P(X< ) 1-P(X> ) A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball pitcher throws 30 curve balls, what is the probability that no more than 16 of them are strikes? Fill in the blanks below to represent the probability
Answer:
19.49% probability that no more than 16 of them are strikes
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 30, p = 0.626[/tex]
So
[tex]\mu = E(X) = np = 30*0.626 = 18.78[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*0.374} = 2.65[/tex]
What is the probability that no more than 16 of them are strikes?
Using continuity correction, this is [tex]P(X \leq 16 + 0.5) = P(X \leq 16.5)[/tex], which is the pvalue of Z when X = 16.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16.5 - 18.78}{2.65}[/tex]
[tex]Z = -0.86[/tex]
[tex]Z = -0.86[/tex] has a pvalue of 0.1949
19.49% probability that no more than 16 of them are strikes
A car increases, then decreases, its speed. Which table could represent the speed of the car?
6
43
5
45
5
45
7
41
7
49
9
43
9
47
o
6
47
Time (min)
Speed (mph)
Time (min)
Speed (mph)
Time (min)
Speed (mph)
Time (min)
Speed (mph)
N00
il colloll
100
5
45
6
45
7
45
41
5
45
6
43
7
41
9
41
41
Answer:
The speed increases (45—>47—>49) then decreases (48—>47) over time.
Step-by-step explanation:
The table that represents the speed of the car that increases and decreases as time increases is Table B.
Option B is the correct answer.
What is speed?Speed is the ratio of the given distance and time.
It shows how fast an object is moving at a given time.
The formula is Distance / Time.
We can find the distance or time when the required values is given using this formula.
We have,
From the table,
We see that,
Time 5 6 7 8 9
Speed 45 47 49 48 47
This indicates that,
As time increases, the speed increased from 5 minutes to 7 minutes and decreases from 7 minutes to 9 minutes.
Thus,
The table that represents the speed of the car that increases and decreases as time increases are in Table B.
Learn more about speed here:
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Which of the following choices is the x intercept of the equation 2y-x=-6
Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
Given
[tex]2y-x=-6[/tex]
Required
Determine the x intercept
To get the value of x intercept; we simply substitute 0 for y;
i.e. y = 0
[tex]2y-x=-6[/tex] becomes
[tex]2(0)-x=-6[/tex]
[tex]0-x=-6[/tex]
[tex]-x=-6[/tex]
Multiply both sides by -1
[tex]-1 * -x=-6 * -1[/tex]
[tex]x=-6 * -1[/tex]
[tex]x = 6[/tex]
Hence, the x intercept is 6
We know that central angles are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because . Then by the congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because .
Answer:
because they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Step-by-step explanation:
Answer:
Complete the missing parts of the paragraph proof.
Proof:
We know that central angles
✔ AOC and BOD
are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because
✔ all radii of a circle are congruent
. Then by the
✔ SAS
congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because
✔ CPCTC.
Gretta created some figures that she calls reebs What attribute do these reebs have in common?
Answer:
Reebs have 1 right angle
Step-by-step explanation:
Look at all the reebs. They all have 1 right angle!
Answer:
C
Step-by-step explanation:
If point OR=20 and point PR=5, what is OP(geometry)? please show work
Answer:
The length of OP is 25.
Step-by-step explanation:
The data provided is:
OR = 20
PR = 5
Assume that OR and PR are straight lines.
O_____________________R______P
Compute the length of OP as follows:
OP = OR + PR
= 20 + 5
= 25
Thus, the length of OP is 25.
What is the range of this function?
A student walk 60m on a bearing of 028 degree and then 180m due east. How is she from her starting point, correct to the nearest whole number?
Answer: she is 215m from her starting point
Step-by-step explanation:
The diagram representing the situation is shown in the attached photo. Triangle ABC is formed with AC representing her distance from her starting point.
