The probability that X is greater than 53
What is probability ?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Formula for calculating the standard score or z score:
z = x-μ/σ, where:
z is the standard score
x is the raw score
μ is the population mean
σ is the population standard deviation
In this question: μ = 61 and σ = 8
The score is greater than 53
Let’s calculate the z score, for x = 53 and then find the probability for x greater than 53
z = (53 - 61)/8
= -8 / 8
= -1
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A new video game has been released. The table shows the proportional relationship between the number of levels completed and the time it should take to complete them.
Number of Levels 2 7
Time (hours) ? 3.5
How many minutes should it take to complete 2 levels?
60 minutes
120 minutes
180 minutes
210 minutes
The number of minutes it takes to complete 2 levels is (a) 60 minutes
How many minutes should it take to complete 2 levels?From the question, we have the following parameters that can be used in our computation:
Number of Levels 2 7
Time (hours) ? 3.5
This table can be represented as follows:
Ratio = Level : Time
So, we have the following representation
Level : Time = 7 : 3.5
At level 2, we have
2 : Time = 7 : 3.5
Express as fraction
Time/2 = 3.5/7
So, we have
Time = 2 * 3.5/7
Evaluate
Time = 1
Express as minutes
Time = 60 minutes
Hence. the time is 60 minutes
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if m, p, and t are distinct positive prime numbers, then m3pt has how many different positive divisors greater than 1 ?
There are 15 different positive divisors (greater than 1) for the number m³pt. Here m, p, and t are distinct prime numbers. This is obtained by the prime factorization method.
How to find the number of positive factors for a number?The following are the steps to find the number of positive factors of a number:
Step 1: Find the L.C.M of the number by using the prime factorization method. For example: consider the number 24. Then, its prime factorization is as follows:
24 = 2 × 2 × 2 × 3
Step 2: Same bases should be added in powers. So, the factors we can write as
24 = 2³ × 3¹
Step 3: To find the number of positive factors of the number, the exponents of the prime factors is multiplied by adding 1.
I,e., N = (3 + 1)(1 + 1) = 4 × 2 = 8.
So, there are 8 factors for the number 32. They are 1, 2, 3, 4, 6, 8, 12, and 24.
Calculation:It is given that, m, p, and t are distinct positive prime numbers.
Then, the number of positive divisors greater than 1 for the number m³pt are
m³× p × t
Since m, p, and t are prime factors, we can multiply their power by adding 1 to them. I.e.,
N = (3 + 1) (1 + 1) (1 + 1) = 4 × 2 × 2 = 16
So, there are a total of 16 factors for the given number (including 1). So, the number of factors greater than 1 is 16 - 1 = 15.
Therefore, there are 15 different positive divisors greater than 1 for the number having prime factors as m³pt.
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I dont know which comes first
Answer:
Step-by-step explanation:
Distribute 3
Subtract 3x
Divide 9
-4/3 = x
Check
write an equation of a line perpendicular to the given equation using the given point given (8,2): x = -4
The equation of line passes through the point (8, 2) will be;
⇒ y = 1/4x
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (8, 2).
And, The slope of perpendicular line is,
⇒ m = - 4
Now,
Since, The equation of line passes through the point (8, 2).
So, We need to find the slope of the line.
Since, The product of slope of the perpendicular line is - 1.
Hence, Slope of the line is,
m = - 1/- 4
m = 1/4
Thus, The equation of line with slope 1/4 is,
⇒ y - 2 = 1/4 (x - 8)
⇒ y - 2 = 1/4 (x - 8)
⇒ y - 2 = 1/4x - 2
⇒ y = 1/4x
Therefore, The equation of line passes through the point (8, 2) will be;
⇒ y = 1/4x
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Given m || n, find the value of x and y.
X =
(7x+18)º
y =
Do
(9x-14)°
m
Answer:
x = 16y = 130Step-by-step explanation:
You want the values of x and y when corresponding angles at parallel lines are marked (9x -14)° and (7x +18)°, and a vertical angle to those is marked y°.
Corresponding anglesCorresponding angles where a transversal crosses parallel lines are congruent:
(9x -14)° = (7x +18)°
2x = 32 . . . . . . . . . . divide by °, add 14-7x
x = 16
Then these angles are ...
(9(16) -14)° = (144 -14)° = 130°
Vertical anglesVertical angles are congruent, so ...
y° = 130°
y = 130
2(log 2x − log y) − (log 3 + 2 log 5)
Answer:
.................=/
Step-by-step explanation:
What is the solution to p + 4 = -9 + p?
