Answer:
Area of sector = 21.195 cm²
length of arc = 4.71 cm
Step-by-step explanation:
Given:
Radius of circle (r) = 9 Cm
Angle at O = 30°
Find:
Area of sector.
length of arc.
Computation:
⇒ Area of sector = [θ/360]πr²
Area of sector = [30/360]3.14(9)²
Area of sector = 21.195 cm²
⇒ length of arc = [θ/360]2πr
length of arc = [30/360]2(3.14)(9)
length of arc = 4.71 cm
A certain town has two kinds of youth basketball teams. One is a school team (S) and the other is a rec team (R). On any given Saturday in December, the probability that a school team will have a game is 0.8, and the probability that a rec team will have a game is 0.7. The probability that both have games us 0.65.
On any given Saturday in December, what is the probability that either a rec team or a school team has a game?
Answer Choices:
0.65
0.7
0.8
0.85
Answer:
D. 0.85
Step-by-step explanation:
Given
Probability of S = 0.8
Probability of R = 0.7
Probability of S and R = 0.65
Required
Probability of S or R
Using probability notations;
P(S) = 0.8
P(R) = 0.7
P(S n R) = 0.65
The question requires that we solve for P(S or R)
For overlapping events S and R; the following formula is applicable.
P(S or R) = P(S) + P(R) - P(S n R)
Substitute the values of P(S), P(R) and P(S n R)
P(S or R) = 0.8 + 0.7 - 0.65
P(S or R) = 0.85
Hence, the probability that either a rec team or a school team has a game is 0.85
A palindrome is chosen at random from the list of all $6$-digit palindromes, with all entries equally likely to be chosen. (Recall that a palindrome is a positive integer that reads the same forward and backwards, such as $387783$. Note: Since these palindromes are being thought of as numbers, rather than simply strings of digits, it is to be understood that the leading digit, the digit in the hundred-thousands place, must be nonzero.) What is the expected value of the chosen number?
Answer:
Expected value 550,000
Step-by-step explanation:
Calculation of the expected value of the chosen number
We should know that each of the digit of the number may likely be thought of what we called a random variable, in which the first digits and the last digits comes uniformly from [1,2,3,4,5,6,7,8,9] while the last digit can't be 0 because of what we called the palindrome condition).
Therefore each of these two digits will have an expected value of 5 while the other four digits will come uniformly from this digits which are [0,1,2,3,4,5,6,7,8,9] in which each of the digits will have an expected value of 4.5.
Thus Expected value is additive, which means we have to also take place the value into account.
Now let find the EXPECTED VALUE
The expected value will be :
(100,000+1)⋅(5)+(10,000+1,000+100+10)⋅(4.5)
Expected value=550,000
Therefore the Expected value will be 550,000
Please help meeeee
The measure of a central angle is 18°. If the length of its intercepted arc is xπ units, what is the circumference of the circle?
A.( x/20)π units
B. (x/18)π units
C. (x/10)π units
D. 18xπ square units
E. 20xπ square units
Answer:
20xπ units
Step-by-step explanation:
Use the formula for the length of an arc.
θ/360 × 2πr
The length of the arc and the central angle is already given.
18/360 × 2πr = xπ
Solve for r.
r = (xπ)/(18/360)/(2π)
r = 10x
The radius is 10x.
The circumference is 2πr.
2π(10x)
20xπ
The circumference of the circle is 20xπ units.
Predict the number of chocolate chips in nine pancakes
━━━━━━━☆☆━━━━━━━
▹ Answer
72 Chocolate Chips
▹ Step-by-Step Explanation
1 Pancake = 8 Chocolate Chips
You can set this up as:
[tex]\frac{1}{8} = \frac{9}{y} \\\\1 * 9 = 9\\8 * 9 = 72\\\\y = 72\\[/tex]
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Find the measures of line segments AD and DC. Show your work.