Angle B = 28 + 90 = 118°
To determine AC, we would apply the law of Cosines which is expressed as
a² = b² + c² - 2abCosA
Where a,b and c are the length of each side of the triangle and B is the angle corresponding to b(AC). Likening the expression to the given triangle, it becomes
AC² = AB² + BC² - 2(AB × BC)CosAC
AC² = 60² + 180² - 2(60 × 180)Cos118
AC² = 3600 + 32400 - 21600Cos118
AC² = 36000 - 21600(-0.46947156)
AC² = 36000 + 10140.59
AC² = 46140.59
AC = √46140.59
AC = 215 m
What is being constructed based on the markings in the following diagram?
Inscribed regular hexagon
inscribed equilateral triangle
perpendicular line through a point off a line
perpendicular line through a point on a line
thank you :)
Answer:
perpendicular line through a point on a line
Step-by-step explanation:
The circle centered at C seems intended to produce point D at the same distance as point B. That is, C is the midpoint of BD.
The circles centered at B and D with radius greater than BC seems intended to produce intersection points G and H. (It appears accidental that those points are also on circle C. As a rule, that would be difficult to do in one pass.)
So. points G and H are both equidistant from points B and D. A line between them will intersect point C at right angles to AB.
Segment GH is perpendicular to AB through point C (on AB).
Answer:
Perpendicular line through a point on a line
Step-by-step explanation:
Please help help❤️help me it would mean a lot
Answer:
B. points C, F and G
Step-by-step explanation:
B. Points G C F
Approximately how many liters are in 18 quarts?
Answer:
18 liquid quarts ≈ 17 litres
Answer:
18 us liquid quart =17.034 liters
Step-by-step explanation:
1) 1 us liquid quart = 0.946 liter
2) Multiply 0.946 *18 = 17.034
Write 9y−211 as a sum or difference.
Answer:Difference
Step-by-step explanation:
What is the value?
I’m so stuck :/
Answer:
15
Step-by-step explanation:
do PEMDAS
do parenthesis first so -3^2 plus 3 times 2
then do exponents so 9 plus 3 times 2
then multiplication so 9 plus 6
then addition so 15
hope this helps
Answer:
Hey!
Your answer is 15!!
Step-by-step explanation:
IF YOU NEED A FURTHER EXPLANATION PLS LET ME KNOW!
HOPE THIS HELPS!!
find the nth term of the following sequence
4, 7, 12, 19, 28
Answer:
[tex]n^2+3[/tex]
Step-by-step explanation:
4, 7, 12, 19, 28
The differences are 7-4=3, 12-7=5, 19-12=7, 28-19=9.
This is an arithmetic sequence since the differences are constant.
There must be [tex]n^2[/tex] in the nth term.
These are the next terms in the sequence:
4, 7, 12, 19, 28, 39, 52, 67, 84, 103, 124, 147, 172, 199, 228, 259, 292, 327, 364, 403, 444, 487, 532, 579, 628, 679, 732, 787, 844, 903, 964, 1027, 1092, 1159, 1228, 1299, 1372, 1447..
[tex]n^2 +c=4[/tex]
[tex]1^2+c=4[/tex]
[tex]c=4-1[/tex]
[tex]c=3[/tex]
Therefore, the nth term is [tex]n^2+3[/tex].
Answer:
nth term = n^2 + 3.
Step-by-step explanation:
4 7 12 19 28
The differences are in an arithmetic sequence so this is a quadratic sequence,
- the differences are 3, 5, 7, 9... which is an A.S.
The common difference of the A.S. is 2 so there is n^2 in the formula for the nth term.
By inspection , we see that each term is 3 more than the term number squared.
1^2 + 3 = 4
2^2 + 3 = 7
3^2 + 3 = 12
4^2 + 3 = 19 and so on.
