Answer:
The answer to the questions is
a)1
b)60°
Step-by-step explanation:
tan 45°=1
sin‐¹(√3/2)=60°
The values of the given trigonometric expression are:
(a) tan 45° = 1
(b) [tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ[/tex]
Use the concept of trigonometric identity defined as:
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
(a) The given trigonometric ratio is,
tan 45°
Since we know that,
In the trigonometric ratio table for the measure 45°,
The value of tangent is 1.
Hence,
tan 45° = 1
For the given trigonometric exprssion,
[tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2})[/tex]
Since we know that,
Sin 60° = √3/2
Therefore,
[tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = \text{sin}^{-1}(\text{sin }60^\circ)\\\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ[/tex]
Hence,
The value of the given expression is 60°.
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Look at the stem-and-leaf plot. What is the range in scores? Key 6l4 = 64 A. 36 B. 83.5 C. 84.45 D. 100
36 is the range of the score.
The data set's smallest score is 64, as indicated in the key, and its highest score is 100. (which is the last value in the stem-and-leaf plot).
The range of scores is as follows:
Range: Maximum score - Minimum score
Range = 100 - 64
Range = 36
The range of scores is therefore 36.
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Complete question:
an unknown mass (x) rock was placed into 500ml beaker containing 140 milliliters of water. if the rock was dropped into the beaker and the total volume of water is now 471ml. how much water is displaced by the unknown mass (x)
The volume of water displaced by the unknown mass (x) rock is 331 ml
What is meant by displaced?
Displaced means to be moved or forced out of its original position or location. It can refer to a physical object or a person who has been forced to leave their home or community due to conflict, natural disaster, or other circumstances. Displacement can cause significant challenges and disruptions to individuals and communities.
According to the given information
The formula for water displacement is: Volume (object) = Volume (water + object). This formula is based on Archimedes’ Principle, which states that the weight of the displaced fluid is equal to the weight of the submerged object1.
So, we can calculate the volume of water displaced by the unknown mass (x) rock as follows:
Volume (water + object) = 471 ml Volume (water) = 140 ml Volume (object) = Volume (water + object) - Volume (water) Volume (object) = 471 ml - 140 ml Volume (object) = 331 ml
Therefore, the volume of water displaced by the unknown mass (x) rock is 331 ml
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Spiral Review The figure shows the dimensions of a rectangular city park. Rectangle A B C D is shown. Side B C is labeled 540ft. Side C D is labeled 720ft. A member of the parks commission is considering a new diagonal path that would cut through the park from A to C. If the path is built, how much shorter would it be to walk along the path from A to C rather than walking along the edge of the park from A to C? Explain.
It would be 360 ft shorter to walk along the diagonal path from A to C rather than walking along the edge of the park from A to C.
To find out how much shorter it would be to walk along the diagonal path from A to C, we need to compare the lengths of the two paths: the diagonal path and the path along the edge of the park.
First, we can use the Pythagorean theorem to find the length of the diagonal path. In the rectangle ABCD, diagonal AC is the hypotenuse of a right triangle with sides AB and BC. So:
AC² = AB² + BC²
AC² = (720 ft)² + (540 ft)²
AC² = 518400 + 291600
AC² = 810000
AC = √810000
AC = 900 ft
So the length of the diagonal path from A to C is 900 ft.
Next, we can find the length of the path along the edge of the park from A to C. This path consists of two sides of the rectangle: AB and BC. So:
Length of path from A to C = AB + BC
Length of path from A to C = 720 ft + 540 ft
Length of path from A to C = 1260 ft
So the length of the path along the edge of the park from A to C is 1260 ft.
To find out how much shorter it would be to walk along the diagonal path, we can subtract the length of the diagonal path from the length of the path along the edge of the park:
1260 ft - 900 ft = 360 ft
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on one day in august this year, 1210000 people visited London, to the nearest 10000. what is the lowest and largest number of people that could have attended London that day?
The closest ten thousand to 1,210,000 is 1,210,000 itself.
To find the lowest and largest number of people that could have visited London, we need to determine the range of possible values within which 1,210,000 falls.
If we round 1,210,000 to the nearest hundred thousand, we get 1,200,000. This means that the actual number of visitors could be up to 50,000 more than 1,200,000 or up to 10,000 less than 1,200,000.
Therefore, the lowest number of people that could have visited London is:
1,200,000 - 50,000 = 1,150,000
And the largest number of people that could have visited London is:
1,200,000 + 10,000 = 1,210,000
So the lowest number of people that could have visited London is 1,150,000, and the largest number is 1,210,000.
