Answer: To estimate the value of csc 120° using the graph of y = csc x, we can locate the point on the graph that corresponds to 120° and read the y-coordinate (csc value) from there.
On the graph of y = csc x, we observe that the csc value is undefined at x = 0° and x = 180° due to vertical asymptotes. Additionally, csc x has maximum and minimum points at multiples of 90°.
To estimate csc 120°, we can look for the nearest maximum or minimum point on the graph. The closest maximum point to 120° is at 90°, and the closest minimum point is at 180°.
Since the maximum value of csc x is 1, we can estimate csc 120° to be approximately 1.
Therefore, the estimated value of csc 120° is 1 (rounded to the nearest tenth).
Step-by-step explanation:
Can someone help me with this please!
Answer:
e^1.4 = 4.05519
to 3dp = 4.055
Step-by-step explanation:
3dp meaning 3 decimal places counting according to the value of 5
You roll a standard number cube. Find P(number greater than 2). 1 1/3 5/6 2/3
The probability of rolling a number greater than 2 on a standard number cube is 2/3.
Since we are interested in the probability of rolling a number greater than 2, we need to count the favorable outcomes and divide them by the total number of possible outcomes.
The numbers greater than 2 on the cube are 3, 4, 5, and 6, which means there are four favorable outcomes.
Since the cube has six possible outcomes in total, the probability of rolling a number greater than 2 is 4/6, which simplifies to 2/3.
Therefore, the probability of rolling a number greater than 2 on a standard number cube is 2/3.
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Which side lengths form a right triangle?
Choose all answers that apply:
A 5,√8,33
B 8, 15, 17
√2, √2,2
Answer:
B and C
Step-by-step explanation:
We can determine which three sides will form a right triangle using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
a and b are the legs,and c is the hypotenuse and the longest sidesThus, a three side lengths can only form a right triangle if the sum of the squares of the shorter sides equal the square of the longest side (the hypotenuse)We can simply check A, B, and C to see which side lengths form a right triangle:A:
5 and √8 (approximately 2.236) are the shorter sides, so we plug these in for a and b in the Pythagorean theorem; 33 is the longest side, so we plug it in for c:5^2 + (√8)^2 = 33^2
25 + 8 = 1089
33 ≠ 1089
Because 33 is not equal to 1089, these three lengths do not form a right triangle.
B:
8 and 15 are the shorter sides, so we plug these in for a and b in the Pythagorean theorem;17 is the longest side, so we plug it in for c:8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
Thus, these three side lengths form a right triangle.
C:
The two √2 (approximately 1.414) are the shorter sides, we plug these in for a and b in the Pythagorean theorem;2 is the longest side, so we plug it in for c:(√2)^2 + (√2)^2 = 2^2
2 + 2 = 4
4 = 4
Thus, these three side lengths also form a right triangle.
x − y = y − x proposition or not?
The proposition x − y = y − x is true.
We are given that;
The equation x − y = y − x
Now,
X − y = -(y - X)
-(y - X) + 2X - 2X = y - X + X - y = y - x.
Similarly, y - x = -(x - y)
-(x - y) + 2y - 2y = x - y + y - x = X - y.
Both sides of the equation are equal.
Therefore, by the given function answer will be true.
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(question 7) calculus
Answer:
A. -0.693147
Step-by-step explanation:
Replace f(x) with y in the given function:
[tex]y=\left(\dfrac{1}{2}\right)^x[/tex]
Take natural logs of both sides of the equation:
[tex]\ln y=\ln \left(\dfrac{1}{2}\right)^x[/tex]
[tex]\textsf{Apply the log power law:} \quad \ln a^n=n \ln a[/tex]
[tex]\ln y=x\ln \left(\dfrac{1}{2}\right)[/tex]
Differentiate using implicit differentiation.
