If his teacher used a 95% confidence interval to correctly estimate the true percentage of correct answers that he should have scored on this exam, what possible grades could the teacher reasonably assign to Gabriel
Answers
The possible range of scores is given as follows:
Anything from 21% to 59%.
The percentage that is typically assigned is given as follows:
40%.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]\pi = 0.4, n = 25[/tex]
Then the lower bound of the confidence interval is given as follows:
0.4 - 1.96 x sqrt(0.4 x 0.6/25) = 0.21.
The upper bound of the confidence interval is given as follows:
0.4 + 1.96 x sqrt(0.4 x 0.6/25) = 0.59.
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Related Questions
what is p(divisor of 6) write your answer as a percentage rounded to the nearest tenth
Answers
The probability of selecting a divisor of 6 is 66.7%.
What is probability?It is expressed as a number between 0 and 1, where 0 represents an impossible event (it will never occur) and 1 represents a certain event (it will always occur).
According to question:1, 2, 3, and 6 can be divided by 6.
To find the probability (p) of selecting a divisor of 6, we need to divide the number of divisors of 6 by the total number of possible outcomes, which is also 6 (since there are 6 positive integers from 1 to 6).
So, p(divisor of 6) = number of divisors of 6 / total number of outcomes
= 4 / 6
= 2 / 3
We can multiply this fraction by 100 to get the percentage:
p(divisor of 6) = 2 / 3 * 100
= 66.7%
Rounded to the nearest tenth, the answer is 66.7%. Therefore, the probability of selecting a divisor of 6 is 66.7%.
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Match each exercise with the first step needed to perform the operation. Do not actually perform the operation.
Choose the correct answer below.
A. Multiply the numerators and multiply the denominators.
B. Multiply the first rational expression by the reciprocal of the second rational expression.
C. Subtract the numerators. Place the difference over a common denominator.
D. Subtract the denominators. Place the difference below a common numerator.
Answers
Two same-sized triangular prisms are attached to a rectangular prism as shown below.
If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?
Answers
Answer:1,208 square centimeters
Step-by-step explanation:
select all values for b that make the equation 8(x - 3) = 2x + b + 6x have no solutions for x. -24 -3 3 24
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{B (-3), C (3), and D (24)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{8(x - 3) = 2x + b + 6x}[/tex]
Find: [tex]\textsf{Which values for b are not a solution}[/tex]
Solution: In order to make it easier for us to determine the answer, let us first simplify the expression that was given to us. We can do that by first combining like terms on the right side of the equation and distributing the 8 on the left side of the equation.
[tex]\textsf{8(x - 3) = 2x + b + 6x}[/tex][tex]\textsf{(8 * x) + (8 * -3) = 8x + b}[/tex][tex]\textsf{8x - 24 = 8x + b}[/tex]We can now subtract 8x from both sides of the equation.
[tex]\textsf{8x - 8x - 24 = 8x - 8x + b}[/tex][tex]\textsf{-24 = b}[/tex]Now that we know that b is equal to -24, that means that any value other than -24 would cause the equation to have no solutions. Therefore, the correct answer would be B (-3), C (3), and D (24).
A table titled dice rolls has 7 rows and 2 columns. In the top row, result is in the first column and number of rolls is in the second column. In the second row, 1 is in the first column and 15 is in the second column. In the third row, 2 is in the first column and 18 is in the second column. In the fourth row, 3 is in the first column and 14 is in the second column. In the fifth row, 4 is in the first column and 16 is in the second column. In the sixth row, 5 is in the first column and 19 is in the second column. In the seventh row, 6 is in the first column and 18 is in the second column.
To find the average result of rolling a six-sided dice, Josh rolls a dice 100 times.
The table shows how many times Josh rolled each number. What is the mean,
or average, of the dice rolls?