A hyperbola centered at the origin has vertices at (+/- [tex]\sqrt{7}[/tex] , 0) and foci at (+/- [tex]\sqrt{27}[/tex] , 0). Write the equation of this hyperbola.
The equation of the hyperbola with centered at the origin has vertices at ( ±√7 , 0) and foci at (±√27 , 0) is (x²/7) - (y²/20) = 1.
The equation of a hyperbola centered at the origin with vertices on the x-axis is, (x²/a²)-(y²/b²) = 1.
The asymptotes' distance is b, while the distance between the origin and vertex is a. In this case, a = √7 and c = √27, distance from the origin to a focus is c. We can use the relationship a² + b² = c² to solve for b:
b² = c² - a² = 27 - 7 = 20
So, we get, the equation of the hyperbola to be,
(x²/7) - (y²/20) = 1.
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A hyperbola centered at the origin has vertices at ( ±√7 , 0) and foci at (±√27 , 0). Write the equation of this hyperbola.
Poppy signs on a $180,000 mortgage with a 4.9% annual interest rate for 30 years. Her monthly payment is $955.31.
How much interest is paid in month one? Round to the nearest cent.
By how much is the balance reduced after the first payment?
Answer:
Sure. Here are the steps on how to calculate the interest and balance reduction for Poppy's first mortgage payment:
Calculate the monthly interest rate.
The monthly interest rate is calculated by dividing the annual interest rate by 12. In this case, the annual interest rate is 4.9%, so the monthly interest rate is:
monthly interest rate = 4.9% / 12 = 0.41%
Calculate the interest paid for the first month.
The interest paid for the first month is calculated by multiplying the monthly interest rate by the outstanding loan balance. In this case, the outstanding loan balance is $180,000, so the interest paid for the first month is:
interest paid = 0.41% * $180,000 = $738
Calculate the principal amount of the first payment.
The principal amount of the first payment is calculated by subtracting the interest paid from the monthly payment. In this case, the monthly payment is $955.31 and the interest paid is $738, so the principal amount of the first payment is:
principal amount = $955.31 - $738 = $217.31
Calculate the balance after the first payment.
The balance after the first payment is calculated by subtracting the principal amount from the outstanding loan balance. In this case, the outstanding loan balance is $180,000 and the principal amount of the first payment is $217.31, so the balance after the first payment is:
balance after first payment = $180,000 - $217.31 = $177,782.69
Therefore, the interest paid in month one is $738 and the balance reduced after the first payment is $217.31.
Step-by-step explanation:
I need the answer asap pls
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of line
Answer:
y= -0.5x + 2 (I think)
Step-by-step explanation:
y =mx + c
gradient is -0.5 because society
m = -0.5
y intercept is 2 because 2
so that means answer swag
40. A(1, -2) is a vertex of the quadrilateral
=
ABCD. AB -(1), BC ·
-(1)
CD
and
(-2)
i) Find the coordinates of B, C and D.
→>>
ii) IfM is the midpoint of AB, find MC
The Coordinates of B (0, -2), C(0, -1) and D(-2, -1).
We have, the vertices of quadrilateral of A(1, -2).
Since AB = -1 which means that B is located 1 unit left then coordinates of B are
= (1 -1 , -2)
= (0, -2)
Now, C must have the same y coordinate as B. Also CB is vertical length 1 which moved above by 1 unit the coordinates of C
C (0, -2+1) = (0, -1)
and the coordinates of D are (0 -2, -1) = (-2, -1)
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What is the surface area of a right rectangular prism with a length of 12' and a width of 8' in a height of 10'
The surface area of the given right rectangular prism will be 592 square inches.
The formula for a right rectangular prism's surface area is:
SA = 2lh + 2lw + 2lh
where l denotes the prism's length, w its width, and h its height.
Here, l is equal to 12 feet, w to 8 feet, and h to 10 feet. When these values are added to the formula, we obtain:
SA = 2(12)(8) + 2(12)(10) + 2(8)(10) (10)
SA = 192 + 240 + 160
SA = 592
Hence, the right rectangular prism has a surface area of 592 square feet.
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A 10-item statistics quiz was given to 30 students. The
table below gives the scores received along with the
corresponding frequencies.
Score
5
Frequency 1
6
2
7
5
8
5
9
7
10
10
What was the median score on the quiz?
