The probability is 0.4444.
What is probability?Probability is a measure of the likelihood of a particular outcome occurring in a given situation. It is the chance that something will happen or is true. Probability is expressed as a number between 0 (impossible) and 1 (certain). Probability is a mathematical way of predicting what will happen in the future based on a given set of data. It is used to analyze the likelihood of various outcomes in a range of scenarios, such as gambling, finance, insurance, and weather forecasting.
The probability of a randomly selected tester from the group of college-bound seniors having a score between 1497 and 1507 can be calculated using the standard normal distribution. First, we need to convert the scores to standard scores, or z-scores. Subtract the mean from the scores and divide by the standard deviation to get z-scores.
For XXX = 1497, z = (1497 - 1497) / 322 = 0.
For XXX = 1507, z = (1507 - 1497) / 322 = 0.31.
Using a standard normal table, we can calculate the area under the normal curve between 0 and 0.31. The probability of randomly selecting a tester with a score between 1497 and 1507 is 0.4444. The probability is therefore P(1497 ≤ XXX ≤ 1507) = 0.4444.
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Complete questions as follows-
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497 ≤ XXX ≤ 1507).
What is the product of 2x 3y )( 2x 3y )? *?
The product of (2x-3y)(2x+3y) is 4x^2-9y^2
Product= (2x-3y)(2x+3y)
Let the product of (2x-3y)(2x+3y) be P
P=2x(2x+3y)-3y(2x+3y)
P= 2x(2x)+2x(3y)-3y(2x)-3y(3y) {using distributive property of multiplication}
This property states that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a-b)(a+b) is equal to a^2 - b^2. This result is used as an identity.
P= 4x^2 +6xy - 6xy -9y^2
solving 6xy-6xy=0
P= 4x^2 - 9y^2
4x^2-9y^2 is the product of (2x-3y)(2x+3y).
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what is 2 2/3 x 3 1/4
Answer:
Step-by-step explanation:
Determine the value of c for each figure
Answer:
can you tell me a little bit more?
The following dotplot shows the centuries during which the 111111 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle. According to the 1.5.IQR rule for outliers, how many high outliers are there in the data set?
The conclusion which we get after analyzing the data given is that there aren't outliers in the displayed data set.
We will calculate the interquartile range and us the rule 1.5 .
The formula to calculate interquartile range is to subtract the value of first quartile by the value of second quartile.
IQR = Q3 - Q1
Therefore, interquartile range becomes,
IQR = 17 - 13
IQR = 4
Now , we will apply rule 1.5 and for that we will multiply 4 by 1.5 first
4 * 1.5 = 6
and then,
17 + 6 = 23
on applying the rue we will get ,
13 - 6 = 7 .
This value means that there is no outlier in the displayed data set.
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9. Which equation is represented by the table?
X
0
1
2.
3
у
40
20
10
5
a. 40(2)^x
b. 40(1/2)^x
Multiply (x-3)(4x+2) using the FOIL method. Select the answer choice showing the FOIL method products
The result of (x-3)(4x+2) using FOIL method is 4x^2 -6x +2x -6.
The FOIL method is a technique used to multiply two binomials. It stands for "First, Outer, Inner, Last" and follows these steps:
First: Multiply the first term of the first binomial by the first term of the second binomial
Outer: Multiply the first term of the first binomial by the second term of the second binomial
Inner: Multiply the second term of the first binomial by the first term of the second binomial
Last: Multiply the second term of the first binomial by the second term of the second binomial
Applying FOIL method to (x-3)(4x+2) we get:
First: 4x * x = 4x^2
Outer: 4x * -3 = -12x
Inner: -3 * 4x = -12x
Last: -3 * 2 = -6
So the result of (x-3)(4x+2) is 4x^2 -12x -12x -6 = 4x^2 -24x -6.
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An aerospace engineer is designing a model of a portion of a new telescope, a cylinder with a cone cut-out as shown below. What is the total volume of the materials used to make the new telescope piece?
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the required figure is not attached to the question.
From the question, we can deduce that the telescope is a composite figure made from a cone and a cylinder.
To get the volume of the materials used, you have to calculate the volume of the cone and that of the cylinder.
The sum of these volumes, is your answer.