4x= 2y + 38; 2 - 3y=x
Simultaneous equation please help
Answer:
x = 59/7, y = -15/7
Step-by-step explanation:
4x= 2y + 38;
2 - 3y=x
We can substitute for x in the first equation since the second equation is solved for x
4(2-3y) = 2y+38
Distribute
8 - 12y = 2y+38
Add 12y to each side
8-12y+12y = 2y+12y+38
8 = 14y+38
Subtract 38 from each side
-30 = 14y
Divide by 14
-30/14 = y
-15/7 = y
Now solve for x
2 - 3y = x
2 - 3*-15/7 = x
2 +45/7 = x
14/7 + 45/7 = x
59/7 =x
how many times do you need to add 5 to 17 to reach the product of 6 and 7
Answer:
5
Step-by-step explanation:
The product of 6 and 7 is 42.
Let x be the number of times needed to add 5 to 17 to reach 42.
17 + 5x = 42
5x = 42 - 17
5x = 25
x = 5
Answer: I’m pretty sure it’s 5
Step-by-step explanation:
Which graph shows the line y- 1 = 2(x + 2)?
Answer:
Graph C
Step-by-step explanation:
The slope is 2 and to find the numbers in the equation are actually the opposite of what they appear, making the point (-2,1).
7th grade math I needs some help
Answer:
Step-by-step explanation:
To find 5e. El change, find the difference between week 1 and 1.
56.92-(-16.54) = 56.92+16.54 = -73.46.
Note: this is negative, because we are calculating the difference.
Hope this helps
What else would need to be congruent to show that ABC= A DEF by SAS?
B
E
Given:
AC DF
ZCZE
А
O A. BC = EF
O B. ZCEF
O C. ZAŁ ZD
O D. AC = DF
Answer:
A.
Step-by-step explanation:
BC ≅ EF
BC needs to be congruent to EF to show that ΔABC ≅ ΔDEF by SAS(Side -Angle-Side) Postulate.
Bill buys and sells laptops. Last month Bill bought 50 laptops. He paid £400 for each laptop. He sold 40 of these laptops at a profit of 30% on each laptop and 10 of these laptops at a profit of 15% on each laptop. Bill's target last month was to sell all 50 laptops for a total of at least £25 000. Did Bill reach this target?
Answer:
Yes, in fact Bill exceeded his target by £2,200.
Step-by-step explanation:
Cost of the laptops = 50 x 400
= 20,000
Sold 40 at 30% profit
(40 x 400) x 1.30
= 20,800
Sold 10 at 15% profit
(15 x 400) x 1.15
= 6900
Total sales value
= 20800 + 6900 = 27,700
Bill's total sales are greater than his target, that is, £25,400>£25,000. So, we can say that Bill reached his target.
What are the different aspects of buying and selling goods?Cost Price(C.P.): Price at which the good is bought.Selling Price(S.P.): Price at which the good is sold.Profit: When S.P. > C.P., profit takes place. Profit = S.P. - C.P.Loss: When C.P. > S.P., loss takes place. Loss = C.P. - S.P.Note: Profit and loss are always calculated on C.P.
How do we solve the given question?Bill buys 50 laptops for £400 each.
∴ His C.P. of each laptop = £400.
He sells them in two parts,
Part 1:
He sells 40 laptops at 30% profit on each laptop.
∴ Profit on each laptop = 30% of C.P. = 30% of £400 = £(0.3*400) = £120
∴ S.P. of each laptop = C.P. + Profit = £400 + £120 = £520
Total sales 1 = Number of laptops * S.P. of each = 40*£520 = £20,800.
Part 2:
He sells 10 laptops at 15% profit on each laptop.
∴ Profit on each laptop = 15% of C.P. = 15% of £400 = £(0.15*400) = £60
∴ S.P. of each laptop = C.P. + Profit = £400 + £60 = £460
Total sales 2 = Number of laptops * S.P. of each = 10*£460 = £4,600.
Bill's total sales after both parts = Total sales 1 + Total sales 2
or, Bill's sales = £20,800 + £4,600 = £25,400.
