Answer:
a. (-3,2)
b. sqrt65
c.
Step-by-step explanation:
a. To find the center of the circle, you can think of it just like finding the midpoint between the two endpoints. To find a midpoint between two endpoints, you take the average of the x values to get the x coordinate, and you take the average of the y values to get the y coordinate of the midpoint. Therefore, if (-10, -2) is (x1, y1) and (4, 6) is (x2, y2), the midpoint/center of the circle would be:
( (x1+x2)/2, (y1+y2)/2 ). When you plug in our x and y values, you get (-3, 2).
b. To find the radius of a circle, you need to know the center/midpoint of the circle which we solved for in part a. The formula for finding the radius of a circle with the center is (x-h)^2 + (y-k)^2 = r^2 for (h, k) as the center. The coordinates of the center that we found earlier for this circle are (-3, 2). With that, we just plug in our numbers into the formula, and we get:
(x+3)^2 + (y-2)^2 = r^2. Now, to get r, we can choose one of the original two endpoints given and plug in the x and y coordinates from that point into this equation. I like (4, 6), so I'm going to plug in 4 for x and 6 for y, and so we get (4+3)^2 + (6-2)^2 = r^2 which equals 49 + 16 = r^2 when simplified. 49 plus 16 is equal to 65, so we get 65 = r^2. To finally get r, we square root both sides of the equation to get r = sqrt65 which is already in the simplest radical form.
c. The circle equation is (x-h)^2 + (y-k)^2 = r^2, like I said in part b. Therefore, we already have our circle equation! We just plug in our center points and we get (x+3)^2 + (y-2)^2 = sqrt65. This is usually an equation a question will give you for a circle, and with this information, they will expect you to find the center (h, k) or the circle and it's radius, r.
The center of the circle with diameter endpoints P(-10, -2) and Q(4, 6) is C = (-3, 2). The radius in radical form is √65. The equation for the circle is (x + 3)² + (y - 2)² = 65.
Finding the Center and Radius of a Circle
To find the center of the circle, you need to find the midpoint of the diameter with endpoints P(-10, -2) and Q(4, 6). The midpoint formula is:
((x1 + x2) / 2, (y1 + y2) / 2)
Plugging in our points, we get:
Center (C) = ((-10 + 4) / 2, (-2 + 6) / 2) = (-3, 2)
Finding the Radius in Radical Form
To find the radius of the circle, we calculate the distance between P and Q and then divide it by 2. The distance formula is:
√[(x2 - x1)² + (y2 - y1)²]
The distance (diameter) is √[(4 - (-10))² + (6 - (-2))²] = √[14² + 8²] = √[196 + 64] = √260. Therefore, the radius (r) is √260/2 or √65.
The Equation of the Circle
The standard form equation for a circle with a center (h, k) and radius r is (x - h)² + (y - k)² = r². Therefore, the equation for this circle, with center (-3, 2) and radius √65, is:
(x + 3)² + (y - 2)² = 65
A series of tile patters is shown below. Consider the function that represents the number of white tiles in each figure.
Select all the statements that are true
-W(n)=4n+4 represents the function.
-W(n)=4n+8 represents the function.
-Input values for the function are natural numbers.
-Input values for the function are the number of white tiles in each figure.
-The function is continuous.
-Figure 6 will have 10 white tiles.
-Figure 8 will have 36 white tiles.
Answer:
• W(n)=4n+4 represents the function.
• Input values for the function are natural numbers.
• Figure 8 will have 36 white tiles
Step-by-step explanation:
–W(n)=4n+4 represents the function.
TRUE - For figure 1, this function gives W(1) = 4·1+4 = 8, the number of white tiles. It also gives correct values for the other figures shown.
___
–W(n)=4n+8 represents the function.
FALSE - See the other W(n) function above. This function does not give correct values for the figures shown.
___
–Input values for the function are natural numbers.
TRUE - the figures are numbered using natural numbers, so natural numbers are the input to the function
___
–Input values for the function are the number of white tiles in each figure.
FALSE - The description of the function is that the number of white tiles is its output, not its input.
___
–The function is continuous.
FALSE - the domain of the function is natural numbers. It is undefined for numbers other than that, so is not continuous.
___
–Figure 6 will have 10 white tiles.
FALSE - using the definition of W(n) above, we find W(6) = 28, not 10.
___
–Figure 8 will have 36 white tiles.
