Answers
Answer:
152°
Step-by-step explanation:
Circle Theorem vocabulary
Secant: a straight line that intersects a circle at two points.
Arc: the curve between two points on the circumference of a circle
Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.
Angles of Intersecting Secants Theorem
If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.
[tex]\implies m \angle PRD=\dfrac{1}{2}\left(m\overset{\frown}{PD}-m\overset{\frown}{QS} \right)[/tex]
From inspection of the given diagram:
[tex]m \angle PRD=50^{\circ}[/tex][tex]m\overset{\frown}{PD}=(12x+8)^{\circ}[/tex][tex]m\overset{\frown}{QS}=(4x+4)^{\circ}[/tex]Substitute these into the formula and solve for x:
[tex]\implies 50^{\circ}=\dfrac{1}{2}\left((12x+8)-(4x+4)\right)^{\circ}[/tex]
[tex]\implies 50^{\circ}=\dfrac{1}{2}\left(8x+4\right)^{\circ}[/tex]
[tex]\implies 100^{\circ}=(8x+4)^{\circ}[/tex]
[tex]\implies 96^{\circ}=8x^{\circ}[/tex]
[tex]\implies x=12[/tex]
Substitute the found value of x into the expression for arc PD:
[tex]\implies m\overset{\frown}{PD}=(12x+8)^{\circ}[/tex]
[tex]\implies m\overset{\frown}{PD}=(12 \cdot 12+8)^{\circ}[/tex]
[tex]\implies m\overset{\frown}{PD}=(144+8)^{\circ}[/tex]
[tex]\implies m\overset{\frown}{PD}=152^{\circ}[/tex]
Therefore, the measure of arc PD is 152°.
Related Questions
If (a + b + c)‐¹= a‐¹+ b‐¹ + c‐¹, show that (a + b + c)³ = a³ + b³ + c³.
Answers
Step-by-step explanation
:We have to prove that (a + b + c)³ - a³ - b³ - c³ = 3(a + b ) (b + c) (c + a).
Considering LHS,
LHS : (a + b + c)³ - a³ - b³ - c³
= [(a + b + c)³ - a³] - (b³ + c³)
Using the algebraic identity,
a³ - b³ = (a - b)(a² + b² + ab)
(a + b + c)³ - a³ = ((a + b + c) - a)((a + b + c)² + a² + (a + b + c)a)
Using the algebraic identity,
(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)
= (b + c)(a² + b² + c² + 2(ab + bc + ca) + a² + a² + ab + ac)
= (b + c)(3a² + b² + c² + 3ab + 2bc + 3ac)
Using the algebraic identity,
a³ + b³ = (a + b)(a² + b² - ab)
b³ + c³ = (b + c)(b² + c² - bc)
So, [(a + b + c)³ - a³] - (b³ + c³) = (b + c)(3a² + b² + c² + 3ab + 2bc + 3ac) - [(b + c)(b² + c² - bc)]
= (b + c)[3a² + b² + c² + 3ab + 2bc + 3ac - (b² + c² - bc)]
= (b + c)[3a² + b² + c² + 3ab + 2bc + 3ac - b² - c² + bc]
= (b + c)[3a² + 3ab + 3bc + 3ac]
= (b + c)[3(a² + ab + bc + ac)]
= (b + c)[3(a(a + b) + c(b + a)]
= (b + c)[3(a + c)(a + b)]
= 3(a + b)(b + c)(a + c)
= RHS
Tell how you can ue mental math to find 45. 8 X 10 to the 3rd power and 45. 8 X 0. 1
Answers
The result of 45.8*10^3 is going to be 45800. Using mental math, 45.8*0.1 will be 4.58.
What is mental math?A set of abilities known as mental math enable people to perform calculations "in their heads" without the aid of paper and pencil or a calculator. Recalling math information, such as 8 x 5 = 40, is one of these abilities. Rounding numbers and estimating calculations are additional abilities. Mathematical calculations made solely with the human brain, without the aid of any materials or tools like a calculator, are referred to as mental calculations. When computing tools are not available, when mental calculation is quicker than other methods, or even in a competitive setting, people may use it.