Answers
Answer:16.7
Step-by-step explanation: So the first step is to add all of the numbers in the second column. (15,18,14,16,19,18). At the end of your problem it says 100. So you have 6 different numbers, and 100. You will do 100 divided by 6. Finally you will get 16.66 and you will just round it.
Determine the equation of the circle with center (-6, -2 containing the point (-9, -2).
Answers
The equatiοn οf the circle is (x + 6)(x+6) + (y + 2)(y+2) = 9.
What is circle ?A circle is a twο-dimensiοnal geοmetric figure that cοnsists οf all pοints that are equidistant frοm a single fixed pοint called the center. A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane in such a way that its distance frοm a fixed pοint is always cοnstant.
Tο find the equatiοn οf a circle, we need the cοοrdinates οf the center and the radius.
The center οf the circle is given as (-6, -2), sο the cοοrdinates οf the center are (h, k) = (-6, -2).
The pοint (-9, -2) is οn the circle, sο its distance frοm the centre is equal tο the radius. We can use the distance fοrmula tο find the radius:
[tex]\rm r = \sqrt{((x_2 - x_1)\times (x_2 - x1) + (y_2 - y_1)\times(y_2 - y_1))}[/tex]
[tex]= \sqrt{((-3)^2 + 0^2)[/tex]
= 3
Therefοre, the radius οf the circle is 3.
Nοw we can use the standard fοrm οf the equatiοn οf a circle, which is:
(x - h)(x-h)+ (y - k)(y-k)= r*r
Substituting the values we fοund, we get:
Simplifying:
(x + 6)(x+6) + (y + 2)(y+2) = 9
Therefοre, The equatiοn οf the circle is [tex](x + 6)(x+6) + (y + 2)(y+2) = 9[/tex].
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You leave your house to go the mall. You drive due north 8 miles, due east 7.5 miles, and due north again 2 miles. Answer b and c.
Answers
Answer:
CD = 1.5 milesAE = 12.5 milesStep-by-step explanation:
Given the figure with triangle ABC similar to triangle EDC and AB=8 mi, ED=2 mi, BD = 7.5 mi, you want the measures of CD and AE.
b. CDSimilar triangles will have corresponding sides proportional. That means ...
ED/CD = AB/CB
2/CD = 8/(7.5 -CD)
Inverting the ratios and multiplying by 8 gives ...
4·CD = 7.5 -CD
5·CD = 7.5 . . . . . . . add CD
CD = 1.5 . . . . . . . . . divide by 5
c. AEThe distance AE is the hypotenuse of a right triangle with side lengths 7.5 and (8+2) = 10. The Pythagorean theorem can be used to find AE:
AE² = 7.5² +10² = 56.25 +100 = 156.25
AE = √156.25 = 12.5
AE = 12.5 miles, the distance to the mall.
__
Additional comment
You may recognize these triangles are 3-4-5 triangles. ABC has a scale factor of 2, so has side lengths 6-8-10. EDC has a scale factor of 1/2, so has side lengths 1.5, 2, 2.5. The triangle with AE as its hypotenuse is the sum of these, so has a scale factor of 2.5 (miles).
AE = (2.5 miles) · 5 = 12.5 miles
A particle moves along the x-axis with velocity given by v(t) = 6t² + 8t - 5
for time t≥ 0. If the particle is at position x = -2 at time t = 2, what is
the position of the particle at time t = 1?
Answers
The position of the particle at time t = 1 would be -1.
Position of a particle at a time, tTo find the position of the particle at time t = 1, we need to integrate the velocity function v(t) from t = 0 to t = 1, and add it to the initial position x = -2:
x(1) = -2 + ∫[0,1] v(t) dt
Integrating v(t), we get:
x(1) = -2 + ∫[0,1] (6t² + 8t - 5) dt
x(1) = -2 + [2t³ + 4t² - 5t] from 0 to 1
x(1) = -2 + [2(1)³ + 4(1)² - 5(1)] - [2(0)³ + 4(0)² - 5(0)]
x(1) = -2 + [2 + 4 - 5]
x(1) = -2 + 1
x(1) = -1
Therefore, the position of the particle at time t = 1 is -1.
