Using the normal approximation to the binomial, it is found that the probabilities are given as follows:
a) 0.0055 = 0.55%.
b) 0.2296 = 22.96%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters of the binomial distribution are given as follows:
n = 150, p = 0.889.
Hence the mean and the standard deviation of the approximation are:
[tex]\mu = E(X) = np = 150 x 0.889 = 133.35[/tex].[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150(0.889)(0.111)} = 3.8473[/tex]Item a:
Using continuity correction, the probability is P(123.5 < X < 124.5), which is the p-value of Z when X = 124.5 subtracted by the p-value of Z when X = 123.5, hence:
X = 124.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{124.5 - 133.35}{3.8473}[/tex]
Z = -2.3
Z = -2.3 has a p-value of 0.0107.
X = 123.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{123.5 - 133.35}{3.8473}[/tex]
Z = -2.56
Z = -2.56 has a p-value of 0.0052.
Hence the probability is 0.0107 - 0.0052 = 0.0055 = 0.55%.
Item b:
The probability is P(112.5 < X < 130.5), which is the p-value of Z when X = 130.5 subtracted by the p-value of Z when X = 112.5, hence:
X = 130.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130.5 - 133.35}{3.8473}[/tex]
Z = -0.74
Z = -0.74 has a p-value of 0.2296.
X = 112.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{112.5 - 133.35}{3.8473}[/tex]
Z = -5.42
Z = -5.42 has a p-value of 0.
Hence the probability is 0.2296 - 0 = 0.2296 = 22.96%.
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what is the sign of f on the interval -5/9 < X < 2/3
Note that the sign of f on the interval -5/9 < x < 2/3 is negative. (Option B)
What is the explanation for the above?To determine the sign of f(x) on the interval -5/9 < x < 2/3, we need to evaluate f(x) at a test point within this interval and determine if it is positive or negative.
Since we know that f(x) has zeros at x = -4, x = -5/9, and x = 2/3, we can use these points as our reference to choose test points.
Specifically, since the zeros at x = -5/9 and x = 2/3 are not included in the interval -5/9 < x < 2/3, we can choose any test point within this interval, such as x = 0.
Evaluating f(x) at x = 0, we get:
f(0) = (3(0) - 2)(0 + 4)(9(0) + 5)
= (-2)(4)(5)
= -40
Since f(0) is negative, we can conclude that f(x) is negative on the interval -5/9 < x < 2/3.
Therefore, the sign of f on the interval -5/9 < x < 2/3 is negative
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Full Question:
f(x) = (3x - 2) (x+4) (9x +5) has zeros at x = -4, x = -5/9, and x = 2/3, that is the sign of f on the interval -5/9 < x < 2/3?
Which graph represents the function
there are 2 more graphs but it won't add it
Answer:
[tex]f(x) = 9x^2+9x - 18/3x + 6\\= 9(x^2 + x - 2)/3(x+2)\\= 3(x^2+x-2)/x+2\\= 3(x+2)(x-1)/x+2\\= 3x - 3[/tex]
so y = 3x - 3
since 3x + 6 is on the bottom,
[tex]3x + 6\neq 0\\3x\neq -6\\x\neq -2[/tex]
so this means it should be the graph of y = 3x - 3, but with a hole at (-2, -9)
Christine splits 4/5 pounds of candy with 5 people. What is the unit rate in pounds per person. In simplest form
Answer:
4/25
Step-by-step explanation:
4/5 ÷ 5 = 4/5 × 1/5 = 4/25
An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. If (h) represents hours, how much will the mechanic charge if they worked 10 hours in one day?
$450
$400
$550
None of these choices are correct.
Answer:
$800
Step-by-step explanation:
per hour $40×10hours=$400
$400÷$50=8 times initial fee
8×$50=$400 total initial fee
$400hours fee+$400 initial fee=$800 total payment
Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]
The area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners. It has one pair of opposite congruent angles and the diagonals of a kite are perpendicular.
We have a quadrilateral shown in the picture.
The diagonal divides the quadrilateral into two triangles
The area of the quadrilateral = area of the triangle ADC + area of the
triangle ADB
= (1/2)3.42×4.39 + (1/2)5.44×3.42
= 7.5069 + 9.3024
= 16.80 square units
Thus, the area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.
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2.
Julia grows flowers in a garden that is the shape of a rectangle. The side lengths of
the garden are shown in the diagram.
5½⁄2 feet
3 feet
Which of these is equal to the area of the garden? Select all that apply.
A. 8
square feet
1
B.
5
feet x 3 feet
2
C.
