Answer:
Step-by-step explanation: you are sped that is the answer black n
Assume 0 is an acute angle.
cot 0 =
4
3
The value of the angle csc θ of the given problem is: 5/4
How to solve the trigonometric ratios?There are different trigonometric ratios such as:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Now, we are given that:
cot θ = 4/3
We know that cot θ = 1/tan θ
Thus:
tan θ = 3/4
Since θ is an acute angle, it means it is less than 90 degrees. Thus, using Pythagoras theorem, we can find the third side which is the hypotenuse to be 5
Now, csc θ = 1/sin θ
Thus: sin θ = 4/5
csc θ = 5/4
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A native wolf species has been reintroduced into a national forest. Originally, 46 wolves were transplanted. Assuming that the population is growing exponentially at a rate of 5.6%, how long will it take for the population to reach 150 wolves? Round your answer to the first decimal place.
An investment banking house conducted a survey to determine how two of its proposed investment plans for three different age categories are used. This table shows the responses they received. Plan I Plan II Neither Ages 26–35 19 14 17 Ages 36–45 14 28 8 Ages 46–55 27 21 2 What percentage of people preferring plan I are from the 36–45 age group, and what percentage of people from the 46–55 age group prefer plan II? Round your answers to the nearest whole number. A. 23% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II. B. 28% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II. C. 23% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II. D. 28% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II. E. 32% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.
The Percentage of people from the 46-55 age group preferring Plan II is 42%.
The percentages, we need to calculate the ratio of people preferring Plan I in the 36-45 age group and the ratio of people preferring Plan II in the 46-55 age group.
Let's start with the first part of the question:
Percentage of people preferring Plan I from the 36-45 age group:
To calculate this percentage, we need to divide the number of people preferring Plan I in the 36-45 age group by the total number of people preferring Plan I, and then multiply by 100 to express it as a percentage.
Number of people preferring Plan I in the 36-45 age group = 14
Total number of people preferring Plan I = 14 + 28 + 21 = 63
Percentage = (14 / 63) * 100 ≈ 22.22 ≈ 22% (rounded to the nearest whole number)
So, the percentage of people preferring Plan I from the 36-45 age group is approximately 22%.
Now, let's move on to the second part of the question:
Percentage of people from the 46-55 age group preferring Plan II:
To calculate this percentage, we need to divide the number of people preferring Plan II in the 46-55 age group by the total number of people from the 46-55 age group, and then multiply by 100 to express it as a percentage.
Number of people preferring Plan II in the 46-55 age group = 21
Total number of people in the 46-55 age group = 27 + 21 + 2 = 50
Percentage = (21 / 50) * 100 = 42%
So, the percentage of people from the 46-55 age group preferring Plan II is 42%.
Based on the calculations, the correct answer is:
A. 23% of people who prefer Plan I are from the 36-45 age group, and 42% of people from the 46-55 age group prefer Plan II.
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(a) Dewi has £460 to buy Chinese yuan.
Calculate
.
the maximum number of CYN Dewi can buy, and
how much, to the nearest penny, this will cost him.
The maximum number of CYN Dewi can buy is 4268.8 CYN and cost in pounds is £453.20.
Maximum number of CYN Dewi can buy:
Since £1 buys 9.28 CYN, Dewi's £460 can be converted to Chinese yuan by multiplying it by the exchange rate:
Maximum CYN = £460 × 9.28 CYN/£1
To calculate this, we multiply the pound amount by the exchange rate:
Maximum CYN = £460 × 9.28 CYN/£1 ≈ 4268.8 CYN
Cost in pounds to the nearest penny:
To calculate the cost in pounds, we divide the desired amount of Chinese yuan by the exchange rate:
Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1
To calculate this, we divide the Chinese yuan amount by the exchange rate:
Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1
= £453.20
Therefore, the cost in pounds, to the nearest penny, will be £453.20.
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Complete question
Buying chinese yuan (CYN) £1 buys 9.28 CYN
Selling chinese yuan (CYN) 9.42 CYN buys £1
(a) Dewi has £460 to buy Chinese yuan.