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On the first
day there were 4 laborers getting time and a half and 20 who were not for a total of $2080. On the
second day there were 2 laborers getting time and a half and 15 who were not for a total of $1440.
How much were the time and a half workers getting per day compared to the laborers who did not get
time and a half.
Answers
Answer:
"time and a half" workers were paid 50% more per day
Step-by-step explanation:
You want to know the relative daily pay rates of laborers making time and a half versus those who were not. 4 getting time and a half and 20 not earned a total of $2080, while 2 getting time and a half and 15 not earned a total of $1440.
SetupWe can let x and y represent the daily pay of time and a half workers, and those not earning time and a half. The two payrolls can be described by ...
4x +20y = 2080
2x +15y = 1440
SolutionSubtracting the first equation from 2 times the second, we have ...
2(2x +15y) -(4x +20y) = 2(1440) -(2080)
10y = 800 . . . . . . . simplify
y = 80 . . . . . . . . . . divide by 10
2x +15(80) = 1440
2x = 240 . . . . . . . . . . subtract 1200
x = 120 . . . . . . . . divide by 2
Workers getting time and a half made $120 per day; workers not getting time and a half made $80 per day. Workers getting time and a half made half again as much as those who didn't: $40 per day more, or 50% more, or half-again as much.
__
Additional comment
"Time and a half" means the pay is 50% more. That's what we see here. You don't need any math to say those getting time and a half were getting 50% more per day.
Solve a triangle with b =7, c =10, and A= 51. round to the nearest tenth
Answers
The sides of the triangle are a ≈ 8.3, b = 7, and c = 10, and the angles are A = 51°, B ≈ 51.5°, and C ≈ 77.5°.
What is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles.
To solve the triangle, we need to find the values of the remaining sides and angles. We can start by using the Law of Sines, which states that:
a / sin A = b / sin B = c / sin C
where a, b, and c are the sides of the triangle, and A, B, and C are the angles opposite to those sides.
Using the given values, we can write:
a / sin 51 = 7 / sin B
a / sin 51 = 10 / sin C
To solve for a, we can use either of the two equations above. Let's use the first one and solve for sin B:
sin B = (7 / sin 51) * sin B
sin B = 7 / (sin 51 / sin B)
sin B = 7 / sin(180 - 51 - B)
sin B = 7 / sin(129 - B)
Using the sine rule, we can determine the angle B:
sin B / 7 = sin(129 - B) / 10
sin B = (7/10) * sin(129 - B)
sin B = (7/10) * (sin 129 * cos B - cos 129 * sin B)
sin B = (7/10) * sin 129 * cos B - (7/10) * cos 129 * sin B
(7/10 + (7/10) * cos 129) * sin B = (7/10) * sin 129 * cos B
sin B = (7/10) * sin 129 * cos B / (7/10 + (7/10) * cos 129)
sin B = sin 51.5
B = sin(sin B)
B = sin(sin 51.5)
B ≈ 51.5°
We can now find the remaining angle, C:
C = 180 - A - B
C = 180 - 51 - 51.5
C ≈ 77.5°
Finally, we can use the Law of Sines again to find the remaining side, a:
a / sin A = c / sin C
a / sin 51 = 10 / sin 77.5
a = (10 * sin 51) / sin 77.5
a ≈ 8.3
Therefore, the sides of the triangle are a ≈ 8.3, b = 7, and c = 10, and the angles are A = 51°, B ≈ 51.5°, and C ≈ 77.5°.
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39÷63=? in simplest form as proper fraction
Answers
Answer:
[tex]\frac{13}{21}[/tex]
Hope this helps!