Assume the following dimensions:
Cone
[tex]r = 5\\[/tex] --- radius
[tex]h = 7[/tex] --- height
Cylinder
[tex]r = 5\\[/tex] --- radius
[tex]h = 20[/tex] --- height
The volume of the cone is:
[tex]Volume = \frac{1}{3} \pi r^2h[/tex]
[tex]V_1= \frac{1}{3} \pi *5^2*7[/tex]
[tex]V_1= \frac{1}{3} \pi *25*7[/tex]
[tex]V_1= \frac{175}{3} \pi[/tex]
The volume of the cylinder is:
[tex]Volume = \pi r^2h[/tex]
[tex]V_2 = \pi * 5^2 * 20[/tex]
[tex]V_2 = \pi * 25* 20[/tex]
[tex]V_2 = 500\pi[/tex]
The total is:
[tex]Volume = V_1 + V_2[/tex]
[tex]Volume = \frac{175\pi}{3} + 500\pi[/tex]
Take LCM
[tex]Volume = \frac{175\pi+1500\pi}{3}[/tex]
[tex]Volume = \frac{1675\pi}{3}[/tex]
Given two points, (3, 2) and (7, 18), determine both the linear and quadratic equations crossing both points. Let f(x) and f(k) be the linear and quadratic equation respectively. Write both in standard form
The linear equation f(x) is 4x - 10 and the quadratic equation f(k) is -5/2k^2 + 4k - 1 for the two given points.
The linear equation can be found using the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept. To find the slope (m) we can use the two points given:
m = (y2 - y1) / (x2 - x1) = (18 - 2) / (7 - 3) = 16/4 = 4
The y-intercept (b) can be found using one of the points and the slope:
b = y - mx = 2 - 4(3) = -10
So the linear equation in standard form is:
f(x) = 4x - 10
For the quadratic equation, we know that it's in the form of y = ax^2 + bx + c. We have 2 points, so we have 2 equations with 2 unknowns. We can use this information to solve for a, b and c.
Let's (3,2) point 1 and (7,18) point 2.
f(k) = ak^2 + bk + c....(1)
point 1: f(3) = 2 = 9a + 3b + c...(2)
point 2: f(7) = 18 = 49a + 7b + c...(3)
Now we have 2 equations and 3 unknowns.
using theirs first equation and substitute it in the second and third equation
18 = 49a + 7b + c
2 = 9a + 3b + c
c = 2 - 9a - 3b
18 = 49a + 7b + (2 - 9a - 3b)
18 = 49a + 7b + 2 - 9a - 3b
18 = 40a + 4b + 2
16 = 40a + 4b
now this equation is used to solve for a and b
b = (16 - 40a) / 4
so a,b and c are
a = -5/2
b = 4
c = -1
so the quadratic equation in standard form is:
f(k) = -5/2k^2 + 4k - 1
4x - 10 is the linear equation f(x) and -5/2k^2 + 4k - 1 is the quadratic equation f(k) for the two given points.
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A line is parallel to y = 4x + 1 and
intersects the point (-2, -5). What is the
equation of this parallel line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x - X1)
Then write the equation in slope-intercept form.
Step-by-step explanation:
(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!
Step-by-step explanation:
Given the system of equation, \left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.{
2x−3y=−19
x+6y=28
, solve by elimination.
\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.{
2x−3y=−19
−2(x+6y=28)
, multiply the top equation by -2.
We get, \left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.{
2x−3y=−19
−2x−12y=−56
+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right. , add the equations together.
We get, -15y=75−15y=75 , we just eliminated the variable, x, we can now solve this equation for y.
-15y=-75 = > y=\frac{-75}{-15}−15y=−75=>y=
−15
−75
, y=\frac{75}{15} = > y=5y=
15
75
=>y=5
We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...
x+6y=28 = > x+6(5)=28 = > x+30=28x+6y=28=>x+6(5)=28=>x+30=28 , subtract the value, 30, from both sides. We get, x=-2x=−2 .
We found the value x, x=-2.
Thus the solution to the given system of equations is (-2,5).
Answer:
Comparing given eqn of line i.e.y=4x + 1 with
y=mx+c,we get,
m=4
We know that parallel lines have same value for m and the line parallel to y=4x+1 passes through the point (-2,-5) i.e (x1,y1)
Now,using point slope formula,we get
y-(-5)=4{x-(-2)}
or,y+5=4(X+2)
or,y+5=4x+8
or,y=4x+8-5
:.y=4x+3 is the req eqn for line parallel to y=4x+1
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CAN YOU HELP ME FAST PLEASE
Q 1 ans supplementary
Q2 ans congurent
Q3 ans neithee
The value of πPhone stock has increased 9% each year for the past several years. In 2020, the stock was worth $75. What will the stock be worth in 7 years? What was the stock worth in 2016?
Answer:
2027 = $122.25
2016 = $48
Step-by-step explanation:
Find 1% of 75
75 / 100 = 0.75
multiply by 9
0.75 * 9 = 6.75
So that's $6.75 each year
Now, lets find our answers for 7 years.
