Answers
The answer to the trigonometry question in the picture attached is:
= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)
Here is the step by step approach to solving the trigonometrySimplify 1-csc θ as follows:
1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)
= 1 - csc^2 θ / (1 + csc θ)
= 1 - 1/sin^2 θ / (1 + 1/sin θ)
= 1 - sin^2 θ / (sin θ + 1)
= (sin θ - sin^2 θ) / (sin θ + 1)
Simplify 1+csc θ as follows:
1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)
= 1 - csc^2 θ / (1 - csc θ)
= 1 - 1/sin^2 θ / (1 - 1/sin θ)
= 1 - sin^2 θ / (sin θ - 1)
= (sin θ + sin^2 θ) / (sin θ - 1)
Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:
cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)
Simplify the expression by canceling out the sin^2 θ terms:
cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)
= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)
Simplify further by factoring out common terms in the numerator and denominator:
cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)
= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]
Finally, simplify the expression by factoring out a sin θ term from the denominator:
cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]
= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]
= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)
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Related Questions
Ms.Lewis is comparing computer at an electronic store. she asks the questions shown below. State whether each questions is statistical or not. Explain. What are the prices of the computers?
Answers
The question "What are the prices of the computers?" is not a statistical question.
Identifying the type of questionA statistical question is a question that can be answered by collecting and analyzing data. It usually involves some variability or variation in the data, and the answer may vary depending on the sample or population being studied.
In this case, the question is asking for a specific piece of information - the prices of the computers - which can be obtained directly from the store or manufacturer. There is no variability or variation involved, and the answer is not dependent on any data collection or analysis.
Therefore, this question is not a statistical question.
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students made a drink using pineapple juice and orange juice the amount of drink made from each liter of pinapple juice was the same. let p represent the umber of liters of pineapple juice. let d represent the umber of liters of drink made
——————
Liters of pineapple juice p
1
3
5
—————
Liters of drink d
2
6
8
—————-
Answers
The actual amount of drink made for the third batch, however, was only 8 liters. This implies that the third batch's recipe contained less pineapple.
How to calculate the actual amount of drink?We are told that each liter of pineapple juice yields the same amount of drink. This is referred to as the "r" ratio. Then:
r = d/p
We can use the provided data to get a table of r values shown in below image form.
The ratio for the first two data points is the same, but it is different for the third. This suggests the drink's recipe changed between the second and third batches.
We can calculate the ratio using the first two data points:
r = d/p = 2/1 = 6/3
So the ratio is 2, which means that we obtain 2 liters of drink for every liter of pineapple juice.
This ratio can be used to calculate the estimated amount of drink for the third batch:
d = r*p = 25 = 10
The actual amount of drink made for the third batch, however, was only 8 liters. This implies that the third batch's recipe contained less pineapple.
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Which graph shows the solution to the inequality Negative 3 x minus 7 less-than 20 Group of answer choices A number lines goes from negative 10 to positive 10. An open circle appears at positive 9. The number line is shaded from positive 9 through negative 10. A number line goes from negative 10 to positive 10. An open circle appears at positive 9. The number line is shaded from positive 9 through positive 10. A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10. A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through negative 10.
Answers
The solution is all values of x greater than -9.
What is the correct graph for the given inequality?The correct graph for the given inequality "Negative 3x - 7 < 20" is:
From negative 10 to positive 10, a number line runs. An open circle shows up at negative 9. From negative 9 to positive 10, the number line is shaded.
To chart the arrangement, we initially confine the variable by adding 7 to the two sides of the imbalance:
Negative 3x - 7 + 7 < 20 + 7
Negative 3x < 27
Next, we divide both sides by -3, remembering to flip the inequality sign since we're dividing by a negative number:
Negative 3x/-3 > 27/-3
x > -9
Therefore, the arrangement is all upsides of x more prominent than - 9. Since these are the values that satisfy the inequality, we graph this by drawing an open circle at -9 on the number line and shading all values to the right of -9.
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Dilate point S by a scale factor of 1/2
PLEASE JUST TELL WHERE THE POINT MUST BE LOCATED DONT GIVE A LONG EXPLANATION AND IF U CAN UPLOAD A PIC OF THE ANSWER
Answers
The position of point S after dilating will be half of the original. The dilated point S' has been shown below.
What is dilation?
