The probability that a dart hits one of the shaded areas is 1/6 when a dart is thrown at a regular hexagon dartboard with the design shown.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions.
Here,
angle of hexagon=360/6=60°
using trigonometric ratios,
area of triangle=bh/2
=(h*h√3/2)/2
=h²√3/4
area of hexagon=6*area of triangle
=6*(h²√3/4)
=3√3*h²/2
area of rectangle=bh
=h*h√3
=h²√3
area of shaded region,
=3√3*h²/2-h²√3
=h²√3/2
area of 1 shaded region=(h²√3/2)/2
=h²√3/4
Probability of hitting one shaded area,
=(h²√3/4)/(h²3√3/2)
=1/6
When a dart is thrown at a standard hexagonal dartboard with the pattern shown, the likelihood that it will land in one of the shaded areas is 1/6.
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The equation y=4–x is graphed on the coordinate plane. Which point(s) will NOT be on the line? Select all that apply.
Answer: (6,1), (2,-1) etc
Step-by-step explanation:
Just pick any points on the graph and see if they aren't on the line and if they aren't, then you can pick that one.
please i need it quick
The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.
How to solve a trigonometric equation
In this problem we need to find the solutions of a trigonometric equation, which can be done by means of algebra properties and trigonometric formulas. Now we proceed to present the entire procedure:
Step 1 - Introduce the trigonometric equation:
cos 2x - cos x = - 1
Step 2 - Use the trigonometric formula cos 2x = cos² x - sin ² x:
cos² x - sin ² x - cos x = - 1
Step 3 - Use fundamental trigonometric formula:
cos² x - 1 + cos² x - cos x = - 1
2 · cos² x - cos x = 0
Step 4 - Use algebra properties to factor the expression:
cos x · (2 · cos x - 1) = 0
Step 5 - Find the solutions of the expression:
cos x = 0 → x = {π / 2, 3π / 2}
2 · cos x - 1 = 0
2 · cos x = 1
cos x = 1 / 2 → x = {π / 3, 5π / 3}
The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.
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Here i a ample data et, 19 39 9 33 15 16 2 33 16 Find the mallet number (Minimum) from the data et Find the firt quartile Q1 Find the median Find the third quartile Q3 Find the larget number (Maximum) from the data et
a) The smallest number is 2
b) The first quartile Q1 is 12
c) The median is 16
d) Third quartile Q3 is 33
e)The largest number is 39
What Is Quartile Formula?
To divide a set of observations into four equal pieces, use the quartile formula. The median and the first term are where the first quartile is located. The median represents the middle quartile. The third quartile represents the midway value that falls between the median and the last term.
Given data set:
19, 39, 9, 33, 15, 16, 2, 33, 16
Arrange the data in ascending order:
2, 9 ,15 ,16 ,16 ,19 ,33 ,33 ,39
a) Smallest number: 2
b) The first quartile Q1 :
number of terms=n=9
Q1= (n+1)/4 th term
Q1= (9+1)/4 = 2.5th terms
This means, Q1=mean of 2nd and 3rd terms= (9+15)/2 = 12
c) Median:
M=(n+1)/2 th term = (9+1)/2 =5th term = 16
d) Third quartile Q3:
Q3= 3[(n+1)/4] th term
Q3= 3[(9+1)/4] = 7.5th terms
This means, Q3=mean of 7th and 8th terms= (33+33)/2 = 33
e) largest number : 39
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1. The difference of a number and 46 is at most 153. What is the largest integer that could be used for the number?
2. Vanessa must earn at least 360 points to make an A in her Pre-Algebra class. If she currently scores of 81, 91, and 89 points from her first three test, how many more points does she need to make an A?
3. The band has been selected to march and play in the holiday parade. The 105 members must raise at least $49,500 for the trip. What is the least amount that each one needs to raise (to the next whole dollar)?
4. All the cars a company sells require a down payment of $2,000 and 48 monthly payments. The contract amount for any of the cars is at least $19,940. What is the least amount of the monthly payment (to the next whole dollar)?
