The equation is an illustration of trigonometry ratios, and the non-negative values of x are 30 and 270 degrees
How to solve the equation?The equation is given as:
2sin²(x) + sin(x) = 1
Let y = sin(x)
So, the equation becomes
2y² + y = 1
Rewrite as:
2y² + y - 1 = 0
Expand
2y² + 2y - y - 1 = 0
Factorize
2y(y + 1) - 1(y + 1) = 0
Expand
(2y - 1)(y + 1) = 0
Split
2y - 1 = 0 or y + 1 = 0
Solve for y
y = 0.5 or y = -1
Recall that: y = sin(x)
So, we have:
sin(x) = 0.5 and sin(x) = -1
Take the arcsin of both sides
x = sin⁻¹(0.5) and x = sin⁻¹(-1)
x = 30 degrees and x = 270
Hence, the non-negative values of x are 30 and 270 degrees
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The car model was built on a 1:36 scale. If the length of the car is 180 inches, how many inches long is the model?
Answer:
the results are
a. 1,080-inch
b. 90 feet
Step-by-step explanation:
there are 4 steps to get to your resluts
Answer number 6 please. Bots don’t answer I’m just trying to get help
Answer:
B
Step-by-step explanation:
20 × 2/5 = 8
15 × 2/5 = 6
5 × 2/5 = 2
p/s : the pic is for question no 7. i thought that you want the number 7 so i solved it first. then i reread your question. then i realized u actually want number six. so...
yeah, your welcome :)
What quadrilateral can you draw the has exactly one pair of parallel sides
Answer:
I belive that will be a trapazoid
Step-by-step explanation:
Both sides on the top and bottom are parallel
Please tell me if im wrong!
Answer:
Trapezium
Step-by-step explanation:
It has exactly one pair of parallel sides
answer this easy please help
Answer:
1320
Step-by-step explanation:
The sample ad 600 chips. They wanted to test 36000 chips. 600*60=36000
If 22 out of 600 chips were defective, and 600*60=36000
Then 1320 chips were defective out of the 36000 because 22*60=1320.
Each railroad car in a train set is 6 inches in length.the railroad track is 5 feet long .how many railroad cars can fit on the track
Answer: 10 cars
Step-by-step explanation:
We know that:
A railroad car is 6 inches long and the railroad track is 5 feet long
Start by converting feet to inches. You can do that by multplying the amount of feet by 12.
5 feet x 12 = 60 inches
Now we can divide the length of the railroad track by the length of the railroad cars to see how many we can fit.
60 ÷ 6 = 10
What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1000?
Using the normal distribution and the central limit theorem, it is found that there is a 0.5934 = 59.34% probability that there is an error of at most $1000.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Researching the problem on the internet, it is found that the population has mean and standard deviation given, respectively, by [tex]\mu = 57300, \sigma = 9600[/tex].
For samples of 64, the standard error is given by:
[tex]s = \frac{9600}{\sqrt{64}} = 1200[/tex]
The probability of an error of at most $1000 is the probability of a sample mean between $56,300 and $58,300, which is the p-value of Z when X = 58300 subtracted by the p-value of Z when X = 56300, hence:
X = 58300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{58300 - 57300}{1200}[/tex]
Z = 0.83
Z = 0.83 has a p-value of 0.7967.
X = 56300:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56300 - 57300}{1200}[/tex]
Z = -0.83
Z = -0.83 has a p-value of 0.2033.
0.7967 - 0.2033 = 0.5934.
0.5934 = 59.34% probability that there is an error of at most $1000.
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If fixed costs to print a certain Bible are $15,000 and
variable costs are $25 per Bible, what must be the selling
price to earn $10 per Bible if 5,000 Bibles are printed?
The selling price to earn $10 per Bible if 5,000 Bibles are printed when the fixed costs per print is $15,000 and variable costs are $25 per Bible, is $38.
What is target profit?The target profit is the profit that is expected by a manufacturer from the sale of its product.
The target profit can be established and used to determine the selling price.
When the target profit is added to the fixed cost per unit and the variable cost per unit, the resultant figure is the selling price.
Data and Calculations:Fixed costs per print = $15,000
Number of Bibles per print = 5,000
Fixed costs per Bible = $3 ($15,000/5,000)
Variable costs per Bible = $25
Expected profit per Bible = $10
The selling price = $38
Thus, the selling price to earn $10 per Bible if 5,000 Bibles are printed when the fixed costs per print is $15,000 and variable costs are $25 per Bible, is $38.
