Answers
Answer:
0.5 cm
Step-by-step explanation:
You are given angles B and C and side b, so you can put those values into the given equation:
sin(105°)/(2 cm) = sin(15°)/c
Multiply this equation by c·(2 cm)/sin(105°) and you get ...
c = (2 cm)·sin(15°)/sin(105°) ≈ 0.535898 cm
c ≈ 0.5 cm
_____
Comment on the given equation
When using the Law of Sines to find side lengths, I prefer to write the proportion in a form with the side length of interest in the numerator:
b/sin(B) = c/sin(C)
or
c/b = sin(C)/sin(B)
Using either of these forms, it is one step to find the value of c: Multiply the equation by the inverse of the coefficient of c.
c = b·sin(C)/sin(B)
Related Questions
Does Red Increase Men’s Attraction to Women? A study1 examines the impact of the color red on how attractive men perceive women to be. In the study, men were randomly divided into two groups and were asked to rate the attractiveness of women on a scale of 1 (not at all attractive) to 9 (extremely attractive). Men in one group were shown pictures of women on a white background while the men in the other group were shown the same pictures of women on a red background. The results are shown in Table 1 and the data for both groups are reasonably symmetric with no outliers. Color n x¯ s Red 15 7.2 0.6 White 12 6.1 0.4 Table 1 Does red increase men’s attraction to women? To determine the possible effect size of the red background over the white, find a 95% confidence interval for the difference in mean attractiveness rating μR-μW, where μR represents the mean rating with the red background and μW represents the mean rating with the white background.
Answers
please attached is your answer
Which of the following is the third term of the expansion (a + b)^n ?
C(n, 2)a^n - 2b^2
C(n, 3)a^n - 3b
C(n, 2)a^2b^n - 2
Answers
Answer:
C(n, 2)a^(n-2)b^2
Step-by-step explanation:
Generally, the expansion is written in decreasing powers of "a", so the first few terms would have variable constellations that look like ...
a^n, a^(n-1)b, a^(n-2)b^2, ...
The coefficients would be (in order), C(n, k) for k increasing from 0, so the coefficient of the 3rd term would be C(n, 2).
If the terminal side of an angle In standard position passes through the point (20, -21), then which of the following functions will be positive?
A. Cosecant
B. Secant
C. Tangent
Answers
Answer:
B
Hope This Helps! Have A Nice Day!!
Answer:
b
Step-by-step explanation:
Measure of angle LOI= 38 degrees
Measure of angle JOP= 84 degrees
Find measure of angle JKP
Answers
Answer:
The measure of angle JKP is 61°
Step-by-step explanation:
we know that
If the measure of angle m<LOI=38°
then
m arc IL=38° -----> by central angle
and
If the measure of angle m<JOP=84°
then
m arc JP=84° -----> by central angle
Remember that
The measure of the interior angle is the semi-sum of the arcs that comprise it and its opposite.
so
m<JKP=(1/2)[arc IL+arc JP]
substitute the values
m<JKP=(1/2)[38°+84°]=61°
Preston wants to create a garden that backs up to an existing fence in his yard. He won't need to enclose the garden with fencing and he only has 85 feet of fencing available. What was the largest dimensions of the garden be if you could encloses the three sides of the garden and use the existing fence as the fourth side? If necessary, round answer to the nearest tenth.
Answers
Answer:
42.5 ft by 21.3 ft
Step-by-step explanation:
The largest area is obtained when half the available fence is used parallel to the existing fence, and the other half is used to fence the two ends of the rectangle. Here, that means the dimension parallel to the existing fence is ...
(85 ft)/2 = 42.5 ft
and the ends of the rectangular garden are ...
(42.5 ft)/2 = 21.25 ft ≈ 21.3 ft
_____
You can figure this as follows:
Let x represent the length of fence parallel to the existing fence. Then the other dimension of the fenced area is (85 -x)/2 and the fenced area is the product of these dimensions.
area = x(85-x)/2
This expression describes a downward-opening parabola with zeros at x=0 and at x=85. The vertex (maximum) will be found where x is halfway between these values, at x = (0 +85)/2 = 42.5.
Area is maximized when 42.5 ft of fencing is used parallel to the existing fence, and the other half of the fencing is used for the other two sides of the enclosure.
How would you convert 276 yards to inches?
Add up the digits
Multiply by 36
Change the unit measure
Answers
Answer:
9936 inch.