Ab = 12in
Bc=5in
Answer:
DC = 1.92 inches
AD = 11.08 inches
Step-by-step explanation:
From the figure given above, angle ABC is a right angle triangle where
AB = 12 inches
BC = 5 inches
Use pythagorean theorem to find AC
AC^2 = AB^2 + BC^2
Substitutes all the parameters into the formula
AC^2 = 12^2 + 5^2
AC^2 = 144 + 25
AC = sqrt ( 169 )
AC = 13 in
Also,
BD^2 = AB^2 - AD^2
Let AD = 13 - x
Substitute all into the formula
BD^ = 12^2 - (13 - x)^2 ..... (1)
Moreso,
BD^2 = BC^2 - DC^2
Let DC = x
Substitute all into the formula
BD^2 = 5^2 - x^2 ...... (2)
Equate equation 1 and 2
12^2 - ( 13 - x )^2 = 5^2 - x^2
144 - (169 - 26x + x^2) = 25 - x^2
Open the bracket
144 - 169 + 26x - x^2 = 25 - x^2
-25 + 26x = 25
Collect the like terms
26x = 50
X = 50/26
X = 1.92 inches
Therefore, DC = 1.92 inches
And AD = 13 - 1.92 = 11.08 inches
Find an equivalent system of equations for the following system: 3x + 3y = 0 −4x + 4y = −8
Answer:
Answer:
3x + 3y = 0
7x - y = 8
Step-by-step explanation:
Can u guys PLEASE answer this question ASAP. if y= (a+2)x+7 is parallel to y=3x-4, find the value of a
Answer:
a = 1
Step-by-step explanation:
The factor in front of x must be the same in both equations.
So (a+2) in the first must be 3 (like it is in the second).
That is the case when a=1.
So the +7 and the -4 are not relevant!
pleeeassee help its quiet simple i promise its just that im young lol please add explanation
Answer:
10c - 4d
Step-by-step explanation:
1. Rearrange the problem so similar variables are closer together
3c + 7c + 5d - 9d
2. Simplify the problem by adding like terms
3c + 7c = 10c
5d - 9d = -4d
3. Rewrite the problem so the variables are in ABC order
10c - 4d
Hope this helps :)
Answer:
10c -4d
Step-by-step explanation:
3c - 9d +7c + 5d
Combine like terms
3c +7c -9d +5d
10c -4d
A store carries four brands of DVD players, J, G, P and S. From past records, the manager found that the relative frequency of brand choice among customers varied. Using the given probability values for each of the four brands, find the probability that a random customer will choose brand J or brand P.
Answer:
The answer is below
Step-by-step explanation:
A store carries four brands of DVD players, J, G, P and S. From past records, the manager found that the relative frequency of brand choice among customers varied. Using the given probability values for each of the four brands, find the probability that a random customer will choose brand J or brand P.
P(J)=0.22, P(G)=0.18, P(P)=0.35, P(S)=0.25
Answer: Probability is the ration of possible outcomes to the total number of possible outcomes. The probability of mutually exclusive events i.e. events that cannot occur at the same time is the sum of their individual probabilities. If two events A and B are mutually exclusive events, then:
P(A or B) = P(A) + P(B)
Given that P(J)=0.22, P(G)=0.18, P(P)=0.35, P(S)=0.25, the probability that a random customer will choose brand J or brand P is given by:
P(J or P) = P(J) + P(P) = 0.22 + 0.35 = 0.57
Translate the sentence into an inequality. Eight times the sum of a number and 20 is greater than or equal to 25. Use the variable y for the unknown number.
Answer:
8x + 20 ≥ 25
Step-by-step explanation:
Well 8 times the sum of a number "x" plus 20,
So we can write the following,
8x + 20
and that should be greater than or equal to 25
8x + 20 ≥ 25
Thus,
as an inequality it is 8x + 20 ≥ 25.
Hope this helps :)
Help
Question 1:
A scale on a map shows that 2 inches = 25 miles.
Part A
How many inches on the map represent 60 miles?
Enter your answer in the box.
inches
Part B
How many miles are represented by
1
4
inch on the map?
