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).
If 2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0, find lim x→2 f(x).
The value of [tex]\lim _{x \rightarrow 2}[/tex] f(x) by Sandwich theorem is 2.
As per the given data the function limits are:
2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0
Here we have to determine the value of [tex]\lim _{x \rightarrow 2}[/tex] f(x)
Hence by Sandwich theorem:
The sandwich theorem, also known as the squeeze theorem, asserts that if two functions, g (x) and h (x), are squeezed between one another and their respective limits at a given position are both equal to L, then the limit of f (x) at that point is also equal to L.
We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" [tex]\frac{sin(x)}{x}[/tex] between two nicer functions and using them to find the limit at x = 0.
[tex]& \lim_{x \rightarrow 2}(2 x-2) \leq\lim_{x \rightarrow 2} f(x) \leq \lim_{x \rightarrow 2}\left(x^2-2 x+2\right) \\[/tex]
[tex]& \Rightarrow 2 \leq \lim _{x \rightarrow 2} f(x) \leq 2 \\[/tex]
Hence [tex]\lim _{x \rightarrow 2}[/tex] f(x) = 2
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i think its one but im not sure
Answer: Commutative property.
Step-by-step explanation: Basically, the commutative property can be expressed as a + b = b + a, which matches this scenario pretty well. You are correct.
Let me know if this is right! :)
Is parallel processing always faster?
Only when each iteration is sufficiently time-consuming in terms of CPU usage does parallel programming become more effective.
Parallel processing: What is it?The term "parallel processing" is used to deliver simultaneous data-processing activities, which is utilized to increase the computing performance of computer systems. Additionally, a parallel processing system has the ability to process input concurrently for quicker execution times.
As an illustration, when an instruction is being carried out in an ALU, the following instruction may be read from memory. The system may be equipped with two or more ALUs and be able to carry out multiple instructions at once.
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When working modulo m, the notation a^-1 is used to denote the residue b for whichab = 1 (mod m), if any exists. For how many integers a satisfying 0 < a < 100 is it true thata(a − 1)−¹ = 4a-¹ (mod 20)?Please hurry up guys!!
There are 10 integers that satisfy 0 < a < 100.
What are integers?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
Here, we have
Given: When working modulo m, the notation a⁻¹ is used to denote the residue b for which ab = 1 (mod m), if any exists.
We have to find integers that satisfy 0 < a < 100.
a(a − 1)⁻¹ ≡ 4a⁻¹ (mod 20)
a ≡ 4a⁻¹(a − 1)(mod 20)
a² ≡ 4(a-1)(mod 20)
a² - 4a + 4 ≡ 0(mod 20)
(a - 2)² ≡ 0(mod 20)
a = 2 + 10n | for n = (0, 1, 2, 3.....9)
Hence, there are 10 integers that satisfy 0 < a < 100.
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In how many ways can Harold, Steve, John, Roslyn, Marian and Connie line up so that no two of Harold, Steve and John are next to each other ?
There are four general arrangents of boy/girl to consider:
BGBGBG, GBGBGB, BGGBGB, and BGBGGB.
For any one of these four basic arrangements, the boys can be
rearranged (permuted) among themselves in 3 × 2 × 1 = 6 different
ways. Similarly, the three girls can be rearranged among
themselves in 6 ways. Since the boys and girls can be rearranged
independently, the number of ways to create any one of the four
basic arrangements is 6 × 6 = 36.
So the total number of ways that 3 boys and 3 girls can line up so
that no two of the three boys are next to each other is
4 × 36 = 144 .
The total number of ways that 3 boys and 3 girls can line up so that no two of the three boys are next to each other is found to be as 144 .
It is given that there are four general arrangements of boys and girls,
Here, the boys can be arranged or rearranged (permuted) among themselves in a total of , 3 × 2 × 1 = 6 different ways.
Similarly, the three girls can be rearranged among
themselves in 6 ways.
We are given that both the groups can arrange themselves independently .
Therefore, the number of ways to create any one of the four basic arrangements is 6 × 6 = 36.
Therefore, the number of ways to arrange them is ,
4 × 36 = 144 .
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B is the circumcenter of △ADG. find AE and DG
When B is the circumcenter of triangle ADG the lengths of AE and DG are 4 and 12 respectively
What is circumcenter in a triangle?The intersection of the perpendicular bisectors of a triangle's sides is known as the circumcenter of that particular triangle.