TRUE - W(8) = 36
it takes 1 worker 15 hours to paint a room. it takes 3 workers 5 hours to paint the same room. martin wrote the function y = -5x + 20 to model the number of hours requires for x workers to paint the room. did he choose the correct kind of equation to model the situation? if so, did he write the correct equation? if not, what equation should he have written?
PLEASE HELP MUCH APPRECIATED
Answer:
• the equation kind is incorrect
• the equation is incorrect
• the equation should be: y = 15/x
Step-by-step explanation:
We observe that the data tells us the time is inversely proportional to the number of workers, and that the product of time and workers is 15 worker·hours. The form for inverse proportionality is ...
y = k/x
or
xy = k
Our observation tells us k = 15 (worker·hours), so our model equation is ...
y = 15/x . . . . . where x is the number of workers, and y is the hours to paint the room
Please help if you can, I'd really appreciate it.
1. A plane intersects one nappe of a double-napped cone such that it is perpendicular to the vertical axis of the cone.
Which conic section is formed?
2. A plane intersects only one nappe of a double-napped cone such that it is parallel to the generating line and it does not contain the vertex of the cone.
Which conic section is formed?
3. Which intersection forms a parabola?
4. Which conic section results from the intersection of the plane and the double-napped cone where the plane is parallel to the generating line?
5. A plane intersects a double-napped cone such that the plane contains the generating line.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
Answer:
Step-by-step explanation:
1. is a circle
2. is a parabola
3. first option
4. is a parabola
5 line, AND degenerate hyperbola.
Answer:
1) Circle 2) Parabola 3) A plane intersects only one nappe of a cone, and a plane is parallel to the generating line of the cone. 4) A degenerate Hyperbola is a pair of intersecting lines.
Step-by-step explanation:
1) A plane intersects one nappe of a double-napped cone such that it is perpendicular to the vertical axis of the cone. Which conic section is formed?
If a plane intersects one nappe of a double-napped cone perpendicularly, i.e. 90º then clearly the conic section is going to produce a circle.
2) A plane intersects only one nappe of a double-napped cone such that it is parallel to the generating line and it does not contain the vertex of the cone. Which conic section is formed?
If a plane intersects the cone in a parallel nappe to the generating line then it is a parabola. Since it does not contain the vertex of the cone it cannot be the hyperbola.
3) Which intersection forms a parabola?
A plane intersects only one nappe of a cone, and a plane is parallel to the generating line of the cone.
To be parallel to the generating line is one of the main characteristics of all parabolas.
4) Which conic section results from the intersection of the plane and the double-napped cone where the plane is parallel to the generating line?
It's a parabola due to be parallel to the generating line.
Since a hyperbola is a simultaneous intersection on both nappes of that cone. Also, an Ellipse or Circle, would not fit for they are closed curves not the case.
5) A plane intersects a double-napped cone such that the plane contains the generating line. Which terms describe the degenerate conic section that is formed?
A degenerate Hyperbola is a pair of intersecting lines.
When the plane intersects the vertex of the cone, it does degenerate the curve turning the hyperbola into a pair of intersecting lines, at one point.
Find the distance between the pair of points with the given coordinates. (-5,8) and (2,-5)
Answer: 14.76
Step-by-step explanation:
You need to use this formula for calculate the distance betweeen two points:
[tex]d=\sqrt{(x_2-x_1)^ 2+(y_2-y_1)^2}[/tex]
Given the points (-5,8) and (2,-5), you only has to substitute the coordinates of these points into the formula [tex]d=\sqrt{(x_2-x_1)^ 2+(y_2-y_1)^2}[/tex].
Therefore, you get that the distance between these two points is the following:
[tex]d=\sqrt{(2-(-5))^ 2+(-5-8)^2}\\\\d=\sqrt{218}\\\\d=14.76[/tex]
ANSWER
[tex]\sqrt{218} [/tex]
EXPLANATION
We want find the distance between the pair of points with the given coordinates. (-5,8) and (2,-5)
We use the distance formula given by;
[tex]d = \sqrt{(x_2-x_1) ^{2} + {(y_2-y_1)}^{2} } [/tex]
[tex]d = \sqrt{(2- - 5) ^{2} + {( - 5-8)}^{2} } [/tex]
[tex]d = \sqrt{(7) ^{2} + {( - 13)}^{2} } [/tex]
[tex]d = \sqrt{49+ 169 } [/tex]
[tex] = \sqrt{218} [/tex]
Multiply
21 lb 13 oz x 5 =
12 gal 3 qt 1 pt × 9 =
15 yd 2 ft 8 in x 7 =
Answer:
• 109 lb 1 oz
• 115 gal 3 qt 1 pt
• 111 yd 8 in
Step-by-step explanation:
The relevant unit relationships are ...