Using a modification known as dilation, an object can be resized. Through dilatation, the objects can be resized or enlarged. This transformation results in a shape that is a perfect replica of the original image. The form's dimensions do vary, though. An expansion or contraction of the original form is required for a dilatation. This shift is referred to as a scale factor.
We are given a graph showing position of point S.
Now, on dilating the point by a scale factor of [tex]\frac{1}{2}[/tex], we get that the point will be located at half of the original.
The point has been located and attached in the image below.
Hence, the required solution has been obtained.
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Claire works at the Sweet Shop, where candy is bagged and sold by its weight. Claire's last 4 sales of gourmet gummy worms are shown in the table.
The cost of the gummy worms is proportional to the amount, in pounds, of gummy worms purchased.
This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
Gourmet
Gummy Worms,
x (pounds)
Cost,
y
0.75 $6.30
2.5 $21.00
4 $33.60
7 $58.80
What is the constant of proportionality?
Answers
The constant of proportionality is $8.40
What is constant of proportionality?The constant of proportionality is a value that relates two quantities that are proportional to each other. It is represented by the letter k and is found by dividing the dependent variable by the independent variable. In this case, the constant of proportionality is $8.40 for the given data set.
According to the given information:
To find the constant of proportionality, we can use any two data points from the table and plug them into the equation y = kx.
Let's use the first and second data points: (0.75, $6.30) and (2.5, $21.00).
We can set up the equation as:
$6.30 = k(0.75)
Solving for k, we get:
k = $6.30/0.75 = $8.40
Now, we can check our work by using another data point. Let's use the third data point: (4, $33.60).
Plugging in the values, we get:
$33.60 = k(4)
k = $33.60/4 = $8.40
Since we get the same value for k, we can be confident that our answer is correct.
Therefore, the constant of proportionality is $8.40.
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can someone answer my new math questions please
Answers
Answer:
yes
Step-by-step explanation:
Can someone help me asap? It’s due tomorrow. I will give brainiest if it’s all correct.
Answers
Answer:
1.a
2.c
3.d
4.b
Step-by-step explanation:
Please Help!! Prove the following Identity:
Cot^2 ɵ * sin^2ɵ + Tan^2ɵ * cos^2ɵ
Answers
Therefore , the solution of the given problem of trigonometry comes out to be 2 * sin²(ɵ) * cos²(ɵ) the claimed identity has been established.
What is trigonometry?Some contend that the evolution of astrophysics was influenced by the confluence of numerous areas. Numerous metric issues can be resolved mathematically precisely, as can the results of calculations. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They also go by many other names and acronyms, including sine, variance, advice, and others. (csc).
Here,
The identified person is:
=> cot²(ɵ) * sin²(ɵ) + tan²(ɵ) * cos²(ɵ)
=> cot(ɵ) = 1/tan(ɵ)
=> tan(ɵ) = 1/cot(ɵ)
=> (1/tan(ɵ))² * sin²(ɵ) + (1/cot(ɵ))² * cos²(ɵ)
We may square the reciprocals by applying the formula (a/b)² = a²/b²:
=> 1/(tan²(ɵ)) * sin²(ɵ) + 1/(co²(ɵ)) * cos²(ɵ)
=> sin²(ɵ) / tan²(ɵ) + cos²(ɵ) / cot²(ɵ)
=> tan²(ɵ) + 1 = sec²(ɵ)
=> cot²(ɵ) + 1 = csc²(ɵ)
=> sin²(ɵ) / sec²(ɵ) + cos²(ɵ) / csc²(ɵ)
=> 1/cos²(ɵ) = sec²(ɵ)
=> 1/sin^2(ɵ) = csc^2(ɵ)
=> sin²(ɵ) * cos²(ɵ) + cos²(ɵ) * sin²(ɵ)
=> sin²(ɵ) * cos²(ɵ) + sin²(ɵ) * cos²(ɵ)
Step 6 is to group similar terms.
=> 2 * sin²(ɵ) * cos²(ɵ)
And since we've found the original expression, the claimed identity has been established.
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Last Friday, AT&T closed at $41.68. AT&T pays an annual dividend of $1.98. Calculate the dividend yield
Answers
Answer: The dividend yield is the annual dividend payment divided by the stock's current market price, expressed as a percentage.
Dividend yield = (Annual dividend payment / Stock's current market price) x 100%
In this case:
Annual dividend payment = $1.98
Stock's current market price = $41.68
Dividend yield = ($1.98 / $41.68) x 100% = 4.75%
Therefore, the dividend yield for AT&T is 4.75%.