Enter your answer in the box.
miles
Save
Answer: A) 4.8 inches
B) 3.125 miles
Step-by-Step Explanation:
[tex]\dfrac{2\ inches}{25\ miles}=\dfrac{x}{60\ miles}\\\\\\\dfrac{2(60)}{25}=x\\\\\\x=\large\boxed{4.8}[/tex]
[tex]\dfrac{2\ inches}{25\ miles}=\dfrac{\frac{1}{4}\ inch}{y}\\\\\\2y=25\bigg(\dfrac{1}{4}\bigg)\\\\\\y=\dfrac{25}{8}\\\\\\y=\large\boxed{3.125}[/tex]
Please help I’m super confused :(
Answer:
[tex]a_{7}[/tex] = [tex]\frac{3}{32}[/tex]
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a. [tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = 6 and r = [tex]\frac{1}{2}[/tex] , thus
a₇ = 6 × [tex](\frac{1}{2}) ^{6}[/tex] = 6 × [tex]\frac{1}{64}[/tex] = [tex]\frac{6}{64}[/tex] = [tex]\frac{3}{32}[/tex]
Please answer it now in two minutes
Answer:
Step-by-step explanation:
C 32 units
Here are the 30 best lifetime baseball batting averages of all time, arranged in
order from lowest to highest:
0.329, 0.330, 0.331, 0.331,0.333, 0.333, 0.333, 0.334, 0.334, 0.334, 0.336,
0.337, 0.338, 0.338, 0.338, 0.340, 0.340, 0.341, 0.341, 0.342, 0.342, 0.342,
0.344, 0.344, 0.345, 0.346, 0.349, 0.356, 0.358, 0.366
A stemplot is one way to display these batting averages, as shown below. In
this type of display, the entry 0.3616 denotes one occurrence of the batting
average
0.3219
0.33 011 3 3 3 4 4 4-6 7 8 8 8
0.34 100 1 1 2 2 2 4 4 5 6 9
0.35 168
0.3616
JEET
O A. 0.360
OB. 0.336
O C. 0.3606
O D. 0 366
Answer:
D. 0.366
Step-by-step explanation:
Hello!
A stemplot is a way of arranging a data set.
In the stem you'll find the integer and first two decimal digits of the batting average, because these values are repeated several times.
In the leafs you'll find the third decimal digit.
So for the first value of the stem "0.32" there is only one observation:
0.329 ⇒ 0.32 | 9
For the second value "0.33" correspond 14 observations: 0.330, 0.331, 0.331,0.333, 0.333, 0.333, 0.334, 0.334, 0.334, 0.336, 0.337, 0.338, 0.338, 0.338
0.33 | 0, 1, 1, 3, 3, 3, 4, 4, 4, 6, 7, 8, 8, 8
For the third value "0.34" correspond 12 observations: 0.340, 0.340, 0.341, 0.341, 0.342, 0.342, 0.342, 0.344, 0.344, 0.345, 0.346, 0.349
0.34 | 0, 0, 1, 1, 2, 2, 2, 4, 4, 5, 6, 9
For the fifth value "0.35" and the sixth value "0.36" there is only one observation, so, as happened with the first one, these values of the stem will only have one "leaf"
0.358 ⇒ 0.35 | 8
0.366 ⇒ 0.36 | 6
So the whole stem plot for this 30 observations is:
Stem | Leafs
0.32 | 9
0.33 | 0, 1, 1, 3, 3, 3, 4, 4, 4, 6, 7, 8, 8, 8
0.34 | 0, 0, 1, 1, 2, 2, 2, 4, 4, 5, 6, 9
0.35 | 8
0.36 | 6
Considering this, the correct option is D
I hope this helps!
In circle P, EG and FH are diameters.
What is m EH?
Answer:
[tex]m(\widehat{EH})[/tex] = 130°
Step-by-step explanation:
Angles subtended at the center by the arcs [tex](\widehat{HG})[/tex] and [tex](\widehat{EF})[/tex] are ∠HPG and ∠EPF.
