The values of Radius PQ if PQ = 24 and OR = 5. is 13 and The radius if PQ has length 24 and 9 units aways from center is 15 .
What is area of circle ?
Area of circle can be defined as product of pi and square of radius.
Given,
In the chord PQ of O , point R is choosen so that OR is perpendicular to PQ.
The radius if PQ = 24 and OR = 5.
r = [tex]\sqrt{(24/2)^2 +5^2 }[/tex]
r = [tex]\sqrt{144+25}[/tex]
r = [tex]\sqrt{169}[/tex]
r = 13.
The radius if PQ has length 24 and 9 units aways from center.
radius = [tex]\sqrt{(24/2)^2 + 9^2}[/tex]
= [tex]\sqrt{(12)^2 + 9^2}[/tex]
= [tex]\sqrt{144+81}[/tex]
= [tex]\sqrt{225}[/tex]
r = 15 .
The far from PQ from the center if it has length 16 and the circle has radius 10 is
PQ = [tex]\sqrt{10^2 - (16/2)^2}[/tex]
PQ = [tex]\sqrt{100-64}[/tex]
PQ = [tex]\sqrt{36}[/tex]
PQ = 6
The value of OR if PQ has length 6[tex]\sqrt{5}[/tex] and radius 9 .
OR = [tex]\sqrt{(9^2) - (3\sqrt{5})^2 }[/tex]
OR = [tex]\sqrt{81-45}[/tex]
OR = [tex]\sqrt{36}[/tex]
OR = 6 .
The value of OP .
OP = [tex]\sqrt{QR^2 + OR^2 }[/tex]
OP = [tex]\sqrt{(2\sqrt{3})^2 + (2\sqrt{2})^2 }[/tex]
OP = [tex]\sqrt{12+8}[/tex]
OP = 2[tex]\sqrt{5}[/tex]
Hence, the values of Radius PQ if PQ = 24 and OR = 5 is 13 and The radius if PQ has length 24 and 9 units aways from center is 15 .
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If a1=3 and an=-2an find f 8
Answer:
a₄ = 25
Step-by-step explanation:
using the recursive formula [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] and a₁ = 4 , then
a₂ = 2a₁ - 1 = 2(4) - 1 = 8 - 1 = 7
a₃ = 2a₂ - 1 = 2(7) - 1 = 14 - 1 = 13
a₄ = 2a₃ - 1 = 2(13) - 1 = 26 - 1 = 25
Find three consecutive integers whose sum is -42
Answer:
-15,-14,-13
Step-by-step explanation:
Let x = the first integer
Let x + 1 = the second integer
Let x + 2 = the third integer
The addition of all three equal -42
x + x + 1 + x + 2 = -42 Combine like terms
3x + 3 = -42 subtract 3 from both sides
3x + 3 - 3 = -42 - 3
3x = -45 Divide both sides by 3
x = -15
Check
-15 + -14 + -13 = -42
-42 = -42
Lucy spends 4 hours a week babysitting. Her sister Lily spends 7/8 as much time babysitting. Does Lily babysit for more or less than 4 hours.
Answer: Lily babysits for less than 4 hours.
Step-by-step explanation:
We can start by multiplying 4 hours by 7/8 to find out how many hours Lily spends babysitting.
4 * (7/8) = 7/2 = 3.5 hours
Since 3.5 is less than 4, Lily babysits for less than 4 hours.
Answer: Less than 4. (3 1/2 hours)
Step-by-step explanation:
When you multiply a number by a number smaller than 1, the answer gets smaller.
Lily babysits for 3 1/2 hours because 4 x 7/8 = 3 1/2
0.006375 g = _________ mcg?
Answer:
6375 mcg
Step-by-step explanation:
hopes this helps :)
Help please!! Find the equation of the linear function represented by the table below in slope-
intercept form.