Here,
45.8*10³=45800
45.8*0.1=4.58
The value of 45.8*10³ will be 45800. The value of 45.8*0.1 will be 4.58 using mental math.
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Please por favor someone help me out (;
Answers
The answers are 1) Distributive property 2) Combining like terms 3) Subtraction property of equality 4) Subtraction property of equality 5) Subtraction property of equality
What is mathematical identities?An identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions.
Given; 4x-2(3+2x) = 2x+11
1) 4x-6-4x = 2x+11 = Distributive property
2) 4x-4x-6 = 2x-11 = Combining like terms
3) -6 = 2x-11 = Subtraction property of equality
4) -17 = 2x = Subtraction property of equality
5) -8.5 = 2 = Subtraction property of equality
Hence, the answers are 1) Distributive property 2) Combining like terms 3) Subtraction property of equality 4) Subtraction property of equality 5) Subtraction property of equality
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56% of what number is 21
Answers
Answer:
The answer is 37.5.
Step-by-step explanation:
In canada, 63% of households speak english as their primary language, and 23% speak french as their primary language. if two canadian households are selected at random, what is the probability that the first household speaks french, but the second household speaks english? (0.23)(0.63) = 0.1449 0.23 0.63 = 0.86 0.23 0.63 – (0.23)(0.63) = 0.7451 startfraction 0.23 over 0.63 endfraction = 0.3650
Answers
The probability that the first household speaks French, but the second household speaks English, is 0.1449. The correct option is a.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
In Canada, 63% of households speak English as their primary language, and 23% speak French as their primary language.
Let A be the event that the household speaks French and B be the event that the household speaks English.
Converting percentage to decimals,
63% = 0.63
and 23% = 0.23
According to the question,
P (A) = 0.23 and P (B) = 0.63.
Then, the probability that the first household speaks French, but the second household speaks English is,
Probability =(0.23) x (0.63)
=0.1449
Therefore, the probability that the first household speaks French, but the second household speaks English is 0.1449.
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Write 0.000000836 in scientific notation.
Answers
The decimal 0.000000836 in scientific notation is 8. 36 × 10^-7
What is scientific notation?Scientific notation can be defined as a way of expressing numbers too small or too large to be conveniently written in decimal form.
It is also referred to as standard index form, standard form and scientific form.
It is commonly used for complex calculations with lengthy numbers.
It is also described as a method of expressing numbers in the terms of a decimal number that is between 1 and 10, and not 10 itself multiplied by a power of 10.
Given the decimal;
0.000000836
In scientific notation, it is written as;
8. 36 × 10^-7
The power is negative because the zeros are counted towards the right side.
Hence, the value is 8. 36 × 10^-7
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Do you know the answer~?
then please help me!!!!!!!!!!!!!!
Answers
The amount of Chemical B needed is 1.6 g.
what is graph?This refers to a diagram that shows a series of one or more points, lines, line segments, curves, or areas that represents the variation of a variable when compared with that of one or more other variables.
The quantity of Chemical B is plotted against the quantity of Chemical A.
Chemical B is plotted on the vertical axis using the scale of 1 cm to represent 2 units. Chemical A is plotted on the horizontal axis using the scale of 1 cm to represent 1 unit.
Therefore, on the graph, the line passing through the origin of the graph shows that when 1.4 g of Chemical A is used 1.6 g of Chemical B is needed.
Calculations:Chemical B is plotted on the vertical axis using the scale of 1 cm to represent 2 units.
To get the amount of Chemical B is on vertical axis = 2 grams
5 boxes
=0.4 g
Tracing the mass of Chemical A used 1.4 g it meets the line passing through the center at 4th line (4th box).