Step-by-step explanation:
Note the measurements:
1 Yard = 3 Feet
1 Feet = 12 Inch
1 Yard = 3 Feet = (12)(3) Inches = 36 Inches; 1 Yard = 36 Inches
Multiply 276 with 36
276 x 36 = 9936
9936 inches is your answer.
~
Which figure shows how a shape can be rotated about an axis to form a hemisphere?
Answers
Answer:
A. (first choice)
Step-by-step explanation:
Examine all options:
A. The diagram shows the arc (1/4 from a circle). While rotating this arc about the given axis, we get the hemisphere.
B. The diagram shows the semicircle (1/2 from a circle). While rotating this semicircle about the given axis, we get the whole sphere.
C. The diagram shows the segment (perpendicular to the axis). While rotating this segment about the given axis, we get the circle (lying in a plane).
D. The diagram shows the segment. While rotating this segment about the given axis, we get the cone.
Please help!! 30 points!! Will mark brainliest!!
Answers
Answer:
x = ab/c
Step-by-step explanation:
The product of the distances from the point of intersection of the chords (secants) to the circle is the same for both chords (secants). (This is true whether the point of intersection is inside or outside the circle.)
ab = cx
x = ab/c
the kerns pen company makes ballpoint pens. the fixed cost of operation for one month averages $53500. the cost of producing one pen is $.75 and the pens are sold for $1.05 each. how many pens must be sold in order for the oay to break even?
Answers
Answer:
178,334 pens
Step-by-step explanation:
The company makes $0.30 above the variable cost on each pen, so must sell $53,500/$0.30 ≈ 178,334 pens to cover the cost of operation.
_____
Sale of 178,333 pens will result in a total cost of $0.10, so doesn't quite make the company break even. Sale of 178,334 pens will result in profit of $0.20.
If one dollar bill is 0.0001 meters thick how many meters tall would a stack of 4 trillion one dollar bills be?
Answers
Answer:
400,000,000
Step-by-step explanation:
4000000000000×.0001 is the answer above
Answer:
[tex]4 \times {10}^{8 }m \: or \: 400,000,000m[/tex]
Step-by-step explanation:
Put them both into standard form.
[tex]0.0001 = 1 \times {10}^{ - 4} \: and \: 4 \: trillion \: is \: 4 \times {10}^{12} [/tex]
Multiply them together.
[tex](1 \times {10}^{ - 4} ) \times (4 \times {10}^{12}) = 4 \times 10^{8} [/tex]
1. Drag and drop an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.
2. Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.
3. The equation for a circle is x2−8x+y2−2y−8=0 .
What is the equation of the circle in standard form?
Answers
Answer:-
Central angle , Ф/2π , A = Ф/2 r²
The ratio is 1/3 , V = 1/3 Bh
The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25
Step-by-step explanation:
* Lets revise the rules of the area of the sector of a circle
- The area of the sector which has a central angle Ф° is
(Ф°/360°) × πr², where 360° is the measure of the circle and r is
the radius of the circle
- The area of the sector which has a central angle Ф radians is
(1/2) r²Ф
* Lets complete the missing in the 1st picture
- The ratio of the sector's area A to the circle's area is equal to the
ratio of the central angle to the measure of a full rotation of the circle
- A full rotation of a circle is 2π. This proportion can written as
A/πr² = Ф/2π
- Multiply both sides by πr² to get A = Ф/2 r² where Ф is the measure
of the central angle and r is the radius of the circle
* Lets revise the rules of the volume of the prism and the volume
of the pyramid, where they have the same base and height
- The volume of the prism = area of the base × its height
- The volume of the pyramid = 1/3 × area of the base × its height
- From them the ratio of the volume of the pyramid to the volume
of the prism is 1/3
- The formula of the volume of the prism is V = Bh, where B is the
area of the base and h is the height, the formula of the volume
of the pyramid is V = 1/3 Bh
* Lets revise the standard form of the equation of a circle with
center (h , k) and radius r
- The equation is: (x - h)² + (y - k)² = r²
∴ x² - 2hx + h² + y² - 2ky + k² - r² = 0
∵ x² - 8x + y² - 2y - 8 = 0
- Lets equate the two equation
∴ x² - 2hx + h² + y² - 2ky + k² - r² = x² - 8x + y² - 2y - 8 = 0
∵ -2h = -8 ⇒ ÷ -2
∴ h = 4
∵ -2k = -2 ⇒ ÷ -2
∴ k = 1
∵ h² + k² - r² = -8
∴ (4)² + (1)² - r² = -8
∴ 16 + 1 - r² = -8
∴ 17 - r² = -8 ⇒ subtract 17 from both sides
∴ -r² = -15 × -1
∴ r² = 25
* Substitute the values of h , k , r in the equation of the standard
form of the circle
∴ (x - 4)² + (k - 1)² = 25
* The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25
Find the perimeter of a triangle with sides measuring 5 centimeters , 9 centimeter, and 11 centimeters
Answers
Perimeter is the distance around an object, so you would add 5+9+11 to get 25 cm
A cricular arena is lit by 5 lights equally spaced around the perimeter of the arena. What is the measure of each angle formed by the lights on the perimeter?