Step-by-step explanation:
[tex]\frac{39}{63}[/tex] ( Simplify both numerator and denominator by 3 )
39 ÷ 3 / 63 ÷ 3
[tex]\frac{13}{21}[/tex]
The wholesale price for a chair is $181. A certain furniture store marks of the wholesale price by 22%. Find the price of the chair in the furniture store. Round your answer to the nearest cent as necessary.
Answers
To find the price of the chair in the furniture store, we need to calculate the retail price, which is the wholesale price plus the markup. The markup is calculated by multiplying the wholesale price by the markup rate as a decimal:
markup = 0.22 x $181 = $39.82
So the retail price is:
$181 + $39.82 = $220.82
Rounding to the nearest cent, we get the final answer:
The price of the chair in the furniture store is $220.82.
A group of randomly selected middle schoolers at SCVCS were asked how many pets they have. The data gathered is listed below.
{2, 0, 1, 3, 2, 5, 1, 2, 2, 4, 1, 3, 2, 7, 0, 2, 4, 2, 1}
What is the mode number of pets?
Mode =
Answers
Answer:
2
Step-by-step explanation:
2 appears the most as we can see theres only
two 0
and few of the other numbers
mode is the most common number in the list of any given numbers like the one abpve
307200/100 in decimal form
Answers
Answer:
Step-by-step explanation:
divide both by 100 to get
3072/1
answer: 3072
Test the equation for symmetry: r = 3 - 3 cos 0. Need answer fast. There are 3 tests of symmetry I need to know what they are.
Answers
Therefore, the line Ф = [tex]\frac{\pi }{2}[/tex], but not with respect to the pole, is the answer to the given equation's problem.
Define equationsComplex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures.
In this case, levelling generates [tex]b+7[/tex] rather than another method that could divide [tex]12[/tex] into two parts, analyse the information provided by [tex]y+7[/tex]and generate [tex]y+7[/tex]
A curve is said to be symmetric with respect to the pole if it does not alter when the pole is reflected across the origin. To test for this symmetry, we replace [tex]r[/tex] with [tex]-r[/tex] and see if the answer is still correct.
∴[tex]r = -3+3cos[/tex]Ф[tex]- r = 3-3(cos[/tex]Ф[tex])[/tex]Ф
Regarding the lineФ[tex]= \frac{\pi }{2}[/tex] there is symmetry. We replace Ф with [tex]\pi[/tex]/Ф and verify to see if the solution holds to see if this symmetry holds.
[tex]r= 3-3cos(\pi -[/tex]Ф[tex])[/tex]
[tex]r= 3-3cos[/tex]Ф
Due to the constant expression, the curve is symmetric with respect to the line Ф = [tex]\pi[/tex]/[tex]2[/tex].
Therefore symmetric with respect to the polar axis and the line Ф = [tex]\pi[/tex]/[tex]2[/tex], but not with respect to the pole.
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Please don't include attachments I'm unable to view them
Answers
The solution of the equation which is a vertex, from plot of the equation is
(-1.6, 0.7)What is a vertex?In mathematics, a vertex (plural: vertices) is a point where two or more lines, curves, or edges meet. The term is commonly used in geometry, graph theory, and other areas of mathematics.
In geometry, a vertex is a point where two or more edges of a polygon or a polyhedron meet. For example, a triangle has three vertices, while a cube has eight vertices.
The graph is attached and other vertices shown
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A report on consumer financial literacy summarized data from a representative sample of 1,669 adult Americans. When asked if they typically carry credit card debt from month to month, 587 of these people responded "yes." Estimate p, the proportion of adult Americans who carry credit card debt from month to month. (Round your answer to three decimal places.)
Answers
The answer is 0.351
To estimate the proportion p of American adults with monthly credit card debt, the sample proportion can be used as an estimate. The sample ratio is simply the number of people in the sample with monthly credit card debt divided by the total number of people in the sample.
p hat = 587/1669
p-hat = 0.3511 (rounded to four decimal places)
Therefore, based on this sample, the percentage of adult Americans with monthly credit card debt is estimated to be approximately 0.351. After rounding to three decimal places, its estimate is 0.351.