To get the amount of Chemical B is on vertical axis = amount of Chemical B per box * the number of line (boxes).
To get the amount of Chemical B is on vertical axis = 0.4 g * 4 lines (boxes)
= 1.6 g
Hence The amount of Chemical B needed is 1.6 g.
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David catches 75 camels, tags them, and releases them. A few weeks later, a helicopter pilot takes an aerial photograph of 310 camels, 25 of which are tagged. To the nearest whole number, what is the best estimate for the camel population?
Answers
Answer:
103
Step-by-step explanation:
[tex]\frac{75}{310} = \frac{25}{p}\\ 25 X \frac{310}{75} = 103[/tex]
finding an irrational number between which given pair of numbers supports the idea that irrational numbers are dense in real numbers? math 3
Answers
If there is another element of the same set between any two members of a set, we can say that the set is dense.
We'll show that the first choice—3.14 and pi—is the right one.
To prove that the set of irrational numbers contains a lot of real numbers, we must first discover an irrational number that lies between two specified real numbers.
In order to extend this to the real set, which is the union of irrational numbers and rational numbers, we should be able to find an irrational number between a rational number and an irrational number (or between an irrational number and a rational number). This is because we know that irrational numbers are dense (between two irrational numbers we can find another irrational number).
The first option, which has one of each, will then be the right choice.
Pi is irrational, while 3.14 is rational.
Finding an irrational number between these two indicates that the real set contains many irrational numbers.
(Note that the third option likewise has an irrational and a rational number, but the first one, [tex]e^{2}[/tex], is larger than the second one[tex]\sqrt{54}[/tex], thus it is written wrongly; for this reason, we did not choose it.)
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if there are five people in a car and 1 person is the driver, how many unique seating arrangements are there
Answers
Answer:
none
Step-by-step explanation: if the person driving is one of the five people than none
What is the address of the element 0 ?
Answers
when there are three treatment groups and 300 participants, what is the degrees of freedom in the denominator of the f-statistic calculation?
Answers
The degrees of freedom in the denominator of the f-statistic calculation is 2.
Explain the term degrees of freedom?The number of distinct bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df.
It is determined by subtracting the number of constraints from the sample size.Normal reporting of the results of a statistical test includes the test statistic and the degrees of freedom in brackets.Its degrees of freedom refers to the quantity of independent data points utilized to generate the statistic.For the stated question-
degrees of freedom df = n - 1
n = 3 groups
df = 3 - 1
df = 2
Thus, the degrees of freedom in the denominator of the f-statistic calculation is 2.
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A group of friends went to a hamburger bar 2/5 of them bought a hamburger, 1/3 of them bought just chips, and the rest bought cola, what fraction of the group bought food? what fraction just bought drinks
Answers
By adding the given fractions, we can see that 11/15 of the friends bought food, and 4/15 bought drinks.
What fraction of the group bought food?
We know that 2/5 of the group bought a hamburger, and 1/3 of them bought chips.
Then the total fraction of friends who bought food is given by the addition of the two fractions above.
2/5 + 1/3
finding a common denominator we will get:
(3/3)*(2/5) + (5/5)*(1/3)
6/15 + 5/15
11/15
So 11/15 of the friends bought food, and the rest:
4/15 bought drinks.
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Theater tickets cost $2.50 for children and $3.50 for adults. The price for 9 tickets was $29.50. How many adult tickets were purchased?
Answers
Answer:
8 is the answer
a) about what percentage of scores were between between 68 and 82? 68 % b) about what percentage of scores were between 61 and 75?
Answers
Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%
What is percentage?One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
Here,
Given: Total number of freshman =500
mean =75 and standard deviation =7
a) the percentage of scores that fell between 68 and 82
340 is the number of freshman whose scores that fell between 68 and 82
thus,
percentage = 340 /500 * 100
=> percentage = 68%
b)the percentage of scores that fell between 61 and 75
237 is the number of freshman whose scores that fell between 61 and 75
thus,
percentage = 237/500 * 100
=> percentage = 47.4%
Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%
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Use the model to answer the question.
a 10 by 10 grid is shown. 5 columns and 1 row are shaded.