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A baseball bat costs $41. This is $9 more than four times the wholesale cost of the bat.Find the bat's wholesale cost.
We can find the bat's wholesale cost by working backwards -
Do $41 - 9 to get $32, then we can divide the 32 by the 4 to get $8.
Therefore, the wholesale cost of the bat is $8.
Happy to help!
Answer:
The bat's wholesale cost is $8
Step-by-step explanation:
You first have to subtract 9 from 41 as that will be 4 times the wholesale cost, which is $32. Then you have to divide 32 by 4, as we want to get the wholesale cost, not 4 times of the wholesale cost, and this would give us the wholesale cost, which is $8.
Find the area of the rug. DO NOT ROUND.
what is the area?
Answer:
[tex]\frac{198}{7} \ \text{feet}^{2}[/tex]
Step-by-step explanation:Given:
Diameter of rug = 6 feetTo find the area of the rug, we need to use the formula "πr² or π(D/2)²"
Where:
r = radius d = diameterSince we do not have the radius, we need to substitute the diameter in the formula "π(D/2)²" to determine the area of the rug.
⇒ [tex]\pi (\frac{D}{2} )^{2}[/tex]
⇒ [tex]\pi (\frac{6}{2} )^{2}[/tex]
⇒ [tex]\pi (3 )^{2}[/tex]
⇒ [tex]\pi (3 )(3)[/tex]
⇒ [tex]9\pi[/tex]
Substituting "22/7" as π:
⇒ [tex]9(\frac{22}{7} )[/tex]
⇒ [tex](\frac{198}{7} )[/tex]
When finding the area of ANY shape, do not forget to include the units.
⇒ [tex]\frac{198}{7} \ \text{feet}^{2}[/tex]
Answer:
28.26 ft²
Step-by-step explanation:
Formula:
[tex]\text{Area of circular rug:} = \pi r^{2}[/tex]
Determining the radius of the circular rug:
To determine the radius, we need to divide the diameter by 2.
Given diameter: 6 feet
[tex]\implies {\dfrac{\text{Diameter}}{2} = \text{Radius}[/tex]
[tex]\implies {\dfrac{\text{6}}{2} = \text{Radius}[/tex]
[tex]\implies 3\ \text{feet} = \text{Radius}[/tex]
Replacing the radius in the formula:
[tex]\implies \text{Area of circular rug:} = \pi (3)^{2}[/tex]
Determining the area of the circular rug:
[tex]\implies \text{Area of circular rug:} = \pi (3)^{2}[/tex]
[tex]\implies \text{Area of circular rug:} = 9\pi[/tex]
Replacing π as 3.14 (Approx. measure of π):
[tex]\implies \text{Area of circular rug:} = 9(3.14)[/tex]
[tex]\implies \text{Area of circular rug:} = 28.26 \ \text{ft}^{2}[/tex]
given the room below describe how you would find the perimeter and area?
If the given is DEFG is a kite how do I prove that triangle EFH is congruent to triangle GFH
Answer:
They both have H hoel
Step-by-step explanation:
\
The polynomial x^3-kx^2+kx+2 has a factor of (x-2). What is the value of k?
[tex]\text{Let}~ f(x) = x^3-kx^2 +kx +2.\\\\\text{If}~ x-2~ \text{is a factor of}~ f(x)~ \text{then,}\\ \\f(2) =0\\\\\implies 2^3-k\cdot 2^2 +2k+2 =0\\\\\implies -4k+2k+8+2=0\\\\\implies 10-2k=0\\\\\implies 2k =10\\\\\implies k= \dfrac{10}2 = 5\\\\\\\text{Hence, the value of k is 5.}[/tex]
Which caculation and answer show how to convert 3/12 to a decimal?