Place d/dx in front of each term of the equation:
[tex]\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln \left(\dfrac{1}{2}\right)[/tex]
Differentiate with respect to x:
[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=\ln \left(\dfrac{1}{2}\right)[/tex]
[tex]\textsf{Apply the log quotient law:} \quad \ln \left(\dfrac{a}{b}\right) = \ln a - \ln b[/tex]
[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=\ln(1)-\ln(2)[/tex]
[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=0-\ln(2)[/tex]
[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=-\ln(2)[/tex]
Multiply both sides by y:
[tex]\dfrac{\text{d}y}{\text{d}x}=-y\ln (2)[/tex]
Substitute back in the expression for y:
[tex]\dfrac{\text{d}y}{\text{d}x}=-\left(\dfrac{1}{2}\right)^x\ln (2)[/tex]
Therefore, the differentiated function is:
[tex]f'(x)=-\ln(2)\left(\dfrac{1}{2}\right)^x[/tex]
To find f'(0), substitute x = 0 into the differentiated function:
[tex]\begin{aligned}x=0 \implies f'(0)&=-\ln(2) \left(\dfrac{1}{2}\right)^0\\&=-\ln(2) \cdot 1\\&=-\ln(2) \\&=-0.693147\; \sf (6\;d.p.)\end{aligned}[/tex]
After a 95% reduction, you purchase a new television on sale for $181. What was the original price of the television? Round your solution to the nearest cent.
Answer:
The original price of the television was $3620.00.
Answer:
$3620.00
Step-by-step explanation:
5% = 181
1% = 36.2
100% = 3620
Which graph represents the function g(x) = 7cosx after a shift of StartFraction 5 pi Over 3 EndFraction units to the right?
The graph of the function g(x) = 7cosx after the shift of 5/3 is shown by the second graph.
What are trigonometric functions?A right-angled triangle's relationship between its angle and sides is represented by a series of functions known as trigonometric functions.
What is Cosine (Cos) Function?
The ratio of the neighbouring side to the hypotenuse is known as the cos function (cosine function) in a triangle.
The range of cosine function lies between -1 to 1.
Calculation for the range of given function:
The given function is, g(x) = 7cosx
Consider x = 0, put in the function.
g(x) = 7cos0
g(x) = 7×1
g(x) = 7
As, for the domain of x = 0 range is 7. the graph will shift upward with 7 units from origin.
Now, according to question, there is a shift of 5/3 of the graph, which means this 7 shift upward will move to 5/3 .
This condition is satisfied by the second graph.
Therefore, the shift for the function g(x) = 7cosx is shown correctly by the second graph.
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Answer:
B
Step-by-step explanation:
I took the test and graph B was the correct one
The function g(x) is a translation 2 units right and 5 units up of fx)-√√x. Which of
the following represents g(x)?
8(x)=√√x-2+5
8(x) = 2√√x+5
8(x) = √√x+5+2
8(x)=√x+2-5
The correct representation of the function g(x) as a translation 2 units right and 5 units up of f(x) = -√√x is:
g(x) = -√√(x - 2) + 5.
To perform a translation 2 units right, the x-coordinate needs to be replaced with (x - 2). This shift moves the entire graph horizontally to the right by 2 units.
Additionally, to shift the graph 5 units up, we add 5 to the function. Thus, the function g(x) is obtained by taking the negative square root of the square root of (x - 2) and then adding 5 to the result.
Among the given options, g(x) = -√√(x - 2) + 5 accurately represents the translation described, while the other options either have incorrect sign placement, incorrect order of operations, or an incorrect translation direction.
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Buying vs Leasing Given the below lease terms at a local car dealership, what is the total cash paid by the end of the lease when at signing the dealership required a down payment, security deposit, acquisition fee at signing and all the monthly payments paid? Length of lease 48 = months MSRP of the car = $29,750 Purchase value of the car after lease = $19,900 Down payment =$2,800 Monthly payment =$595 Security deposit =$575 Acquisition fee =$400
Eli made a wooden box in the shape of a rectangular prism. The box has a length of 5 inches, a width of 3 1/2 inches, and a height of 7 inches.
Part A. Eli wants to paint the entire box green and give the box to his dad as a gift. What is the total area that he will paint? Explain how you found your answer.
Part B. Can the box hold 200 cubic inches of packing peanuts? Explain how you know.
BE FAST!!!
Answer:
Part A:
122.5 cubic inches
Part B:
No
Step-by-step explanation:
Part A:
The volume of a rectangular prism is the product of its length, width, and height. Volume = 5 x 3.5 x 7 = 122.5 cubic inches Since the volume of the box is less than 22 cubic inches.