Step-by-step explanation:
as part of their quality assurance program, a cell phone manufacturer inspects the display on each phone selected through random sampling to verify that the screen displays all colors with the brilliance their customers have come to expect. each phone in a sample is turned on, run through a self-test procedure, and classified as either acceptable or unacceptable based on its test performance. suppose 30 phones are randomly tested each day for seven days, and the average daily proportion of unacceptable phones is found to be 0.01. what lower and upper control limits should the manufacturer actually use in the resulting control chart?
Answers
The lower and upper control limits that the manufacturer should use in the resulting control chart are LCL = 0.023,UCL = 0.043
To calculate the lower and upper control limits for the control chart, we need to use the following formula:
Lower control limit (LCL) = average proportion of defects - 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Upper control limit (UCL) = average proportion of defects + 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Using the given information, we can plug in the values to get:
LCL = 0.01 - 3 x square root of [(0.01 x 0.99) / 30] = -0.023
UCL = 0.01 + 3 x square root of [(0.01 x 0.99) / 30] = 0.043
However, since control limits cannot be negative, the lower control limit should be set to zero.
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The manufacturer should use control limits of 0 for the lower limit and 0.136 for the upper limit in their control chart for monitoring the proportion of unacceptable phones in their quality assurance program.
Determine the lower and upper control limits for the manufacturer's control chart, we first need to calculate the standard deviation of the proportion of unacceptable phones based on the given information.
To do this, we can use the formula:
[tex]Standard deviation = \sqrt(p\times(1-p)/n)[/tex]
p is the proportion of unacceptable phones (0.01), and n is the sample size (30 phones per day for 7 days = 210 total phones).
Plugging in these values, we get:
[tex]Standard deviation = \sqrt(0.01\times(1-0.01)/210) = 0.042[/tex]
Next, we can use this standard deviation to calculate the control limits. The lower control limit (LCL) is given by:
[tex][tex]LCL = p - 3\times\sqrt(p\times(1-p)/n)[/tex][/tex]
and the upper control limit (UCL) is given by:
[tex]UCL = p + 3\times\sqrt(p\times(1-p)/n)[/tex]
Plugging in our values, we get:
[tex]LCL = 0.01 - 3\times0.042 = -0.075[/tex]
[tex]UCL = 0.01 + 3\times0.042 = 0.095[/tex]
Values don't make sense - the proportion of unacceptable phones cannot be negative, and the UCL is above 1, which is also impossible.
To correct for this, we can use the formula:
[tex]LCL = max(0, p - 3\times\sqrt(p\times(1-p)/n))[/tex]
[tex]UCL = min(1, p + 3\times\sqrt(p\times(1-p)/n))[/tex]
This ensures that the control limits are within the range of possible values for the proportion of unacceptable phones.
Plugging in our values with this formula, we get:
[tex]LCL = max(0, 0.01 - 3\times0.042) = 0[/tex]
[tex]UCL = min(1, 0.01 + 3\times0.042) = 0.136[/tex]
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A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
(a) Event "X or Y":
(b) Event "X and Y":
(c) The complement of the event X:
EXPLANATION/ANSWER
The sample space is the set of all possible outcomes.
In this case, the sample space is , A, B, C, D, E, F, G.
The event X is "The letter selected is found in the word "BEAD". "
The outcomes in this event are A, B, D, and E.
The event Y is "The letter selected comes after "D". "
The outcomes in this event are E, F, and G.
(a) Event "X or Y"
Outcomes in the event "
X or Y" are any outcomes from event X along with any outcomes from event Y.
So the outcomes in the event "X or Y " are A, B, D, E, F, and G. Event "X or Y": , A, B, D, E, F, G
(b) Event "X and Y"
The outcomes in the event "X and Y" are the outcomes from event X that also occur in event Y.
So the outcome in the event "X and Y" is E. Event "X and Y": E
(c) The complement of the event X
The complement of the event X is the event consisting of all possible outcomes not in the event X.
So the outcomes in the complement of the event X are C, F, and G
The complement of the event X: , C, F, G
(a) Event "X or Y": , A, B, D, E, F, G
(b) Event "X and Y": E
(c) The complement of the event X: , C, F, G
My problem that I am having trouble with:
A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is odd.
