cos\theta\right)\cdot \cos\theta}[/tex]
Distribute:
[tex]\displaystyle =\frac{\sin\theta}{1-\cos^2\theta}[/tex]
Recall from the Pythagorean Theorem that sin²θ + cos²θ = 1. Hence, 1 - cos²θ = sin²θ. Substitute and simplify:
[tex]\displaystyle =\frac{\sin\theta}{\sin^2\theta} \\ \\ =\frac{1}{\sin\theta}[/tex]
We can convert this to cosecant if we wish.
People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below. Pink lemonade: 156 males, 72 females Yellow lemonade: 104 males, 48 females The events "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6. P(female | pink lemonade ) = P(pink lemonade) = 0.3. P(pink lemonade | female) = 0.3 and P(pink lemonade) = 0.6. P(female | pink lemonade ) = 0.3 and P(pink lemonade) = 0.6.
Answer:
[tex]P(pink) = P(pink |\ female) = 0.6[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}{} & {Male} & {Female} & {Pink} & {156} & {72} \ \\ {Yellow} & {104} & {48} \ \end{array}[/tex]
Required
Why [tex]prefers\ pink\ lemonade[/tex] and [tex]female[/tex] are independent
First, calculate [tex]P(pink |\ female)[/tex]
This is calculated as:
[tex]P(pink |\ female) = \frac{n(pink\ \&\ female)}{n(female)}[/tex]
[tex]P(pink |\ female) = \frac{72}{48+72}[/tex]
[tex]P(pink |\ female) = \frac{72}{120}[/tex]
[tex]P(pink |\ female) = 0.6[/tex]
Next, calculate [tex]P(pink)[/tex]
[tex]P(pink) = \frac{n(pink)}{n(Total)}[/tex]
[tex]P(pink) = \frac{156 + 72}{156 + 72 + 104 + 48}[/tex]
[tex]P(pink) = \frac{228}{380}[/tex]
[tex]P(pink) = 0.6[/tex]
So, we have:
[tex]P(pink) = P(pink |\ female) = 0.6[/tex]
Hence, they are independent
Answer:
P(pink lemonade | female) = P(pink lemonade) = 0.6.
Step-by-step explanation:
A
Let ℤ be the set of all integers and let, (20) 0 = { ∈ ℤ| = 4, for some integer }, 1 = { ∈ ℤ| = 4 + 1, for some integer }, 2 = { ∈ ℤ| = 4 + 2, for some integer }, 3 = { ∈ ℤ| = 4 + 3, for some integer }. Is {0, 1, 2, 3 } a partition of ℤ? Explain your answer.
Answer:
[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z
Step-by-step explanation:
Given
[tex]$$A _ { 0 } = \{n \in \mathbf { Z } | n = 4 k$$,[/tex] for some integer k[tex]\}[/tex]
[tex]$$A _ { 1 } = \{ n \in \mathbf { Z } | n = 4 k + 1$$,[/tex] for some integer k},
[tex]$$A _ { 2 } = { n \in \mathbf { Z } | n = 4 k + 2$$,[/tex] for some integer k},
and
[tex]$$A _ { 3 } = { n \in \mathbf { Z } | n = 4 k + 3$$,[/tex]for some integer k}.
Required
Is [tex]\{0, 1, 2, 3\}[/tex] a partition of Z
Let
[tex]k = 0[/tex]
So:
[tex]$$A _ { 0 } = 4 k[/tex]
[tex]$$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0[/tex]
[tex]$$A _ { 1 } = 4 k + 1$$,[/tex]
[tex]A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1[/tex]
[tex]A _ { 2 } = 4 k + 2[/tex]
[tex]A _ { 2} = 4 *0 + 2$$ \to A_2 = 2[/tex]
[tex]A _ { 3 } = 4 k + 3[/tex]
[tex]A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3[/tex]
So, we have:
[tex]\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}[/tex]
Hence:
[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z
Represent pictorially:
3x2/6 = 6/6 or = 1
Answer:
yes is correct 6/6 = 1 / 3*2=6 =1
Answer:
nonsense. what's the difference between 6/6 or 1 .
PLEASE HELP WILL GIVE BRAINLIEST
Sarah uses 23 of her supply of cheese to make pizza and 19 of her supply of cheese to make lasagna. If Sarah uses 213 pounds of cheese, how many pounds of cheese were in her supply?
A.)3 pounds
B.)6 pounds
C.)8 pounds
D.)9 pounds
Answer:
C.) 8 pounds
Hope that can help
3 - 11 x = - 118
what is the answer?