Since Bill's total sales are greater than his target, that is, £25,400>£25,000. So, we can say that Bill reached his target.
Learn more about the different aspects of buying and selling goods at
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Please help with answers A and B :)
cereal is on sale for $3.60 for a 9-ounce box. what is the price per ounce?
Answer:
$0.40 per oz
Step-by-step explanation:
given that the cereal is $3.60 for a 9 oz box
i.e
9 oz ----> costs $3.60
1 oz ----> costs $3.60 ÷ 9 = $0.40
hence the unit rate is $0.40 per oz
Answer:
0.40 per ounce
Step-by-step explanation:
The question asks is to find the unit rate, or price per ounce.
To find this, we need to divide the price by the number of ounces.
price/ ounces
It costs $3.60 for 9 ounces of cereal.
$3.60/9 ounces
Divide $3.60 by 9 (3.60/9=0.4)
$0.4/ounce
It costs $0.40 per ounce of cereal.
find the smallest square number that is divisible by each of the number 8,12,18 and 30
Answer:
3600.
Step-by-step explanation:
8 = 2*2*2
12= 2*3
18= 2*3*3
30 = 2*3*5
The lowest common multiple of the these is
2 * 2 * 2 * 3*3* 5 = 360.
So the smallest square number = 2*2*2*2*3*3*5*5
(We make all the sets of factors a square).
So it's 16 * 9 * 25 = 3600.
Answer:
3600
Step-by-step explanation:
Write a mathematical sentence that expresses the information given below.
Use g as your variable name. If necessary:
type < = to mean <
or > Fito mean >.
The number of gallons of gas that were in the tank plus 13 more adds up to
76 gallons.
Answer:
g + 13 = 76
Step-by-step explanation:
We are told to use the variable "g" for the number of gallons of gas in the tank. When we add 13 to that, we are told the sum is 76. When all numbers are in gallons, this translates to ...
g + 13 = 76
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
Answer:
Yes, because both figures are rectangles and all rectangles are similar (B)
Question:
The complete question related to this found at brainly (question Id: 2996738) is stated below:
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
a. Yes, because corresponding sides are parallel and have lengths in the ratio 1/4
b. Yes, because both figures are rectangles and all rectangles are similar.
c. No, because the center of dilation is not at (0, 0).
d. No, because corresponding sides have different slopes
Step-by-step explanation:
Coordinates of rectangle EFGH
E (-4,4), F(4,4), G(-4,0), H (4,0)
EF = 8
FG =4
GH= 8
HE= 4
Coordinates of rectangle ABCD
A (-3,3), B(3,3), C(-3,0), D (3,0)
AB = 6
BC = 3
CD = 6
DA = 3
Find attached the diagram.
Image = EFGH, pre-image = ABCD
Scale factor = (sides of the image)/(sides of the pre-image)
= 8/6 = 4/3
Similar shapes have same shapes but different sizes. From the result obtained, the two shapes are similar with different sizes.
Rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin.
Reason: the lines connecting the coordinates of both shapes meet at the origin. And also both figures are rectangles and all rectangles are similar (B)
Four lines extend from point K. The space between lines K J and K N is 58 degrees. The space between lines K N and K M is 61 degrees. The space between lines K M and K L is 61 degrees. Which statement must be true about the diagram? Point K is a midpoint of Line segment J L. mAngleJKN = One-halfmAngleJKM Ray KM is an angle bisector of AngleNKL. JK = One-halfKL
Answer:
Ray KM is an angle bisector of [tex]\angle NKL[/tex].
Step-by-step explanation:
Given that there are 4 lines that are extended from a point K.
Angle between KJ and KN is [tex]58^\circ[/tex] i.e. [tex]\angle JKN =[/tex] [tex]58^\circ[/tex]
Angle between KN and KM is [tex]61^\circ[/tex] i.e. [tex]\angle NKM =[/tex] [tex]61^\circ[/tex].