6.75 * 7 = $47.25
75 + 47.25 = $122.25
The stock will be $122.25 in 2027
Now for 2016.
$6.75 * 4 = $27
$75 - $27 = $48
The stock was $48 in 2016
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given few inequalities and some operations are performed on them
For first inequality:
=> 4 < 7
Multiply both sides by 3, then by 2, then by 4, then by 9
=> 4 *3 * 2 * 4 * 9 < 7 *3 * 2 * 4 * 9
=> 864 < 1512
there is no change in the inequality sign and it is still true.
For the second inequality:
=>11 > -2
Add 3 to both sides, then add 3, then add (-4)
=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)
=> 13 > 0
there is no change in the inequality sign and it is still true.
For the third inequality:
=> -2 ≤ -2
Subtract 6 from both sides, then 8, and then 2
=> -2 -6 -8 -2 ≤ -2 -6 -8 -2
=> -18 ≤ -18
there is no change in the inequality sign and it is still true.
For the fourth inequality:
=> -4 < 8
Divide both sides by -4
=> -4 / -4 < 8 / -4
Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign
=> 1 > -2
Divide both sides by -2
=> -1/2 < 1
there are two times a change in the inequality sign and it is still true.
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NO LINKS HELP During a sale, a store owner offers a discount depending on how much money a customer spends. The function p(x) represents the total amount owed by a customer during the sale when purchasing items totaling a value of x dollars.
How much does a customer owe for items with a total value of $140, in dollars and cents?
9514 1404 393
Answer:
$125
Step-by-step explanation:
For x = 140, the function definition for x ≥ 100 is used.
p(140) = 95 +0.75(140 -100) = 95 +30 = 125
The customer will owe $125 for items with a value of $140.
A. the function has a maximum value of 1
B.the function has a minimum value of 1
C.the function has a maximum value of -2
D.the function has a minimum value of -2
Answer:
A) The function has a maximum value of 1
Step-by-step explanation:
Since the parabola opens downward, then its maximum would be 1 and its minimum would be -∞
Find the probability that a point chosen at random will lie in the shaded area.
A) 32%
B)62%
C)94%
D)2%
36-x=-36 what's the answer to It
Answer:
x = 72
Step-by-step explanation:
36 - x = -36
*subtract 36 from both sides*
-x = -72
*divide by -1*
x = 72
Answer:
0 is the answer of the equation
Kelsey starts downloading a file. After 4 seconds, her computer says 40% of the file has downloaded."
How many seconds will it take in all to download the file at this rate?
Answer:
6 seconds left, 10 seconds total.
Step-by-step explanation:
40 / 4 = 10
Increases by 10% each second
60% left, so 60 / 10 = 6
Answer:
6 seconds left, 10 seconds total.
Step-by-step explanation:
40 / 4 = 10
Increases by 10% each second
60% left, so 60 / 10 = 6
Step-by-step explanation:
Type the correct answer in each box. The coordinates of the point that corresponds to an angle of radians in the unit circle are (, ).
On solving the provided question, we can say that coordinates of the point in the unit circle S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] ) => S= ( 0 , -1 )
What is circle?Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
S = (0, -1 )
coordinates of the point in the unit circle
S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] )
S= ( 0 , -1 )
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test form 1a answers 6th grade three times Geoff's age plus 3 is myrkas age. myrka is 48. what is Geoff's age
Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.
What does a math reshuffle mean?Rearranging terms in an equation to get the solution is known as "solving by rearranging." Keep these guidelines in mind when solving by rearranging: To shift terms from one side to the other, do the reverse operation.Rearranging terms in an equation to get the solution is known as "solving by rearranging." Keep these guidelines in mind when solving by rearranging: To shift terms from one side to the other, do the reverse operation.Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.Age of Myrka = 3x + Age of Geoff
3x + 3 = 48
3x = 48 - 3
3x = 45 x = 15
Geoff is therefore 15 years old.
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What evidence from Gilgamesh a new English version best supports the conclusion that Gilgamesh is an epic hero?
In "Gilgamesh: A New English Version," several pieces of evidence support the conclusion that Gilgamesh is an epic hero.
Gilgamesh is the king of Uruk: He is the main character of the story, and his actions and deeds are the focus of the epic. As a king, he holds a position of power and authority and is responsible for the well-being of his people.
Gilgamesh undertakes a quest: He embarks on a journey to find immortality after the death of his dear friend Enkidu. His quest takes him to the ends of the earth and shows his determination and courage.