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calculate the area of the shaded region. the apothem is 2 ft, and the shaded area is 110 degrees. the figure is a circle.
Answers
The area of the shaded region is 1.916 ft²
What is Area?Area is a measure of the amount of space inside a two-dimensional shape, such as a square, rectangle, triangle, circle, or any other shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, or square meters.
To calculate the area of the shaded region, we need to find the area of the entire circle and subtract the area of the unshaded portion.
The central angle corresponding to the shaded region is 110 degrees. The entire circle has a central angle of 360 degrees.
The unshaded portion of the circle is the sector that corresponds to the central angle of 360 - 110 = 250 degrees. The area of a sector of a circle with radius r and central angle θ is given by the formula:
A = (θ/360)πr²
Substituting θ = 110 degrees and r = 2 ft, we get:
A = (110/360)π(2)
A = (0.305)π(2)
A = (0.305)π(2)
A = 0.61π
A = 1.916 ft²
Therefore, the area of the shaded region is 1.916 ft².
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Complete question:
Calculate the area of the shaded region. the apothem is 2 ft, and the shaded area is 110 degrees. the figure is a circle
Please help. Find x.
Answers
Step-by-step explanation:
because the circle arcs are equal, it also means that the lengths of the chords (WV and XY) are equal.
9x - 34 = 4x + 1
5x - 34 = 1
5x = 35
x = 35/5 = 7
x subtract 2 x subtract 2 multiply 3 in expression
Answers
Assuming you meant "x - 2(x - 2) * 3" as the expression, here is how you can simplify it:
x - 2(x - 2) * 3= x - 2(3x - 6) // Distribute the 2
= x - 6x + 12 // Distribute the -2
= -5x + 12 // Simplify
Therefore, the simplified expression is -5x + 12.
ANOTHER SCENARIOTo simplify the expression "x subtract 2 x subtract 2 multiply 3," we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, we need to simplify the multiplication by 3 inside the parentheses:
x - 2x - 2(3)Next, we can simplify the subtraction of 2x:
-x - 2(3)
Finally, we can simplify the multiplication of 2 and 3:
-x - 6
Therefore, the simplified expression is "-x - 6".
Solve the systems by graphing.
y =x+3
y = -2x - 6
Answers
Answer: (-3, 0)
Step-by-step explanation:
First, we will graph these equations. See attached. One has a y-intercept of 3 and then moves right one unit for every up down (we get this from the slope of 1). The other has a y-intercept of 4, and then moves down two units for every unit right (we get this from the slope of 1).
The point of intersection is the solution, this is the point at which both graphed lines cross each other. Our solution is:
(-3, 0) x = -3, y = 0
Answer:
(-3, 0)
Step-by-step explanation:
When we graph the equations:
y = x + 3,
y = -2 - 6,
we can see that they intersect at (-3, 0).
Therefore, that is the solution to the system.
— Extra note —
When graphing a line from a slope-intercept form equation (y = mx + b), we know the following:
m is the line's slope (rise over run)
b is the y-coordinate of the line's y-intercept
In a large population, 58 % of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Answers
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693
If 58% = 58÷100 of the people have been vaccinated, then;
1 - (58/100) = 42% = 42÷100 of the people who have not been vaccinated.
Now:
Probability, P( > 1 ), that at least one of the selected four has been vaccinated is given by;
P( > 1 ) = 1 - P(0) -----------(1)
Where;
P(0) = probability that all of the four have not been vaccinated.