Calculate the maximum number of CYN Dewi can buy, and
how much, to the nearest penny, this will cost him.
Explain where the hands of an analog clock point at 1:27.
The hands of an analog clock point at 1:27 is at 1o'clock position
How to determine the pointAt 1:27 on an analog clock, the hour hand focuses straightforwardly at the numeral "1" on the clock confront, demonstrating that it is within the 1 o'clock position.
The miniature hand, on the other hand, focuses between the numerals "2" and "3" on the clock confront, roughly midway between them.
Since there are 60 minutes in an hour and the diminutive hand moves around the clock confront at a consistent rate, it shows that 27 minutes have passed since the hour started.
Hence, the miniature hand is closer to the numeral "3" but not however at it. The moment hand may be anyplace on the clock confront, because it moves persistently.
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pls answer this question, I don't understand it.
The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.
Here, we have,
given that,
the product of two number in scientific notation is: 0.0258 × 10⁻⁸
now, let the two numbers be:
0.43× 10⁻⁵ and, 0.06× 10⁻³
we get,
0.43× 10⁻⁵ × 0.06× 10⁻³
= 0.43 × 0.06× 10⁻⁵ × 10⁻³
= 0.43 × 0.06 × 10⁻⁵⁻³
=0.43 × 0.06× 10⁻⁸
=0.0258 × 10⁻⁸
Hence, The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.
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What is the solution to the proportion 2/3 m/9
Need the answer ASAP
Answer: A. x=3 y= -1 z=4
Step-by-step explanation:
I plugged it into my graphing calculator.
>2nd Matrix
>Edit >A
>choose 3x3
>Enter all coefficients as they look
>2nd Matrix
>Edit >B
>Choose 3x1
>Enter answers as they look
Go to main page
[tex][A]^{-1} [B]\\[/tex]
Answers end up being 3, -1, 4
Please help ASAP 7p-13p+4-5p
Hello!
[tex]7p-13p+4-5p\\\\= 7p-13p-5p+4\\\\= -6p-5p+4\\\\\Large\boxed{= -11p + 4}[/tex]
Can u help me please fill in the square
The equation of the circle is (x + 4)² + (y - 1)² = 81
Given is an equation of a circle we need to convert it in standard form,
x² + y² + 8x - 2y = 64,
To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.
The standard form of a circle equation is:
(x - h)² + (y - k)² = r²
where (h, k) represents the center of the circle, and r represents the radius.
Let's convert the given equation to standard form step by step:
x² + y² + 8x - 2y = 64
Rearrange the equation to group the x-terms and y-terms:
x² + 8x + y² - 2y = 64
Now, complete the square for the x-terms.
Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:
x² + 8x + 16 + y² - 2y = 64 + 16
Simplify:
(x + 4)² + y² - 2y = 80
Complete the square for the y-terms.
Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:
(x + 4)² + y² - 2y + 1 = 80 + 1
Simplify:
(x + 4)² + (y - 1)² = 81
Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.
Hence the equation of the circle is (x + 4)² + (y - 1)² = 81
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Question 3 of 10
The slope of the line below is 4. Which of the following is the point-slope form
of the line?
(-3,-4)
A. y+4= -4(x+3)
B. y-4 = -4(x-3)
C. y+ 4 = 4(x+3)
D. y-4 = 4(x-3)
Answer:
C. y + 4 = 4(x+3)
Step-by-step explanation:
Point slope form: y-y1 = m(x-x1)
Substitute the given slope 4 and point (-3, -4)
y-(-4) = 4(x - (-3))
Simplify
y + 4 = 4 (x+3)
write an explicit formula for an the nth term of the sequence 6, 12, 18
Answer:
[tex]a_{n}[/tex] = 6n
Step-by-step explanation:
there is a common difference between consecutive terms, that is
12 - 6 = 18 - 12 = 6
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 6 and d = 6 , then
[tex]a_{n}[/tex] = 6 + 6(n - 1) = 6 + 6n - 6 = 6n
Multiply out
5x(3x-2)=
The solution is the multiplication is: 5x × (3x-2) = 15x² - 10x.