Gilgamesh faces challenges and monsters: During his journey, Gilgamesh faces several challenges and monsters, such as the giant Humbaba and the Bull of Heaven. His bravery in overcoming these obstacles demonstrates his heroic qualities.
Gilgamesh has supernatural strength and abilities: He is two-thirds god and one-third man, which means he is gifted with supernatural strength, speed and endurance. He is able to perform deeds that would be impossible for a mortal.
Gilgamesh demonstrates wisdom and self-awareness: Throughout his journey, Gilgamesh comes to understand the limitations of human life and the importance of living a meaningful existence. He demonstrates wisdom and self-awareness which are the hallmark of a true epic hero.
These examples of Gilgamesh's character and actions support the conclusion that he is an epic hero and his story is an epic.
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can someone pls help
The surface area of this regular pyramid is 1040 cm2. The base is a regular pentagon with side b = 16 cm and slant height l =15 cm. Find its apothem (a).
show work please. i will give brainliest ! :)
Answer:
(a) = 11 cm
Step-by-step explanation:
The formula for finding the surface area of a regular pyramid is B + (1/2*P*l), with B being the area of the base, p being the perimeter of the base, and l being the slant of the pyramid.
The area of a pentagon can be solved using the formula 1/2*a*p, with a being the apothem and p being the perimeter of the pentagon.
B + (1/2*80*15) = 1040B + 600 = 10401040 - 600 = 440 (440 is the area of pentagon)1/2*a*(16*5) = 44040*a = 440440/40 = 11The apothem is 11 cm. Hope this helps!
Is 8 15 17 a right triangle?
No, the sides of a right triangle do not include 8, 15, and 17. The sides of a right triangle must follow the Pythagorean theorem, so the sum of the squares of the two shorter sides must equal the square of the longest side. 8² + 15² does not equal 1
8² + 15² = 64 + 225 = 289
17² = 289
Therefore, 8, 15, and 17 are not the sides of a right triangle.
The Pythagorean theorem is an important mathematical concept used to determine if three numbers form the sides of a right triangle. This theorem states that the sum of the squares of the two shorter sides must equal the square of the longest side. In the case of 8, 15, and 17, 8² + 15² does not equal 17², so it is not a right triangle. To test this, we can calculate 8² + 15² = 289, and then 17² = 289. Since the two values are not equal, we can conclude that 8, 15, and 17 are not the sides of a right triangle.
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if two lines in a plane intersect then they are not parallel true or false
Answer:
true because parallel means lines that doesnt meet
Answer:true, parallel line never intersect, I hope this helps!!
Cute cat btw<3
Pls help me anyone
I don’t get this pls
Answer:
1. Y=-2x+3
2. Y=3x+2/3
I'm sorry I can't get them all but I know these are right
Question 2 of 5
Simplify.
(m3)6 +m18
A. m4
B. 1
C. m
D. m-9
SUBMIT
Using the first index law, the solution provided indicates that this has a value of 1.
What is the first index law?X to the power of A multiplied by X to a power of B results in X to the power of A + B, according to the first law of indices. Keep in mind that adding the indices when multiplying terms with them means that the base must remain constant throughout.
What exactly is index theory?A topological invariant of a certain class of differential operations on a manifold is studied in index theory, as well as the invariant's local formula in terms of the manifold's geometry. inspirational cases. operator elliptic The index theorem by Atiyah-Singer.
According to the given information:(m³)⁶/m¹⁸ = m³ˣ⁸/m¹⁸
= m¹⁸/m¹⁸
= 1
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Tell whether (0, -1) is a
is a solution of the inequality whose graph is shown.
Answer:
No, the point isn't in the shaded area
Step-by-step explanation:
1/4 - 7/1 (pls i nee answer)
Answer:3/4 is the answer
Step-by-step explanation:
Answer:(s)
1/4 - 7/1 = - 27/4
Decimal: - 6.75
Mixed number: - 6 3/4
Step-by-step explanation:
1/4 - 7/1 = - 27/4 or - 6.75 or - 6 3/4
LCM: 4, 1 = 4
Adjust Fraction Based On LCM:
1/4 - 28/4
Apply The Fraction Rule:
a/c - b/c = a - b/c
1 - 28/4
Subtract the numbers:
1 - 28 = - 27
= -27/4
Apply Fraction Rule:
- a/b = - a/b
Thus:
1/4 - 7/1 = - 27/4
Decimal: - 6.75
Mixed Number Form - 6 3/4
I hope that helps you!!!
a small ior shows the data is
Answer:
Don't have enough infromation to answer that.
Step-by-step explanation:
x < 5 and x + 2y ≥ 1
Answer:
-1
Step-by-step explanation: