The probability that the sample mean will lie between 1070 and 1120 is .7001 to .8500.
To find the probability that the sample mean will lie between 1070 and 1120, we use the Z-score formula:
Z = (x - μ) / σ
where x is the value we are looking for (in this case 1070 or 1120), μ is the population mean (1100), and σ is the population standard deviation (100).
Using this formula, we can calculate the Z-scores for 1070 and 1120, which are -0.3 and 0.2 respectively.
We can then use a Z-table to find the probability associated with each of these Z-scores. The probability associated with a Z-score of -0.3 is 0.6179, and the probability associated with a Z-score of 0.2 is 0.7886.
The probability that the sample mean will lie between 1070 and 1120 is the difference between these two probabilities, which is 0.1707. This is equivalent to a probability of 0.7001 to 0.8500.
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Given: ΔPQR ≅ ΔPNM
What is the measure of PM?
Responses
A - b
B - c
C - a
D not enough information
Answer:
A
Step-by-step explanation:
since the triangles are congruent then corresponding sides are congruent.
Δ PQR congruent to Δ PNM
PR and PM are corresponding sides , then
PM = PR = b
Convert 7π/21 to degrees.
Converting 7π/21 to degrees will be 60°.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees. Although it is not a SI unit—the radian is the SI unit of angular measure—it is mentioned as an accepted unit in the SI brochure.
Angles are measured in terms of radians. Angles are measured using the degree and radian units. In calculus and the majority of other branches of mathematics, angles are typically or generally measured in radians.
It should be noted that in order to convert radians yo degrees, you've to multiply by 180/π since a full circle is 360°.
This will be illustrated as:
= 7π / 21 × 180 / π
= 7/21 × 180
= 60°
The value is 60°.
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5/6 X +3 equals 13 
Answer:
Step-by-step explanation:
The answer is 12
Answer:
x=12
Step-by-step explanation:
[tex]\frac{5}{6}x+3=13\\\frac{5}{6}x+3-3=13-3\\\frac{5}{6}x=10\\6(\frac{5}{6}x)=10(6)\\5x=60\\(\frac{1}{5})5x=60(\frac{1}{5})\\x=12[/tex]
a car is traveling at 50 mph due south at a point 1 mile north of an intersection. a police car is traveling at 40 mph due west at a point 1 mile east of the same intersection. at that instant, the radar in the police car measures the rate at which the distance between the two cars is changing. what does the radar gun register?
If a car is traveling at 50 mph due south at a point 1 mile north of an intersection. the radar gun register at -62.6 mph.
What is distance?Distance can be defined as how far an object is from another object.
Distance of the first car north of the intersection point =y
Distance of the police car west of the intersection =x
Distance between the cars =s
s² =x² +y²
x=1.4 miles or 0.25 miles
y =1/2 miles or 0.50 miles
Pythagoreans theorem
Distance between cars
s =√x²+y²
s=√(0.25 miles)² +(0.50 miles)²
s =0.559 miles
Hence,
ds/dt = [0.25 miles/ 0.559 miles (-40 mph)] + [0.50 miles/0.559 miles (-50 mph)
ds/dt = -17.89 + -44.7
ds/dt = - 62.59mph
ds/dt =- 62.6 mph (Approximately)
Therefore the distance is 62.6 mph.
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Erin is selling books for $12 each. She wants to make more than $180 in book sales. Write an inequality that can be used to determine the number of books, b, she must sell in order to meet her goal, then solve for b.
The inequality that can be used to determine the number of books, b, Erin must sell in order to meet her goal of making more than $180 in book sales is 12b ≥ 180.
2. The solution to the inequality 12b ≥ 180 is that b ≥ 15.
What is inequality?Inequality is a mathematical statement that two or more mathematical expressions are unequal because their solutions are not equivalent in value.
Inequalities are depicted as less than (<), more than (>), not equal to (≠), less than or equal to (≤), and more than or equal to (≥).
