Using the normal distribution, it is found that the probability that a data value is between 28 and 35 is given by:
A. 29.6%.
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.Researching the problem on the internet, the mean and the standard deviation are given by:
[tex]\mu = 26, \sigma = 4[/tex].
As a proportion, the probability that a data value is between 28 and 35 is the p-value of Z when X = 35 subtracted by the p-value of Z when X = 28, hence:
X = 35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 26}{4}[/tex]
Z = 2.25
Z = 2.25 has a p-value of 0.988.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 26}{4}[/tex]
Z = 0.5
Z = 0.5 has a p-value of 0.692.
0.988 - 0.692 = 0.296 = 29.6%, which means that option A is correct.
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question 2. write the product using exponents
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given expression ,
[tex] \frac{1}{8} . \frac{1}{8} .y.y.y \\ [/tex]
this can also be written as ,
[tex] \frac{1}{8} \times \frac{1}{8} \times y \times y \times y \\ \\ \longrightarrow \: \frac{y {}^{3} }{64} [/tex]
hope helpful ~
What is the volume of the triangular prism?
12 cm
3 cm
8 cm
Answer:
Find the area of the triangle side, then multiply by the length of the prism.Area of triangle = 1/2 x height x baseArea = 1/2 x 2 x 3 = 3 square cmVolume = 3 x 4 = 12 cubic cm.Answer is A)
Step-by-step explanation:
mary drove for four hours on an interstate highway at a constant rate of 60 miles per hour. during the next hour, she drove on a state road at a slower rate of 40 miles per hour. how many miles did mary travel on her trip?
Step-by-step explanation:
speed = distance/time
distance = speed × time.
so, for the first 4 hours
distance = 60 m/h × 4 h = 240 miles
and for the next hour
distance = 40 m/h × 1 h = 40 miles
she traveled therefore
240 + 40 = 280 miles
the answer was 280, Take your chances with it, I did it on edgeinuity but it wont let me show the screenshot i took
is the only plane shape in which every point on the figure is the exact same distance from the center.
The only plane shape in which every point on the figure is the exact same distance from the center is; The Circle
How to Identify a Circle?
There are different types of plane shapes such as Square, rectangle, Circle, Trapezoid, Parallelogram, Rhombus, Kite, Triangle e.t.c.
Now, Except for the circle and Triangle, every other listed plane shape above is a quadrilateral because they have 4 sides. Now, no quadrilateral has all its' sides equal from the center. Likewise, no triangle has all its' sides equal from the center.
The only plane shape with all its' sides equal from the center is the circle because the radius is equal all through.
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the jar contains 22 marbles 12 purple 8 red and 2 green one marbles drawn and put back then a 2nd marble is drawn, what is the probability that both marbles were red?
Explanation:
There are 8 red marbles out of 22 total
8/22 = 4/11 is the probablity of randomly selecting red.
If the first marble is put back, then that probability will not change.
The probability of two red marbles in a row is (4/11)*(4/11) = 16/121
Side note: 16/121 = 0.1322 = 13.22% approximately
In ΔRST, = 93 inches, ∠S=123° and ∠T=28°. Find the length of r, to the nearest 10th of an inch
Answer:
<r=29
Step-by-step explanation:
what is the answer ?
The angle B will be equal to ∠B=53.13 degrees.
What is the triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
It is given that:-
Three sides of the triangle are:- a= 3, b=4 and c =5
The angle B will be calculated by the following formula;-
[tex]\angle B=Cos^{-1}\dfrac{a^2+c^2-b^2}{2ac}\\\\\\\angle B=Cos^{-1}\dfrac{3^2+5^2-4^2}{2\times 3\times 5}\\\\\\\angle B=Cos^{-1}(0.6)\\[/tex]
∠B=53.13 degrees
Hence the angle B will be equal to ∠B=53.13 degrees.
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Expand and simplify 3(x-4)(2x+5)
3(x-4)(2x+5)
= 3×(x-4)×(2x+5)
= (3x-12)(2x+5)
= 6x²+15x-24x-60
= 6x²-9x-60
[tex]3( {2x }^{2} + 5x - 8x - 20) \\ 3( {2x}^{2} - 3x - 20) \\ {6x}^{2} - 9x - 60 \\(6x + \frac{5}{2} )(x - 4)[/tex]
To divide x3y by x4y, first divide y by y to get x3/x4. Which of these would you do next to solve?
An expression is defined as a set of numbers, variables, and mathematical operations. The solution of the division of x³y by x⁴y is equal to 1/x.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The division of x³y by x⁴y can be done as,
x³y/x⁴y
= x⁽³⁻⁴⁾ y⁽¹⁻¹⁾
= x⁻¹
= 1/x
Hence, the solution of the division of x³y by x⁴y is equal to 1/x.