Answer:
x = 11
Step-by-step explanation:
I assume you want x, so I simply rearranged the terms, subtracted, and simplified.
Last year there were 221 students and 12 teachers at Hilliard School. This year there are 272 students. The principal wants to keep the same student to teacher ratio as last year. Which proportion can the principal use to find x, the number of teacher needed this year?
Answer:
3264:221
Step-by-step explanation:
If by last year there were 221 students and 12 teachers at Hilliard School, then;
221students = 12teachers
To find the equivalent ratio for 272students, we can say;
272students = x teachers
Divide both expressions
221/272 = 12/x
Cross multiply
221 * x = 272 * 12
221x = 3264
x = 3264/221
x = 3264:221
This gives the required proportion
pls help me i’m so stuck
Answer:
Step-by-step explanation:
If a point (x, y) is reflected across y = -x, coordinates of the image point will be,
(x, y)→ (-y, -x)
Following this rule,
Vertices of the triangle will be,
(3, 1) → (-1, -3)
(3, -2) → (2, -3)
(6, -3) → (3, -6)
Therefore, image of the given triangle A will be,
(-1, -3), (2, -3) and (3, -6)
Can someone please help?
Answer:
f(x) = (x + 4)^2 - 5
Step-by-step explanation:
Parent function: f(x) = x^2
To show this in a way that may look more familiar, f(x) = 1(x - 0)^2 + 0
Vertex form: f(x) = a(x - h)^2 + k
We know a = 1, because the slope is the same as the parent function.
Vertex: (h,k)
We can see that the vertex of the graph is (-4, -5)
So h = -4 and k = -5
Now all we need to do is plug the variables into our equation.
f(x) = a(x - h)^2 + k
f(x) = 1(x + 4)^2 - 5
f(x) = (x + 4)^2 - 5
What is the equation of the following line?
Answer:
The equation of the line is y=7x
What is (f.g)(x)?
f(x)=x^3 - 4x + 2
g(x)=x^2 + 2
Answer:
f(g(x)) =
[tex] {x}^{6} + 6 {x}^{4} + 8x^{2} + 2[/tex]
Step-by-step explanation:
put g(x) instead of any x in f(x)
[tex] {(x ^{2} + 2) }^{3} - 4( {x}^{2} + 2) + 2[/tex]
What is 3/4 divided by 1/2
Answer:
6/4 or 1 1/2
Step-by-step explanation:
You have to use the Keep Change Flip technique.
Keep 3/4.
Change the division symbol to a multiplication one
Flipi 1/2 to 2/1
and when you multiply the answer is 6/4 = 1 1/2
Which of the following is the constant ratio of the relation shown in the table?
Answer:
hello!
where are you from ?
Step-by-step explanation:
option 4 is correct ...there is no constant ratio.
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
Answer:
There is no actual question here, this is just a statement.
re-read the question .... i assume it says "what is the highest that she will get during a dive?"
highest point is at t = 33/32
– 16(33/32)^2 + 33(33/32) + 4 =
62.015625
Step-by-step explanation:
Lindsey will be 30 feet in the air at approximately 1.09 seconds and 2.48 seconds.
To find the time at which Lindsey will be 30 feet in the air, we need to solve the quadratic equation y = -16x² + 33x + 45 for x when y = 30.
Setting y equal to 30, we have:
30 = -16x² + 33x + 45
Rearranging the equation, we have:
16x² - 33x - 15 = 0
To solve this quadratic equation, we can factor or use the quadratic formula. In this case, factoring might be more challenging, so we'll use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values from our equation, we have:
x = (-(-33) ± √((-33)² - 4(16)(-15))) / (2(16))
Simplifying, we get:
x = (33 ± √(1089 + 960)) / 32
x = (33 ± √(2049)) / 32
Calculating the square root of 2049, we have:
x = (33 ± √(2049)) / 32
x ≈ 1.09 or x ≈ 2.48
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Complete question is:
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x² + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
At what time will Lindsey be 30 feet in air?