Answer:
X
1
2
3
4
y
-1
-3
-5
-7
The slope intercept form is y= 2x+1
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let's take 2 points :
(x1,y1) = ( 1, -1)
(x2,y2) = ( 2, -3)
slope , m = (y2-y1) /(x2-x1)
= (-3-(-1))/(2-1)
= (-3+1)/1
= -2
Slope intercept form:
y-y1=m(x-x1)
y-(-1) = -2 (x-1)
y+1=-2x+2
=> y=2x+2-1
=> y= 2x+1
Thus, the slope intercept form is y= 2x+1
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Carlos is building a prop for the school play and he needs to calculate the amount of lumbet needed to make it. the prop is shaped like a tower and the radius of the base of the tower is 2.5 feet. if the tower is hollow and has no base, what is the approximate surface area of the tower? round your answer to the nearest tenth.
The approximate surface area of the tower is 156.33 feet².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
The given tower is a composite of a cylinder and a cone.
But cylinder does not have the bases and cone also does not have it's base.
Surface area of the curved surface of cylinder = 2π r h
where r is the radius of the base and h is the height of the cylinder.
Given h = 8 feet and r = 2.5 feet
Curved surface area of cylinder = 2π × 2.5 × 8 = 40π feet²
Surface area of the curved surface of the cone = π r √(h² + r²)
where r is the radius of the base of the cone and h is the perpendicular height of the cone.
Given r = 2.5 feet and h = 3 feet
Curved surface area of cone = π × 2.5 [√(2.5² + 3²)]
= 9.76π feet²
Total surface area = 40π + 9.76π
= 156.33 feet²
Hence the total surface area of the tower is approximately 156.33 feet².
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What is the range of the conic section?
(yl-3≤y≤3)
Answer:
1the answer for this is easy it is 4.4
Kendra and Jamal are standing in line. The number line shows their positions in meters with
positive numbers representing positions to the right. Help please
the solution of number line is all the options are correct.
What is number line?A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.
Here,
Kendra and Jamal are standing in line. The number line shows their positions in meters with positive numbers representing positions to the right.
The position of Kendra is -6 and Jamal is 0.
Kendra is 6 meters left of Jamal.
Kendra and Jamal are 1-6 meters apart.
Jamal is 6 meters right of Kendra.
Hence, all the options are correct.
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HELP MEEEEEE
10 Answer:
Evaluate the expression 7 + x + (-3) when x = 2:
11 Answer:
Evaluate the expression 4x2 + 2 when x = 2.
12 Answer:
Evaluate the expression |x + 10| when x = -12.
13 Answer:
Evaluate the expression |2x + 1| when x = 3/2.
14 Answer:
Evaluate the expression (x - 3)/4 when x = 4.
15 Answer:
Evaluate the expression (5 - x)/6 when x = 3.
The value of expression is ,
10) 6
11) 18
12) 2
13) 4
14) [tex]\frac{1}{4}[/tex]
15) [tex]\frac{1}{3}[/tex]
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression
10) 7+x+(-3)
Put x=2 then
=> 7+2-3
=> 7-1 = 6
11) 4[tex]x^2[/tex]+2
put x=2 then
=> [tex]4*2^2+2[/tex]
=> 4*4+2
=> 16+2=18
12) Ix+10I
put x=-12 then
=> I-12+10I
=> I-2I = 2
13) |2x + 1|
put x= 3/2 then
=> I2*[tex]\frac{3}{2}[/tex]+1I
=> I3+1I
=> I4I = 4
14)(x - 3)/4
put x=4 then
=> [tex]\frac{4-3}{4}[/tex]
=> [tex]\frac{1}{4}[/tex]
15) (5 - x)/6
put x=3 then
=> [tex]\frac{5-3}{6}[/tex]
=> [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
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A cruise ship has 2,400 regular passengers. Children makes up 120 of them, 23 are teenagers and the rest are adult passengers. What fractional part of the regular passengers are the adult passengers?