5. A particular type of TV is being sold for $1,200 cash for $500 down with 48 monthly payments. Find the amount of the monthly payment if the plan resusts in charges of at least $1,484 over the life of the contract. Find the amount of interest paid if the monthly payment plan is chosen.
please help, its due tomorrow. thank you.
The basic calculation values are;
1. The largest number is 199
2. The score Vanessa needs is 99 points
3. Each person should raise approximately $471
4. The approximate minimum monthly payment is $374
5. The approximate monthly payment is $55.9
The interest is 123.[tex]\overline {6}[/tex]
What are basic mathematical operations?Basic mathematical operations includes addition, subtraction, multiplication, division, and combinations of the above operations.
1. Let x represent the number, we have;
x - 46 ≤ 153
x ≤ 153 + 46 = 199
x ≤ 199
The largest integer that could be used for the number is 199
2. Vannesa's current scores are;
81 points, 91 points, 89 points
The score Vannesa requires so as to get an A is 360 points
The score Vannesa needs = 360 - (81+91+89) = 99
Vannesa needs 99 points to get an A
3. The number of members in the band = 105
The amount the band needs to raise = $49,500
The amount each one should raise therefore is 49500 ÷ 105 ≈ 471
Each one needs to raise $471
4. The down payment is $2,000
Number of monthly payment = 48
Least contract amount = $19,940
The monthly payment = (19,940 - 2,000)/48 ≈374
The least monthly payment ≈ $374
5. The cash price for the TV = $1,200
The down payment = $500
The charges = $1,484
Number of monthly payment = 48
Total payment = $1,200 + $1,484 = $2,684
The monthly payment = 2,684 ÷ 48 ≈ 55.9
The monthly payment is approximately $55.9
The interest is therefore;
[tex] \dfrac{1484}{1200}\times 100 = 123.\overline 6 \%[/tex]
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Given: If a triangle is equilateral, then the triangle is isosceles.
Identify the following statements as the inverse, the converse and the contrapositive.
To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.
So, inverse of the given statement is "If △ABC is not equilateral , then it is not isosceles"
We have to find the inverse of the given statement:
" If ∆ABC is equilateral, then it is isosceles."
A triangle is said to be equilateral if all of the three sides are equal in measure and a triangle is said to be isosceles if two sides of a triangle are equal in measure.
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Two Triangles are similar. The
scale factor of the smaller
triangle to the larger triangle is 1/3.
If the perimeter of the larger
triangle is 27 m, what is the
perimeter (in m) of the smaller
triangle?
The perimeter of the smaller triangle is 3m.
What is a perimeter of a triangle?
The total of a triangle's three sides is the perimeter. The Greek words "peri" (which means around) and "metron," which means measure, are combined to get the English word perimeter. The perimeter of any 2D shape is the total distance encircling it. Since a shape's perimeter indicates how long its boundary is, it is stated in linear units.
Here,
The ratio of given perimeters is 1:3 so the ratio of their sides and their altitudes will also be in the ratio of 1:3.
The ratio of the areas is 1^2/3^2=1/9. (ratio of their sides: a/b, ratio of their areas: a^2/b^2)
Now, we have 1/9=A/27
where A = area of the smaller triangle
Now, cross-multiply the given quantity
1*27=9*A
27=9A
A=27/9
A=3 m is the area of the smaller triangle.
Hence, the perimeter of the smaller triangle is 3m.
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Write a mathematical sentence that expresses the information given below.
Use p as your variable name. If necessary:
type <= to mean <
or > = to mean 2.
A football team had 52 players at the start of the season, but then some
players left the team. After that, the team had 43 players.
The mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season or p = 52-43.
According to the question,
We have the following information:
A football team had 52 players at the start of the season, but then some players left the team. After that, the team had 43 players.
Now, let's take the number of players who left the team to be p.
So, we have the following expression:
p = 52-43
p = 9
Hence, the mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season.
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Convert meters to centimeters. 9.2 m = afers x 1. cm m) cm)
A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomrua in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from "Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomrua in Older Adults," by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min. Does zopiclone appear to be effective?
A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
What is a confidence interval?
A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.