The easiest way to convert a fraction to a decimal is to divide the numerator (the top of the fraction) by the denominator (the bottom of the fraction)
3/12=0.25
The function f(x) = x2 6x 3 is transformed such that g(x) = f(x − 2). find the vertex of g(x). (−1, −8) (−3, −4) (−1, −6) (−5, −6)
Answer: (-1,-6)
Step-by-step explanation:
x^2+6x+3
g(x) = f(x-2)
replace all value of x in the f(x) function to (x-2)
(x-2)^2 + 6(x-2) + 34
(x-2)(x-2) + 6(x-2) + 34
expand through FOIL and distribution
x^2-4x+4+6x-12+3
combine like terms
x^2+2x-5
-b/2a = x value of vertex
-2/2(1) = x value
x value = -1
plug in -1 for all values of x in the g(x) equation to solve for y value
(-1)^2+2(-1)-5
1-2-5 = -6
y = -6
x = -1
(x,y) = (-1,-6)
The vertex of the considered function g(x) = f(x − 2) is given by: Option c: (-1,-6)
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
How to convert the given equation to vertex form?We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.
So, we're given that:
[tex]f(x) = x^2 + 6x + 3[/tex][tex]g(x) = f(x-2)[/tex]Thus, we get:
[tex]g(x) = f(x-2) \\g(x) = (x-2)^2 + 6(x-2) + 3 \\g(x) = x^2 -4x + 4 + 6x - 12+3\\ g(x) = x^2 + 2x -5[/tex]
Converting g(x) to vertex form:
[tex]g(x) = x^2 + 2x - 5\\g(x) = x^2 + 2x + 1 - 1 -5\\g(x) = (x+1)^2 -9\\g(x) = (x - (-1) )^2 -6\\g(x) = (x-(-1))^2 + (-6)[/tex]
Comparing this with [tex]a(x-h)^2 + k[/tex], we get (h,k) = (-1,-6) as the coordinate of the vertex of the graph of g(x), as shown below.
Thus, the vertex of the considered function g(x) = f(x − 2) is given by: Option c: (-1,-6)
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Which statement is true about the ordered pair (1 , 7)? A. To plot the ordered pair (1 , 7), travel seven units to the right on the x-axis and one unit up on the y-axis, from the origin. B. To plot the ordered pair (1 , 7), travel one unit to the right on the y-axis and seven units up on the x-axis, from the origin. C. To plot the ordered pair (1 , 7), travel one unit to the right on the x-axis and seven units up on the y-axis, from the origin. D. To plot the ordered pair (1 , 7), travel seven unit to the right on the y-axis and one units up on the x-axis, from the origin.
Answer:
C is the correct answer.
Step-by-step explanation:
You're trying to find a true statement about the point (1,7)
A. To plot the ordered pair (1 , 7), travel seven units to the right on the x-axis and one unit up on the y-axis, from the origin.
B. To plot the ordered pair (1 , 7), travel one unit to the right on the y-axis and seven units up on the x-axis, from the origin.
C. To plot the ordered pair (1 , 7), travel one unit to the right on the x-axis and seven units up on the y-axis, from the origin.
D. To plot the ordered pair (1 , 7), travel seven unit to the right on the y-axis and one units up on the x-axis, from the origin.
_____________________________________________________
Solving:
A is incorrect because it shows the point (7,1).
D is incorrect because that isn't the proper way to graph a coordinate.
B is incorrect because it says travel one unit to the right on the y axis which is the incorrect axis to graph the point (1,7).
C is your correct answer because you need to move 1 unit to the right on the x-axis to get to the coordinate (1,0). Then, you need to go 7 units up on the y-axis to reach (1,7).
What is the area of the playground shown? The edges of the playground meet at right angles, except for the edge whose length is not given. Show all work.
Answer:
520,000
Step-by-step explanation:
1400 x 200 = 280000
(400 + 800) x 400 /2 = 240000
240000 + 280000 = 520000
The area of the playground is 520000 square feet.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
Given that the edges of the playground meet at right angles, except for the edge whose length is not given.
And to find the area of the composite figure,
find all the areas separately.
There is a square with a side length of 400 feet.
A rectangle with dimensions 200 feet by 600 feet.
Another rectangle with dimensions 1400- 600 = 800 feet by 200 feet.
And a triangle with a base of 400 feet and a height of 400 feet.
The area of the playground = (400 x 400) + (200 x 600) + (800 x 200) + (1/2 x 400 x 400)
The area of the playground = 160000 + 280000 + 80000
The area of the playground is 520000 square feet.
Therefore, the area is 520000 square feet.
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What is the value of z so that -3 and 3 are both solutions of x2 + z = 25?