The selling price per book = $12
The total sales revenue expected is ≥ $180
The number of books = b
Inequality describing the situation = 12b ≥ 180
b ≥ 180 ÷ 12
b ≥ 15
Thus, we can conclude that Erin needs to sell 15 or more books to earn $180 or more from the book sales.
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URGENT HELP PLEASEEE :)
a) The probability of rolling a total of 5 is 1/9.
b) If a pair of fair dice 360 times, then 40 times you will get a total of 5.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
The number of 5 in the table is 4.
The total number of outcomes is 6 × 6 = 36
The number of outcomes of favorable event is 4.
Total number of outcomes is 36.
The probability getting total of 5 after rolling the pair of dice is
=4/36
Divide the denominator and numerator by 4:
= 1/9
If 360 time the pair of dice rolled, the number of times to get total 5 is
360 × (1/9)
= 40.
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If they are similar, find the value of x
For figure 2) the value of the 'x' would be x = 14.
and for figure 3) the value of the 'x' would be x = 17 or x = 1 .
What is the Basic Proportionality Theorem?
The Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.
Figure 2)
By using the Basic Proportionality Theorem, we can write
[tex]\frac{11}{22}=\frac{x}{42-x}\\\\\frac{1}{2}=\frac{x}{42-x}\\\\42-x=2x\\\\3x=42\\\\x=14[/tex]
Now for figure 3)
By using Pythagoras' theorem, we can write
[tex]24^2+(x+7)^2=(2x-10)^2\\\\576+x^2+14x+49=4x^2-40x+100\\\\3x^2-54x+51=0\\\\x^2-18x+17=0\\\\x^2-17x-x+17=0\\\\(x-17)(x-1)=0\\\\x=17 $ or $ x=1[/tex]
Hence, for figure 2) the value of the 'x' would be x = 14.
and for figure 3) the value of the 'x' would be x = 17 or x = 1 .
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.........i need help past due
Answer:
[tex]\frac{85}{17}[/tex]
Step-by-step explanation:
[tex]\frac{8.5}{1.7}[/tex] multiply the top and bottom by 10
[tex]\frac{85}{17}[/tex]
HELP MEE !! 45 points!!
Solve. What is “u” in the inequality? –11 < 6u+ 4u
Answer:
u > -11/10
Step-by-step explanation:
the lacrosse team sold s team booster sweatshirts, and 19 of them were adult sizes. write an expression that shows how many sweatshirts were not adult sizes.
The expression that shows how many sweatshirts were not adult sizes is s - 19 .
Given :
the lacrosse team sold s team booster sweatshirts, and 19 of them were adult sizes.
Expression :
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Expression = number of sold sweatshirts - number of adult sizes.
= s - 19.
This gives the number of sweatshirts that are not adult sizes
if s = 25
then not adult sizes sweatshirts = s - 19
= 25 - 19
= 6
Hence the expression is s - 19.
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The first side of a triangle is 3cm longer than the second. The third side is twice as long as the second. The perimeter is 31cm. Find the length of each side.
Answer:
7 cm ; 10 cm ; 14 cm
Step-by-step explanation:
x = y + 3
z = 2y
x + y + z = 31
y + 3 + y + 2y = 31
4y = 31 -3
4y = 28
4/4 y = 28/4
y = 7
z = 7(2) = 14
x = 7 + 3 = 10
The volume of a cylinder having height one and half of the radius is 12,936 m3 what minimum square cm of paper is needed to cover the curved surface area of the cylinder? The answer should be 1848m2. please solve my question.