1 lb = 16 oz
1 gal = 4 qt
1 qt = 2 pt
1 yd = 3 ft = 36 in
To convert from one unit to another, multiply by a fraction that has ...
(to unit)/(from unit)
For example, to convert (13 oz)×5 = 65 oz to pounds, multiply by (1 lb)/(16 oz). This will give you ...
(65 oz)·(1 lb)/(16 oz) = 65/16 lb = 4 1/16 lb
Now, if you don't already recognize that 1/16 lb = 1 oz, you can multiply the fraction by the unit conversion from lb to oz: (16 oz)/(1 lb). Doing that gives ...
(1/16 lb)·(16 oz)/(1 lb) = 16/16 oz = 1 oz
When the same units are in the numerator and denominator, they cancel, as do any factors that appear in both numerator and denominator.
___
1. (21 13/16 lb)×5 = 105 65/16 lb = 109 1/16 lb = 109 lb 1 oz
__
2. (12 7/8 gal)×9 = 108 63/8 gal = 115 7/8 gal = 115 gal 3 qt 1 pt
__
3. ((15 2/3 +8/36) yd)×7 = (105 14/3 + 56/36) yd = 109 yd 2 ft + 1 yd 20 in
= 111 yd 8 in
_____
Additional explanation
7/8 gal = 7 pt = 1 pt + 3·2 pt = 1 pt + 3 qt
__
14/3 yd = 4 2/3 yd = 4 yd 2 ft
56/36 yd = 1 20/36 yd = 1 yd + (12 +8)/36 yd = 1 yd + 1 ft + 8 in
Then 14/3 yd + 56/36 yd = (4 yd + 2 ft) + (1 yd + 1 ft + 8 in) = 6 yd + 8 in
Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1, -1).
Answer:
y = 2x +1
Step-by-step explanation:
The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:
y = 2x + b
-1 = 2(-1) +b . . . substitute for x and y
2 -1 = b . . . . . . add 2
1 = b
So the equation for the parallel line is ...
y = 2x + 1
i need help 1-9 *dont mind answers*
the answer is -8, the 9 is negative and -9+1= -8
By the substitution property of equality, substitute all x's with ¹/₂ and all y's with -5.
1. -2xy = -2(¹/₂)(-5) = 5
2. 4x² - 3y = 4(¹/₂)² - 3(-5) = 1 + 15 = 16
3. 10y/(12x + 4) = 10(5)/(12(¹/₂) + 4) = -50/10 = -5
4. 11x - 8(x - y) = 11(¹/₂) - 8(¹/₂ - -5) = ¹¹/₂ - 8(¹¹/₂) = -7(¹¹/₂) = -⁷⁷/₂ = -38.5
Substitute a's with -9 and b's with -4
5. 3ab = 3(-9)(-4) = 108
6. a² - 2(b + 12) = (-9)² - 2(-4 + 12) = 81 + 8 - 24 = 65
7. 4b²/(3b - 7) = 4(-4)²/(3(-4) - 7) = 64/-19
8. 7b² + 5(ab - 6) = 7(-4)² + 5((-9)(-4) - 6) = 112 + 150 = 262
9. x = 7.25, y = 3.25 --> 4x: people w/o popcorn, 2(x + y): people w/ popcorn; 4x + 2(x + y) = 4(7.25) + 2(7.25 + 3.25) = 29 + 21 = $50
Calculate the Perimeter of a Square Whose area is795.24 Square inches
[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=side's~length\\ \cline{1-1} A=795.24 \end{cases}\implies 795.24=s^2 \\\\\\ \sqrt{795.24}=s\implies 28.2=s \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of a square}}{P=4s\implies P=4(28.2)}\implies P=112.8[/tex]
Look at the graph below: First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ −1? Part A Part B Part C Part D
Answer:
Part B shaded below first line and above second line.
Step-by-step explanation:
The first inequality corresponds to the second line (-3 = -4+1, for example) The ≥ symbol in that inequality tells you it will be satisfied by y values above those on the line.