A particle is projected vertically upwards . It attains a height h after 2 seconds and again after 10 seconds . the height h is numerically equal to
Answer:
320m
Step-by-step explanation:
that is the procedure above
I need someone to please explain how to turn this into a simplified fraction. (NOTE: please explain!!) __ 3.541 The repeating sign is only above the 41, not the five
the way to do these recurring decimals is by firstly separating the repeating part or recurring part and then multiply it by some power of 10 so we move it to the left, lemme show
[tex]3.5\overline{41}\implies \cfrac{35.\overline{41}}{10}\qquad \stackrel{\textit{say that the repe}\textit{ating part is }~\hfill }{x = \overline{0.41}\qquad \qquad \textit{so that }35.\overline{41}=35+\overline{0.41}=35+x}[/tex]
now, let's multiply that repeating part by some power of 10 that moves the 41 to the left, well, we have two repeating decimals, 4 and 1, so let's use two zeros, namely 100 or 10², thus
[tex]100\cdot x = 41.\overline{41}\implies 100x - 41+\overline{0.41}\implies 100x = 41+x\implies 99x=41 \\\\\\ \boxed{x =\cfrac{41}{99}}\qquad \qquad \textit{so then we can say that}~~\cfrac{35.\overline{41}}{10}\implies \cfrac{35+\frac{41}{99}}{10} \\\\\\ \cfrac{~~\frac{3506}{99}~~}{10}\implies \cfrac{~~\frac{3506}{99}~~}{\frac{10}{1}}\implies \cfrac{3506}{99}\cdot \cfrac{1}{10}\implies \cfrac{3506}{990}\implies \blacktriangleright \stackrel{\textit{which simplifies to}}{\cfrac{1753}{495}} \blacktriangleleft[/tex]
Can someone help and explain this to me,if you do it means a lot :)
Answer:
0 zero
Step-by-step explanation:
you must find gf(x) first
g[ f(x) ] = g [ 2 + 1 ]
= 3-2+x which is you sub fx tu g
g [ f (-1) ] = 3-2-1
=0
What function is graphed below?
Answer:
[tex]y\ =\ \ \tan\theta\ +2[/tex]
Step-by-step explanation:
Match the base to the corresponding height.
Answer:
I can't see the picture
Step-by-step explanation:
SORRY :(
Which linear inequality represents the graph below? (-2, 3) & (0, -2)
Answer:
no hablo inglés wey perdón corona y gracias
(NEED THIS ASAP)
Tests show that the hydrogen ion concentration of a sample of apple juice is 0.0003 and that of ammonia is 1.3 x 10-9. Find the approximate pH of each liquid using the formula pH = -log (H+), where (H+) is the hydrogen ion concentration The pH value of the apple juice is___ The pH value of ammonia is____
1.pH of apple juice
A. 8.11
B. 1.75
C. 3.5
D. 2.1
2. pH of ammonia
A. 1.1
B. 7.0
C. 5.4
D. 8.9
Answer: I believe but not 100% sure
1) C
2) B
Step-by-step explanation:
The pH value of the apple juice is 3.5, option C) is the correct answer.
The pH value of the ammonia is 8.9, option D) is the correct answer.
What is pH of solution?The pH of a solution is defined as the logarithm of the reciprocal of the hydrogen ion concentration [H+] of the given solution.
From the formular;
pH = -log[ H⁺ ]
Given the data in the question.
For the Apple juice;
hydrogen ion concentration H⁺ = 0.0003 pH of the apple juice pH = ?pH = -log[ H⁺ ]
pH = -log[ 0.0003 ]
pH = 3.5
The pH value of the apple juice is 3.5
Option C) is the correct answer.
For the ammonia;
hydrogen ion concentration H⁺ = 1.3 × 10⁻⁹pH of the ammonia pH = ?pH = -log[ H⁺ ]
pH = -log[ 1.3 × 10⁻⁹]
pH = 8.9
The pH value of the ammonia is 8.9
Option D) is the correct answer.
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1/5 + 3/4 + 1/2
please helpppo asap
Answer:
29/20 or 1 9/20 or 1.45
Answer:
[tex]\frac{1}{5}+\frac{3}{4}+\frac{1}{2}[/tex]
lease common multiplier of 5,4,2 is 20
[tex]\frac{4}{20}+\frac{15}{20}+\frac{10}{20}[/tex]
[tex]Add\: 4+15+10= 29[/tex]
[tex]1/5+3/4+1/2=29/20[/tex]
[tex]Answer :\frac{29}{20}[/tex]
--------------------------
hope it helps
have a great day!!