P(0) = P(1) x P(2) x P(3) x P(4)×p(5)
Where;
P(1) = Probability that the first out of the four has not been vaccinated
P(2) = Probability that the second out of the four has not been vaccinated
P(3) = Probability that the third out of the four has not been vaccinated
P(4) = Probability that the fourth out of the four has not been vaccinated
P(5)=Probability that the fifth out of the five has not been vaccinated
Remember that 42÷100 of the population has not been vaccinated. Therefore,
P(1) = 42÷100
P(2) = 42÷100
P(3) = 42÷100
P(4) = 42÷100
P(5)=42÷100
P(0) = (42÷100) x (42÷100) x (42÷100) x (42÷100)×(42÷100)
P(0) = (42÷100)⁵
P(0) = (0.42)⁵
P(0) = 0.013067
Therefore, from equation (1);
P( > 1 ) = 1 -0.013067
P( > 1 ) = 0.98693
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693
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PLEASE HELP ASAP!!! THANKS
Answers
Answer: 28/52
Step-by-step explanation: its easy
Answer:
28/52. You will get it right.
Moussa and Anand own competing taxicab companies. Both cab companies charge a
one-time pickup fee for every ride, as well as a charge for each mile traveled. Moussa
charges a $3 pickup fee and $2.20 per mile. The table below represents what Anand's
company charges.
Anand's Taxicab Company
Miles (2) Total Cost (y)
10
$25
20
$48
30
$71
40
$94
Use the dropdown menu and answer-blank below to form a
true statement.
Anand's company charges
per mile than Moussa's
options are more/less
Answers
Anand's business charges $25 for a 10-mile ride, which is less than Moussa's overall expenses.
How to calculate Anand's expense per mile?In comparison to Moussa, Anand's business costs less per mile.
Let's examine why by contrasting the costs charged by the two businesses for a 10-mile trip:
With a $3 pick-up fee and $2.20 per mile,
Moussa's business costs a total of $3 + $2.20*10 = $25.
Less than Moussa's overall expense,
Anand's business charges $25 for a 10-mile ride.
For all other distances mentioned in the table, we can verify that Anand's business charges less per mile than Moussa's. Thus, it is accurate that
"Anand's company charges less per mile than Moussa's."
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can you always divide by e^x? and what example can you give to prove this statement
Answers
Answer: No, you cannot always divide by e^x. When e^x equals zero, dividing by it would result in an undefined value or division by zero error.
For example, consider the function f(x) = e^x. We know that e^x is never equal to zero for any value of x. Therefore, we can always divide by e^x for any value of x, and the resulting quotient will be well-defined.
However, if we consider the function g(x) = 1 / e^x, we cannot always divide by e^x. When e^x equals zero, g(x) will be undefined. In fact, there is no value of x for which e^x is equal to zero, so the function g(x) is well-defined for all values of x.
In summary, dividing by e^x is allowed for most cases, except when e^x equals zero.
Step-by-step explanation:
Which of the following is the value of a when the function f(x) = 3|x| written in the standard form of an absolute value function?
–1
–3
1
3
Answers
Answer: -1 Is the answer.
Consider a triangle ABC like the one below. Suppose that A = 27°, b=42, and c= 72. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
Continue
Breaking
news
B
Search
B = ₁₁ c = 0₁₁a = 0
a
□ OD
X
No
solution
Ś
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99+
Answers
The solution to the triangle is: a ≈ 22.4, b = 4 , c ≈ 77.2 ,A = 27° ,B ≈ 42.5°
C ≈ 110.5° we got the answer by using law of sine
what is law of sine?
The Law of Sines, also known as the Sine Rule, is a mathematical formula used in trigonometry to relate the sides and angles of a non-right-angled triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
In the given question,
Using the law of sines and the fact that the angles of a triangle sum up to 180 degrees, we can solve for the missing parts of the triangle:
sin(A)/a = sin(B)/b = sin(C)/c
sin(27)/a = sin(B)/42 = sin(C)/72
We can use the first equation to solve for a:
a = b(sin(A)/sin(B)) = 42(sin(27)/sin(B)) ≈ 22.4161
Next, we can use the second equation to solve for sin(B):
sin(B) = b(sin(A)/a) = 42(sin(27)/a) ≈ 0.6822
Taking the inverse sine, we find that B ≈ 42.4827 degrees.