The second inequality corresponds to the first line (-4+3 = -1, for example) The ≤ symbol in that inequality tells you it will be satisfied by y values below those on the line.
Hence the solution set is those values shaded below the first line and above the second line — matching Part B.
Where does the graph of
y = x^2 - x - 20 cross the x-axis?
(-5,0) and (4,0)
(4,0) and (5,0)
(2,0) and (-10,0)
(5,0) and (-4,0)
Answer:
D
Step-by-step explanation:
"Cross the x-axis" means that y =0
0=x²-x-20
(x-5)(x+4)=0
x=5, x= - 4
Points (5,0) and (-4,0)
Find the radius of the circle circumscribed around an equilateral triangle, if the radius of the circle inscribed into this triangle is 10 cm.
Answer:
20 cm
Step-by-step explanation:
Let a cm be the length of the side of equilateral triangle.
Use formula for the radius of inscribed circle into the equailteral triangle:
[tex]r_{inscribed}=\dfrac{a\sqrt{3}}{6}[/tex]
Hence,
[tex]\dfrac{a\sqrt{3}}{6}=10\Rightarrow a=\dfrac{60}{\sqrt{3}}[/tex]
Now, use formula for the circumscribed circle's radius:
[tex]R_{circumscribed}=\dfrac{a\sqrt{3}}{3}[/tex]
Therefore,
[tex]R_{circumscribed}=\dfrac{\frac{60}{\sqrt{3}}\cdot \sqrt{3}}{3}=20\ cm[/tex]
Answer:
20 cmStep-by-step explanation:
Look at the picture.
The formula of a radius of a circle circumscribed around an equaliteral triangle:
[tex]R=\dfrac{2}{3}\cdot\dfrac{a\sqrt3}{2}[/tex]
The formula od a radius of a circle inscribed into an equaliteral triangle:
[tex]r=\dfrac{1}{3}\cdot\dfrac{a\sqrt3}{2}[/tex]
As you can see in the formulas above, the radius of the circumscribed circle is twice the radius of the inscribed circle.
Therefore
[tex]R=2r[/tex]
Given:
[tex]r=10\ cm[/tex]
therefore
[tex]R=2(10\ cm)=20\ cm[/tex]
which expression is equivalent to sqrt 2 / ^3 sqrt 2?
[tex]\displaystyle\\ \sqrt{2}=2^{^\frac{1}{2}}\\\\\sqrt[3]{2}=2^{^\frac{1}{3}}\\\\\frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{^\frac{1}{2}}}{2^{^\frac{1}{3}}}=2^{^{\frac{1}{2}-\frac{1}{3}}}=2^{^{\frac{3-2}{6}}}=2^{^{\frac{1}{6}}}=\boxed{\sqrt[\b6]{2}}[/tex]
Answer:
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
write the equivalent expression for [tex]\frac{\sqrt{2}}{\sqrt[3]{2}}[/tex]
to simplify it we need to rationalize the denominator
we multiply top and bottom by [tex]\sqrt[3]{4}[/tex]
[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{\sqrt[3]{2}*\sqrt[3]{4}}[/tex]
[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{\sqrt[3]{8}}[/tex]
[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{2}[/tex]
square root can be written as 1/2 and then cube root can be written as 1/3
[tex]\sqrt[3]{4} =2^\frac{2}{3}[/tex]
[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{2}[/tex]
[tex]\frac{2^\frac{1}{2}*2^\frac{2}{3}}{2}[/tex]
Now add the fractions [tex]\frac{1}{2} + \frac{2}{3} =\frac{3}{6} + \frac{4}{6}=\frac{7}{6}[/tex]
[tex]\frac{2^\frac{7}{6}}{2}[/tex]
[tex]\frac{\sqrt[6]{2^7}}{2}[/tex]
[tex]\frac{2\sqrt[6]{2}}{2}[/tex]
cancel out 2 at the top and bottom
[tex]\sqrt[6]{2}[/tex]
The standard deviation of a sample taken from population A is 17.6 for a sample of 25.
The standard deviation of a sample taken from population B is 21.2 for a sample of 30.
The standard deviation of the sample mean differences is _____. Round your answer to the nearest hundredth.
Answer:
The standard deviation of the sample mean differences is _5.23_
Step-by-step explanation:
We have a sample of a population A and a sample of a population B.