0 41
016
09
o 22
Answer:
I think it is B (16)
Step-by-step explanation:
A spinner and 4 cards are shown below:
A spinner with 5 equal sectors is shown in the figure. The colors Green, Blue, Purple, Yellow, and Red are marked on it. The arrow points at the purple color. Four cards are shown on the right side. The colors Red, Yellow, Blue, and Pink are marked on them.
Jane spins the spinner and selects a card without looking. What is the probability that the spinner stops at purple and a pink card is selected?
1 over 20
1 over 5
1 over 4
9 over 20
Answer:
1 over 20
Step-by-step explanation:
Given that:
a spinner and 4 cards
A Spinner ⇒ 5 equal sectors;Color: Blue,Purple,Yellow,Red,Green
Arrow point at purple
Four cards ⇒ Color : Red,Yellow,Blue,Pink
Jane spins the spinner & selects card without looking.
To Find - Probability spinner stops at purple & select pink card.
Solve:
Multiply 4 (the number of cards) with 5 (The number of equal sectors)
[tex]\frac{1}{5}\times\frac{1}{4}=\frac{1}{20}[/tex] {1 × 1 = 1} {5×4=20}
~lenvy~
Answer:
1 over 20
Step-by-step explanation:
Given the following:
1 spinner and 4 cards
A Spinner which has 5 equal sectors;Color: Green, Blue,Purple,Yellow,Red.
{Arrow point at purple}
Four cards ⇒ which color are Red,Yellow,Blue,Pink
Jane spins the spinner & selects card without looking.
To Find → Probability spinner stops at purple & select pink card.
Since, purple and pink only has one in each of Spinner/card
Thus,
Spinner (5 equal sectors - 1/5}
Card {4 cards - 1/4}
1/4 × 1/5 = 1/20
Hence, probability spinner stops at purple & select pink card is [A] 1/20
[RevyBreeze]
A local band spent $2,000 to record and make 400 CDs. They sold all of their CDs and made a profit of $500. How much did they charge for each CD?
Answer:
$6.25 for each CD
Step-by-step explanation:
6.25 x 400 = 2,500
2,500 - 2,000 = 500
there is a 500 profit
2. Solve the inequality and graph the solution
V-6 ≥ 4
Answer:
V≥10
Step-by-step explanation:
V−6≥4
Add 6 to both sides.
V≥4+6
Add 4 and 6 to get 10.
V≥10
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Hoped this helped :)
Find the area of the following triangle. Show each of the math steps that you use to find the area. Then explain how to go about finding the area of this particular triangle (explain each one of the steps that you showed with your math).
100 POINTS IF YOU ANSWER CORRECTLY AND ILL GIVE BRAINLIEST
Semi perimeter:-
[tex]\\ \rm\rightarrowtail s=\dfrac{a+b+c}{2}[/tex]
[tex]\\ \rm\rightarrowtail s=\dfrac{1.8+2.4+3}{2}[/tex]
[tex]\\ \rm\rightarrowtail s=\dfrac{7.2}{2}=3.6cm[/tex]
Apply heron s formula
Area:-
[tex]\\ \rm\rightarrowtail \sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]\\ \rm\rightarrowtail \sqrt{3.6(3.6-1.8)(3.6-3)(3.6-2.4)}[/tex]
[tex]\\ \rm\rightarrowtail \sqrt{3.6(1.8)(0.6)(1.2)}[/tex]
[tex]\\ \rm\rightarrowtail \sqrt{4.6656}[/tex]
[tex]\\ \rm\rightarrowtail 2.16cm^2[/tex]
Answer:
[tex]\sf Area \ of \ a \ Triangle=\dfrac12bh[/tex]
(where b is the base of the triangle and h is the height)
Given:
base = 2.4 cmheight = 1.8 cmSubstitute the given values into the formula:
[tex]\sf \implies Area=\dfrac12 \cdot 2.4 \cdot 1.8[/tex]
[tex]\sf =2.16 \ cm^2[/tex]
x^2-x-42=0
Help I just need the line of symmetry
Answer:
Step-by-step explanation:
answers: x = 7
x = -6
let me know if you need anymore help.
mark me brainliest please.
Determine the oreadred pair for (-10,3) when it has been reflected over the y-axis
Answer:
(10 , 3)
Step-by-step explanation:
When you reflect over the y-axis, you are flipping the sign of the x-coordinate.