Answers
Answer:
108°
Step-by-step explanation:
Suppose that circle with center A is a circular arena. Points B, C, D, E and F are 5 lights. These 5 points form regular pentagon (because these 5 lights are equally spaced around the perimeter of the arena).
The sum of all interior angles of pentagon can be calculated using following formula
[tex](n-2)\cdot 180^{\circ},\\ \\(5-2)\cdot 180^{\circ}=3\cdot 180^{\circ}=540^{\circ}[/tex]
All interior angles in regular pentagon are of equal measure, so
[tex]\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]
Thus, the measure of each angle formed by the lights on the perimeter is 108°.
Answer:
D. 108
Step-by-step explanation:
I just did the test yourself
A couple is planning to have 3 children. Assuming that having a boy and having a girl are equally likely, and that the gender of one child has no influence on (or, is independent of) the gender of another, what is the probability that the couple will have exactly 2 girls? The "random experiment" in this case is having 3 children, as odd as that may sound in this context. The next and most important step is to determine what all of the possible outcomes are, and list them (i.e., list the sample space S). In this case, each outcome represents a possible combination of genders of 3 children (note that examples with the same number of boys and girls but a different birth order must be listed separately).
Answers
Answer:
44.444%, (B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)
Step-by-step explanation:
We will start with the second part of the question, listing out all of the possible combinations that can occur from this data set. There is a 50/50 chance of having a girl or a boy, and there are three children. For now we'll use B to represent a boy and G for a girl. It goes as follows:
(B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)
I often find it easy to write out a branch diagram to help me visualize this problem and make sure I have all possibilities. (See attached image)
Count the total number of combinations (9). Next, count the number that include exactly 2 girls (4). With this information, we now know that there is a 4 out of 9 chance of having exactly 2 girls and one boy. 4/9 is in simplest form, so all you have to do is find the percentage (44.444%)
Answer:
C or .375
Step-by-step explanation:
Someone explain to me how I do this law of sines problem
Answers
Answer:
44.1 cm
Step-by-step explanation:
In order to find the length of side "a", you need to know the measure of angle A. That is found by making use of the fact that the sum of angles in a triangle is 180°.
102° + 28° + A = 180°
A = 180° -130° = 50°
Now, you can fill in the given information in the given equation and solve for "a":
sin(A)/a = sin(B)/b
sin(50°)/a = sin(28°)/(27 cm)
Multiplying by a(27 cm) gives ...
sin(50°)(27 cm) = a·sin(28°)
Dividing by the coefficient of "a", we get ...
a = (27 cm)sin(50°)/sin(28°) ≈ 44.0563 cm
Rounded to the nearest tenth, this is ...
a ≈ 44.1 cm
_____
Since we're looking for a side length (not an angle), I prefer to write the Law of Sines formula "upside down" from that shown:
a/sin(A) = b/sin(B) = c/sin(C)
Then it is one step to get to ...
a = b·sin(A)/sin(B) . . . . . . multiply by sin(A)
Suppose you graphed every single point of the form $(2t + 3, 3-3t)$. For example, when $t=2$, we have $2t + 3 = 7$ and $3-3t = -3$, so $(7,-3)$ is on the graph. Explain why the graph is a line, and find an equation whose graph is this line.
Answers
Answer:
see below for explanation
3x +2y = 15
Step-by-step explanation:
The x-coordinate and the y-coordinate are both linear functions of t, so their relationship to each other is linear. A graph of those (x, y) points must be a line.
___
You can find an equation by solving one of the expressions for t, then substituting that into the other.
x = 2t +3
t = (x -3)/2
Substituting into the y expression, we get ...
y = 3 -3(x -3)/2
y = (-3/2)x + 15/2
3x +2y = 15 . . . . . . . add 3/2x and multiply by 2 to put into standard form
_____
The attached graph shows a portion of the line defined parametrically (0 ≤ t ≤ 1). It is dotted so you can see it overlays the line defined by the linear equation in x and y.