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alfredo va a comprar 850 dolares si cada dolar cuesta en promedio 2945 pesos cuanto dinero en pesos debe llevar alfredo
Answer:
He will need $2,503,250 pesos.
Step-by-step explanation:
2,945 x 850 = 2,503,250
g(t)=-3t +2 h(t)=t-4 find (g o h)t)
Answer:
3t-10
Step-by-step explanation:
g(h(t))=g(t-4)
=3(t-4)+2
=3t-12+2
=3t-10
A gallon of milk cost 3.79. because of inflation, the price increases by 5% per year . write an equation that models the growth in the price of milk
A, B & C form a triangle where Z
BAC = 90°.
AB = 3.3 mm and CA = 7.7 mm.
Find the length of BC, giving your
answer rounded to 1 DP.
Answer:
BC≈8,38
Step-by-step explanation:
AB=a
BC=c
CA=b
a²+b²=c²
3.3²+7.7²=c²
√70,18=√c²
c≈8,38
344/299 = x
what is x?
Answer:
Mixed Number Form: x = 1 45/299
Decimal Form: x = 1.15050167…
Step-by-step explanation:
Solve for x
58° 22 X
Answer:
x = 13.75 units
Step-by-step explanation:
Right triangle
tan 58 = opposite side / adjacent side
tan 58 = 22/x
x = 22/ (tan 58) = 13.75
Which is the next step in the following construction of an equilateral triangle?
circle with center P and point A along circles edge, arcs along the circle at points B, C, D, E, and F in alphabetical order, and a line segment connecting points A and C
Connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have:
Circle with centre P and point A along the circle's edge, arcs along the circle at points B, C, D, E, and F in alphabetical order, and a line segment connecting points A and C.
A triangle with three sides that are all the same length and three angles that are all the same size (60°) is called an equilateral triangle.
Connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
Thus, connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
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Ms Hieronymus goes through 1/2 a package of pencils every 1/8 a month for her students How many packages does Ms Hieronymus need for 10 months
Answer:
Every 1/8 month (ie about 4 days) she uses 1/2 a package
So every month she will use 8 x (1/2) = 4 packages
So in 10 months she will use 4 x 10 = 40 packages
What is the interquartile range of the set of data this box-and-whisker plot represents?
The interquartile range = upper quartile - lower quartile = 18 - 15 = 3 (option A).
What is Interquartile Range (IQR)?The interquartile range (IQR) of a data = upper quartile - lower quartile.
In the box-and-whisker plot given:
Upper quartile = 18Lower quartile = 15Interquartile range (IQR) = 18 - 15Interquartile range (IQR) = 3Learn more about the interquartile range on:
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can someone help me with this question
Answer:
the answer will be 1 7/3 I believe
John spins a fair spinner with 5 equal sections numbered 1 through 5. His spin lands on the number 2. What is the probability that John's next three spins land on the number 2
Using it's concept, it is found that the probability that John's next three spins land on the number 2 is of [tex]\frac{1}{125}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that out of 5 numbers, one is 2, hence the probability of three consecutive spins landing on two is given by:
[tex]p = \left(\frac{1}{5}\right)^3 = \frac{1}{125}[/tex].
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The first four terms of a sequence are shown on the graph below.
What can be concluded about the sequence?
The common ratio of the sequence is 2.
The common difference of the sequence is 2.
The next term of the sequence is represented by the point (5, 64).
The next term of the sequence is represented by the point (5, –64).
Answer:
The next term of the sequence is represented by the point (5, –64)
Step-by-step explanation:
From inspection of the graph, the first four terms of the sequence are:
(1, -4)(2, 8)(3, -16)(4, 32)Each x-value increases by 1 for each consecutive term.
Each y-value is the previous y-value multiplied by -2.
Therefore, it is a geometric sequence with a common ratio of -2.
Following the above rule, if the last term in the sequence is (4, 32), then the next term in the sequence will be:
x = 4 + 1 = 5y = 32 × -2 = -64So, the next term of the sequence is represented by the point (5, –64)
ST is tangent to OQ. What is m
Sum of the interior angle of any triangle must equal to 180 degrees thus :
[tex]53 + 90 + t = 180[/tex]
[tex]143 + t = 180[/tex]
[tex]t = 37[/tex]
Thus angle T has a measure of 37° .
Answer: 37
Explanation: Angle S is a right triangle because ST is tangent to circle Q.
180 - 90 - 53 = 37
A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a
scale factor of 3/4. Find the perimeter of the preimage, the original triangle, before its
dilation. Round your answer to the nearest tenth, if necessary.