Answer: No solution
Step-by-step explanation:
First take away p from both sided and then you get 4 = -9 but you can't really do anything else
Deanna and lulu are playing games at the arcade. Deanna starts with $15, and the machine she is playing costs $0. 75 per game. Lulu starts with $13, and her machine costs $0. 50 per game. Choose the correct expressions to write an equation that could be used to find after how many games the two friends will have the same amount of money remaining. Let g represent the number of games.
After 8 number of games both has equal amount of money.
Deana starts with $15 and the machine she is playing costs $0.75 per game
lulu starts with $13 and the machine she is playing costs $0.50 per game
Let us after x number of games both has same money
Deana spends 0.75*x amount of money after playing x number of games.
Deana has remaining amount of money 15 - 0.75*x.
lulu spends 0.50*x amount of money after playing x number of games.
lulu has remaining amount of money 13 - 0.50*x.
We have assumes that after x number of games both has same amount of money.
[tex]15-0.75*x = 13 - 0.50*x[/tex] --- this is the correct expression to write an equation that could be used to find after how many games the two friends will have the same amount of money.
15 - 13 = 0.75*x - 0.50*x
2 = 0.25*x
x = 2/0.25
x = 8.
So After 8 number of games both has equal amount of money.
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8) Which ratio would be equivalent to 1/9 ? *
OA) 3/18
OB) 2/27
OC) 3/27
D) 3/10
Answer: c) 3/27
Step-by-step explanation:
To make equivalent fractions, we multiply the numerator and denominator with the same number so that on cancelling we get the original fraction...
Therefore, 1/9=
1 x 3 / 9 x 3 = 3/27
Which can also be written as 3:27
So, the answer is c) 3/27
Michael typed 430 minutes in 5 minutes. If she continues at this rate, how many words could Michael type in 12 minutes?
When Michael continues at this rate, the words Michael type in 12 minutes will be 1032.
How to calculate the rate?It is important to note that a rate demonstrates how many times one number can fit into another number. Rates contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Here, Michael typed 430 words in 5 minutes. The words ler minutes will be:
= 430 / 5
= 86
If he continues at this rate, thr words Michael type in 12 minutes will be:
= 86 × 12
= 1032 words.
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Complete question
Michael typed 430 words in 5 minutes. If she continues at this rate, how many words could Michael type in 12 minutes?
Hurricanes are large storms that form over warm waters out in the ocean. hurricanes are associated with low-pressure regions in the atmosphere. how does the low pressure associated with a hurricane help them to grow big and powerful?
A hurricane is a big rotating storm system that develops over warm ocean waters and usually travels westward toward the American mainland.
An Atlantic Ocean hurricane or a northern Pacific Ocean hurricane is a tropical storm. In most years, hurricanes develop between June 1 and November 30. The Taino Indian word "hurakan," which means "god of wind," is where the word "hurricane" originates.
A hurricane is a big rotating storm system that develops over warm ocean waters and usually travels westward toward the American mainland. Depending on the maximum sustained wind speeds, hurricanes are either classed as tropical storms or hurricanes. Hurricanes have winds of 74 mph or more, whereas tropical storms have winds of 39 to 73 mph.
The hurricane's eye, which is a calm, clear region encircled by powerful winds, is the most hazardous component of the storm. The hurricane's eye, which can be up to 30 miles across, frequently experiences the storm's greatest rains and highest winds.
A hurricane's landfall can result in flooding from storm surges, strong winds, and heavy rains. The increase in sea level that happens as a cyclone nears land is known as a storm surge. Along with coastal locations, this increase in water level has the potential to inflict significant harm and flooding.
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The equation c = 6.99p represents the proportional relationship between the total cost (c) and the number of pounds (p) of shrimp at a grocery store.
Which description is true, based on the equation of the proportional relationship?
For $1, you can buy 6.99 pounds of shrimp.
For $6.99, you can buy 6.99 pounds of shrimp.
For $6.99, you can buy 1 pound of shrimp.
For $0.01, you can buy 1 pound of shrimp.
For $6.99, you can buy 1 pound of shrimp, therefore, the third option is correct
What is a Ratio?A ratio indicates the number of times one number contains another.
The given equation is c = 6.99p, where c is the cost and p is the weight in pounds.
c = 6.99p
substitute p = 1:
c = 6.99
Hence, for $6.99, you can buy 1 pound of shrimp, therefore, the third option is correct.