Angle between KM and KL is [tex]61^\circ[/tex] i.e. [tex]\angle MKL =[/tex] [tex]61^\circ[/tex]
Please refer to the attached image for the conditions and dimensions of angles given in the question statement.
Now, let us have a look at the options given:
1. Point K is a midpoint of Line segment JL
JL is not a straight line first of all, and secondly there is no condition given about the line segments.
So, it is incorrect.
2. [tex]m \angle JKN = \dfrac{1}{2}m \angle JKM[/tex]
[tex]\angle JKN =[/tex] [tex]58^\circ[/tex] and
[tex]m \angle JKM =58+61=139^\circ\\\Rightarrow \dfrac{1}{2} m \angle JKM = 64.5^\circ[/tex]
So, it is also incorrect.
3. Ray KM is an angle bisector of [tex]\angle NKL[/tex].
Ray KM divides the [tex]\angle NKL[/tex] into two equal angles [tex]\angle NKM =[/tex] [tex]61^\circ[/tex] and [tex]\angle MKL =[/tex] [tex]61^\circ[/tex] so it is correct.
The given line passes through the points (-4, -3) and (4.
1)
What is the equation, in point-slope form of the line that is
perpendicular to the given line and passes through the
point (-4, 3)?
V-3 -2(x+4)
3-
2-
+
Oy-3 =-{(x+4)
Ov-3 = {(x + 4)
-2
y-3 =2(x + 4)
-3
(-3)
9514 1404 393
Answer:
y -3 = -2(x +4)
Step-by-step explanation:
The slope of the given line is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-3))/(4 -(-4)) = 4/8 = 1/2
The perpendicular line will have slope -1/(1/2) = -2.
__
The point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
For point (-4, 3) and slope -2, the equation is ...
y -3 = -2(x +4)
The ratio of the same side interior angles of two parallel lines is 33:3. Find the measures of all eight angles formed by the parallel lines and transversal.
9514 1404 393
Answer:
all 4 acute angles: 15 degrees
all 4 obtuse angles: 165 degrees
Step-by-step explanation:
The sum of same-side interior angles between parallel lines is 180°. The smallest of them will be 3/(33+3) = 1/12 of 180°, or 15°. The largest will be 180° -15° = (33/3)(15°) = 165°. All remaining angles are congruent to one or the other of these.
All four acute angles are 15°; all four obtuse angles are 165°.
Estimate 6 8 9 ( 1 9 10 ) by rounding to the nearest whole number. The estimate is the actual product because
Answer:
[tex]6\frac{8}{9} (1\frac{9}{10}) = 13[/tex]
Step-by-step explanation:
Given
[tex]6\frac{8}{9} (1\frac{9}{10})[/tex]
Required
Estimate
To do this; we start by converting both fractions to improper fraction
[tex]6\frac{8}{9} (1\frac{9}{10})[/tex]
[tex]\frac{62}{9} (1\frac{9}{10})[/tex]
[tex]\frac{62}{9} (\frac{19}{10})[/tex]
Open Bracket
[tex]\frac{62}{9} * \frac{19}{10}[/tex]
Combine to form a single fraction
[tex]\frac{62 * 19}{9 * 10}[/tex]
Multiply numerators and denominators
[tex]\frac{1178}{90}[/tex]
Convert fraction to decimal
[tex]13.0888888889[/tex]
Approximate to nearest whole number
[tex]13[/tex]
Hence, [tex]6\frac{8}{9} (1\frac{9}{10}) = 13[/tex]
Answer:
First box: 14
Second box: greater than
Third box: both factors were rounded up.
Step-by-step explanation:
I JUST DID IT AND GOT IT RIGHT!
HOPE IT HELPS!
Can I have some help please? Thanks!
Answer:
(22/7)/6=0.523809
Step-by-step explanation:
V=4/3πr^3
V=4/3π(1/2)^3=π/6
or (22/7)/6=0.523809