Here, we have,
given that,
the expression is:
5x(3x-2)
now, we have to Multiply out
so, we have,
5x × (3x-2)
= 5x×3x - 5x×2
=15x² - 10x
Hence, The solution is the multiplication is: 5x × (3x-2) = 15x² - 10x.
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Given below are lease terms at the local dealership. What is the total cash due at signing?
Terms:
Length of lease: 30 months
MSRP of the car $15,500
• Purchase value of the car after lease: $9900
Down payment $2500
Monthly payment $425
-Security deposit $375
Acustion fee $500
A. 375
B. 3375
C. 3800 (✅️)
D. 3400
Molly used 192 beads to make a necklace AND a bracelet. It takes 5 times as many beads to make a necklace as it does a bracelet. How many beads are used to make the necklace?
Examining the word problem we can say that, Molly used 160 beads to make the necklace.
How to find the number of beadsLet's assume the number of beads used to make the bracelet is x.
We also know that Molly used a total of 192 beads for both the necklace and the bracelet. and It takes 5 times as many beads to make a necklace as it does a bracelet, So,
x + 5x = 192
6x = 192
solve for x
x = 192 / 6
x = 32
Molly used 32 beads to make the bracelet.
number of beads used to make the necklace
Number of beads used for the necklace = 5 * 32
Number of beads used for the necklace = 160
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Vertex for y=2(x-3)^2 +1
The vertex of the equation of the parabola y = 2( x - 3 )² + 1 is (3,1).
What is the vertex of the parabola?Given the equation of the parabola in the question:
y = 2( x - 3 )² + 1
To determine the vertex of the parabola, we use the vertex form of a parabola which is expressed as:
Vertex form: y = a(x - h)² + k
Where (h, k) represents the vertex of the parabola.
The given equation is already in the vertex form:
y = 2( x - 3 )² + 1
Hence, comparing the given equation, y = 2(x - 3)² + 1, with the vertex form, we can see that:
h = 3 and k = 1
Therefore, the vertex is (3,1).
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Which is the equation for the function shown? A parabola that opens upward graphed on a coordinate plane. The vertex is negative 1, negative 2, and the parabola passes through the points negative 3, 2, and 1, 2. A. f(x) = (x − 1)2 + 2 B. f(x) = (x + 1)2 − 2 C. f(x) = (x − 2)2 + 1 D. f(x) = (x + 2)2 − 1
The equation for the function shown is f(x) = (x + 1)² - 2. Option B
How to determine the equationFrom the information given, we have the deductions;
The vertex of the parabola is given as (-1, -2)
Using the form;
f(x) = a(x - h)^2 + k
Such that (h, k) represents the vertex coordinates.
Substitute the vertex coordinates into formula, we get;
f(x) = a(x - (-1))² + (-2)
= a(x + 1)² - 2
Now, substitute the value for a, we get;
2 = a(-3 + 1)² - 2
find the square and collect like terms
4 = a(4)
a = 1
Put value back into the equation
f(x) = 1(x + 1)² - 2
Multiply the value, we get;
f(x) = (x + 1)² - 2
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Calculate the area of the composite figure
1. The area of composed figure is 52.26 cm².
2. The area of composed figure is 74 ft².
1. Area if Triangle
= 1/2 x b x h
= 1/2 x 6 x 8
= 24 cm²
Area of semicircle
= πr²/2
= 3.14 x 3 x 3
= 28.26 cm²
So, area of composed figure
= 28.26 + 24
= 52.26 cm²
2. Area of Trapezium
= 1/2 (7 + 13) x 5
= 1/2 x 20 x 5
= 50 ft²
Area of Triangle
= 1/2 x b x h
= 1/2 x 8 x 6
= 24 ft²
So, area of composed figure
= 24 + 50
= 74 ft²
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Derrick Rolls a die many times and Records the number of times he rolls a three arrange the following situations in order from the situation that gets the largest difference between relative frequency and actual probability to the situation that gives the smallest difference
The order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:
Situation 1: Derrick rolls the die 10 times.