Likewise, when you reflect over the x-axis, you are flipping the sign of the y-coordinate.
In this case, you are reflecting over the y-axis, and the pair given to you is (-10, 3). When you reflect over the y-axis, you must flip the sign of the x-coordinate.
(-10 , 3) reflected over the y-axis is (10 , 3).
~
42 ft.
30 ft
Both triangles are similar The area of the larger triangle is about 382 ft
Answer:
just awnsering for the points sorry man
Step-by-step explanation:
Find the volume of the cone below.
Answer:
C. 2027.4 m^3
Step-by-step explanation:
volume = (1/3) · π · r^2 · h
volume = (1/3) · π · 8.8^2 * 25
volume = (1/3) · π · 1936
volume = (1/3) · 1936π
volume = 2027.4 m^3
Pierre throws a snowball up in the
air. The height of the snowball in
feet, h(x), can be represented by
h(x) = -0.5x2 + 6x + 4, where x is
the horizontal distance the snowball
travels in feet. Pierre wants to
know how far the snowball has
traveled when the height is 20
feet.
Using the given function, it is found that the snowball traveled 4 feet when the height is 20 feet.
What is the function for the ball's height?The height when x feet are traveled is given by:
h(x) = -0.5x² + 6x + 4.
When the height is of 20 meters, we have that h(x) = 20, hence:
20 = -0.5x² + 6x + 4.
0.5x² - 6x + 16 = 0
x² - 12x + 32 = 0
(x - 8)(x - 4) = 0
For the first time: x - 4 = 0 -> x = 4.
The snowball traveled 4 feet when the height is 20 feet.
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A lender estimates the closing costs on a home loan will be 3.75% of the loan amount of $120,000. the actual closing costs are listed below. closing cost charge loan origination $300 title insurance $600 attorney’s fees $1,250 appraisal $550 inspection $525 recording fees $125 escrow $2,000 evaluate the lender’s good faith estimate. a. the lender made an excellent estimate; it was equal to the actual closing costs. b. the lender made a very good estimate; it was within 0.25% of the actual closing costs. c. the lender made a fairly good estimate; it was between 0.25% and 0.5% of the actual closing costs. d. the lender made a poor estimate; it was off by more than 0.5% of the actual closing costs.
The lender’s good faith estimate is that he made a poor estimate; it was off by more than 0.5% of the actual closing costs.
What is closing cost?All the expenduture and charges charged by a lander and other parties is called the closing cost.
A lender estimates the closing costs on a home loan will be 3.75% of the loan amount of $120,000. Thus, the estimate closing cost is,
[tex]C_{ec}=\dfrac{3.75}{100}\times120000\\C_{ec}=4500[/tex]
The actual closing costs are listed below.
Loan origination $300Title insurance $600 Attorney’s fees $1,250 Appraisal $550 Inspection $525 Recording fees $125 Escrow $2,000.The total annual cost is,
[tex]C= $300 +$600 +$1,250 +$550 +$525 +$125 +$2,000\\C=4800[/tex]
Total annual cost is $300 more than the estimate closing cost. In the percentage form,
[tex]p=\dfrac{4800-4500}{4500}\times100\\p=6.66\%[/tex]
Thus, the lender’s good faith estimate is that he made a poor estimate; it was off by more than 0.5% of the actual closing costs.
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Answer:
Its D trust me
I got it right from the other person
Please Help there are 3 questions.
Answer:
1) There are 15 in it, which means we need to find the 8th. The 8th is 6, which means the median is 6. We then need to find the other quartiles.
8/2=4, which means we need to look at the 4th,5th and 12th,13th.
The first one is FIVE, and the second is SEVEN. Therefore, the FIRST ONE.
2)113
3)37
Levi spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -14.1°F. Between 9am and noon, the temperature rose 17.8°F. Between noon and 3pm, the temperature went down 16.8°F. Between 3pm and 6pm, the temperature dropped 12.3°F. What was the temperature at 6pm?
Answer:
-25.4°F
Step-by-step explanation:
-14.1 + 17.8 = 3.7
3.7 - 16.8 = -13.1
13.1 - 12.3 = -25.4
Use the points in the diagram to name the figure.
D) Line JK
<----->
JK
Hope it helps :)