Here,
From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,
98%C.I. = µ ± z * σ / n = 98.90 ± 2.33 * 42.30 / sqrt of 16 = 98.90 ± 24.64 = 74.26 to 125.54
The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.
Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
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A sheet of metal 10 inches by 8 inches is to be used to make a open box. Squares of equal sides x are cut out of each corner then the sides are folded to make the box. Find the value of x (correct to 2 decimal places) that makes the volume a maximum.
Answer:
1.81 inches
Step-by-step explanation:
Zayne wants to join a gym.
Get Fit Gym charges a $140 enrollment fee and $50 per month.
Fit R Us charges a $245 enrollment fee and $35 a month.
He thinks Get Fit Gym is the better deal. Do you agree or disagree? Explain you're answer
Zayne is right as Get Fit Gym is the better deal.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Zayne who wants to join a gym. Get Fit Gym charges a $140 enrollment fee and $50 per month. Fit R Us charges a $245 enrollment fee and $35 a month. He thinks Get Fit Gym is the better deal.
The price for one month at Get Fit Gym will be -
C[G] = 140 + 50 x 1 = 140 + 50 = $190
The price for one month at Fit R Us will be -
C[F] = 245 + 35 x 1 = 245 + 35 = $280
Therefore, Zayne is right, Get Fit Gym is the better deal.
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A discount of 25 % is allowed on an article marked at rs 17 500. calculate the discount.
Answer:
$4375
Step-by-step explanation:
25 percent *17500 =
(25:100)*17500 =
(25*17500):100 =
437500:100 = 4375
This morning, Ravi's car had 15.04 gallons of fuel. Now, 4.9 gallons are left. How much fuel did Ravi use
gallons
Through subtraction method, we find out that the gallons of fuel used by Ravi is equal to 10.14 gallons.
It is given that -
The original gallons of fuel that Ravi had in the morning = 15.04 gallons
Now, the gallons of fuel left = 4.9 gallons
We have to find out the gallons of fuel used by Ravi.
The amount of fuel Ravi used =
Original gallons of fuel - Gallons of fuel left
= (15.04-4.9) gallons
= 10.14 gallons.
Thus, through subtraction method, we find out that the gallons of fuel used by Ravi is equal to 10.14 gallons.
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Leticia is selling raffle tickets for her class fundraiser. Her class receives four-fifths of the money raised from selling the raffle tickets. Prior to the selling of raffle tickets, her class fund had a balance of $200.00.
Which function can be used to find m, the amount of money in Leticia's class fund, based on t, the amount of money Leticia has made from selling raffle tickets?
The function for the given situation is m=200+0.8t.
Given that, Leticia is selling raffle tickets for her class fundraiser. Her class receives four-fifths of the money raised from selling the raffle tickets.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the amount of money in Leticia's class fund=m and the amount of money Leticia has made from selling raffle tickets is t
Now, the function is
m=200+4/5 t
⇒m=200+0.8t
Therefore, the function for the given situation is m=200+0.8t.
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2(x-3)^2-12=116 help
Step-by-step explanation:
[tex]2(x - 3) {}^{2} - 12 = 116 \\ [/tex]
[tex]2 \times ( {x}^{2} - 6x + 9) - 12 = 116[/tex]
[tex] {2x}^{2} - 12x + 18 - 12 = 116[/tex]
[tex] {2x}^{2} - 12x - 110 = 0[/tex]
[tex] {x}^{2} - 6x - 55 = 0[/tex]
[tex] {x}^{2} - 11x + 5x - 55 = 0[/tex]
[tex]x(x - 11) + 5(x - 11) = 0[/tex]
[tex](x +5 )(x - 11) = 0[/tex]
What is the area of a quadrilateral with vertices at (1, 1), (5, -1),
(1,5), and (5,5)?
The area of the quadrilateral is = 15 square units.