Một lô hàng chứa rất nhiều sản phẩm, trong đó tỷ lệ sản phẩm loại tốt là 70%. Chọn ngẫu nhiên từ lô hàng ra 5 sản phẩm. Gọi X là số sản phẩm tốt có trong 5 sản phẩm chọn ra: a. Hãy tìm bảng phân phối xác xuất b. Xác định kỳ vọng và phương sai của X c. Tìm số sản phẩm tốt được lấy ra có khả năng xảy ra nhiều nhất
Answer:
lâp bảng
Step-by-step explanation:
X=0 thì xác suất lấy ra được sản phẩm tốt là 5*30%=1,5%
X =1 thì xác suất lấy ra được là 1* 70%*4*30%=0,84%
X=2 thì xác suất lấy ra được sản phẩm tốt là 2*70%*3*30%=1,26%
X=3 thì xác suất lấy ra được sản phẩm tốt là 3*70%*2*30%=1,26%
X=4 thì xác suất lấy ra được sản phẩm tốt là 4*70%*1*30%=0,84%
X=5 thì xác suất lấy ra được sản phẩm tốt là 5*70%=3,5%
X 0 1 2 3 4 5
P 1,5 0,84 1,26 1,26 0,84 3,5
b,
E(x)= 1,5*0+ 0,84*1+1,26*2+1,26*3+0,84*4+3,5*5=28
E(x^2)=1,5*0^2+0,84*1^2+1,26*2^2+1,26*3^2+0,84*4^2+3,5*5^2=118,16
===> V(x)= (E(x))^2-E(x^2)=28^2-118,16=665,84
An item was marked down 64% from its original price,x . The amount discounted was $30. Which equation can be used to find the original price
Answer:
OP = discount amount × 100 / discount %
Step-by-step explanation:
if I understand this correctly, the actual sale price was 36% (100-64) of the originally marked price.
original price (OP) = 100%
64% of OP = 30
1% of OP = 30/64
OP (100%) = 100 × 30/64
this could be simplified to 100 × 15/32, but this hinders is finding the global formula :
OP = discount amount × 100 / discount %
A 90 % confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. the interval was ($133, 306, $150, 733). To make useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?
A) Increase the sample size and increase the confidence level.
B) Decrease the sample size and increase the confidence level.
C) Decrease the sample size and decrease the confidence level.
D) Increase the sample size and decrease the confidence level.
Answer: D) Increase the sample size and decrease the confidence level.
Step-by-step explanation:
A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.
A smaller confidence interval will also lead to a reduced interval width because it means that the chances of the prediction being correct have increased.
The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer. What is the probability that the sample mean would differ from the true mean by more than 1.1 dollars if a sample of 38 5-gallon pails is randomly selected? Round your answer to four decimal places.
Answer:
Probability[(X - μ) < 1.1] = 0.6046
Step-by-step explanation:
Given:
σ² = 64
Mean μ = 34
Find:
Probability[(X - μ) < 1.1]
Computation:
Standard deviation σ = √σ²
Standard deviation σ = √64
Standard deviation σ = 8
Probability[(X - μ) < 1.1] = Probability[-1.1 < (X - μ) < 1.1]
Probability[(X - μ) < 1.1] = Probability[-1.1/(8/√38) < (X - μ) < 1.1/(8/√38)]
Using z table
Probability[(X - μ) < 1.1] = 0.6046
I NEED HELP ASAP!!!!!!!!!!!PLEASE
Answer:
74.8% approximately
Step-by-step explanation:
Area of circle is pi×r^2=pi×4^2=16pi=50.27 approximately
Area of pentagon (assumption regular pentagon)=5/2×apothem×side length=5/2(3.2)(4.7)=37.6
So the probability that it lands in the red is 37.6/50.27 approximately =74.8% approximately
A shopkeeper allows discount of 12% on the marked price of a certain article and makes a profit of 10%. if the article costs the shopkeeper Rs.420. what price should be the marked price?
Answer:
rs288
Step-by-step explanation:
MP of the article = 210×120100×10087.5= Rs.288210×120100×10087.5= Rs.288
Part of solved Discount questions and answers : >> Aptitude >> Discount
WILL MARK BRAINLIEST
Please help solve problems with common tangents.
Answer:
not sure, sorry : p
Step-by-step explanation:
can anyone help with integers?
Fill in the blanks.
6) 83 + 17 = 17 +
7) |46| – |50| =
8) 42 – 2 + (18 – 10) =
9) 18 – (3 – 1) =
10) 8 - 0 =
Answer:
a) 83,b) -4,c) 48,d) 16,e) 8
Use the quadratic formula to find both solutions to the quadratic equation
given below.
3x2 - x + 4 = 0
Answer:
[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex] or [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]
Step-by-step explanation:
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
We have a = 3; b = -1; c = 4.
[tex] x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(4)}}{2(3)} [/tex]
[tex]x = \dfrac{1 \pm \sqrt{1 - 48}}{6}[/tex]
[tex]x = \dfrac{1 \pm \sqrt{-47}}{6}[/tex]
[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex] or [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]