If 15% of the customer's total is $22.05, then the customer's total is _______."
Answers
let's say is "x", so "x" is then 100% of the whole bill.
we know 15% is 22.05, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 22.05&15\\ x&100 \end{array}\implies \cfrac{22.05}{x}=\cfrac{15}{100}\implies 2205=15x \\\\\\ \cfrac{2205}{15}=x\implies 147=x[/tex]
Answer:
$147
Step-by-step explanation:
15% over 100 is .15
So you get .15x= 22.05
Get x by itself by dividing .15 by .15
whatever you do to one side you have to do to the other so divide 22.05 by .15 and you get $147
Which of the following quadratic functions are in standard form?
(Picture attached)
Answers
E and F
The standard form for a quadratic function is f(x) = ax^2 + bx + c.
E follows this pattern. a = -2; b = -8; c = 3
F also follows this pattern. a = 1/2; b = -2; c = 0
Please help, I need an explanation because I'm confused on how to do this.
Answers
Answer:
15°
Step-by-step explanation:
If CB is a diameter, the arc BKAC is a semicircle and has a degree measure of 180. If the measure of angle BCK is 20 and it is an inscribed angle, then the measure of the arc it intercepts is twice that. So arc BK measures 40 degrees. That means that arc KA has a measure that is found by subtracting arc AC and arc BK from 180. 180 - 40 - 110 = 30. If that arc is 30 and the angle that intercepts it is inscribed, then the angle measure is half the measure of the arc. So the angle is 15°
{35 POINTS} A factory produces t-shirts. The production cost, C(x), for x t-shirts can be modeled by a quadratic function.
Each of the following functions is a different form of the quadratic model for the situation given above. Which form would be the most helpful if attempting to determine the number of t-shirts that would minimize cost?
A.
C(x) = 0.02(x2 - 720x + 144,600)
B.
C(x) = 0.02(x - 360)2 + 300
C.
C(x) = 0.02x2 - 14.4x + 2,892
D.
C(x) = 0.02x(x - 720) + 2,892
Answers
Answer:
B. C(x) = 0.02(x - 360)2 + 300
Step-by-step explanation:
The minimum of a quadratic function is found at its vertex. The vertex form of the equation lets you read the coordinates of the vertex directly, so that is the form most helpful for finding minimum cost.
___
Perhaps the next most helpful form is that of option D, sometimes called "intercept form." The vertex is located halfway between the intercepts, so will be halfway between 0 and 720. Of course, the vertex location at 360 is read directly from the vertex form of option B.
Answer:
A
Step-by-step explanation:
Please use " ^ " to denote exponentiation: x^2 (not x2).
To determine the number of t-shirts that would minimize cost, we'd want to have a quadratic function graph that opens up, and to determine the vertex (which point would also be the minimum cost).
Equation A is the one we want. Why? because we can ignore the coefficient 0.02 in determining the minimum cost. We see immediately that the coefficient of the x^2 term is a = 1 and that of the x term is b = -720.
Recall that the axis of symmetry passes through the vertex / minimum, and has equation
720
x = -b / (2a). With a = 1 and b = -720, x = - --------- = 360
2
Again, A is the correct answer. The miminim cost occurs at x = 360 (shirts).
Can someone please help me with this problem
Answers
Answer:
745.5 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the trig function relating the hypotenuse and the side opposite an angle. It tells you ...
Sin = Opposite/Hypotenuse
The line marked x (the hypotenuse of the triangle) is a transversal crossing the two parallel horizontal lines. That means the interior angle of the triangle at lower right (the angle of elevation) has the measure 28°. That angle is opposite the side marked 350 ft. So, you have ...
sin(28°) = (350 ft)/x
Multiplying by x/sin(28°), this equation becomes ...
x = 350 ft/sin(28°)
x ≈ 745.5 ft
Martin ordered a pizza with a 16-inch diameter. Ricky ordered a pizza with a 20-
inch diameter. What is the approximate difference in area of the two pizzas?
Answers
Answer:
113 inches^2
Step-by-step explanation:
write a function to model the situation.
a digital image is reduced or enlarged by dragging the corner. the height to width ratio is always maintained as that the width is 1.25 times the height. write a function to model the area of the image as a function of its height.
please help and thank you !!
Answers
Answer:
a(h) = 1.25h²
Step-by-step explanation:
The formula for the area of a rectangle is ...
A = HW . . . . . where H represents the height and W represents the width
If the image has a height of h, then the width is 1.25 times that, or 1.25h. Putting these values into the formula, we have ...