151/11
square feet
D. 16
16¹ square feet
E. 5 feet +
11/12
F. (5 feet x 3 feet) +
foot + 3 feet
for
foot
The area of the rectangular garden given the length and width is 16 1/2 square feet
Area of the gardenLength = 5 1/2 feetWidth = 3 feetArea of a rectangular garden = length × width
= 5 1/2 feet × 3 feet
= 11/2 × 3
= 33/2
= 16 1/2 square feet
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If the odds on a bet are 7:1 against, what is the probability of winning? Express your answer as a fraction.
Probability helps us to know the chances of an event occurring. The probability of winning the bet is 0.125.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given the odds on a bet are 7:1, therefore, there are a total of 8 cases out of which only one case is of winning. Thus, the probability of winning the bet will be,
Probability = 1/8 = 0.125
Hence, the probability of winning the bet is 0.125.
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urgent algebra 2 help please
Answer:
y = 4x - 5
Step-by-step explanation:
y = mx + b
By putting above values in equation (i)
-1 = 4 (1) + b
-1 = 4 + b
-5 = b
b = -5
y = 4x - 5
HELP pls. Which statement correctly demonstrates using limits to determine a vertical asymptote of
Answer:
Step-by-step explanation:
Suppose f(x)=x²+4 and g(x)=2x+1.
Find the value of f(-2)g(-2).
Answer: -24
Step-by-step explanation:
I am assuming you want the value of (f × g)(-2)
[tex]f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8[/tex]
[tex]g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3[/tex]
8 × -3 = -24
please help me asap :)
Answer:
They are not similar because corresponding sides are not proportional.
ExplainationCondition for similarity of two triangles -
The ratio of corresponding sides should be equal.
Condition for congruence of two triangle -
Any of the following -
Side side side
side angle side
angle angle
angle side angle
Which equation describes the same line as y-5=-2(x+4)
what is the least common multiple of the numbers 8 and 12?
A. 24
B. 8
C. 4
D.96
Answer:
A. 24
Step-by-step explanation:
Least common multiple of 8 and 12 = 24
8× 1 = 8 12×1 = 12
8×2 = 16 12×2=24
8×3 = 24
L.C.M (8,12) = 24
The greatest multiple that occurs in both the multiples of 8 and 12, is 24.
Hence, the least common multiple here is 24.
Let f(t) represent the temperature of a turkey baking in an oven as a function of time (t) in the oven (in minutes). This means time (t) is the independent variable and temperature of the turkey f(t) is the dependent variable. The turkey was in the oven for 360 minutes and then removed. Note that when something is baked in an oven, the temperature of the oven stays constant. The graph of the function is shown below.
Describe the rate of change pattern over each interval of the graph listed below.
a. 0 < t < 345
b. 345 < t < 360
c. t > 360
Explain what is happening in each interval of your graph in terms of the turkey and its temperature, using complete sentences.
Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation.
Answer:
a. When the time is greater than 0, but less than 345 minutes, the temperature of the turkey is increasing at roughly a linear rate.
b. When the time ranges from 345 to 360 minutes, the temperature of the turkey stays constant, at 165 degrees.
c. When the time is greater than 360 minutes, the temperature of the turkey decreases.
f(x)= 2x^3 + 6x^2 -5x - 3, g(x)= 3x-4 find (f-g)(x)
The difference in the given functions is 2x^3 + 6x^2 -8x + 1
Difference of functionsGiven the following function a shown
f(x)= 2x^3 + 6x^2 -5x - 3
g(x)= 3x-4
Take the difference
(f-g)(x) = f(x) - g(x)
Substitute
(f-g)(x) = 2x^3 + 6x^2 -5x - 3 - (3x - 4)
Expand
(f-g)(x) = 2x^3 + 6x^2 -5x - 3 - 3x + 4
(f-g)(x) = 2x^3 + 6x^2 -8x + 1
Hence the difference in the given functions is 2x^3 + 6x^2 -8x + 1
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A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The difference is only 0.04, but that is still a significant change.
The margin of error is quite small compared to the change year over year, so it is a significant issue.
The change of 0.09 is not a lot and thus should be ignored.
The margin of error is larger than the increase, so we should consider it an issue of just extra information and thus can be ignored.
The correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.
What is the margin of error(MOE)?It is defined as an error that provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]
Where Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
We have:
A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C.
As the value of MOE is 0.13 degrees
It is a serious problem because the margin of error is quite narrow in comparison to the shift from year to year.
Thus, the correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.
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Which expression is modeled by this arrangement of tiles?
40 positive tiles are broken up into 10 groups of 4 positive tiles.