Situation 2: Derrick rolls the die 100 times.
Situation 3: Derrick rolls the die 1,000 times.
Situation 4: Derrick rolls the die 10,000 times.
Situation 5: Derrick rolls the die 1,000,000 times.
To determine the order of situations from the largest difference between relative frequency and actual probability to the smallest difference, we need to consider the concept of relative frequency and actual probability.
Relative frequency refers to the observed proportion of an event occurring in an experiment or trial, while actual probability represents the theoretical or expected probability of that event occurring.
Situation 1: Derrick rolls the die 10 times.
In this situation, the relative frequency of rolling a three can vary, but with a limited number of trials, the relative frequency might not accurately reflect the actual probability. Therefore, the difference between relative frequency and actual probability is likely to be larger compared to situations with more trials.
Situation 2: Derrick rolls the die 100 times.
With a larger number of trials, the relative frequency is expected to converge towards the actual probability. The difference between relative frequency and actual probability would likely be smaller compared to the previous situation.
Situation 3: Derrick rolls the die 1,000 times.
Increasing the number of trials further enhances the convergence of relative frequency to the actual probability. The difference between relative frequency and actual probability would be smaller than in the previous two situations.
Situation 4: Derrick rolls the die 10,000 times.
With an even larger number of trials, the relative frequency becomes more reliable and closely approximates the actual probability. The difference between relative frequency and actual probability would be smaller compared to the previous situations.
Situation 5: Derrick rolls the die 1,000,000 times.
In this situation, the large number of trials greatly increases the reliability and accuracy of the relative frequency. The observed relative frequency is expected to be very close to the actual probability, resulting in the smallest difference between the two.
Therefore, the order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:
Situation 1: Derrick rolls the die 10 times.
Situation 2: Derrick rolls the die 100 times.
Situation 3: Derrick rolls the die 1,000 times.
Situation 4: Derrick rolls the die 10,000 times.
Situation 5: Derrick rolls the die 1,000,000 times.
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2.
5 m
50 m
18 m
25 m
As per the given data, the area of the rectangular field is approximately 204 square meters.
To find the area of the rectangular field, we need to multiply its length by its width.
Given that the length is 18 2/5 m and the width is 11 2/23 m, we need to convert these mixed fractions into improper fractions for easier calculation.
Length: 18 2/5 m = (5 * 18 + 2)/5 = 92/5 m
Width: 11 2/23 m = (23 * 11 + 2)/23 = 255/23 m
Now, we can calculate the area of the rectangular field:
Area = Length * Width
= (92/5) m * (255/23) m
= (92 * 255)/(5 * 23) m^2
= 23460/115 m^2
= 204 m^2 (rounded to the nearest whole number)
Therefore, the area of the rectangular field is approximately 204 square meters.
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Your question seems incomplete, the probable complete question is:
A rectangular field is 18 2/5 m long and 11 2/23 m wide. Find its area.
give the rule in words of this pattern 10,13,17,238
Answer:
a set of numbers in order of least to greatest
77th term of the sequence 16,19,22,25
The 77th term of the given Sequence is 244.
The given sequence is an arithmetic progression with a common difference of 3. To find the 77th term of the sequence, we can use the formula for the nth term of an arithmetic progression.
The formula for the nth term of an arithmetic progression is:
_ = _1 + ( − 1),
where _ is the nth term, _1 is the first term, is the position of the term in the sequence, and is the common difference.
In this case, _1 = 16 and = 3. Plugging in these values into the formula, we get:
_77 = 16 + (77 − 1) × 3.
_77 = 16 + 76 × 3.
_77 = 16 + 228.
_77 = 244.
Therefore, the 77th term of the given sequence is 244.