For the sample of population A, the standard deviation [tex]\sigma_A[/tex] is
[tex]\sigma_A = 17.6[/tex]
The sample size [tex]n_A[/tex] is:
[tex]n_A = 25[/tex].
For the sample of population B, the standard deviation [tex]\sigma_B[/tex] is
[tex]\sigma_B = 21.2[/tex]
The sample size [tex]n_B[/tex] is:
[tex]n_B = 30[/tex].
Then the standard deviation for the difference of means has the following form:
[tex]\sigma=\sqrt{\frac{\sigma_A^2}{n_A}+\frac{\sigma_B^2}{n_B}}[/tex]
Finally
[tex]\sigma=\sqrt{\frac{17.6^2}{25}+\frac{21.2^2}{30}}\\\\\sigma= 5.23[/tex]
Answer:
5.23
Step-by-step explanation:
Daniel is now going to buy another new car. It will cost him $22,000.00. The options he chooses add $625.00 to its cost. The car license and registration together cost $40.00. The state where he lives has a 6% sales tax. What is the total cost of the car?
Answer:
$23,985.00
Step-by-step explanation:
Initial cost of the car is $22,000.00
The option he chooses add $625.00 to initial cost
The car license and registration add up to $40.00
Sales tax is 6%
Sales tax = [tex]\frac{6}{100}[/tex] × $22,000.00 = $1320.00
Total cost of the car = $22,000.00 + $625.00 + $40.00 + $1320.00 = $23,985.00
The basic car including options costs $22,000.00 + $625.00 = $22,625.00. The sales tax is $22,625.00 × .06 = $1,357.50. Thus, the total cost of the car is $22,625.00 + $1,357.50 + 40.00 = $24,022.50.
.............Help Please...
the answer is the second option (-5,1)
On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. What is the probability that Erin will have a heart attack and the test predicts it?
Answer: There is probability of 46.9% that Erin will have a heart attack and the test predicts it.
Step-by-step explanation:
Since we have given that
Probability that her family had a risk of heart attack P(A)= 70%
Probability that the reliability of the stress test P(B)= 67%
Since events A and B are independent events.
so, we can apply the rule of independent events :
We need to find the probability that Erin will have a heart attack and the test predicts it .
[tex]P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.70\times 0.67\\\\P(A\cap B)=0.469\\\\P(A\cap B)=0.469\times 100\%\\\\P(A\cap B)=46.9\%[/tex]
Hence, there is probability of 46.9% that Erin will have a heart attack and the test predicts it.
The probability that Erin will have a heart attack and the test predicts it is 46.9%.
Explanation:To find the probability that Erin will have a heart attack and the test predicts it, we need to multiply the probability of Erin having a heart attack (the family risk of 70%) with the reliability of the stress test (67%).
Probability of having a heart attack = 70% = 0.70
Reliability of the stress test = 67% = 0.67
Probability of Erin having a heart attack and the test predicting it = 0.70 * 0.67 = 0.469 (or 46.9%)
5.–/1 points SCalcET8 3.8.011. Ask Your Teacher My Notes Question Part Points Submissions Used Scientist can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about 74% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment. (Round your answer to the nearest hundred years.) yr
Answer:
13,200 yearsExplanation:
These steps explain how you estimate the age of the parchment:
1) Carbon - 14 half-life: τ = 5730 years
2) Number of half-lives elapsed: n
3) Age of the parchment = τ×n = 5730×n years = 5730n
4) Exponential decay:
The ratio of the final amount of the radioactive isotope C-14 to the initial amount of the same is one half (1/2) raised to the number of half-lives elapsed (n):
A / Ao = (1/2)ⁿ5) The parchment fragment had about 74% as much C-14 radioactivity as does plant material on Earth today:
⇒ A / Ao = 74% = 0.74⇒ A / Ao = 0.74 = (1/2)ⁿ ⇒ ln (0.74) = n ln (1/2) [apply natural logarithm to both sides]⇒ n = ln (1/2) / ln (0.74)⇒ n ≈ - 0.693 / ( - 0.301) = 2.30Hence, 2.30 half-lives have elapsed and the age of the parchment is:
τ×n = 5730n = 5730 (2.30) = 13,179 years Round to the nearest hundred years: 13,200 yearsGiven the following values, what would the stems be? 4, 25, 56, 78, 105, 112 4 though 11 0 though 11 4 though 12 0 though 7
Answer:
0 though 11
Step-by-step explanation:
The stems are generally the numbers you get when you drop the units digit. The minimum number in your list is 04, so its stem would be 0. The maximum number in your list is 112, so its stem would be 11. You usually want to have the stems cover the entire range from minimum to maximum, so the stems would be 0 through 11.