Choose the numbers to find the product shown by the model.
0.5 × ____ = _____
Answers
The complete model will be;
⇒ 0.5 × 0.1 = 0.05
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A 10 by 10 grid is shown.
And, 5 columns and 1 row are shaded.
Now,
Since, 5 columns and 1 row are shaded.
Hence, The complete model will be;
⇒ 0.5 × 0.1 = 0.05
Thus, The complete model will be;
⇒ 0.5 × 0.1 = 0.05
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The product of two consecutive numbers is 3306. What are the numbers?
Answers
The winner of a 1000 mile race drove his car to victory at a
rate of 131.3009 mph. What was his time (to the nearest
thousandth of an hour)?
Answers
He took 7.616 hours for victory at the speed of 131.3009 and cover 1000 miles.
What is distance?
The distance between two sites is the length of the route. The metre is the SI unit for distance.
What is speed?
The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.
What is time?
The amount of time that something happens, goes through a process, or remains the same.
Speed= 131.3009 mph
Total distance= 1000 miles
Speed = distance/ time
time= distance/ speed
time= 1000/131.3009
(nearest thousandth means round off upto 3 decimal places)
time= 7.616 hours
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Look at picture !!!!
Slope=
Y-intercept=
Equation=
Answers
Answer:
y = -5x -2
Step-by-step explanation:
Equation y=mx+b
Slope m=(y2-y1)/(x2-x1)
Slope m=(-7- -2)/(1 - 0)
Slope m=(-7 + 2)/(1 - 0)
Slope m=(-5)/(1)
Slope m= -5
Point-slope form = y − y 1 = m ( x − x 1 )
Point-slope form = y − -2 = -5 ( x − 0 )
Point-slope form = y + 2 = -5x − 0
Point-slope form = y = -5x -2
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(1 point) how many different ways can a race with 6 runners be completed? (assume there is no tie.) your answer is : 36
Answers
There are 720 different ways can a race with 6 runners be completed.
What is a combination?
The process of combining or the condition of combining. a combination of things; an amalgamation of concepts. a grouping of notes: A chord is a grouping of notes. a grouping of people or entities acting together to impede commerce.
Here, we have
The winner can be chosen from all 6 runners, the second person can be chosen from 5 people, the third - from 4, and so on.
So the total number of possible results can be calculated as:
n = 6×5×4×3×2×1= 6!
= 720
Hence, there are 720 different ways can a race with 6 runners be completed.
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Three times the sum of x and 7 is 27. What is x?
Answers
Answer:
2
Step-by-step explanation:
it says 3 times the sum of x and 7 equals 27 so 1st divide 27 by 3 which gives you 9 and then subtract 7 which is given and that gives you 2 for your answer
Please help me, I need this for tomorrow’s test
Answers
Answer:
12
Step-by-step explanation:
14 + 7 = 21
14 / 21 = ⅔
AE = 18
x / 18 = ⅔
x = 18 x ⅔
x = 12
what effect does increasing the sample size have on the probability? provide an explanation for this result.
Answers
Increasing the given sample size will decreases the probability because σx will decreases as n value increases.
In Statistitics whenever we test a hypothesis for testing a statistic, we use confidence interval. Confidence interval is on either side of an assumed value a margin of error. Margin of error is calculated as critical value * sigma/sqrt of n. Thus we find that whenever n increases, margin of error decreases.
Thus making confidence interval narrower and thus making probability for accepting null hypothesis a less value. As the pattern sizes increase, the range of every sampling distribution decreases so they emerge as more and more leptokurtic. The variety of the sampling distribution is smaller than the variety of the authentic populace. Therefore, as a pattern length increases, the pattern imply and general deviation might be nearer in fee to the populace imply μ and general deviation σ.