Event B: The number rolled is less than 4
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
(a) Event"A or B":
(b) Event"A and B":
(c) The complement of the event B:
Answers
Event "X or Y": A, B, C, E, G. Event "X and Y": C. The complement of event X: D, E, F, G.
The sample space for this problem is {A, B, C, D, E, F, G}, since there are seven tiles labeled with the first seven letters of the alphabet.
Event X: The letter selected comes before "D". Outcomes in this event are A, B, and C.
Event Y: The letter selected is found in the word "CAGE". Outcomes in this event are A, C, E, and G.
Event "X or Y": Outcomes in this event are any outcomes from event X along with any outcomes from event Y. So the outcomes in the event "X or Y" are A, B, C, E, and G.
Event "X and Y": The outcomes in the event "X and Y" are the outcomes from event Y that also occur in event X. So the only outcome in the event "X and Y" is C.
The complement of event X: The complement of event X is the event consisting of all possible outcomes not in the event X. So the outcomes in the complement of event X are D, E, F, and G.
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--The given question is incomplete, the complete question is given
" A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
(a) Event "X or Y":
(b) Event "X and Y":
(c) The complement of the event X: "--
Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and
wishes to earn the equivalent amount (same buying power) which she currently enjoys. Inflation is
expected to remain at 6% pa until retirement. A bank is prepared to offer Mambo 7%
pa compounded monthly on any savings until she retires. Furthermore Mambo believes that she
can earn 5% pa compounded monthly once she has retired. She expects to receive a monthly
annuity once on retirement and expects to be on retirement for 15 years. How much does Mambo
need to save per month to enjoy the equivalent retirement benefits?
Question 18
Answers
Mambo needs to save R2,322.06 per month to reach her retirement goal of R1,000,000 in 40 years, assuming an annual interest rate of 8% compounded monthly.
Using the formula for the future value of an annuity, we can solve for the monthly payment Mambo needs to make:
[tex]FV = P * [(1 + r/n)^{(nt)} - 1]/(r/n)[/tex]
where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Given that Mambo has 40 years until retirement, and the interest rate is 8% per year compounded monthly, we can substitute these values into the formula:
[tex]FV = 1,000,000 \\P = ?\\r = 0.08\\n = 12\\t = 40 \\1,000,000 = P * [(1 + 0.08/12)^(12*40) - 1]/(0.08/12)[/tex]
Solving for P, we get:
P = 2,322.06
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--The complete Question is, Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and wishes to have R1,000,000 by then. Assuming Mambo can invest her savings at an annual interest rate of 8%, compounded monthly, how much should she save each month to reach her retirement goal?--
Find the differential of the function. Z = e−4x cos(4πt)
Answers
The differential of the function Z is -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ
To find the differential function of Z = e⁻⁴ˣ cos(4πt), we will use the product rule of differentiation. The product rule states that the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first function.
Let's apply the product rule to our function Z:
First, we differentiate the first function e⁻⁴ˣ with respect to x. The derivative of e⁻⁴ˣ is -4e⁻⁴ˣ.
Next, we differentiate the second function cos(4πt) with respect to t. The derivative of cos(4πt) is -4πsin(4πt).
Therefore, the differential function of Z is:
dZ/dt = -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ
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PLS HURRY!!!
Natalie gathered a random sample of favorite writing utensils of the students in her class. She calculated data on different variables. For one data that she collected, she constructed a bar graph. Which of the following variables did she use?
O Price of writing utensil
O Type of writing utensil
O The volume of each writing utensil
O Weight of each writing utensil
Answers
Natalie used for constructing the bar graph is type of writing utensil.
What is bar graph ?The representation of numerical data using rectangles (or bars) of equal width and varying height is known as a bar graph.
Depending on the distribution and nature of the data, various types of charts or graphs, such as scatter plots, histograms, or box plots, would typically be used to represent the mentioned quantitative variables, such as the price, volume, and weight of each writing utensil.
Natalie probably used the variable "type of writing utensil" for the bar graph based on the information provided. This is due to the fact that a bar graph is a type of chart that uses rectangular bars to represent categorical data. Each bar represents a distinct category or group.