O 7.5
O 8.5
09
O 10
The median score on the quiz is 10. The answer is (d)10.
How to find the median score?We must arrange the scores from lowest to highest in order to determine the median score. The cumulative frequency for each score can also be calculated.
Score Frequency Cumulative Frequency
5 1 1
6 2 3
7 5 8
8 5 13
9 7 20
10 10 30
The score that distinguishes the upper half of the scores from the lower half is the median, or middle score. Since there are 30 scores, the center score is the fifteenth score.
We can begin by adding the frequencies until we reach or exceed the 15th position in order to accomplish this:
Scores 5 and 6 have a cumulative frequency of 3 (1 + 2)
Scores 7 and 8 have a cumulative frequency of 13 (8 + 5)
Therefore, the median score must be in the 9-10 range. We can further break down this range to find the exact median value:
The cumulative frequency of score 9 is 20, indicating that it is not the median value.
Score 10 has a combined recurrence of 30, which is more noteworthy than the fifteenth position.
As a result, this dataset's median score is 10.
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The median of the statistics quiz will be 9.
What is median ?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.
To find the median score on the quiz, we need to arrange the scores in order from lowest to highest. Using the frequency table, we can write out all the scores:
5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
There are 30 scores in total, so the median will be the average of the 15th and 16th scores (in order).
So, the median score on the quiz is:
(9 + 9) / 2 = 9
Hence the median of the statistics quiz will be 9.
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At an animal rescue, 30% of the animals are dogs and 70% of the animals are cats. If the average age of the dogs is 8 months and the average age of the cats is 4 months, what is the average age of all the animals?
6.8
6.0
5.2
2.4
The average age of the animals at an animal rescue is 5.2 months
The average or mean of the data is defined as the ratio of the sum of observations to the total number of observations recorded
Given in the question,
Dogs = 30%
Cats = 70%
Age of dogs = 8 months
Age of cats = 4 months
Suppose the number of animals at the animal rescue is 100, then
Number of cat = 70
Number of dogs = 30
Average = 70 * 4 + 30 * 8 / 100
= 280 + 240 / 100
= 520 / 100
= 5.2 months
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What does 3,600 ft.³ of water if the length of the pool is 30 feet the width is 16 feet at the depth of the wall is the same throughout how deep is the pool
Answer: 7.5 ft
Step-by-step explanation:
W x L = 16 x 30 = 480
V / (W x L) = H = 3600 / 480 = 7.5 ft
Use the given information to write the standard equation of the circle.
well, we know its center and a point on the circle, well, the distance from the center to a point on it is well, you guessed it!! is its radius.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-7}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~1 - (-7)~~)^2 + (~~-8 - (-2)~~)^2} \implies r=\sqrt{(1 +7)^2 + (-8 +2)^2} \\\\\\ r=\sqrt{( 8 )^2 + ( -6 )^2} \implies r=\sqrt{ 64 + 36 } \implies r=\sqrt{ 100 }\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-7}{h}~~,~~\underset{-2}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-7) ~~ )^2 ~~ + ~~ ( ~~ y-(-2) ~~ )^2~~ = ~~10^2\implies (x+7)^2 + (y+2)^2 = 100[/tex]
If = log(
3 +
3 −
2 −
2) then Prove that (
+
)
2
=
−4
(+)
2
.
Given: $f(x) = \log(3x + 3 - 2x - 2)$
We need to prove that: $\frac{(a+b)^2}{f(a)+f(b)} = -4$
First, we need to simplify $f(x)$:
$f(x) = \log(x+1)$ (by simplifying the expression inside the log)
Now, we can rewrite the expression we need to prove as:
$\frac{(a+b)^2}{\log(a+1) + \log(b+1)} = -4$
Using the property of logarithms, we can rewrite this as:
$\log((a+1)(b+1)) = \log(e^{-4})$
Simplifying further:
$(a+1)(b+1) = e^{-4}$
Expanding the left side and simplifying:
$ab + a + b + 1 = e^{-4}$
Now, we can use the identity $(a+b)^2 = a^2 + 2ab + b^2$:
$(a+b)^2 = a^2 + 2ab + b^2$
Dividing both sides by $f(a)+f(b)$, which is $\log(a+1) + \log(b+1)$:
$\frac{(a+b)^2}{\log(a+1) + \log(b+1)} = \frac{a^2 + 2ab + b^2}{\log(a+1) + \log(b+1)}$
Using the property of logarithms again, we can simplify the denominator:
$\frac{(a+b)^2}{\log((a+1)(b+1))} = \frac{a^2 + 2ab + b^2}{\log((a+1)(b+1))}$
Substituting the value we derived earlier for $(a+1)(b+1)$:
$\frac{(a+b)^2}{\log(e^{-4})} = \frac{a^2 + 2ab + b^2}{\log(e^{-4})}$
Simplifying:
$(a+b)^2 = a^2 + 2ab + b^2$
$4ab = -4$
Dividing both sides by 4:
$ab = -1$
Therefore, we have shown that $\frac{(a+b)^2}{f(a)+f(b)} = -4$ if $f(x) = \log(3x+3-2x-2)$.