Since these angles are the vertical angles both will be equal.
m∠HPG ≅ m∠EPF
3x - 10 = 2x + 10
3x - 2x = 10 + 10
x = 20
Therefore, [tex]m(\widehat{HG})=(3\times 20) - 10[/tex]
= 50°
Similarly [tex]m(\widehat{EF})[/tex] = 50°
In the same way angles subtended at the center will be equal.
m∠EPH ≅ m∠FPG
and [tex]m(\widehat{EH})=m(\widehat{FG})[/tex]
Since [tex]m(\widehat{EH})+m(\widehat{FG})+m(\widehat{EF})+m(\widehat{HG})=360[/tex]°
[tex]m(\widehat{EH})+m(\widehat{EH})+50+50=360[/tex]
[tex]2m(\widehat{EH})=360-100[/tex]
[tex]m(\widehat{EH})=130[/tex]
Therefore, measure of arc EH = 130°
On a coordinate plane, a line goes through (negative 3, 3) and (negative 2, 1). A point is at (4, 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)?
Answer:
y = -2x + 9
Step-by-step explanation:
(1-3)/(-2--3) = -2/1 = -2 = m
y = mx + b
1 = -2(4) + b
9 = b
y = -2x + 9
Which statement is true regarding the graphed functions? A) f(4)=g(4) B) f(4)=g(-2) C) f(2)=g(-2) D) f(-2)=g(-2)
Answer:
Option (D)
Step-by-step explanation:
If the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are lying of the line.
Slope of the line represented by the function 'f' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Two points are lying on the line are (-2, 4) and (0, -2).
Slope of the line passing through these points 'm' = [tex]\frac{4+2}{-2-0}[/tex]
m = -3
Y-intercept of the line 'b' = -2 [From the graph]
Therefore, equation of the function will be,
f(x) = (-3)x - 2
f(x) = -3x - 2
Similarly, for other function represented by the line in red,
Slope of the line passing through (-6, 0) and (0, 6) = [tex]\frac{6-0}{0+6}[/tex]
m' = 1
Y-intercept of g(x) = 5 [From the graph]
Equation that represents the function g(x) = 1.x + 5
g(x) = x + 5
For g(x) = f(x)
-3x - 2 = x + 6
-3x - x = 2 + 6
-4x = 8
x = -2
Therefore, for x = -2 both the functions will have the value.
f(-2) = g(-2)
Option (D) will be the answer.
PLEASE HELP ASAP!!!! what is 3/5x + 22 = 28? Explain!
Hi someone please help me I'm not sure how to do thissss
If the longer base of triangle XYZ is three times the length of the shorter base, a, what is the length of the hypotenuse in terms of the shorter base?
Answer: The length of the hypotenuse is √(10)*a
Step-by-step explanation:
Remember the Pythagorean theorem.
If b is the larger base, and a the shorter base, and H is the hypotenuse:
a^2 + b^2 = H^2
now, we know that b = 3*a.
(3*a)^2 + a^2 = H^2
10*a^2 = H^2
√(10)*a = H
Then we have the length of the hypotenuse in terms of the shorter base, B.
Given that abc=def, m
Answer:
ABC. def, m is a brain training site. off work at abc .bac. cab .equal abcdef
8. Kamau and Mutisya started to walk from
the same point towards opposite
directions. After some time, each had
made 40 strides. If Kamau's and Mutisya's
strides were 75 cm and 77 cm respectively,
what was the distance between them after
the 40 strides?
Answer:
6080 cm OR 60.8m
Step-by-step explanation:
75 x 40 = 3000 cm
77 x 40 = 3080 cm
They are moving in perfectly opposite directions, which makes a straight line.
3000 + 3080 = 6080 cm = 60.8m
find x.
help please !!
Answer:
x = 95°
Step-by-step explanation:
[tex]x = ?\\Sum -of- interior -angles=?\\Shape = pentagon\\No -of - sides= 5\\Sum- of- interior- angles = (n-2)180\°\\=(5-2)\times180\°\\3\times180\°\\Sum-of-interior-angles=540\°\\104\°+117\°+100\°+124\°+x\°=540\°\\445\°+x\° = 540\°\\x\° = 540\°-445\°\\x = 95\°[/tex]
WILL MARK BRAINLIEST PLEASE HELP ME! In a complete sentence, describe the angle relationship between ∠APD and ∠CPB. Then write and solve an equation based on the relationship you identified in order to find the measure of ∠APD.