In other terms, the circumcenter is the point at which the bisector of a triangle's sides coincides.
The perpendicular lines radiating from the sides of the triangle are the bisectors hence the line it radiates from shares the is shared into two halves at that point
Having this in mind
AE = DE = 4
and
DF = GF = 6
Also, DF + GF = DG
DG = DF + DF
DG = 6 + 6
DG = 12
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write the frraction 7/14 in simplest form
Answer:
To find the simplest form is to find a number than can evenly go into both numbers. 7/14=1/2. 1/2 as you can divide 7 into 7 one time and 7 into 14 twice. A half (1/2). Because 7 is the half of 14, so the simplest form is 1/2. At first look you think it's already in its simplest form, but
explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{7}{14}}\\\\\\\mathsf{= \dfrac{7\div7}{14\div7}}\\\\\\\mathsf{= \dfrac{1}{2}}\\\\\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{\dfrac{1}{2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
I need help with this please
Answer in explanation:
*change the problem to [tex]\frac{5}{6}[/tex] x [tex]\frac{3}{1}[/tex]
(change 3 into a fraction by putting 1 in the place of a denominator)
next cross multiply
5 x /1
/2 1
3 can go into 6- 1 time
since anything multiplied by 1 is 1, the answer is [tex]\frac{5}{2}[/tex]
Hope this helps ya!
*(disclaimer lol: alternatively, you could cross multiply without changing 3 to a fraction and get the same answer-- however, I wanted to explain as clearly as possible, and figured it was less confusing this way!)
How would I do this?
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{28p^5-8p^4 + 40p^2}{4p^3}\implies \cfrac{28p^5}{4p^3}-\cfrac{8p^4 }{4p^3}+\cfrac{ 40p^2}{4p^3}\implies 7p^5 p^{-3}-2p^4 p^{-3}+10p^2p^{-3} \\\\\\ 7p^{5-3}-2p^{4-3}+10p^{2-3}\implies 7p^2-2p+10p^{-1}\implies 7p^2-2p+\cfrac{10}{p}[/tex]
Four thousand two hundred carnations were reserved for use on thge float. If this was 7/10 of the flowers needed, how many glowers would be on the float
The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.
How to count a set of objects using fractions?Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.
For example:
1/4 (one-fourth)2/5 (two-fifth)It means one of four parts and two of five parts.
We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!
The carnations of a set of flowers is 7/10. It is 4200 carnations.
The carnations part is 7 and the whole part of flowers is 10.
Using fraction, the whole flowers would be
= 10/7 × 4200
= 6.000 flowers
Hence, the number of flowers needed to be on the float is 6.000 flowers.
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Pls help me do this i need hwlp if any one can figure if out
Considering that the quadrilateral EFGH is similar to quadrilateral IJKL the side LI is calculated to be
30.6How to find the side LIThe side LI is calculated using the concept of similar polygons. This concept allows for the sides to be proportionally equal to each other.
This implies that the factor used for any side will produce same result
let the factor be r and using side HG and JK to solve for the factor r
HG * r = JK
where
HG = 16
JK = 51
substituting the values and solving for r
HG * r = JK
16 * r = 51
r = 51/16
and HE * r = LI
where HE = 9.6
LI = 9.6 * 51/16
LI = 30.6
hence side LI = 30.6
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The rectangular floor of a classroom is 30 feet in length and 36 feet in width. A scale drawing of the floor has a length of 5 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRYYYYYYYYYYYYYY
Answer:
30 in.²
Step-by-step explanation:
Real:
length 30 ft
width 36 ft
Scale:
length 5 in.
width ?
30/36 = 5/x
30x = 5 × 36
x = 6
The scale width is 6 inches.
Scale area:
area = length × width
area = 5 in. × 6 in.
area = 30 in.²
The area, of the floor in the scale drawing is 30 in.²
What is the unitary method?The area is the total amount of space that an object's shape or a flat (2-D) surface occupies.
Given that rectangular floor of a classroom is 30 feet in length and 36 feet in width. A scale drawing of the floor has a length of 5 inches.
length 30 ft
width 36 ft
Scale: length 5 in.
Then we have
30/36 = 5/x
30x = 5 × 36
x = 6
The scale width is 6 inches.
Scale area:
The area = length × width
area = 5 in. × 6 in.
area = 30 in.²
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22. The table shows the number of students
going on a field trip. One chaperone is
needed for every 12 students.