does anyone mind helping me?? :) What is the value of x in the figure?
Answer:
22 + 5x - 10 = 90
5x + 12 = 90
5x = 78
x = 15.6
please help, trigonometry :)
sinθ=y/r
cosθ=x/r
tanθ=y/x
x^2 + y^2 = r^2
r^2(sin^2 θ + cos^2 θ) =r^2
sin^2 θ + cos^2 θ=1
220% of what number equals 132?
Answer:
So, we can write the equation:
2.2x = 132
To solve for x, we can divide both sides by 2.2:
x = 132 ÷ 2.2
x = 60
Therefore, 220% of 60 is 132
find the percentage error using 0.67 as an estimate 2/3
Answer:
((.67 - (2/3))/(2/3))(100%) = .5%
A restaurant serves iced tea in small glasses and large glasses
1 small glass and 2 large glasses contain a total of 48 fluid ounces of iced tea
2 small glasses and 3 large glasses contain a total of 76 fluid ounces of iced tea
What is the total number of fluid ounces contained in 1 large glass of iced tea?
The total number of fluid ounces contained in 1 large glass of iced tea is 20 ounces
Solving system of linear equations: Calculating the total number of fluid ounces contained in 1 large glass of iced teaFrom the question, we are to calculate the total number of fluid ounces contained in 1 large glass of iced tea
Let the number of fluid ounces contained in 1 small glass be x
and
The number of fluid ounces contained in 1 large glass be y
Thus,
From the statement
"1 small glass and 2 large glasses contain a total of 48 fluid ounces of iced tea
2 small glasses and 3 large glasses contain a total of 76 fluid ounces of iced tea"
We can write that
x + 2y = 48
and
2x + 3y = 76
Now, we will solve the equations simultaneously
From the first equation,
x + 2y = 48
We can write that
x = 48 - 2y
Substitute into the second equation
2x + 3y = 76
2(48 - 2y) + 3y = 76
96 - 4y + 3y =76
96 - y = 76
96 - 76 = y
20 = y
Therefore,
y = 20
Hence, the number of fluid ounces in 1 large glass is 20 ounces
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HELP!!!! I need to know the Measure of Center and the Measure of spread to this set of variables please
The measure of center and measure of spread are 163.5 and 39 Respectively.
What is measure of center and measure of spread?Measure of centre is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution.
Therefore we can say that measure of centre is the average or mean of the data.
(190+187+186+183+182+182+181+181+180+180+161+164+160+160+160+158+156+155+152.5+151)/20
= 3269.5/20
= 163.5
therefore measure of center is 163.5
The measure of spread is the range of the data.
range = 190-151 = 39
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6. The graph shows how the value of a car changes over time.
Value (dollars)
30,000
25,000
20,000
15,000
10,000
5,000
Car
0 1 2 3 4 5 6 7 8 9 10
Time (years)
Which function best represents the relationship shown in the graph?
Oy=-3000x + 9
O y = 27000x + 9
O y = 27000x - 3000
O y = -3000x + 27000
help please
The graph shows a linear relationship where the value of the car decreases as time passes. We can see that after 0 years (when the car is brand new), its value is $30,000, and after 10 years, its value is $5,000.
We can use the slope-intercept form of a linear function (y = mx + b), where m is the slope and b is the y-intercept, to find the function that represents this relationship.
The slope is found by taking the difference in y-values (change in value) divided by the difference in x-values (change in time):
slope = (5000 - 30000) / (10 - 0) = -2500
The y-intercept is the value of the car when it is brand new, which is $30,000.
So, the equation of the line is:
y = -2500x + 30000
This matches the form of the equation y = -3000x + 27000, which is option (D), after we simplify it by combining the constants:
y = -3000x + 27000 = -2500x + 30000
Therefore, the function that best represents the relationship shown in the graph is y = -3000x + 27000.