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Gary is collecting stamps and wants to collect the same number of stamps each week. He currently has 520 stamps. He only has 6 more weeks to collect the remaining stamps that he needs for his collection. He needs a total of at least 1000 stamps before he is done. Graph the answer to the inequality.
Answers
Answer:
Step-by-step explanation:
1000-520=480
480/6=80
x+6+520=1000 (-6)
x+514=1000
x=486
Giving Brainly to whoever helps! Thanks.
Answers
Answer:
140 hamburgers
Step-by-step explanation:
to find the answer we must first use a let statement and write an equation
let x = hamburgers
hamburgers * 2 is cheeseburgers and added together that is 420
so
x + 2x = 420
now solve
3x = 420
x = 140
140 hamburgers were sold
Answer:
Step-by-step explanation:
240 divided by 3= 80
80+80=160
160 hamburgers sold altogether on Wednesday.
Cynthia is a real estate agent. In one of her properties, a large square
room has an area of 405 square feet. To find the length of one side of
the room, Cynthia writes V405 feet. Simplify this expression, using the
first rule of radicals.
Answers
The expression after simplifying with the first rule of radicals is 9√5.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is side²
We have,
Area of a square = side² _______(1)
Area = 405 square feet _______(2)
From (1) and (2) we get,
405 square feet = Side²
Side = √405 feet
[ 405 = 81 x 5 ]
Side = √(81 x 5)
[ 9² = 81 ]
Side = 9√5
Thus,
The side length is 9√5 feet.
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A year hence a father will be 5 times as old as his son. Two years ago, he was three times as old as his his son will be four years hence. Find their present age.
Answers
y = father’s age
5(x + 1) = y + 1
3(x + 4) = y - 2
First equation simplified:
5x + 5 = y + 1
y = 5x + 4
Plug into second equation:
3x + 12 = 5x + 4 - 2
-2x = -10
x = 5 (age of son)
y = 5(5) + 4 = 29 (age of father)
First try was incorrect
Hercules ate 6 hot dogs every 16 minutes. At that rate, how long,
minutes, will it take to eat 18 hot dogs?
Answers
Answer:
48 minutes
Step-by-step explanation:
6 : 16 = 18 : x
x = 16 * 18 / 6
x = 16 * 3
x = 48
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad. The probability of drawing a bag with bad potatoes is less than 1. The probability of drawing a bag with good potatoes is greater than 0. What is the probability of drawing a bag with bad potatoes? what is the expected probability of the complement of the event?.
Answers
Probability of drawing bad potatoes = 0.1
The probability of drawing a bag with bad potatoes is less than 1.
The probability of drawing a bag with good potatoes is greater than 0
The probability of drawing a bag with bad potatoes as a decimal .
The probability is 20% which means 20 by hundred , which means there is a chance of being its ok.
probability of bad potatoes = 2/20
=1/10
=0.1
To find the probability of the outcomes = Number of favourable outcome / Number of total outcome.
Probability of event 1 and 2
probability of event 1 =Number of favourable outcome / Number of total outcome.
probability of event 2 = 1 -( probability of event 1)
probability of good potatoes = 1- ( probability of bad potatoes)
Probability of the given event( probability of the bad potatoes = 1-(0.1)
Thus,
Probability of the bad potatoes in the 2 of the bags are=0.9
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What is the domain of the function of x graphed below?
(-6.-5)
A {xx>-1}
(-1.3)
Cx-5
B {x-6
D {xx<3}
Answers
Answer:
Step-by-step explanation:
B is the answer
Create a line from-6,-5 to the x axis to -6 and draw a line from -1,3 down to x axis because that is your domain. Make sure to look at your open circles or closed circles at end of the line, if closed there are block brackets, If open then it is parenthesis. If it is a coordinate it is curly brackets. So therefore the answer is B