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x^2-2y=5 and 4y+z=7 write z in terms of x
The equation is written as z = 7 + (20 -4x²/2)
How to make the subject
From the information given, we have that the equations as;
x²-2y=5 ( 1)
4y+z=7 (2)
From equation (1), make y the subject of formula, we have;
-2y= 5 - x²
Divide both sides by the coefficient of the variables, we have;
y = 5 - x²/-2
y = -5 + x²/2
Now, substitute the value of y in (2), we have;
4 (-5 + x²/2) + z = 7
expand the bracket
-20 + 4x²/2 + z = 7
collect the like terms, we have;
z = 7 + (20 -4x²/2)
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: B
Step-by-step explanation: 63.3 in^2
The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022. Andre visited Dubai over winter break. He stood 1000 meters away from the building, looked up at a 39.62 degree angle using a laser rangefinder and spotted the top of the building.
Andre
If every floor is 5.079 meters tall, how many floors are there in the Buri Khalifa?
The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022, there are approximately 148 floors in the Burj Khalifa.
We can make use of the data given to determine the Burj Khalifa's floor count.
Andre is known to have stood 1,000 metres away from the structure and turned his head to look up at a 39.62 degree angle.
Let's write "h" for the Burj Khalifa's height and "d" for Andre's distance from the building's base.
tan(39.62°) = h / d
h = d * tan(39.62°)
h = 1000 * tan(39.62°) ≈ 753.7 meters
So, as per this, Number of floors = h / floor height
Number of floors = 753.7 meters / 5.079 meters
Number of floors ≈ 148.4 floors or 148 floors.
Thus, 148 floors are there in Burj Khalifa.
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WILL GIVE BRAINLIEST TO THE CORRECT ANSWER!!
This scale drawing shows a enlargement in a figure.
What is the value of x?
Enter your answer in the box.
X =
Answer:
18
Step-by-step explanation:
is a 1/3 scale
6-12-?
8-16-24
simple :)
I have 12 teams that will play each other once, but have activities that each team will only play once. How many weeks and activities do I need.
==============================================
Explanation:
The formula to use is n*(n-1)/2
Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = 66
That formula is from the nCr combination formula when r = 2.
---------------------
Here's a visual way to see why that rule works.
Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}[/tex]
In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}[/tex]
Let's also cross out any cell below the main diagonal.
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}[/tex]
We do this because a mirrored copy is found above the diagonal.
We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.
Those 6 matchups are:
A vs BA vs CA vs DB vs CB vs DC vs DThe order doesn't matter. A matchup like "A vs B" is the same as "B vs A".
We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.
Then we split that in half to get the formula n(n-1)/2.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
To determine the radius of each wheel, we can use the formula for the circumference of a circle:
Circumference = 2πr,
where "Circumference" represents the circumference of the wheel and "r" represents the radius of the wheel.
Given that the circumference of each wheel is 22 inches, we can set up the equation as follows:
22 = 2πr.
To solve for the radius, we'll isolate "r" by dividing both sides of the equation by 2π:
22 / (2π) = r.
Using a calculator for the approximation, we get:
r ≈ 3.5 inches.
Therefore, to the nearest length, the radius of each wheel is approximately 3.5 inches.
Answer:
C) 3.5 inch
Step-by-step explanation:
b) 9 mm 6 mm 7 mm surface area for this question
The surface area of the rectangular prism is 318 square mm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
9 mm by 6 mm by 7 mm
The surface area of the rectangular prism is calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (9 * 6 + 9 * 7 + 6 *7)
Evaluate
Area = 318
Hence, the area is 318 square mm
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Question
The net of a rectangular prism and its dimensions are given as 9 mm 6 mm 7 mm. What is the total surface area of the rectangular prism in square inches?
Which choice is a solution to this system of equations? -x=y-4 y=4x+9
The solution to the system of equations is x = 5.4 and y = -1.4
How to determine the solution to the system of equations?From the question, we have the following parameters that can be used in our computation:
-x=y-4 y=4x+9
So, we have
-x = y - 4
y = 4x + 9
Rewrite the equation as
x = -y + 4
y = 4x + 9
So, we have
y = 4(-y + 4) + 9
Open the bracket and evaluate
5y = 9 - 16
So, we have
y = -1.4
Recall that
x = -y + 4
So, we have
x = 1.4 + 4
Evaluate
x = 5.4
Hence, the solution is x = 5.4 and y = -1.4
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