What is area of the quadrilateral ?The quantity of territory contained within a quadrilateral determines its area. Let's review the definition of a quadrilateral. A closed shape with four line segments enclosing it is referred to as a quadrilateral. Both regular and irregular quadrilaterals exist. A quadrilateral with regular sides is one with equal-length sides. An irregular quadrilateral is a quadrilateral that is not regular. There are six different kinds of quadrilaterals.square \srectangle \sparallelogram \strapezoid \srhombus \skite.The area of a quadrilateral is nothing but the region enclosed by the sides of the quadrilateral. It is measured in square units such as m2, in2, cm2, etc.acc to our quesstion-
There are two sets of Y values identical ( 0 and 5 ).There are two sets of identical X values ( -1 and 2)This makes a rectangle.The length is 5-0 = 5The width is 2 - -1 = 3Area = Length x width = 5 x 3 = 15 square units.hence,The area of the quadrilateral is = 15 square units.
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How do I put 8x=26+14y in standard form
The given equation written in standard form is 8x - 14y = 26
Writing a linear equation in standard formFrom the question, we are to write the given linear equation is standard form.
From the given information, the given linear equation is
8x = 26 + 14y
The standard form of linear equation is given as
Ax + By = C
Where x and y are the variables
A, B, and C are the constants
Now, we will write the given equation in standard form
8x = 26 + 14y
Subtract 14y from both sides of the equation
8x - 14y = 26 + 14y - 14y
8x - 14y = 26
Hence, the equation is 8x - 14y = 26
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In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive 13 miles closer to the mountain, the angle of elevation is 9.
The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.
It is given that:
In traveling across flat land you notice a mountain directly in front of you.
Applying tan ratio:
tan3.5 = h/(15+x)
Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.
h = (15 + x) tan3.5
h = x tan9
(15 + x) tan3.5 = x tan9
x = 9.44
h = 9.44 tan9
h = 1.49 miles
Thus, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.
The complete question is:
In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive 13 miles closer to the mountain, the angle of elevation is 9.
Approximate the height of the mountain. (Round your answer to one decimal place.)
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Select all of the roots of x3 + 2x2 – 16x– 32.
–1
–2
–4
1
4
5
Answer:
-4, -2, 4
Step-by-step explanation:
You want the roots of the polynomial x³ +2x² -16x -32.
FactorsThe polynomial can be factored by grouping:
x³ +2x² -16x -32
= (x³ +2x²) -(16x +32) . . . . . . group pairs of terms
= x²(x +2) -16(x +2) . . . . . . . . factor each group
= (x² -16)(x +2) . . . . . . . . . . . . factor out the common factor
Now, the difference of squares can be factored:
= (x -4)(x +4)(x +2)
RootsThe zero product rule tells us the roots are the values of x that make the factors zero:
x -4 = 0 ⇒ x = 4
x +4 = 0 ⇒ x = -4
x +2 = 0 ⇒ x = -2
The roots of the polynomial are {-4, -2, 4}.
__
Additional comment
The factorization of the difference of squares is a special form:
a² -b² = (a +b)(a -b)
Answer:
-2, -4, and 4 are the correct answers on edge
Step-by-step explanation:
Josh has to walk 9/10 of a kilometre to school.He is 1/3 of the way there. How much further will he have to walk?
Jenny wants to record 15 minutes of songs for a film.
The table shows the playing time of 3 songs she has recorded.
Song
A
B
C
Playing time
4 minutes and 33 seconds
3 minutes and 42 seconds
3 minutes and 06 seconds
How much more time, in minutes and seconds, does she need to record?
a 14-ounce can of green beans contains two teaspoons of salt. how much sodium is present in 2 teaspoons (11.5 grams) of salt?
The percentage of salt in green beans can is 2.89%.
It is important to know about the percentage first, the percentage is a part of the sample in the population. It can be determined by this formula
A% = x / N . 100%
where A% is the percentage, x is the sample and N is the total population
From the question above, we know that :
x = 11.5 grams
N = 14 ounce = 396.89 grams
By substituting the parameter to the equation, we get
A% = x / N . 100%
A% = 11.5 / 396.89 . 100%
A% = 2.89%
Hence, the total salt in the can is 2.89%
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Find the least common denominator for this pair of algebraic fractions:
p/4 and p/16
The least common denominator for this pair of algebraic fractions: p/4 and p/16 is 16.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In the case, the fraction is illustrated as p/4 and p/16.