Answer:
[tex] \frac{2257}{2400} [/tex]
Step-by-step explanation:
2400 - (120+23)
=2400 - 143
=2257
Therefore,
2257
2400
Hi, please help me with this very easy maths question. Thanks
The quadratic expression for the curves is written as
The curve opening up y = a(x + 4)² - 7
The curve opening down y = -1/8(x - 4)² + 3
How to write the equation of the curveThe equation of the quadratic equation is written using the formula
y = a(x - h)² + k
where h and k are points of the vertex v(h, k)
The curve opening up
h = -4 and k = ?
using points C and B
-5 = a(0 + 4)² + k, -5 = 16a + k
1 = a(4 + 4)² + k, 1 = 64a + k
solving simultaneously
-5 = 16a + k
1 = 64a + k
subtraction
-6 = -48a
a = 1/8
solving for k
-5 = 16a + k
-5 = 16 * 1/8 + k
k = -7
substituting the values
y = a(x + 4)² - 7
The curve opening down
A is the vertex (4, 3)
y = a(x - 4)² + 3
using D (0, 1) to solve a
1 = a(0 - 4)² + 3
1 - 3 = 16a
a = -1/8
hence the equation is y = -1/8(x - 4)² + 3
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A high speed boat travels from the mainland to an island 170 miles away in 2.34 hours. What is the boat's average speed? If necessary, round to two decimal places
Answer:
Average speed = Total distance travelled / Total time taken
= 170 miles / 2.34 hours
= 72.65 miles per hour or 72.65 mph
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A recipe requires 3½ cups of nonfat milk. A person already has ¾ cup. How much more is needed?
A. 2¾
B. 2¼
C. 3¼
D. 1¾
Show work please
Answer:
A. 2¾
Step-by-step explanation:
The person needs the difference. This is a subtraction problem.
3 1/2 - 3/4 =
3/4 is just a fraction, but you can think of 3/4 as a mixed numeral by writing 3/4 as 0 3/4. The whole part is 0 and the fractional part is 3/4.
= 3 1/2 - 0 3/4
Now we are subtracting two mixed numerals. You need to subtract the whole part, 0, from the whole part, 3, and the fractional part, 3/4, from the fractional part, 1/2.
For the fractional parts, we need a common denominator of 4.
= 3 2/4 - 0 3/4
Now we have both fractions with a common denominator of 4, but since we cannot subtract 3/4 from 2/4, we borrow 1 from 3 as 4/4.
3 goes down 1 to 2, and the 1 which is borrowed as 4/4 is added to the 2/4 to give you 2 6/4. 2 6/4 has the same value as 3 2/4. Now we have:
= 2 6/4 - 0 3/4
We subtract 0 from 2, and we subtract 3/4 from 6/4.
= 2 3/4
Answer: 2 3/4
The announcer said, ‘Ingrid won the 100 metre race in 13.9 seconds.’
Her time was originally measured to 2 decimal places.
What was the slowest time she could have run?
Answer:
So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.
Step-by-step explanation:
Ingrid's time of 13.9 seconds was originally measured to 2 decimal places, which means that her actual time could be rounded to 13.9 seconds. To find the slowest time she could have run, we need to find the greatest value that could have been rounded down to 13.9 seconds.
Since the time was measured to 2 decimal places, this means that the hundredths place is known and the thousandths place can be anything between 0 and 9. So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.
Three candy bars and one soda costs $5.63.
At the same price, one candy bar and four sodas
cost $4.81. How much does a candy bar cost?
The cost of a candy bar is equal to $1.61.
How to determine the cost of a candy bar?In order to write an equation that model this situation, we would assign variables to the cost of candy bars and the cost of soda respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the cost of candy bars.Let the variable y represent the cost of soda.Next, we would translate the word problem into an algebraic equation based on the fact that three (3) candy bars and one (1) soda costs $5.63 as follows;
3x + y = 5.63 ...equation 1.
Additionally, one candy bar and four sodas cost $4.81 at the same price;
x + 4y = 4.81 ...equation 2.
x + 4(5.63 - 3x) = 4.81
x + 22.52 - 12x = 4.81
11x = 22.52 - 4.81
x = 17.71/11
x = $1.61
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Write an equation in slope-intercept form for the line through the points (2, -1) and (10, 3).