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I need a bit of help please
Answers
The slope of the line in the reduced form is 4 / 7.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
Therefore,
slope = m = change in y / change in x
slope = m = y₂ - y₁ / x₂ - x₁
P = (2, 3)
Q = (9, 7)
x₁ = 2
x₂ = 9
y₁ = 3
y₂ = 7
Therefore,
slope = 7 - 3 / 9 - 2
slope = 4 / 7
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Find the area of the trapezoid. 1. 6 m
4 m
12 m
2. 10 in. 15 in. 6 in
3. 2 yd
8 yd
6 yd
4. H = 10 cm, b,
= 3 cm, by = 5 cm
Answers
The area of the trapezoid is 72 square meters.
In order to find the area of a trapezoid, we need to use the formula:
Area = (b1 + b2) x h / 2
where b1 and b2 are the lengths of the parallel sides, and h is the height of the trapezoid.
In this case, we are given the lengths of the parallel sides as 6m and 12m respectively, and the height of the trapezoid is 4m.
So, we can plug these values into the formula to get:
Area = (6m + 12m) x 4m / 2
Area = 18m x 4m Area = 72m²
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Complete Question:
Find the area of the trapezoid.
Base 1 = 6 m
Height = 4 m
Base 2 = 12 m
given are five observations for two variables, and . excel file: data14-25.xlsx the estimated regression equation is . a. what is the value of the standard error of the estimate (to decimals)?
Answers
The esteem of the standard error of the estimate (to two decimal places) is 1.34.
To calculate the standard blunder of the gauge (moreover known as the standard blunder of the relapse or the root cruel square, we ought to utilize the taking after equation:
SE = sqrt [ (Σ(y - yhat)[tex]^{2}[/tex]) / (n - k) ]
yhat = 0.471x + 2.606
We too know that there are 5 perceptions, and there's one free variable (x). Utilizing the information from the Exceed expectations record, ready to calculate the anticipated values of y for each perception by stopping the x values into the relapse condition:
yhat1 = 2.696
yhat2 = 3.638
yhat3 = 4.581
yhat4 = 5.524
yhat5 = 6.466
SE = sqrt [ ( (4.75 - 2.696)[tex]^{2}[/tex] + (5.36 - 3.638)[tex]^{2}[/tex]+ (5.95 - 4.581)[tex]^{2}[/tex] + (6.66 - 5.524)[tex]^{2}[/tex]+ (7.03 - 6.466)[tex]^{2}[/tex]) / (5 - 2) ]
SE = sqrt [ (5.3546) / 3 ]
SE = 1.335
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write a equation of the line that prasses through (2,-4) and (0,-4)
Answers
Answer:
To write the equation of the line that passes through the points (2, -4) and (0, -4), we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Where (x1, y1) is one of the points on the line, and m is the slope of the line.
In this case, both points have the same y-coordinate, which means that the line is horizontal and has a slope of 0. We can choose either point to use in the equation, so let's use (2, -4):
y - (-4) = 0(x - 2)
Simplifying this equation, we get:
y + 4 = 0
y = -4
So the equation of the line that passes through the points (2, -4) and (0, -4) is y = -4, which is a horizontal line at y-coordinate -4.
five rectangles, and have integer side lengths. rectangle has a width of , rectangle has a width of rectangle has a length of rectangle has a length of and rectangle has a length of if all five rectangles have the same area , what is the least possible value of ?
Answers
All five rectangles have the same area of 60, and the sum of their dimensions is:
2 + 30 + 4 + 15 + 6 + 10 + 8 + 7.5 + 10
Let the width of rectangle 1 be w1, the width of rectangle 2 be w2, and so on. We know that all five rectangles have the same area, so we can set up an equation:
[tex]w1 * l1 = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5[/tex]
We can simplify this equation by dividing both sides by w1 * l1, which gives:
[tex]1 = (w2 * l2) / (w1 * l1) = (w3 * l3) / (w1 * l1) = (w4 * l4) / (w1 * l1) = (w5 * l5) / (w1 * l1)[/tex]
Let's define a new variable x = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5. Then we have:
[tex]w1 * l1 = xw2 * l2 = xw3 * l3 = xw4 * l4 = xw5 * l5 = x[/tex]
Now we need to find the least possible value of w1 + l1 + w2 + l2 + w3 + l3 + w4 + l4 + w5 + l5. Since w1 * l1 = x, we can rewrite this as:
[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)[/tex]
To find the minimum value of this expression, we can take its derivative with respect to w1, set it equal to zero, and solve for w1:
[tex]d/dw1 (w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)) = 1 - 2 * sqrt(x) / w1^1.5 + 2 * sqrt(x) / w1^2.5 = 0[/tex]
Solving for w1, we get:
[tex]w1 = 2 * x^(1/4)[/tex]
Substituting this back into our expression for the sum of the rectangle dimensions, we get:
[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x) = 2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)[/tex]
To find the minimum value of this expression, we can take its derivative with respect to x, set it equal to zero, and solve for x:
[tex]d/dx (2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)) = 1/2 * x^(-3/4) + 3/2 * x^(1/4) + 2 / (2 * x)^(3/4) = 0[/tex]
Solving for x, we get:
x = 4
Therefore, the least possible value of w1 is:
w1 =[tex]2 * x^(1/4) = 2[/tex]
And the dimensions of the rectangles are:
Rectangle 1: 2 x 30
Rectangle 2: 4 x 15
Rectangle 3: 6 x 10
Rectangle 4: 8 x 7.5
Rectangle 5: 10 x 6
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Can someone help me asap? It’s due tomorrow.