If the scale factor is 3/4. Then the perimeter of the original triangle will be 66.67 units.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a scale factor of 3/4.
Then the perimeter of the preimage, the original triangle, before its
dilation will be
Let c be the perimeter of the original triangle.
Then we have
[tex]\rm \dfrac{3}{4} \times x = 50\\\\x = 66.67[/tex]
Then the perimeter of the original triangle is 66.67 units.
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Handedness: 18 left-handed
22 right-handed
The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. if there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.)
A) 0.410
B) 0.357
C) 0.333
D) 0.250
If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N=rT. This relationship is known as Little's law.
The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.
Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?
Answer:
Let x be the number of left handed female students and let y be the number of left handed male students.
Then the number of right handed female students will be 5x and the number of right handed male students will be 9y. Since the total number of left handed students is 18 and the total number of right handed students is 122, the following system of equations must be satisfied.
x+y=18 and 5x+9y=122
Solving this system gives x=10 and y=8.
Thus, 50 of the 122 right handed students are female. Therefore, the probability that a right handed student selected at random is female is the fraction 50/122
which to the nearest thousandth is 0.410.
T is average time spend by shoppers in minutes
N average number of shoppers.
Here, shoppers/hour =84.
Hence r=
60
84
T=5
Hence N=rT=
60
84
×5=7
Average number of shoppers waiting at checkout =7
Answer:
EMMA ITS KAIDN. text back.
Step-by-step explanation:
I had already answered this.
Someone help please answer question 1
Answer:
Reflection in line x=1
Step-by-step explanation:
If you draw a line of all values where X = 1. It forms a line between the 2 shapes and by reflecting in that line, you will get Shape B from shape A
What is the sum of the solution 4|3x-5|-5=-1
4|3x-5|-5=-1
|12x-20|-5= -1
|12x-20|= -1+5
|12x-20|= 4
x1-> 12x-20= 4
12x= 4+20
x= 24/12
x=2
x2-> -12x+20 = 4
-12x = 4-20
-12x= -16
x= -16/-12
x= 4/3
i just dont know the answer
Answer:
(3,7) (4,4) (1,2)
Step-by-step explanation:
180 degrees: (x, y) —> (-x, -y)
1-Find the measure of
1. 226 degrees
2. 113 degrees
3. 134 degrees
4. 67 degrees
2-Find the circumference of the circle 7 cm. Use 3.14 for pi.
1. 21.98 cm
2. 38 cm
3. 3.5 cm
4. 7 cm
3-Classify the triangle by its sides and angles: 15.5 in, 15.5 in and 15.5 in.
1. Scalene, right
2. Equilateral, right
3. Equilateral, acute
4. Isosceles, acute
4-What are the coordinates of the image of point L(4,2) after a reflection over the line y = -1.
1. (-5,2)
2. (4,-4)
3. (3,1)
4. (4,-2)
5-A point P has coordinates (3.2). What are it’s new coordinates after reflecting point P over the y-axis.
1. (-3,-2)
2. (3,-2)
3. (3,2)
4. (-3,2)
Im honestly so confused and need help with it because i just want to go on to the next question♀️
Answer:
1.05 (0.2x + 1/2y + 0.75z)
Step-by-step explanation:
Finding the cost of each item :
1 Sweatshirt
Cost = $xDiscount = 80% offPrice = (100% - 80%)(x)Price = 0.2x2 T-shirts
Cost = $yDiscount = Buy one, get one 50% offPrice = (50%)(y)Price = 1/2y1 Pair of Pants
Cost = $zDiscount = 25% offPrice = (100% - 25%)(z)Price = 0.75zNow, the final cost (after applying sales tax) is :
1.05 (0.2x + 1/2y + 0.75z)Option #1An equilateral triangle has a side length of $12 \sqrt{3}.$ The triangle is rotated about one of its altitudes as an axis, sweeping out a cone in space. Find the volume of the cone.
The volume of the cone is 254.85 cubic units
How to determine the volume of the cone?The side length of the equilateral triangle is given as:
l = 12√3
Calculate the radius (r) of the cone using:
r = l/2
r = 12/2√3
r = 6√3
Calculate the height of the cone using:
[tex]h = \sqrt{l^2 + (l/2)^2[/tex]
This gives
[tex]h = \sqrt{(12\sqrt 3)^2 + (6\sqrt3)^2[/tex]
Evaluate
[tex]h = \sqrt{540[/tex]
h = 22.24
The volume of the cone is then calculated as:
V = 1/3πr²h
This gives
V = 1/3π * (6√3)² * 22.24
Evaluate
V = 254.85
Hence, the volume of the cone is 254.85 cubic units
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