Part B:
The box cannot hold 200 cubic inches of packing peanuts.Show all work on each of the 8 problems
2.
You are building a rectangular chest. You want the length to
be 6 feet, the width to
be 2 feet, and the volume to be 24 cubic feet. What should
the height be?
ne.
The height of the rectangular chest should be 2 feet.
To determine the height of the rectangular chest, we can use the formula for the volume of a rectangular prism:
Volume = Length * Width * Height
We are given that the length is 6 feet, the width is 2 feet, and the volume is 24 cubic feet. Let's substitute these values into the formula and solve for the height:
24 = 6 * 2 * Height
Dividing both sides of the equation by (6 * 2):
24 / (6 * 2) = Height
24 / 12 = Height
2 = Height
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answer from the 4 options.
ASAP
Answer :
From the figure XY and WZ are opposite sides and XW and YZ are the opposite sides.
Opposite sides of Parallelogram are equal.XY = WZ
3a - 4 = a + 2
3a - a = 2 + 4
2a = 6
a = 6/2
a = 3
Now put the value of a in XY
XY = 3a - 4
XY = 3(3) - 4
XY = 9 - 4
XY = 5Similarly,
XW = YZ
2b = b + 1
2b - b = 1
1b = 1
b = 1
Now put the value of b in YZ
YZ = 2b
YZ = 2 × 1
YZ = 2XY = 5 and YZ = 2Answer :
D. XY = 5 , YZ = 2Step-by-step explanation :
As We Know that Opposite sides of the Parallelogram are equal.
SO,
(i) YZ = XW (opposite sides)
YZ = 2bXW = b + 1→ 2b = b + 1
→ 2b - b = 1
→ b = 1
Since, YZ = 2b
→ YZ = 2 × 1
→ YZ = 2.
Also,
(ii) XY = WZ (opposite sides)
XY = 3a - 4WZ = a + 2→ 3a - 4 = a + 2
→ 3a - a = 2 + 4
→ 2a = 6
→ a = 6/2
→ a = 3 .
Since, XY = 3a - 4
putting the value of a = 3.
=> 3(3) - 4
→ 9 - 4
→ 5
XY = 5.
Therefore, Option D is the required answer.
What kind of geometric transformation is shown in the line of music?
translation
glide reflection
reflection
Answer:
translation
Step-by-step explanation:
What equation is equivalent to 8.8 x 10^9 divided by 2.2 x 10^-3?
Solve for c.
(5c-3) ÷ 4 = 8
c = [?]
A group of scientists is conducting an experiment on the effects of media on children. They randomly select 100 children and randomly assign each child to one of four treatment groups. Each treatment group has a specific amount of screen time during a one-week time frame. The first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time.
After the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments.
Which statements about this study are true?
This study uses blocking.
This study uses a repeated measures design.
This study uses blinding.
This study uses random sampling.
This study uses a control group.
This study uses a repeated measures design, random sampling, and a control group.
What is Repeated Measures Design?Repeated measures design is used because each child experiences all treatments over time. Random sampling is present as children were randomly selected.
The control group is the group with no screen time. Blocking isn't used as participants aren't grouped based on shared characteristics affecting the response. Blinding isn't used as it's not mentioned that participants or researchers are unaware of the treatment given, which would prevent bias.
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The temperature was 40 degrees at noon at midnight the temperature was -10 degrees, which integer describes the change in temperature
Answer:
The temperature change from noon to midnight is 50 degrees. The temperature at noon was 40 degrees and at midnight it was -10 degrees. Therefore, the change in temperature is 40 - (-10) = 50 degrees.
Line contains points (−4,0)
and (0,−2). Find the distance between line and the point P(4,1). Round your answer to the nearest hundredth, if necessary.
The distance between line and the point P(4,1) is,
⇒ d = 4.47
We have to given that;
Line contains points (- 4,0) and (0, - 2).
Since, The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Hence, The equation of line is,
⇒ y - 0 = (- 2 - 0) / (0 - (- 4)) (x - (- 4))
⇒ y = - 2/4 (x + 4)
⇒ y = - 1/2 (x + 4)
⇒ y = - 1/2x - 2
⇒ 2y = - x - 4
⇒ 2y + x + 4 = 0
So, The distance between the line 2y + x + 4 = 0 and the point P(4, 1) is:
⇒ d = (2 × 1 + 4 + 4) / √(2² + 1)
⇒ d = 10 / √5
⇒ d = 2√5
⇒ d = 2 x 2.23
⇒ d = 4.47
Thus, The distance between line and the point P(4,1) is,
⇒ d = 4.47
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help me please so hard
Gradient is another word for slope.