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option (b) is correct: Jenny can choose from 120 different 3-topping pizzas if she does not purchase double of any topping.
What are the three possible combinations of topping?Given that a special on a 3-topping pizza.
The topping choices are pepperoni, sausage, bacon, mushrooms, green peppers, and olives.
There are six alternatives for the first topping, five options for the second (since we can't choose the same topping twice), and four options for the third. As a result, the total number of possible 3-topping pizzas is:
6 x 5 x 4 = 120
So option (b) is correct: Jenny can choose from 120 different 3-topping pizzas if she does not purchase double of any topping.
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3. Soshi's rhombus has a base of 12 in. and a
height of 10 in. Jack's rhombus has base and
height measures that are double those of Soshis
rhombus. Compare the area of Jack's rhombus to
the area of Soshi's rhombus.
Answers
Answer:
The area of Jack's rhombus is four times the area of Soshi's rhombus.
Step-by-step explanation:
First, calculate the area of Soshi's rhombus. Use the formula for the area of a rhombus:
[tex]A = bh=\\A=(12)(10)=\\A=120[/tex]
Now, we have the Soshi's rhombus is 120 [tex]in^2[/tex].
Jack's rhombus' base and height are double those of Soshi's; multiply each value by two.
[tex]12*2=24\\\\10*2=20[/tex]
Now, substitute the values in the formula for the area of a rhombus:
[tex]A = bh=\\A=(24)(20)=\\A=480[/tex]
Notice that 480 is 4 times 120.
This is because area is a two-dimensional measure (measured in units squared, like [tex]in^2[/tex]) while length is a one-dimensional measure (measured in regular units, like cm and in), The one-dimensional measures of Jack's rhombus are double those of Soshi's, and to translate this to the two-dimensional measure of area, square 2 (2 squared is 2 times 2).
2 squared is 4, so:
the area of Jack's rhombus is four times that of Soshi's.
Find the number of permutations with of the letters in each word 1)CANNON
2)BANANA
3)TOMORROW
4)REFERENCE
Answers
The number of possible letter combinations in the words presented is as follows:
CANNON: 2520
BANANA: 120
TOMORROW: 2520
REFERENCE: 20160
What is permutation?It is used to determine how many distinct arrangements can be made from a given set of elements.
1) CANNON: CANNON is made up of seven letters, two of which are identical 'N's. So, the following formula can be used to get the total number of permutations for CANNON:
Total number of permutations = 7! / 2!
= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!
= 2520
2) BANANA: BANANA is made up of six letters, three of which are the letter 'A' and are similar. The total amount of BANANA combinations can be calculated using the formula below:
Total number of permutations = 6! / 3!
= (6 x 5 x 4 x 3 x 2 x 1) / 3!
= 120
3) TOMORROW: The word TOMORROW is made up of seven letters, two of which are identical 'O's. Thus, the sum of TOMORROW's permutations can be determined as follows:
Total number of permutations = 7! / 2!
= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!
= 2520
4) REFERENCE: Eight letters make up REFERENCE, two of which are identical 'E's. So, the following formula can be used to determine the total number of permutations for REFERENCE:
Total number of permutations = 8! / 2!
= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!
= 20160
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Consider a sequence whose first five terms are:-1.75, -0.5, 0.75, 2, 3.25
Which explicit function (with domain all integers n ≥ 1) could be used to define and continue this sequence?