Fifth grade students 310
Sixth grade students 305
Seventh grade students 225
Write two equations with variables that you can use to find a number of chaperones needed
How many chaperones are needed?
Answer:
Step-by-step explanation: i'd say jus divide
What is the range of f?
A. -3<_f(x)<_7
B. The f(x)-values -3,3,6, and 7
C. -6<_f(x)<_6
D. The f(x)-values -6,-4,-3, and 6
The range of f is C.
What is range?
Range is the difference between the highest and lowest values in a set of data. It is a measure of variability, providing an indication of how widely values in the data set are dispersed from one another. In statistics, range is an important tool that helps to describe and summarize data. Range is also used to measure the dispersion of data within a data set, including the degree of spread or variability in the data.
-6<_f(x)<_6. This means that the f(x)-values range from -6 to 6, including -4 and -3. The range of f does not include -3, 3, 6, and 7, which are not within the range of -6 to 6.
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A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $26. Option B is a commission rate of 5% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
The total amount of sales he must make should be of $20800.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $26. Option B is a commission rate of 5% on weekly sales
Assume that the amount of sales he needs to make is of ${x}. So, for same amount, we can write -
(26 x 40) = 5% of {x}
(26 x 40) = (5/100) x {x}
{x} = (26 x 40 x 100)/5
{x} = (26 x 40 x 20)
{x} = 26 x 800
{x} = 20800
Therefore, the total amount of sales he must make should be of $20800.
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if crystals room measures 10.5 ft long and 7 feet wide and 9 feet tall how much paint will be needed to paint her bedroom
Answer:
She needs 18,731.6 Litres of paint to paint her bedroom.
Step-by-step explanation:
Given;Length (l) = 10.5 ftWidth (w) = 7 feetHeight (h) = 9 feetTo Find;How much paint will be needed to paint her bedroom.Formula;V = l × w × hSo,
V = l × w × h
V = 10.5 × 7 × 9 feet
V = 661.5 cubic feet
We know that,
1 cubic foot = 28.317 litresSo,
661.5 × 28.317 = 18,731.6 Litres
Thus, She needs 18,731.6 Litres of paint to paint her bedroom.
How many times would you expect to roll a 5 if you rolled a fair die 1,300 times? Round your answer, if needed.
A.
0.1667
B.
1,083
C.
217
D.
95
Answer: C, 217
Step-by-step explanation:
(Find the value of): 2m x 2-m
49x+ 0.10= 117.90
I need help please
Subtract 0.1 from both sides49x+ 0.10= 117.90
49x+0.1-0.1=117.9-0.1
x=2.404
What is meant by variables?A quantity that may assume any one of a set of values. : a symbol representing a variable. : something that is variable. : a factor in a scientific experiment that may be subject to change.A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables49 x+0.1=117.9Move 0.1 to the right side49 x=117.8Divide both sides by 4949 x/49=117.8/49Simplifyx=2.40408To learn more about variables refers to:
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How do you find the slope of x =- 4?
The slope of x= -4 is unidentified.
The x= -4 is a vertical line and slope cannot be found.
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; the reason for this usage is unclear, although it may be found in O'Brien's (1844)[2] and Todhunter's (1888][3] formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope.
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What will be the minimum value of the expression 3x² 6x 6?
The minimum value of the expression 3x² + 6x + 6 is 3.
Therefore the answer is 3.
A quadratic mathematical expression contains a variable of highest degree of 2 and it is of the general form ax² + bx + c, where a, b and c are constants.
Minimum value of a quadratic equation of form ax² + bx + c is when
x = -b/ 2a
Then minimum value is
a( -b/ 2a )² + b( -b/ 2a ) + c
= (b²a + -2ab² + 4a²c)/ 4a²
= ( - b² + 4ac)/ 4a
= c - b²/4a
In the expression 3x² + 6x + 6, a = 3, b =6 and c = 6. So minimum value is
= 6 - 6²/ (4×3)
= 3
--The question is incomplete, answering to the question below--
"What will be the minimum value of the expression 3x² + 6x + 6?"
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James is building a doll house that is proportional to his own house. He is using a scale of 0. 5inch = 1foot. If the doll house is 12. 3inches tall, how tall is his house. ?
James's house is 24.6 feet tall because he is using a scale of 0.5 inch per 1 foot. To get this measurement, he multiplied 12.3 inches (the height of the doll house) by 2.