Matias has a planter that is full of soil. The planter is a rectangular prism that is 1 1/2 ft high, 3 2/3 ft long, and 2 ft wide. Matias pours all the soil into a new planter. The new planter is a rectangular prism that has a base of 8 1/4. What is the height of the soil in the new planter
The height of the soil in the new planter is 4/3 feet
Consider the old planter
The height of the prism = [tex]1\frac{1}{2}[/tex] feet = 3/2 feet
The length of the prism = [tex]3\frac{2}{3}[/tex] feet = 11/3 feet
The width of the prism = 2 feet
The volume of the rectangular prism = Length × width × height
= 11/3 × 2 × 3/2
= 11 cubic feet
The area of the base of the new planter = [tex]8\frac{1}{4}[/tex] square feet = 33/4 square feet
The volume of both planter will be equal
The base area × height = volume
33/4 × h = 11
h = 11 / (33/4)
h = 11 × 4/11
h = 4/3 feet
Therefore, the height of the new planter is 4/3 feet
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Find the next two terms in this
sequence.
50, 40, 31, 23, 16, | ? ],[?]
Answer:
8, 0
Step-by-step explanation:
there are 25 animals on a farm. 10 of them are cows. what percentage of animals on the farm are cows?
Answer: 40%
Step-by-step explanation:
Take 10 divided by 25; then times 100 = 40%
What kind of transformation converts the graph of f(x)= – 7|x|+7 into the graph of g(x)=7|x|–7?
The transformation from f(x) = -7|x| + 7 to g(x) = 7|x|- 7 is-
The graph of f(x) has been moved 14 units down. Then it is rotated upwards to get the graph of g(x)
What is rotation?
The mathematical transformation which turns a geometrical figure about a fixed point is called rotation. The fixed point is called center of rotation.
f(x)= –7|x|+7
g(x) = 7|x|- 7
At first the graph of f(x) has been moved 14 units down. Then it is rotated upwards to get the graph of g(x)
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Need Help for this Answer on this screenshot
Answer:
<
A
Step-by-step explanation:
What is the value of f(x) = 1/2x + 5 when x = 4?
Answer:
f(x)=7
Step-by-step explanation:
f(x)= 1/2x+5 ; x=4
f(4)= 1/2(4)+5
f(4)= 2+5
f(x)=7
Hope this helps, because I just did this lesson and I was confused at first, but with practice you will get it!
Please help me out I really need this answer please please
Answer:
A. Imaginary Square is 1 so ye ignore
If the constant of Proportionality between X and Y is 2.5, Which equation represents their relationship
A) Y= 2.5X
B)2Y=5X
C)5Y=2X
D)Y=X divided by 2.5
Y= 2.5x equation represent their relationship .
What is equation?An equation is a formula that is express the equality of two expressions ,by the connecting them with the equal sign .
The process of equting one thing with another is called the equation of science with objective .
The equation is representing direct proportion is, by the connecting them with in the equal sign.
y = kx ← k is the constant of proportion
Here k = 2.5 , thus
y = 2.5x ← equation of proportion.
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On a 60-mile road there are 7 rest stops placed at.
equal intervals, including one at each end of the
road, as shown above. What is the distance, in feet,
between two consecutive rest stops?
(Note: 1 mile = 5,280 feet)
A) 31,680
B) 36,960
C) 45,257
D) 52,800
Answer:
C. 45,257
Step-by-step explanation:
5280 * 60 = 316,800
316,800 ÷ 7 = 45,257
The distance between two consecutive rest stops is 45257 feet.
What is division?Division is the process of dividing a number by a given number.
Given that, the 60-mile road is divided into 7 equal parts.
The length of each part is:
60/7 mile
Given that;
1 mile = 5280 feet
Therefore;
60/7 mile = (60/7)5280 feet
60/7 mile ≈ 45257 feet
Hence, the distance between two consecutive rest stops is 45257 feet.
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there are 10 students in the class. two th them should be selected as the best students in the class. how many different ways can be done
There are 45 different ways in which two of them can be selected as the best students in the class.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations).
A k-combination of a set S is officially defined as a subset of S's k unique elements.
Total number of students = 10
Number of students to be selected = 2
No. of ways = 10C2
= (10*9)/2
= 5*9
= 45
Hence, there are 45 different ways in which two of them can be selected as the best students in the class.