Now we can use the fact that the angles of a triangle sum up to 180 degrees to solve for C:
C = 180 - A - B ≈ 110.5173 degrees.
Finally, we can use the law of sines again to solve for the remaining side, c:
c = a(sin(C)/sin(A)) = 22.4161(sin(110.5173)/sin(27)) ≈ 77.2352
Therefore, the solution to the triangle is:
a ≈ 22.4
b = 42
c ≈ 77.2
A = 27°
B ≈ 42.5°
C ≈ 110.5°
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Multiply the following to put them in standard form
-4 (5x-2)=
Answers
Answer:
-2x × 10^1 + 8 × 10^0
or
-2x × 10 + 8 × 1
Step-by-step explanation:
Multiply the following to put them in standard form
-4 (5x-2)=
-20x +8
standard form
-2x × 10^1 + 8 × 10^0
or
-2x × 10 + 8 × 1 (remember PEMDAS)
Denice is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 12 inches × 15 1/4 inches. She needs to cut another rectangle that is 10 1/3 inches by 10 1/4 inches. How many total square inches of construction paper does Denice need for her project?
Answers
The total area of construction paper needed for the project is:
180.25 + 127.5833... = 307.8333... square inches (rounded to four decimal places)
What is Area?Area is the measure of the amount of surface inside a closed boundary, usually measured in square units. It is used to express the size or extent of a two-dimensional region or shape, such as a square, rectangle, circle, or triangle.
To find the total area of the construction paper needed for the project, we need to find the area of each rectangle and then add them together.
For the first rectangle with dimensions of 12 inches by 15 1/4 inches, the area is:
12 × 15 1/4 = 180 + 45/4 = 180.25 square inches
For the second rectangle with dimensions of 10 1/3 inches by 10 1/4 inches, the area is:
10 1/3 × 10 1/4 = (31/3) × (41/4) = 127.5833... square inches (rounded to four decimal places)
Therefore, the total area of construction paper needed for the project is:
180.25 + 127.5833... = 307.8333... square inches (rounded to four decimal places)
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A large toy top is a cone with a slant height of
10
cm
and radius of
6
cm
. The handle of the toy top is a cylinder with a diameter of
2
cm
and height
2
cm
. Determine the approximate volume of the top. Use
π
≈
3.14
.
Answers
For the given cone, the approximate volume of the toy top is 106.81 cubic centimeters. The three dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.
What is volume?Volume is a three-dimensional quantity that measures the amount of space occupied by an object or a region in space.
The volume of the toy top can be calculated by finding the volumes of the cone and cylinder and then adding them together.
The volume of the cone is given by the formula V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius and h is the height of the cone. In this case, the slant height is given, so we need to use the Pythagorean theorem to find the height:
h = [tex]\sqrt{(l^2 - r^2)[/tex] = [tex]\sqrt{(10^2 - 6^2)[/tex] = √(64) = 8 cm
Therefore, the volume of the cone is:
V_cone = (1/3)π[tex]r^2[/tex]h = (1/3)π([tex]6^2[/tex])(8) ≈ 100.53 [tex]cm^3[/tex]
The volume of the cylinder is given by the formula V = π[tex]r^2[/tex]h, where r is the radius and h is the height of the cylinder. In this case, the diameter is given, so we need to divide by 2 to get the radius:
V_cone = (1/3)πh = (1/3)πr = d/2 = 1 cm = 2 cm
Therefore, the volume of the cylinder is:
V_cylinder = π[tex]r^{2}[/tex]h = π([tex]1^{2}[/tex])(2) ≈ 6.28
The total volume of the toy top is:
V = V_cone + V_cylinder ≈ 100.53 + 6.28 ≈ 106.81 T
Therefore, the approximate volume of the toy top is 106.81 cubic centimeters.
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