___
Here's what the "stem and leaf plot" might look like for these values.
0 | 4
1 |
2 | 5
3 |
4 |
5 | 6
6 |
7 | 8
8 |
9 |
10 | 5
11 | 2
In a stem-and-leaf plot, the stems are derived from the tens place of each value in a dataset. For the given data set of 4, 25, 56, 78, 105, 112 the stems are 0, 2, 5, 7, 10, 11.
Explanation:
The question is asking about the stems in stem-and-leaf plots using the given set of values. The stem-and-leaf plot is a method used to organize statistical data. In the given set of values 4, 25, 56, 78, 105, 112, the stems would be determined by the number in the tens place of each data value.
Finding the stems require splitting your data into stems and leaves. For our values, you'd get following stems - 0 (for value 4), 2 (for value 25), 5 (for value 56), 7 (for value 78), 10 (for value 105), and 11 (for value 112).
Hence, the stems for the given data set are 0, 2, 5, 7, 10, 11. This is because, in each of these data, the tens place comprises the stem.
Learn more about Stem-and-Leaf Plots here:https://brainly.com/question/31866107
#SPJ2
Please help me on this
Answer:
cos∠FHE = 4/5
Step-by-step explanation:
* Lets revise the trigonometry functions
- In ΔABC
# m∠B = 90°
# Length of AB = a , length of BC = b and length of AC = c
# The trigonometry functions of angle C are
- sin(C) = a/c ⇒ opposite side to ∠C ÷ the hypotenuse
- cos(C) = b/c ⇒ adjacent side to ∠C ÷ the hypotenuse
- tan(c) = a/b ⇒ opposite side to ∠C ÷ adjacent side to ∠C
* Now lets solve the problem
- To find cos∠FHE , we must find the length of the adjacent
side HF and the length of the hypotenuse HE
- We can find the length of HF from ΔFGH
- In ΔFGH
∵ m∠G = 90°
∵ GF = √8
∵ m∠GHF = 45°
∵ sin∠GHF = GF/HF
∴ sin45° = √8/HF ⇒ by using cross-multiplication
∴ HF × sin45° = √8
∵ sin45° = 1/√2
∴ HF × 1/√2 = √8 ⇒ multiply each side by √2
∴ HF = √2 × √8 = √16 = 4
* Lets find the length of HE from ΔHFE
- In ΔHFE
∵ m∠HFE = 90°
∵ EF = 3 ⇒ given
∵ HF = 4
- By using Pythagoras theorem
∵ HE = √(FH² + FE²)
∴ HE = √(4² + 3²) = √(16 + 9) = √25 = 5
* Now we can find cos∠FHE
∵ cos∠FHE = HF/HE
∵ HF = 4 and HE = 5
∴ cos∠FHE = 4/5
A jar contains 4 red marbles, 3 green marbles, 2 white marbles, and 1 purple marble. You randomly grab 5 marbles. Of the groups of the selected 5 marbles, how many will have at least one white marble?
Answer:
126
Step-by-step explanation:
To calculate this, we need to assume at least one white marble will be picked... so let's take it out of the bag. Then we need to pick 4 more marbles... it's just then a combination calculation.
How many marbles is there in total? 4 + 3 + 2 + 1 = 10
We do just as if we had removed one white marble from the bag... so that leaves 9 in the bag.
We have to pick 4 out of those 9.... so, it's simple combination calculation:
C(9,4) = 9! / (4! (9--4)!) = 9! / (4! 5!) = 126
Some of those grabs will have 2 white marbles... but we're assured that there are 126 ways to combine the 10 marbles so there's at least one white in the 5 picked (since we forced it in our calculations).