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Con la finalidad de otorgar los materiales suficientes para un óptimo trabajo de limpieza, se hizo la siguiente pregunta al personal de intendencia, ¿qué utensilio se gasta más?. Acomoda las etiquetas de los utensilios por debajo de las barras según corresponda.
Answer:
D=Trapeador
A=Cubeta
C=Escoba
B=Recogedor
Step-by-step explanation:
chloe is 5 feet 4 inches tall.There are 2.54 centimeters in 1 inch .What is Chloes height in centimeters
Answer:
Step-by-step explanation:
When ABCD is Drawn to scale
would the lines AD and Bc be
Parallel or not?
Answer:
No they would be perpendicular
Step-by-step explanation:
Exponential functions
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = ax
Where a>0 and a is not equal to 1.
x is any real number.
If the variable is negative, the function is undefined for -1 < x < 1.
Here,
“x” is a variable
“a” is a constant, which is the base of the function.
An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.
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suppose you were hired to conduct a study to find out which of four brands of soda college students think taste better. in your study, students are given a blind taste test. you randomly divide your sample of students into one of four groups, with one fourth of the students tasting each drink. the ratings are given on a scale of 1 (awful) to 5 (delicious). which type of hypothesis test would be the best to compare these ratings?
The type of hypothesis test would be the best to compare these ratings are that it is sample test.
The Independent Samples t Test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.
The Independent Samples t Test is a parametric test. This test is also known as: Independent t Test.In independent samples (or unpaired sample), the values come from two or more different groups. For example, if the group of men and the group of women are asked about their income, independent samples exist. In this case, a person from one sample cannot be assigned to a person from the other sample
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Which transformation is modeled by the function?
The transformations of f(x) are (b) horizontally shrunk by a factor of 1/4, vertically stretched by a factor of 5 and then reflected across the x-axis
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x²
g(x) = -5(4x)²
Mathematically, these equations can be represented as
g(x) = -5f(4x)
The above equations implies that, we have the transformation to be:
The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4The -5 implies that the function f(x) is vertically stretched by a factor of 5 and then reflected across the x-axisHence, the transformed function is (b(
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a poll is conducted the day before an election for state senator. there are two candidates running. the poll shows that 53% of the voters surveyed favor the republican candidate, with a margin of error of 2.as percentage points. should the republican be confident that she'll have a victory party? why or why not?
The lower limit of the confidence interval is 51%, which is above 55%, so the Republican should expect to win.
What does confidence interval mean?
Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.
If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty. In statistics, confidence is another word for probability.
A confidence interval of proportions has two bounds, a lower bound and an upper bound.
These bounds depend on the sample proportion and the margin of error.
The lower bound is the sample proportion subtracted by the margin of error.
The upper bound is the margin of error added to the sample proportion.
In this problem, we have that:
Sample proportion 53%
Margin of error 2%
53 - 2 = 51%
53 + 2 = 55%
Hence, the lower limit of the confidence interval is 51%, which is above 55%, so the Republican should expect to win.
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9. a travel agency will plan tours for groups of 25 or larger. if the group contains exactly 25 people, the price is $300 per person. however, the price per person is reduced by $10 for each additional person above 25. you want to find what size group will produce the largest revenue for the agency. when x is the number of people added to the 25, the total revenue will be r(x)
If more than 25 people are added, the total revenue will be r(x) = $ 50, with the x = 5 size group producing the highest revenue for the agency.
what is marginal revenue ?The law of diminishing returns dictates that marginal revenue will eventually begin to decline as output level rises, even though it can remain constant above a certain threshold of output.
calculation
If a group of 25 people or more, a travel agency will organize the excursion.
The cost is $300 per person, if the group has exactly 25 participants. However, the cost per person drops by $10 for each additional person beyond the calculated maximum of 25.
R(X) = ( 25 + x ) ( 300 - 10x ) ( 300 - 10x )
evaluate in relation to x = R'(X) = 300 - 10x - 250 - 10x = 50 - 20x
We now have 30 people, which means that there are 5 more persons than 25.
Marginal revenue equals $50 when x = 5 and R'(X) = 50 - 20(5).
The revenue will drop by $50 for the following individual (31st ).
If more than 25 people are added, the total revenue will be r(x) = $ 50, with the x = 5 size group producing the highest revenue for the agency.