A = h·(1.25h)
A = 1.25h²
In function form, we can write a(h), area as a function of height, as ...
a(h) = 1.25h²
Look at the picture below
Answers
ANSWER
Option A
EXPLANATION
The graph of g(x) has equation:
[tex]g(x) = \sqrt[3]{ x + 2 } - 4[/tex]
The parent function is
[tex]f(x) = \sqrt[3]{x} [/tex]
To obtain the graph of g(x), we must shift f(x) 2 units to the left and 4 units down.
The graph of this function is shown in the attachment.
The correct choice is option A.
If 2n + 3(2- 2n) = 14 what is the value of n? (Please give the correct answer, I will give brainliest)
Answers
Answer:
n = -2
Step-by-step explanation:
Eliminating parentheses, you have ...
2n +6 -6n = 14
Combining terms and subtracting 6, you get ...
-4n = 8
Dividing by the coefficient of n gives ...
n = -2
_____
Check
2(-2) +3(2 -2(-2)) = 14
-4 +3(2+4) = 14
-4 +3(6) = 14
-4 +18 = 14 . . . . answer checks OK
please help and explain the answer!
Answers
Answer:
462 cm^2
Step-by-step explanation:
The centerline of the cloth area has a radius of (28 cm + 14 cm)/2 = 21 cm, so its length will be 1/4 of the circumference of a circle of that radius:
cloth centerline length = (1/4)·2πr = (π/2)·21 cm = (22/7)/2 · 21 cm = 33 cm
The width of the cloth portion is ...
28 cm - 14 cm = 14 cm
so the area of the cloth portion will be the product of centerline length and width:
(33 cm)(14 cm) = 462 cm^2
How does the range of g(x)=6/x compare with the range of the parent function f(x)=1/x?
Answers
The range of the function g(x)=6/x is the same as the range of the parent function f(x)=1/x, which is all real numbers except zero, despite the scaling factor '6'. This is because transformations other than shifts do not change the range.
Explanation:The comparison between the functions g(x)=6/x and f(x)=1/x lies in the understanding of how modifications to a parent function affect its range. The function f(x)=1/x is a parent function and its range is all real numbers except for zero. This is because as x approaches zero, the output of the function approaches infinity, thus, zero is not included in the range.
When we look at the function g(x)=6/x, the multiplier '6' just scales the values of the parent function by a factor of 6. This means the range will still be all real numbers except for zero, just like in the parent function. This is because the function transformations do not affect the range of the function that has a rational form like f(x)=1/x unless there are additional horizontal or vertical shifts.
Learn more about Function Transformations here:https://brainly.com/question/26896273
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What is 125% of 332?
Answers
Answer:
W = 415
Step-by-step explanation:
Is means equals and of means multiply
W = 125% * 332
Change to decimal form
W = 1.25 *332
W = 415
Dalia has 9 hamsters and 4 fish at her house. Choose the ratio of fish to the total number of pets. (Select all that apply.)
A) 4 to 9
B) 4 to 13
C) 9 to 13
D) 4:9
E) 4:13
F) 13:4
Answers
Answer:
4 to 13
4:13
Step-by-step explanation:
I finished my test and these were the answers
The ratio of the number of fish to the total number of pets Dalia has is 4 to 13 or 4:13.
Explanation:The subject of this question is the calculation of a ratio. In this case, the asked ratio is the number of fish to the total number of pets that Dalia has. Dalia has 4 fish and a total of 9 hamsters + 4 fish = 13 pets. Therefore, the correct answer is the ratio of 4 (fish) to 13 (total pets). This ratio can be represented in two ways: B) 4 to 13 or E) 4:13. The other options represent different ratios and do not correctly answer the question.
Learn more about Ratio Calculation here:https://brainly.com/question/31549749
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The sum of two numbers is 842. The difference is 314. Find the numbers.
Answers
Let's call the two numbers x and y.
We know that x+y = 842 and that x-y = 314
Now that we have two equations, we can solve using substitution by solving for one variable in one of the equations, and plugging that in for the same variable in the other equation.
Lets solve for x in the second equation to get:
x = 314 + y
Now plug in 314+y for x in the first equation:
(314 + y) + y = 842
Combine like terms:
314 + 2y = 842
Now solve for y:
2y = 842-314
2y = 528
y = 264
Finally, plug 264 in for y to solve for x:
x + 264 = 842
x = 842-264
x = 578
The two numbers are 578 and 264.