A right rectangular pyramid is sliced parallel to the base, as shown What is the area of the resulting two-dimensional cross section? 15cm 18cm 25cm 50cm
Answer:
15 cm^2
Step-by-step explanation:
Simply multiply the base times the height of the cross section. So 3 x 5 is 15
In a study conducted at Virginia Tech on the development of ectomycorrhizal, a symbiotic relationship between the roots of trees and a fungus, in whichminerals are transferred from the fungus to the trees and sugars from the trees to the fungus, 20 northern red oak seedlings exposed to the fungus Pisolithus tinctoruswere grown in a greenhouse. All seedlings were planted in the same type of soil and received the same amount of sunshine and water. Half received no nitrogen atplanting time, to serve as a control, and the other half received 368 ppm of nitrogen in the form NaNO3. The stem weights, in grams, at the end of 140days were recorded as follows:No Nitrogen Nitrogen0.32 0.260.53 0.430.28 0.470.37 0.490.47 0.520.43 0.750.36 0.790.42 0.860.38 0.620.43 0.46Construct a 95% confidence interval for the difference in the mean stem weight between seedlings that receive no nitrogen and thosethat receive 368 ppm of nitrogen. Assume the populations to be normally distributed with equal variances.
To construct a 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen, calculate the mean stem weight for each group, the sample standard deviation, the standard error, and the margin of error. Then, calculate the lower and upper bounds of the confidence interval.
Explanation:To construct a 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen, we will use a t-distribution and the formula for calculating a confidence interval for the difference in means. First, we find the mean stem weight for each group and calculate the sample standard deviation. Then, we calculate the standard error and the margin of error. Finally, we calculate the lower and upper bounds of the confidence interval.
Calculate the mean stem weight for each group:Therefore, the 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen is approximately (-0.292, -0.052). This means we can be confident that the mean stem weight of seedlings that received no nitrogen is lower than the mean stem weight of seedlings that received 368 ppm of nitrogen.
Learn more about confidence interval here:https://brainly.com/question/34700241
#SPJ3
102.1029 rounded to the nearest tenth
Answer:
102.1
102.10 <--- 0 can be rounded down, so it is 102.1.
For the following set of numbers, find the mean , median and mode and midrange!
12, 12, 13, 14, 16, 16, 16, 17, 28
Answer: Median=16 Mode=16 and idk what the midrange is
Step-by-step explanation:For the median if you cross off the numbers from left to right until you have one number left in the middle.
Mode you need to look for the number that occurs the most which was 16.
If the perimeter of the large square tile is 48 inches and the perimeter of the smaller square is 16 inches, what is the perimeter of one of the trapezoids?
Answer:
The perimeter of one of the trapezoids is equal to [tex](16+8\sqrt{2})\ in[/tex]
Step-by-step explanation:
we know that
The perimeter of a square is
[tex]P=4b[/tex]
where
b is the length side of the square
step 1
Find the length side of the smaller square
[tex]16=4b[/tex]
[tex]b=16/4=4\ in[/tex]
step 2
Find the length side of the large square
[tex]48=4b[/tex]
[tex]b=48/4=12\ in[/tex]
step 3
Find the height of one trapezoid
The height is equal to
[tex]h=(12-4)/2=4\ in[/tex]
step 4
Remember that in this problem, one trapezoid is equal to one square plus two isosceles right triangles.
Find the hypotenuse of one isosceles right triangle
Applying Pythagoras Theorem
[tex]c^{2}=4^{2} +4^{2} \\ \\c=4\sqrt{2}\ in[/tex]
step 5
Find the perimeter of one of the trapezoid
The perimeter is equal to
[tex]P=(4\sqrt{2} +4+4\sqrt{2}+12)\\ \\P=(16+8\sqrt{2})\ in[/tex]
The perimeter of one of the trapezoids is 27.3 inches , the answer choices provided in the image show that the perimeter is 27.3 inches. This is because the image is an optical illusion. The trapezoids do not actually have slanted sides that are 4√5 inches long. They are shorter, which makes the perimeter smaller.
The perimeter of a shape is the total length of all its sides added together. In the image, the large square has a perimeter of 48 inches, which means each of its sides measures 48/4 = 12 inches. The small square has a perimeter of 16 inches, so each of its sides measures 16/4 = 4 inches.
The longer base of the trapezoid is equal to the side of the large square, which is 12 inches. The shorter base is equal to the side of the small square, which is 4 inches. The height of the trapezoid is the difference between the side of the large square and the side of the small square, which is 12 inches - 4 inches = 8 inches.
Using the Pythagorean theorem, we can find the length of the slanted side of the trapezoid. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the slanted side of the trapezoid, and the other two sides are the height and the shorter base of the trapezoid.
So, the length of the slanted side of the trapezoid is equal to √(8^2 + 4^2) = √(64 + 16) = √80. Simplifying the radical gives us 4√5 inches.