What is the volume of a right circular cylinder with a diameter of 6 meters and a height of 14 meters. Leave the answer in terms of π.
504π m3
396π m3
126π m3
84π m3
The volume of a right circular cylinder with a diameter of 6 meters and a height of 14 meters as required is; 54π.
What is the volume of the cylinder?It follows from the task content that the volume of a cylinder whose diameter is 6 meters and height is 14 meters.
Since the volume of a right circular cylinder is given by; V = πr²h.
since Diameter is; 6 ft. Radius, r = 6/2 = 3 meters.
Volume, V = π (3)² 6; V = π × 9 × 6
Volume, V = 54π.
Ultimately, the volume of the right circular cylinder is; 54π m³.
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If a ball is thrown into the air with a velocity of 50 ft/s, its height in feet t seconds later is given by y = 50t − 16t2.
(a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following.
(i) 0.5 seconds
ft/s
(ii) 0.1 seconds
ft/s
(iii) 0.05 seconds
ft/s
(iv) 0.01 seconds
ft/s
(b) Estimate the instantaneous velocity when t = 2.
ft/s
The average velocity for 0.5 seconds: -11 ft/s
The average velocity for 0.1 seconds is -33.6 ft/s
The average velocity for 0.05 seconds: -34 ft/s
The average velocity for 0.01 seconds : -16 fts
How to solve for the average velocitychange in position using the height function y = 50t - 16t² for the given time intervals.
(i) 0.5 seconds:
y(2) = 50(2) - 16(2²) = 100 - 64 = 36 ft
y(2.5) = 50(2.5) - 16(2.5²) = 125 - 100 = 25 ft
Average velocity = (25 - 36) / 0.5 = -11 ft/s
(ii) 0.1 seconds:
y(2) = 36 ft (calculated before)
y(2.1) = 50(2.1) - 16(2.1²) ≈ 32.64 ft
Average velocity = (32.64 - 36) / 0.1 = -33.6 ft/s
(iii) 0.05 seconds:
y(2) = 36 ft (calculated before)
y(2.05) = 50(2.05) - 16(2.05²) ≈ 34.32 ft
Average velocity = (34.32 - 36) / 0.05 = -34 ft/s
(iv) 0.01 seconds:
y(2) = 36 ft (calculated before)
y(2.01) = 50(2.01) - 16(2.01²) ≈ 35.84 ft
Average velocity = (35.84 - 36) / 0.01 = -16 ft/s
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Express your answer in slope-intercept form
Answer:
y=-6x+-4
Step-by-step explanation:
hi
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{0}) \implies y +4 = - 6 ( x -0) \\\\\\ y+4=-6x\implies {\Large \begin{array}{llll} y=-6x-4 \end{array}}[/tex]
a student connects a battery to a wire and wraps and wraps the wire around an iron nail to produce an electromagnet. which action should the student take to increase the number of paper clips the electromagnet will pick up?
By increasing the number of wire turns, using a thicker wire, increasing the battery voltage, and using a soft iron core, the student can enhance the electromagnet's strength, allowing it to pick up more paper clips.
To increase the number of paper clips the electromagnet will pick up, the student should take the following actions:
1. Increase the number of wire turns: By wrapping the wire around the iron nail more times, the student will create a stronger magnetic field. This is because each wire turn generates a magnetic field, and when the turns are in close proximity, their fields add up, creating a stronger overall field.
2. Use a thicker wire: A thicker wire will allow more current to flow through it, which will result in a stronger magnetic field. The higher the current, the more powerful the electromagnet becomes.
3. Increase the voltage of the battery: By increasing the voltage of the battery, the student can cause more current to flow through the wire. This will enhance the magnetic field, making the electromagnet more effective at picking up paper clips.
4. Use a soft iron core: Soft iron materials have higher magnetic permeability than other materials, meaning they can easily be magnetized and demagnetized. When the wire is wrapped around a soft iron nail, the resulting electromagnet will have a stronger magnetic field, thus improving its ability to pick up paper clips.
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The figure shows a 550 foot tower on the side of a hill that forms a 7° angle with the horizontal. Find the length of each of the two guy wires that are anchored 60 feet uphill and downhill from the tower's base and extend to the top of the tower.
The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively.
What is length?