40 divided by (negative 10)
40 divided by 10
40 divided by 40
40 divided by 40
Answer:
40 divided by 10
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Needa line segment has endpoints P(-8,7) and Q(6,-3). What is the midpoint of the segment?
Answer:
1/2(6-8), 1/2(-3+7)=-1,2
Answer: C - (-1, 2)
Step-by-step explanation:
NEED HELP ASAP !!!
Simplify: √16r
O 47²
O 473
87²
O 8-3
Answer:
4 r^3
Step-by-step explanation:
sqrt ( 16 r^6 ) = sqrt ( 4^2 * (r^3)^2 ) = 4 r^3
Find the 7th term in the
sequence
-, -1, -5, -25, . . .
Hint: Write a formula to help you.
1st term. Common Ratio (desired term - 1)
Enter
Answer: -15625
Step-by-step explanation:
The explicit formula for the sequence is
[tex]a_{n}=-1(5)^{n-1}\\\\\implies a_{7}=-1(5)^{7-1}=\boxed{-15625}[/tex]
There are 10 USB drives in a box and 3 are defective. Two drives are to be selected, one after the other. What is the probability of selecting a defective USB followed by another defective USB?
[tex]|\Omega|=10\cdot9=90\\|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{90}=\dfrac{1}{15}\approx6.7\%[/tex]
pls help oooooooooooo
Answer:
110
Step-by-step explanation:
Suppose lines EH and BD are parallel:
Angle <GFE and angle <ABC are supplementary so their sum is equal to 180
2x + 10 + x + 20 = 180 add like terms
3x + 30 = 180 subtract 30 from both sides
3x = 150 divide both sides by 3
x = 50
We are asked the value of <ACD
<ABD and <ACD are also supplementary so we can find the value od <ACD:
x + 20 + <ACD = 180 we know x = 50 so we can replace x with that
50 + 20 + <ACD = 180
70 + <ACD = 180 subtract 79 from both sides
<ACD = 110
If f(x) =
√2x+3
6x-5
a. 1
b. -2
then f() =
C. -1
d. - 13
Answer:
put 1/2as a value of x in the equation and then solve .then the answer will be -1
Answer:
[tex]C.\ f\left( \frac{1}{2} \right) =-1[/tex]
Step-by-step explanation:
[tex]f\left( x\right) =\frac{\sqrt{2x+3} }{6x-5}[/tex]
In order to calculate f(1/2) ,all we have to do
is replacing x by 1/2 in the expression of f.
Then
[tex]f\left( \frac{1}{2} \right) =\frac{\sqrt{2\left( \frac{1}{2} \right) +3} }{6\left( \frac{1}{2} \right) -5 }[/tex]
[tex]=\frac{\sqrt{1+3} }{3-5}[/tex]
[tex]=\frac{\sqrt{4} }{-2}[/tex]
[tex]=\frac{2}{-2}[/tex]
[tex]=-1[/tex]
Hey I need help with statistics
what is next number in pattern 7, 11, 2, 18, -7
Answer:
the answer is -7+-25=-32
Can you please help meee
Answer: y = 4x + 5/4
Step-by-step explanation: Plug in the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y-intercept, and such that m, b ≠ 0.
Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t.
Which is the equation for y?
Answer:
y = -t
Step-by-step explanation:
Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.
⇒ parametric equation of line passing through a point (a₁, b₁, c₁)
and parallel to a vector <a, b, c> is given by :
x =a₁ + at , y = b₁ + bt , z = c₁ + ct
now according to question:
given -
point, P(1, 0, -3)
line, x = −1 + 2t , y = 2−t, and z = 3+3t.
so from the line the vector is= <2, -1, 3>
now using above formula,
equation of line is = x = 1 + 2t , y = −t, and z = -3+3t.
we have to solve for 'y' only,
⇒ y = -t (answer)
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Please answer both questions I will give u brainliest if ur right
first one b 315, second d
Step-by-step explanation:
18*=3*+315
7*+4*=a*
5 ice creams cost 6.50 pounds. How much do 11 ice creams cost
Answer:
14.30
Step-by-step explanation:
6.50/5=1.3
so one ice cream is 1.30 pounds
1.30X11=14.3
so 11 ice creams is 14.30 pounds
Let −5, 3 be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.
The value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have (−5, 3) be a point on the terminal side of θ.
Perpendicular = -5
Base = 3
From Pythagoras' theorem:
Hypotenuse² = (3)² + (-5)²
Hypotenuse = √34
cosθ = 3/√34
cscθ = -√34/5
tanθ = -5/3
Thus, the value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.
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