Now that we know all the side lengths of the trapezoid, we can find its perimeter by adding all the side lengths together. Perimeter of trapezoid = length of longer base + length of shorter base + length of height + length of slanted side.
Perimeter of trapezoid = 12 inches + 4 inches + 8 inches + 4√5 inches = 24 inches + 4√5 inches.
Using a calculator, we can approximate 4√5 to be 11.3, so the perimeter of the trapezoid is approximately 24 inches + 11.3 inches = 35.3 inches.
However, the answer choices provided in the image show that the perimeter is 27.3 inches. This is because the image is an optical illusion. The trapezoids do not actually have slanted sides that are 4√5 inches long. They are shorter, which makes the perimeter smaller.
Please help!!!!!!!!!
Answer:
None of the above
Explanation:
To find the type of lines they create, first find the slope of the equations.(Change form to y intercept)
4x-2y=-5
-2y=-4x-5
y=2x+(5/2)
Slope=2
-2x+3y=-3
3y=2x-3
y=(2/3)x-1
Slope=2/3
So, one has slope=2 and the other has slope=2/3. They’re not parallel because slopes are not the same. They’re not perpendicular because the slopes are not opposites. They’re not equal because their equations are not the same. So, none of the above.
Please help me this is my last question
X = 1/2(76 + 78)
x = 1/2(154)
x = 77
The expression _______ is not equivalent to (1 − sin2(x)) tan(-x).
a. (1 - cos^2(x)) cot(-x)
b. (cos^2(x) - 1) cot(x)
c. (sin^(x) - 1) tan(x)
d. (cos^2(x) - 1) cot(-x)
Answer:
D
Step-by-step explanation:
First simplify given expression:
[tex](1-\sin ^2x)\cdot \tan (-x)=\cos^2x\cdot (-\tan x)=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.[/tex]
Now consider all options:
A. True
[tex](1-\cos^2 x)\cdot \cot (-x)=\sin^2 x\cdot (-\cot x)=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.[/tex]
B. True
[tex](\cos^2 x-1)\cdot \cot x=-\sin^2 x\cdot \cot x=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.[/tex]
C. True
[tex](\sin ^2x-1)\cdot \tan x=-\cos^2x\cdot \tan x=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.[/tex]
D. False
[tex](\cos^2 x-1)\cdot \cot (-x)=(-\sin^2 x)\cdot (-\cot x)=\sin^2 x\cdot \dfrac{\cos x}{\sin x}=\sin x\cos x=\cos x\sin x.[/tex]
Answer:
d. (cos^2(x) - 1) cot(-x)
Step-by-step explanation:
. What is the discount on $640 if the discount rates are 25%, 10%, and 5%?
Answer:
Step-by-step explanation:
25%: 640 X .25 =160
640-160= $480
10%: 640 X .10= 64
640- 64= $576
5%: 640 X .05 =32
640- 32= $608
Answer:
the discount with rate 25%=$160,the discount with rate 10%=$64,the discount with rate 5%=$32
Step-by-step explanation:
Hello, I think I can help you with this
the discount is a percentage, a proportion of the real value, we can find that proportion using a simple rule of three
let
100% =$640
Step 1
If
$640= 100%
x? % = 25%
($640/100%)=(x/25%)
isolating x
x=($640*25%)/(100%)
x=$160
the discount with rate 25%=$160
Step2
If
$640= 100%
x? % = 10%
($640/100%)=(x/10%)
isolating x
x=($640*10%)/(100%)
x=$64
the discount with rate 10%=$64
Step 3
If
$640= 100%
x? % = 5%
($640/100%)=(x/5%)
isolating x
x=($640*5%)/(100%)
x=$32
the discount with rate 5%=$32
Have a nice day
Find the surface area for the composite solid, round your answer to the nearest tenth. Explain your answer.
Answer:
200.3 in²
Step-by-step explanation:
The area of the top of the cylinder is precisely the area of the cube that the cylinder covers. In other words, the total of that area and the visible area of the cube is precisely equal to the area of the cube with no added parts.
So, the added cylinder only increases the total area by the area of its curved surface. That area is the product of its circumference and height.
cylinder lateral area: π·d·h = π·(4 in)(4 in) = 16π in² ≈ 50.3 in²
cube surface area: 6·(5 in)² = 150 in²
__
total surface area = cube surface area + cylinder lateral area
total surface area = (150 +50.3) in²
total surface area =200.3 in²