Answer:
Since slope of line passing through two points (x
1
,y
1
) and (x
2
,y
2
) is m=
x
2
−x
1
y
2
−y
1
We now find the slope of the line passing through the points (2,3) and (4,6) as shown below:
m=
4−2
6−3
=
2
3
Therefore, the slope of the line is
2
3
.
Now use the slope and point (2,3) to find the y-intercept.
y=mx+b
⇒3=(
2
3
×2)+b
⇒3=3+b
⇒b=3−3=0
Write the equation in slope intercept form as:
y=mx+b
⇒y=
2
3
x+0
⇒y=
2
3
x
Step-by-step explanation:
2. Regina Aguirre deposits $2,000 into an ordinary annuity after each 6-month period for 4 years. The account
pays 6% interest compounded semiannually. Find the a) future value, and b) total interest earned.
Hlep me with this question and find f 8
-1
8 is bigger than 0, so according to the function, we need to use the third one so it would be -1
Find the place value of the 4 in the the number 16,952,874.
Answer:
one's place
Step-by-step explanation:
Please help me !!! I need help asap
After calculating The perimeter of rectangle is 46.52 in the given rectangle.
What is area of rectangle?
area of rectangle can be defined as the product of length and breadth.
Given ,
A rectangle has a length 20 5 /6 and
breadth = 2 3/7
The perimeter of rectangle = 2 (l+b)
length = (120 + 5 ) / 6 = 125/ 6
breadth = (14+3) / 7 = 17/7
perimeter = 2 (125/6 + 17/7 )
= 2 ( (125*7 + 17 * 6) / 42 )
= 2 (875+102) / 42
= 2 * 23.26
= 46.52
Hence, after calculating The perimeter of rectangle is 46.52 in the given rectangle.
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What’s the diameter of O
The diameter of the circle is 16.66 units.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
Given a circle,
and two segments intersect at a point and form a right angle,
the length of the segment to the point of intersection is 6 units and 8 units as given in the figure,
and a segment pass from the center of the circle,
let the distance from point of intersection to center be x
so radius of circle be 6 + x from figure,
it forms a right triangle as shown in the figure, with hypotenuse 6 + x, base x, and perpendicular 8 units,
using Pythagoras theorem
h² = b² + p²
(6 + x)² = x² + 8²
36 + x² + 12x = x² + 64
12x = 64 - 36
12x = 28
x = 28/12
x = 2.333
radius of circle = 6 + x = 6 + 2.33 = 8.33
diameter of circle = 2r = 2 x 8.33 = 16.66 units
Hence the diameter is 16.66 units.
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help with this please
Answer:
A, B and E
Step-by-step explanation:
A rectangular school banner has a length of 44 inches and a perimeter of 156 inches. The cheerleaders make signs similar to the banner. The length of a sign is 11 inches. What is its perimeter?
Answer: The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width of the rectangle.
We know that the rectangular school banner has a length of 44 inches and a perimeter of 156 inches. And we can use the formula above to find the width of the rectangular school banner:
P = 2L + 2W = 156 inches
P = 2(44) + 2W = 88 + 2W = 156 inches
So the width of the rectangular school banner is W = 156 inches - 88 inches = 68 inches
Now, we know that the cheerleaders make signs similar to the banner. the length of a sign is 11 inches, we can use the same formula to find the perimeter of the sign.
P = 2L + 2W = 2(11) + 2W
So the perimeter of the sign is P = 22 + 2W inches
Since we don't know the width of the sign (W) we can't find the perimeter of the sign.
Step-by-step explanation:
A plant is already 51 centimeters tall, and it will grow one centimeter every month. The plant's height,
centimeters), after m months is given by the following function.