1. Take the height of the doll house (12.3 inches).
2. Multiply 12.3 inches by 2.
3. The result is 24.6 feet which is the height of James's house.
James is building a doll house that is proportional to his own house. He is using a scale of
0.5 inch = 1 foot,
which means that for every 0.5 inch in the doll house, 1 foot is represented in his house. To calculate how tall his house is, we need to figure out how many inches the doll house is. The doll house is 12.3 inches tall. To get the height of James's house, we need to multiply this by 2. Thus, 12.3 inches multiplied by 2 equals 24.6 feet, which is the height of James's house. This is because for every 0.5 inch in the doll house, 1 foot is represented in his house. Therefore, with the scale of 0.5 inch = 1 foot, the height of James's house is 24.6 feet.
1. Determine the scale of the doll house (0.5 inch = 1 foot).
2. Measure the height of the doll house (12.3 inches).
3. Multiply 12.3 inches by 2.
4. The result is 24.6 feet which is the height of James's house.
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Chose the best 3 options
The beat three options are: The slope of the line is 1/5, (2) The possible equation if the line is y=1/5x, (3) The slope and the y intercept are the same
What is slope of a line?Lope is the rate of change of y with respect to x. slope is also the increase in y over increase in x vice versa
Slope is denoted by rise/run
The Possible solutions from the graph are:
The slope and y-intercept are the sameThe possible equation of the line is y=1/5xThe slope of the line is 1/5Taking any two points on the graph : (4, 1) and -4, -1,)
We can find the slope as (1--1)/4--4
Therefore, the Slope = 2/3≡1/5
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How do you add a function in FG?
To add a function in FG, open the functions. php file in your theme folder, add the code for the function at the bottom of the file, save the file, and add the code for the function in the template files where you want it to appear.
To add a function in FG, you first need to open the functions. php file in your theme folder. This is where all the functions for your theme will be stored. Once you have the file open, you can add the code for the function that you want to create. This code should go at the bottom of the file. After you have added the code, save the file. Now, you need to add the code for the function in the template files where you want it to appear. To do this, add the following code: <?php your_function_name(); ?>. This code will call the function that you created in the functions.php file. Once you have added this code, save the file and the function should now appear in your theme.
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Peggy completed 5/6 of the math homework and Al completed 4/5 of the homework. Did Peggy or Al complete more hoof the math homework?
Peggy completed more of the math homework than Al
What does division of fractions mean?
A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.
we know that
In order to be able to compare fractions more easily it is recommended that both have the same denominator
Peggy
5/6 x 5 = 25/30
Al
4/5 x 6 = 24/30
Peggy completed more of the math homework
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A geologist visits 60 volcanoes in Alaska and California. What if 40% of the volcanoes were in California? How many volcanoes would the geologist have visited in California and how many in Alaska?
Answer : in California there are 24 volcanoes while in Alaska there are 36 volcanoes.
Step-by-step explanation:
Total number of volcanoes = 60.
40% of the volcanoes where in California.
i.e 100% - 40% = 60%.
60% of the volcanoes were in Alaska.
In California = 40/100 × 60 = 24 volcanoes.
In Alaska = 60/100 × 60 = 36 volcanoes.
Totally T's is a company that makes t-shirts. Workers go on strike and the factory is closed. What will happen to the supply of t-shirts?
Answer the 3 questions below related to this scenario.
Complete sentences are not required. Please number each answer.
1. Will there be an increase or decrease?
2. Which way will the graph shift?
3. What is the determinant?
A car uses 1 liter of gas every 12 kilometers. How many meters can the car travel on 3 liters of gas
Answer: 360,000
Step-by-step explanation: First you would convert 12 kilometers to meters, which is 120,000. Then multiply that by 3. You get 360,000 meters. Therefore, the car can travel 360,000 meters on liters of gas.
Thomas wants to buy a new baseball bat. The one he likes costs $130, but it is on sale for $104. What is the percent of the discount Tomas will get if he buys the bat
On solving the provided question we can say that the percentage discount will be equal to 20%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
Tomas wants to buy a new baseball bat. T
he one he likes costs $130, but it is on sale for $104.
The discount percentage will be calculated as:-
( $130 - $104) = $26
( 26 / 130) x 100 = ( 2600 / 130 ) = 20%
the discount will be equal to 20%.
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What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Consequently, it follows that the greatest possible quotient as required is; 25.
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