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What’s the square root of 9 ? Explanation
Answer:
The square root of 9 is equal to 3.
Step-by-step explanation:
Square roots are essentially x squared = y. In this case, y is 9. x squared makes x = 3 because 3 * 3 * 3 = 9
Kathryn runs from the north west corner to the southeast corner of a rugby field and Mia runs from the northeast corner to the southwest corner. Mia says she ran farther
Mia is incorrect, as they both ran the same distance, which is the hypotenuse of a right triangle of dimensions 10m and 16m.
What is the Pythagorean Theorem?The Pythagorean Theorem is a geometry axiom which states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the lengths of the sides squared.
The sides are between the angle of 90º, while the hypotenuse is the segment that connects the sides.
From the image given at the end of the answer, the distances ran from each of them are equal, which is the hypotenuse of a right triangle of dimensions 10 m and 16 m, thus the distance is obtained as follows:
d² = 10² + 16²
d = square root of (10² + 16²)
d = 18.87m.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Pedro Romar's savings account statement shows a previous balance of $895.00 and $3.50 in interest. He made a deposit of $210.00 and had a withdrawal of $20.50. What is his new balance?
а. $1,088.00
b.$1,088.50
c. $1,098.00
d. $1,098.50
Answer: A
Step-by-step explanation: To find Pedro Romar's new balance, we need to add his previous balance and the interest to the deposit, and then subtract the withdrawal. This gives us $895.00 + $3.50 + $210.00 - $20.50 = $1,088.00. Therefore, the correct answer is $1,088.00 or option (a).
Use fundamental identities to solve the equation.
csc^3 (x) - csc^2 (x) - csc (x) + 1
x = ± π/2 + 2kπ with k ∈ Z is the solution of fundamental identities
What is fundamental identities?
An equation is referred to as an identity if it has one or more variables and holds true for any replacement value of each variable that is specified on both sides of the equation.
y = cscx
y³ - y² - y + 1 = 0 has a root for y = 1
= y³ - y² - y + 1
= ( y² - 1 ) ( y - 1 )
= ( y + 1 ) ( y - 1 )²
cscx = ± 1
sinx = ± 1
or
x = ± π/2 + 2kπ with k ∈ Z
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Triangle ABC has vertices A(-4,1), B(-2,1), and C(-1,-2) on a coordinate grid. If it is rotated 180 degrees about the origin, what are the coordinates of A'B'C'?
Answer: A' (-4,-1) B' (-2,-1) C' (-1,2)
Step-by-step explanation: The reasons these are the correct answers because if you look at the rule of a rotation, it states that: The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
Write a story or situation that can be represented by the given equation.
4a + 5=12a − 11
story that represented equation, Maria, who liked cookie packages, did the arithmetic and discovered that the price of 4 cookie packages plus $5 is equivalent to the price of 12 cookie packages less $11.
What is a equation?A mathematical equation is a formula that connects two expressions with the equal sign = to express equality.
As a fan of cookie packages, Maria did the math and found that the cost of 4 packages of cookies + $5 is equal to the cost of 12 packages of cookies less $11.
[tex]'a'[/tex] represents the expense of a box of cookies,
On one side of the equation, we have the 4 packages of cookies plus $5.
[tex]4a + 5[/tex]
additionally, the 12 packages of cookies less 11 dollars on the other side of the equation.
[tex]12a - 11[/tex]
Now,
[tex]4a + 5 = 12a - 11[/tex]
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if my annual fee is $37,000 a year and i get a 5% raise every year what would be my annual salary in 14 years
Answer: $62900
Step-by-step explanation:
Find 5% of 37000 by taking 37000 timed 0.05 = $1850
Then find the total rise after 14 years by taking 1850 timed 14 = $25900
Then we add the original 37000 with 25900 = $62900
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Answer: around 62900 Dollars in 14 years
Step-by-step explanation:
find the percentage of the raise per year
1850
Multiply by 14
25900
add the starting amount of salary per year
25900+37000
73257
a boat leave a dock and sails 8 km north and then 13 km east how far is the boat from the dock
PLS HELP!!!! 100 PTS I ONLY HAVE 5 MINS!!!
The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than a certain number of inches.
Write two different expressions to represent the area of this rectangle.
Answer:
Area= 2(x-3)
Area= (x-3)2
Step-by-step explanation:
not sure if that's right but I think it is
Please help me with this question in the picture
Answer:c
Step-by-step explanation: decreasing