It should be noted that the lowest common multiple for 4 and 16 is 16. This is the denominator.
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8-3-3-4-5-6-7-8= the answer is -28
Answer: Correct, the answer is -28
Step-by-step explanation:
8-3=5
5-3=2
2-4=-2
-2-5=-7
-7-6=-13
-13-7=-20
-20-8=-28
What is an equation of the line that passes through the point (-4,7) and is parallel to the line 3x-y=4
Answer:
y=3x+19
Step-by-step explanation:
pls mark
How many edges does the following shape have?
Answer:
6
Step-by-step explanation:
what is an equivelent fraction of 8x^4 * 5x ^3
The equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question as:
8x⁴ × 5x³
We have to determine the equivalent fraction of the given expression.
⇒ 8x⁴ × 5x³
⇒ 8 × 5 × x⁴× x³
Multiply the coefficients in the above expression,
⇒ 40 × x⁴× x³
Add the exponents in the above expression,
⇒ 40 × x⁴⁺³
⇒ 40x⁷
Thus, the equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.
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HELP ASPPP PLEASE THANK SHOW UR WORK PLEASE
Step-by-step explanation:
y + 4 = 8 ( x - 6 )
Multiple 8 by -6 and x
y+4 = 8x -48
Subtract 4 from both sides
y = 8x -52
Take two points from this equation, I took (7,4) and (8,12)
Find the slope with these points, which should give you 8
Step-by-step explanation:
when we have the equation in the form of
y = ax + b
then "a" is the slope.
in our equation
y + 4 = 8(x - 6)
the only thing that contributed to the factor of x is
8(x ...)
so, in the end the equation is (we sit need to bother about the rest)
y = 8x ...
so, the slope is 8.
question 9
this is trickier.
again, we want the form
y = ax + b
we have
6y - 3x = 12
6y = 3x + 12
y = 3/6 x + 2 = 1/2 x + 2
so, the slope is 1/2.
suppose that five microchips in a production run of fifty are defective. a sample of seven is to be selected to be checked for defects. (a) how many different samples of seven can be chosen from the production run of fifty? (b) how many samples will contain at least one defective chip? the set of samples that do not contain any defective chips and the set of samples that contain at least one defective chip are ---select--- sets. so, the number of samples with at least one defective chip is . (c) what is the probability (as a percent) that a randomly chosen sample of seven contains at least one defective chip? (round your answer to one decimal place.) %
The answer to following parts are and this can be solved by using probability.
a) 15,890,700 different samples can be chosen
b) 6,523,881 will contain at least one defective chip
c) 41.1%
What is probability?
A probability is the number of desired outcomes divided by the number of total outcomes.
Main body:
The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
Cₙ,ₓ is the number of different combinations of x objects from a set of n elements, given by the following formula.
Cₙ,ₓ =[tex]\frac{ n!}{x!(n-x)!}[/tex]
(a) How many different samples can be chosen?
Samples of 6 from a set of 50.
Then
C₅₀,₆ = [tex]\frac{50!}{6!(50-6)!}[/tex] =15,890,700
15,890,700 different samples can be chosen
(b) How many samples will contain at least one defective chip?
Either a sample contains no defective chip, or it contains at least one. From a), the sum of them is 15890700.
Then
No defective chips:
Four are defective.
So 50-4 = 46 are not.
This is samples of 6 from a set of 46.
C₄₆,₆ = 46!/6!*40!
9,366,819 samples contain no defective chips.
At least one:
9366819 + n = 15890700
n = 6523881
6,523,881 will contain at least one defective chip
(c) What is the probability (as a percent) that a randomly chosen sample of six contains at least one defective chip
6,523,881 out of 15,890,700
6,523,881/15,890,700 = 0.411
As a percent
41.1%
Hence the answer are as follows.
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Find the area of the triangle.
A=?in^2
Answer:
A = 7.5 in^2
Step-by-step explanation:
the formula for a triangles area is [(h)(b)]/2
2.5 is the h (height) and 6 is the b (base)
first multiply h and b
2.5 * 6 = 15
now divide by 2
15 / 2 = 7.5
that is your answer