H (m)=51+m
What is the plant's height after 36 months?
centimeters
X
Step-by-step explanation:
fufj5655 and I hope that you will be able to help me with the following to help me with the application for the role of the temple and many other people in the forest and a small village known as change in indirect speech to be the oldest
in the fruit bowl that are 10 times. 5 peachse and 2 mangoes select the correct choice from the drop down
The probability of randomly picking a peach from from the fruit bowl is 29 %
How to find the probability ?To find the probability of picking a peach from the fruit bowl at random, you first need to sum up the number of fruit :
= 10 Limes + 5 peaches + 2 mangoes
= 17 fruit
The probability of picking a peach from the fruit bowl can then be found to be :
= Number of peaches in fruit basket / Number of fruit in the fruit basket
= 5 / 17
= 29 %
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The rest of the question is:
The probability of randomly picking a peach from from the fruit bowl is _________.
29%14%52%32%Larry has some money that he has saved. He starts a new job. The graph shows the total amount of money Larry will have y after working x hours. Find and interpret the rate of change and initial value.
The rate of change is $6 per hour while the initial value is $20
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
Let y represent the total amount of money that Larry would have after working x hours.
From the graph, the y intercept is at (0, 20). Using point (0, 20) and (5, 50):
Slope = (50 - 20)/(5 - 0) = 6
The slope is $6 per hour
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Sketch a plot of the line y =-2x+16
Step-by-step explanation:
hope this helps!:).....
Kira gave 5/9 of her baseball collection away to her best friend. If she had 45 cards how many did she give away
Answer:
25
Step-by-step explanation:
5/9 x 45 Cross cancel the 9 and 45. 9 goes into 9 once and 9 goes into 45 5 times
5/1 x 5/1 = 25/1 = 25
Decide whether parallelogram JKLM is a rectangle, a rhombus, or a square. Give all names that apply.
J(-2,7), K(7, 2), L(-2,-3). M-11,2)
rectangle
rhombus
square
Explain your reasoning.
The diagonals are neither perpendicular nor congruent.
The diagonals are perpendicular but not congruent.
The diagonals are congruent, but not perpendicular.
The diagonals are congruent and perpendicular.
Answer:
rhombus
(b) The diagonals are perpendicular but not congruent.
Step-by-step explanation:
You want to know what sort of figure the parallelogram JKLM is, given the vertices J(-2,7), K(7, 2), L(-2,-3), M(-11,2).
ObservationThe x-values of points J and L on diagonal JL are the same, so that diagonal is a vertical line. Its length is 7 -(-3) = 10.
The y-values of points K and M on diagonal KM are the same, so that diagonal is a horizontal line. Its length is 7 -(-11) = 18.
The diagonals are perpendicular and not congruent, so the parallelogram is a rhombus.
it is generally believed that nearsightness affects about 15% of al children. a local elementary school registered 120 incoming kindergarteners.
Note that this scenario is talking about a sampling distribution sincer this school is a sample size 120, therefopre, you will need to calculate the standard deviation using a formula before using the normalcdf aqnd invNorm commands.
(a) what is the mean of the sampling distribution of all samples like this
(b) what is the standard deviation of the sampling distributrion of all samples like this
(c) what is the probability that less tahn 10%of the incoming kindergarteneres are nearsighted?
(d) if this school measutre at the 80th percentile for all incoming kindergarten classes of size 120, what proportion of incoming kindergarteners are nearsighted?
The mean is of 0.15. The standard deviation is of 0.0326.0.1774 of incoming kindergarteners are nearsighted.
Find the mean and S.D ?The central limit theorem and the normal distribution are used to determine that:
a) A 0.15 is the mean.
b) A standard deviation of 0.0326 is present.
c) There is a 0.063 = 6.3% chance that fewer than 10% of the kindergarten applicants have nearsightedness.
d) 0.1774 percent of kindergarten students have nearsightedness.
The mean is of 0.15.
Item b:
s = p (1-p)/n = 0.15(0.85)/120
= 0.0326.
The standard deviation is of 0.0326.
Item c:
The probability is the p-value of Z when X = 0.1.
By the Central Limit Theorem
Z= 0.1 -0.15/ 0.0326.
= -1.53
Z = -1.53 has a p-value of 0.063.
There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.
Item d:
X = 0. 1774
The proportion is X when Z has a p-value of 0.8, so X when Z = 0.84.
0.1774 of incoming kindergarteners are nearsighted.
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