Answer:
∠APD and ∠CPB are Vertical Angles
Equation: 6x - 10 = 4x + 8
Step-by-step explanation:
We use the Vertical Angles Theorem to solve for x:
Step 1: Set up equation
6x - 10 = 4x + 8
Step 2: Subtract 4x on both sides
2x - 10 = 8
Step 3: Add 10 to both sides
2x = 18
Step 4: Find x by dividing 2 on both sides
x = 9
Step 5: Plug in x for 9 to find degree measure
m∠CPB = 4(9) + 8
m∠CPB = 36 + 8
m∠CPB = 44°
m∠CPB = m∠APD (Vertical Angles)
m∠APD = 44°
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
∠APD and ∠CPB are vertically opposite angles
The equation is 6x-10=4x+8
[tex]6x-10=4x+8\\6x-4x=8+10\\2x=18\\x=9[/tex]
Plug x as 9 for the angle.
[tex]4(9)+8\\36+8\\44[/tex]
∠APD and ∠CPB = 44 degrees
The segments shown below could form a triangle.
Answer:
B. False
Step-by-step explanation:
In order for segments to form a triangle, the sum of the lengths of the shorter two must be at least as much as the length of the longest one.
The sum of the shorter two is 6 + 5 = 11. This is not as great as 12, the length of the longest one, so no triangle can be formed.
The difference in the x-coordinates of two points is 3. and the difference in the y-coordinates of the two points is 6
What is the slope of the line that passes through the points?
2
3
6
9
Answer:
slope = difference in y / difference in x
slope = 6/3 = 2 <===
What is the solution to the equation? n = 2 n = 4 n = 7 n = 14
Answer:
n = 2
Step-by-step explanation:
[tex]\sqrt{2n+28}-4\sqrt{n}=0\\\\\\\sqrt{2n+28} = 4\sqrt{n}\\\\[/tex]
Take square,
[tex](\sqrt{2n+28})^{2}=( 4\sqrt{n})^{2}\\\\ 2n + 28 = 16n\\\\28 = 16n -2n\\\\28 =14n\\\\14n=28\\\\n=\frac{28}{14}\\\\n=2[/tex]
Answer:
n=2
Step-by-step explanation:
got it right on edge
For the diagram shown, which angles are corresponding angles ∠3 and ∠7 ∠8 and ∠6 ∠4 and ∠7 ∠3 and ∠5
Answer:
< 3 and < 7
Step-by-step:
Corresponding angles mean that two angles are on the same side of the line. In this situation, the line is "t". Angles 3 and 7 are the only angles on the same side as each other.
Hope this helps!
Answer:
<3 and <7
Step-by-step explanation:
look at pic
Which of the following are steps in practical problem solving? Solve the sentence for the variable. Assign an identifying variable to the quantity to be found. Make a guess at the value of the variable. Write a sentence stating conditions placed on the quantity. Check if the value is correct.
Answer:
A, B and D
Step-by-step explanation:
Following are steps in practical problem solving:
=> Assign an identifying variable to the quantity to be found.
=> Write a sentence stating conditions placed on the quantity.
=> Solve the sentence for the variable.
Answer:
Assign an identifying variable to the quantity to be found.
.Write a sentence stating conditions placed on the quantity.
Solve the sentence for the variable.
1/ n+5 - n2-10n/n3 +4125
Answer:
Here you go mate!
Step-by-step explanation:
Not sure if it's right though
A political poll reports a candidate has a 67% unfavorable rating with a 4% margin of error. Find an interval estimate for the candidate
Answer:
[tex] \hat p-ME = 0.67-0.04= 0.63[/tex]
[tex] \hat p+ME = 0.67+0.04= 0.71[/tex]
And we can conclude that the etimated unfavorable rating is between 63 and 71%
Step-by-step explanation:
For this case we know that the estimated unfavorable rating is given by:
[tex]\hat p=0.67[/tex]
And the margin of error for this estimate is given by:
[tex]ME= 0.04[/tex]
If we want to find the confidence interval we just need to do the following:
[tex] \hat p-ME = 0.67-0.04= 0.63[/tex]
[tex] \hat p+ME = 0.67+0.04= 0.71[/tex]
And we can conclude that the etimated unfavorable rating is between 63 and 71%