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The ale price of a wimming pool after a 18. 5% dicount i 1206. 20. Find the original lit price of the pool
The swimming pool was on sale for $1206.2, which is 18.5% less than its initial $1429.35 cost.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
Here,
Sale price after discount=$1206.2
Discount percent=18.5%
Original price=1206.2+18.5%*1206.2
=$1429.35
The original price of the swimming pool was $1429.35 as It was at sale price of $1206.2 with the discount of 18.5%.
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Let point A be (2,7) and point B be (-6,-3). What point is on the segment connecting A and B such that the distance from the point to B is 4 times the distance from the point to A?
Answer:
The point on the segment connecting A and B that is 4 times as far from B as it is from A is (-8, 8).
Answer:
or the distance to be 4 times the distance from B as A the segment must be divided into (4+1) = 5 segments
so we want the point that is 1/5 of the way from A to B
x from A to B is 2 to - 6 = -8 units 1/5 * -8 + 2 = 0.4
y from A to B is 7 to -3 = -10 units 1/5 * -10 + 7 = 5
PLEASE AWNSER ASAP!!
The Double box plot shows the number of car shows attended by two car clubs each year.
What is the Mean of The Cruisers?
A. 9
B. 10
C. 11
D. Unable to determine given the Data
9 is the mean of clusters
What are equivalent equations?
Equivalent equations are algebraic equations that are having identical roots or solutions. By adding or subtracting the same number or expression to both side of an equation we get an equivalent equation. Also by multiplying or dividing both sides of an equation by the same non zero number we get equivalent equation.
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A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles. How many blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4?.
32 more blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4
A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles.
we need to find the numbar of blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4
Let the number of blue marbles added be n,
required probability P = 3/4
Total marbles = 10 + 7 + 3
= 20
Number of blue marbles=7
Using definition of probability,
(7 + n)/(20+n) = 3/4
4(7+n)=3(20+n)
28+4n=60+3n
n = 32
Therefore, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.
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Evaluate x³-2xy² + y³ when x= -2 and y=3
Answer:
5
Step-by-step explanation:
[tex] {x}^{3} - {2xy}^{2} + {y}^{3} \\ {( - 2)}^{3} - 2( - 2)(3) {}^{2} + {3}^{3} \\ - 8 + 4 - 18 + 27 \\ 31 - 26 = 5[/tex]
Answer:
55
Step-by-step explanation:
1. Substitute in the values
-2^3 - ( 2 * -2 * 3^2 ) + 3^3
2. Simplify the powers
-8 - ( 2 * -2 * 9 ) + 27
3. Solve the brackets
-8 - ( -4 * 9 ) + 27
-8 - ( -36 ) + 27
-8 + 36 + 27
4. Solve
-8 + 63
55
Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. Find r (in mph).
His original speed was r =mph.
Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. The value of r is 16.
What is speed ?
The speed at which an object's position changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it only has a direction and no magnitude, speed is a scalar quantity.
144/r= t
144/(r-4)-144/r = 3
LCM r(r-4)
144r-144(r-4)/r(r-4)=3
Simplify [tex]$\frac{144 r-144(r-4)}{r(r-4)}: \frac{576}{r(r-4)}$[/tex]
[tex]\frac{576}{r(r-4)}=3[/tex]
Multiply both sides by r(r-4)
[tex]\frac{576}{r(r-4)} r(r-4)=3 r(r-4)[/tex]
Simplify
576=3 r(r-4)
Solve [tex]$576=3 r(r-4): \quad r=16, r=-12$[/tex]
r=16, r=-12
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PLS HELP EASY EASY EASY
Answer:
x = 30 degrees
Step-by-step explanation:
By Parts-Whole Postulate, x + 100 = 130, meaning that x = 30 degrees.
Answer: 30
Step-by-step explanation: 130-100=30
I need help with my homework
Answer:
60
Step-by-step explanation1
135 = 2x+15 => corresponding angles
2x= 135-15
2x= 120
x= 60