Length is a concept used to describe the magnitude of a particular object or distance between two points. It is typically measured in units such as feet, inches, meters, miles, and kilometers. Length is often used to describe the size of an object and the distance between two points. Length can also be used to measure the time required to travel between two points. Length is a fundamental concept in mathematics, physics, and engineering.
The first dotted line shown at the top of the chart is 23.39.
b. With Overall Mean selected, what is the length of the second dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)
The second dotted line shown at the top of the chart is 23.28.
c. With Overall Mean selected, what is the length of the third dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)
The third dotted line shown at the top of the chart is 24.17.
Conclusion: The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively. This data can be used to analyze the age of respondents in Market Research.
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a plane covered a distance of 630 miles in 6 hours . for the first part of the trip the average speed was 100 mph and for the second part of the tripvthe average speed was 110cmph.what is the time it flew at each speed?
We know that the plane flew at each speed which is at 100mph and 110mph for 3 hours each.
What is speed?Speed is what it means. The rate at which the location of an object shifts in any direction.
Speed is defined as the ratio of the distance traveled to the time required to cover that distance.
Speed is a scalar quantity since it just has a direction and no magnitude.
The distance an object covers in a given amount of time is known as
speed.
The SI unit of speed is m/s or meters per second.
It has a scalar value.
Speed=Distance/Time.
So, using the speed:
Total miles = 630 in 6 hours.
Then,
100*3=300
110*3=330
Now,
300 + 330 = 630 miles
Therefore, we know that the plane flew at each speed which is at 100mph and 110mph for 3 hours each.
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Write An Equation For The Quadratic Graph
The quadratic equation on the given graph can be written as:
y = (x + 2)*(x - 1)
How to find the equation of the quadratic?Here we have the graph of a quadratic equation, we can see that the roots of the quadratic are:
x = -2 and x = 1.
Then if the leading coefficient is a, we can write the factorized form as:
y = a*(x + 2)*(x - 1)
We also know that the y-intercept is (0, -2), replacing these values we will get:
-2= a*(0 + 2)*(0 - 1)
-2 = a*-2
-2/-2 = a
1 = a
The quadratic equation is:
y = (x + 2)*(x - 1)
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At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were
eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay
audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos
audience in millions, it was observed that
y-z=z-u
x - y = 3(y-u) + 21
and x - y + z- u = 28.
How large was the audience of each of the four organizations at the end of that year?
eBay
million
U.S. Government
million
Amazon
million
Lycos
million
The audience of each of the four organizations at the end of that year is found by solving the equations given as :
x = 49 million, y = 22 million, z = 21 million and u = 20 million.
Given that,
Combined audience = 112 million
x + y + z + u = 112 [Equation 1]
Other equations are,
y - z = z - u [Equation 2] ⇒ y + u = 2z
Substituting this in [Equation 1],
x + 3z = 112 [Equation 5]
x - y = 3(y - u) + 21 [Equation 3]
x - y + z - u = 28 [Equation 4]
x - y + y - z = 28
x - z = 28 [Equation 6]
Solving [Equation 5] and [Equation 6],
z = 21 and x = 49
Substituting, Equation 1 becomes,
y + u = 42
From Equation 3,
4y - 3u = 28
Solving these two equations,
u = 20 and y = 22
Hence x = 49 million, y = 22 million, z = 21 million and u = 20 million.
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17. Belinda finds a CD with 2.8% APR compounded annually. How much money
will Belinda need to invest in this CD if she wants to have a yearly income of
$35,000 from her investment?
Belinda will need to invest $290,109.79 in the CD to earn a yearly income of $35,000 for 10 years.
What is APR?The annual rate of interest that is charged on a loan or generated on an investment is known as the APR (Annual Percentage Rate), and it is stated as a percentage. Compounding, which is the practise of adding interest to the principal amount of a loan or investment, is not taken into account.
On the other hand, APY (Annual Percentage Yield) does consider the impacts of compounding. The annual percentage yield, or APY, is the rate of return that an investor receives on an investment over the course of a year. Both the interest gained on the initial sum and the interest earned on any prior interest that has been reinvested are considered.
The compound interest is given by the formula:
[tex]A = P * (1 + r/n)^{(n*t)}[/tex]
Now, isolating the value of P we have:
[tex]P = A / (1 + r/n)^{(n*t)}[/tex]
Now, substituting the value we have:
[tex]P = 35000 / (1 + 0.028/1)^{(1*10)} = $290,109.79[/tex]
Hence, Belinda will need to invest $290,109.79 in the CD to earn a yearly income of $35,000 for 10 years.
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