Slope = rise/run = (y2-y1)/(x2-x1)
So pick 2 points.
Let's do line A first.
(1,1) and (2,4)
slope = (1-4)/(1-2)
= -3/-1 = 3
The slope (aka gradient) of line A = 3.
Line B.
(0,5) and (1,1)
slope = (5-1)/(0-1)
= 4/-1
= -4
The slope (aka gradient) of line B = -4.
Question 2 of 9
17 - (9 - 10) = (17- 9) - 10
O A. True
3
B. False
“y varies jointly as x and z”. Write the appropriate joint-variation equation, and then find “y” for the given value of “x” and “z”.
y = 12 when x = 4 and z = 5, find “y” when x = 6 and z = 3.
Answer:
y = kxz. y = 10.8
Step-by-step explanation:
y = kxz, where k is a constant.
12 = k(4)(5) = 20k
k = 12/20 = 0.6.
y = kxz
= (0.6) (6) (3)
= 10.8
there are 148 legs in a farmyard full of goats and chickens. there are 62 total animals, how many of each are there
Answer:
Let’s use x to represent the number of goats and y to represent the number of chickens. We know that there are 62 animals in total, so x + y = 62. We also know that there are 148 legs in total, so 4x + 2y = 148 (since goats have four legs and chickens have two).
We can solve for x and y by using substitution or elimination method. Let’s use substitution method here. From x + y = 62, we can get x = 62 - y. Substituting this into 4x + 2y = 148 gives us:
4(62 - y) + 2y = 148 248 - 4y + 2y = 148 248 - 2y = 148 100 = 2y y = 50
So there are 50 chickens on the farmyard. Substituting this into x + y = 62 gives us:
x + 50 = 62 x = 12
So there are 12 goats in the farmyard.
Therefore, there are 12 goats and 50 chickens on the farmyard.
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PLEASE HELP-TIMED-30pts!!
Answer each question individually
___________________________
1. The list below shows the ages of the first 20 customers at a new computer game
store. ⬇️
6, 7, 9, 10, 14, 15, 16, 17, 20, 26, 26, 29, 31, 34, 35, 38, 40, 51, 59, 67
a) Decide what class intervals to use, and then create a frequency table for the
ages.
b)use the frequency table from Part A to create a histogram
We are able to count the frequency of ages falling within each interval using class of 10 years. The histogram is drawn for the frequency table as well below.
What class intervals should we used?To create class intervals, we will use range of 10 years each. Starting from the minimum age of 6, we can use the following intervals [tex]6-15, 16-25, 26-35, 36-45, 46-55, 56-65, 66-75.[/tex]
Now, we can count the frequency of ages falling within each interval:
Class - Frequency
6-15: 3
16-25: 3
26-35: 4
36-45: 2
46-55: 2
56-65: 1
66-75: 1
To create histogram, we will represent the class intervals on the x-axis and the frequency on the y-axis. Each interval's frequency is represented by the height of a bar.
The representation of the histogram using the frequency table i as follows:
4 |
3 | x
2 | x x x
1 | x
-----------------------------
6-15 16-25 26-35
The x represent the bars of the histogram.
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Lindsey is debt-free, has a fully funded emergency fund, and is ready to start saving for a house! She makes $4,000 per month in take-home pay and is looking to purchase a home worth $140,000. She’s trying to figure out how much to save for a down payment on her new home.
The Lindsey should save around $28,000 for the down payment. If she wants to expedite her savings, she can look into cutting down expenses or increasing her income.
Congratulations to Lindsey for being debt-free and having a fully funded emergency fund! As for her question, the down payment for a house usually ranges from 3% to 20% of the home's purchase price.
Based on Lindsey's desired home worth $140,000, the down payment can range from $4,200 (3%) to $28,000 (20%).