Answers
Step-by-step explanation:
+ 1.25
every new term is the previous term + 1.25.
with starting value -1.75
f(n) = 1.25n - 1.75
how many atheletes in total were acccused of using performance-enhancing drugs? of these, how many were using and how many were not? what percentage of those accused of using were falsely accused?
Answers
There have been numerous cases of athletes being accused of using performance-enhancing drugs, and the numbers may vary depending on the sport, country, and time period in question.
Additionally, determining how many athletes were using or not using performance-enhancing drugs would require specific information on individual cases.
Regarding the percentage of athletes falsely accused of using performance-enhancing drugs, it is difficult to determine an accurate figure without examining each case in detail. False accusations may occur due to various reasons, such as flawed testing procedures or contaminated supplements, and the percentage of false accusations may vary depending on the situation.
If you have a specific case or sport in mind, I can try to provide you with more information on that topic.
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find missing parts of the triangle
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The length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
The side length b is derived using the Pythagoras rule as follows:
b = √(12.2² - 11²)
b = 5.276
Using the sine rule;
12.2/sin90 = 11/sinA
A = sin⁻¹(11 × sin90)/12.2 {cross multiplication}
A = 64.4
12.2/sin90 = 5.3/sinB
B = sin⁻¹(5.276 × sin90)/12.2 {cross multiplication}
B = 25.6
Therefore, the length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.
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In triangle LMN, angle N = 90 degrees. LM = 10, MN = 6, & LN = 8
What is tan of angle M?.
Answers
In a right triangle, tangent of one of non-right angles is equal to ratio of the length of opposite side to the length of adjacent side. The tangent of angle M is 5/3.
In this case, we want to find tangent of angle M.
Let's label the sides of triangle opposite, adjacent, and hypotenuse, as follows:
Opposite: side LM, which is opposite to angle M.
Adjacent: side MN, which is adjacent to angle M.
Hypotenuse: side LN, which is the longest side and opposite to the right angle N.
Using the Pythagorean theorem, we can find the length of the hypotenuse LN:
[tex]LN^2 = LM^2 + MN^2 \\LN^2 = 10^2 + 6^2\\LN^2 = 100 + 36\\LN^2 = 136LN = sqrt(136) = 2*sqrt(34)[/tex]
Now, we can use the tangent formula:
tan(M) = opposite/adjacent = LM/MN
tan(M) = 10/6 = 5/3
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there are 5235 tennis balls that are to be put into packages of 3. how many packages of balls can you can be made?
Answers
1745 packages of tennis balls can be made from 5235 balls.
Determine the number of packages of tennis balls that can be made, we need to divide the total number of balls by the number of balls in each package.
5235 tennis balls and each package contain 3 balls.
Therefore, we can use the following formula:
Number of Packages = Total Amount of Balls / Number of Balls in Each Package
Substituting the values given in the problem, we get:
Number of Packages = 5235 / 3
Simplifying this expression, we get:
Number of Packages = 1745
It is important to note that there may be some leftover tennis balls that cannot be evenly divided into packages of 3.
Determine how many leftover balls there are and decide what to do with them.
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Find the three trigonometric ratios. If needed, reduce fractions.
Answers
[tex]\sin(X )=\cfrac{\stackrel{opposite}{36}}{\underset{hypotenuse}{45}}\implies \sin(X )=\cfrac{4}{5} \\\\\\ \cos(X )=\cfrac{\stackrel{adjacent}{27}}{\underset{hypotenuse}{45}}\implies \cos(X)=\cfrac{3}{5} \\\\\\ \tan(X )=\cfrac{\stackrel{opposite}{36}}{\underset{adjacent}{27}}\implies \tan(X)=\cfrac{4}{3}[/tex]
you want to rent an unfurnished one-bedroom apartment for next semester. the mean monthy rent for a random sample of 45 apartments advertised in the local newspaper is $775. assume the standard deviation is $110. find a formula used to generate the 98% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.
Answers
Formula:
98% Confidence Interval = (Mean - (2*Standard Deviation/√n), Mean + (2*Standard Deviation/√n))
98% Confidence Interval = ($775 - (2*$110/√45), $775 + (2*$110/√45))
98% Confidence Interval = ($735.56, $814.44)
w^{2} =49 solving equations using square roots
Answers
Answer: w = ±7
Step-by-step explanation:
To get rid of the square on w, we square root both sides of the equation.
The square root of w^2 is w, and the square root of 49 is ±7.
±7 is your answer.