However, it's recommended to aim for a 20% down payment to avoid private mortgage insurance (PMI) and to lower monthly payments. Best of luck to Lindsey on her journey towards homeownership
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How can I simplify this
The result should be three
The image you provided is a mathematical expression written in a non-standard format. To simplify it and obtain the result of 3, we can break it down step by step.
The expression can be written as follows:
(8c8) * (8x83)
Let's simplify each part separately:
(8c8):
The term "8c8" represents the combination or binomial coefficient. In general, the combination "nCr" is calculated as n! / (r! * (n-r)!), where "!" denotes factorial. When r = n (as is the case here with 8c8), the combination simplifies to 1. Therefore, 8c8 equals 1.
(8x83):
The term "8x83" represents multiplication between the numbers 8 and 83, which equals 664.
Now, let's put it all together:
(8c8) * (8x83) = 1 * 664 = 664
According to the given expression, the simplified result is 664, not 3. Please double-check the expression or provide further clarification if needed.
Need the answer for this please!!
In the given diagram, we have a triangle with two angles labeled as (3x + 10)° and (5x - 30)°. We need to solve for the value of x.
According to the properties of triangles, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the following equation:
(3x + 10) + (5x - 30) + 90 = 180
Let's simplify the equation:
3x + 10 + 5x - 30 + 90 = 180
8x + 70 = 180
Next, we'll isolate the variable term by subtracting 70 from both sides of the equation:
8x = 180 - 70
8x = 110
To solve for x, we'll divide both sides of the equation by 8:
x = 110 / 8
Now, let's calculate the value of x:
x ≈ 13.75
Therefore, the value of x is approximately 13.75.
Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.
en una oficina trabajan 8 profesionales
The number of professionals in the office, given that 8 professionals is 20 % would be 40 professionals.
How to find the number of professionals ?To calculate the total number of staff in the office, use the following formula :
Total staff = ( Professionals / Percentage ) x 100
Professionals = 8 professionals
Percentage = 20 %
Plugging in the values, we get :
Total staff = ( 8 / 20 ) x 100
Total staff = 0. 40 x 100
Total staff = 40 professionals
In conclusion, the office would have a total of 40 professionals if 8 professionals are 20 % of staff.
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Full question is:
en una oficina trabajan 8 profesionales haciendo un porcentaje de 20%. calcular el numero del personal de tal oficina
Translated is:
8 professionals work in an office making a percentage of 20%. Calculate the number of staff in such an office.
Suppose you own 125 shares of a stock that pays a dividend of $0.29 per
share per year. How much will you receive in dividends over 6 years,
assuming the dividends stay the same and you buy no more stock?
OA. $161.25
OB. $217.50
C. $174.00
D. $36.25
PREVIOUS
Hello !
125 * $0.29 * 6 = $217.50
which order pair satisfies the relation 2x+y= -3 ?
a(-1,4)
b(-2,-1)
c(0,-3)
d(-3,-3)
The ordered pair (0, -3) satisfies the relation 2x + y = -3.
To determine which ordered pair satisfies the relation 2x + y = -3, we can substitute the values of x and y from each option into the equation and check if the equation holds true.
a) (-1, 4):
2(-1) + 4 = -2 + 4 = 2 (not equal to -3)
b) (-2, -1):
2(-2) + (-1) = -4 - 1 = -5 (not equal to -3)
c) (0, -3):
2(0) + (-3) = -3 (equal to -3)
d) (-3, -3):
2(-3) + (-3) = -6 - 3 = -9 (not equal to -3)
Therefore, the ordered pair (0, -3) satisfies the relation 2x + y = -3.
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A box contains 19 large marbles and 11 small marbles. Each marble is either green or white. 3 of the large marbles are green, and 4 of
the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green? Express your
answer as a fraction or a decimal number rounded to four decimal places.
The probability of selecting a large or green marble is 0.7333.
The probability of selecting a large marble is 19/30 (19 large marbles out of 30 total marbles). The probability of selecting a green marble is 3/30 (3 green marbles out of 30 total marbles).
To find the probability of selecting a large or green marble, you need to find the probability of selecting a marble that is either large or green. This is known as the union of two events. The union of two events is found by adding the individual probabilities of each event together.
The probability of selecting a large or green marble is 19/30 + 3/30 = 22/30 = 0.7333.
Therefore, the probability of selecting a large or green marble is 0.7333.
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