The probability she makes at least 65 is 0.0139.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
[tex]\begin{aligned}P(x \geq 65) & =1-P(x < 65) \\& =1-P\left(\frac{x-\mu}{n} < \frac{65-56}{4.0988}\right) \\& =1-P(z < 2.1958) \\& =1-0.9861 \\& =0.0139\end{aligned}[/tex]
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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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Linear quadratic systems
The solution of the given system of equations is (-1, 2).
What is system of equations?
A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.
Consider, the given system of equations.
x^2 - x + 3y - 8 = 0 ..(1)
x - y + 3 = 0 ..(2)
From equation (2),
x = y - 3 ..(3)
Plug the value of x in equation (1).
⇒ (y - 3)^2 - (y - 3) + 3y - 8 = 0
y^2 - 6y + 9 - y + 3 +3y - 8 = 0
y^2 - 4y + 4 = 0
y^2 - 2y - 2y + 4 = 0
y(y - 2) - 2(y - 2) = 0
(y - 2)(y - 2) = 0
(y - 2)^2 = 0
y = 2
Now plug y = 2 in equation (3)
x = 2 - 3
x = -1
hence, the solution of the given system of equations is (-1, 2).
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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?
What is the product of 7x -4 and 8x +8
Answer:
56x-32
Step-by-step explanation:
7x-4 Times 8x+8
7xtimes8x
56x-4times8
56x-32
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
If you can, please give me a Brainliest, I only need 1 more to become an Ace, thank you!
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
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:
Can you please help me find why these are perpendicular
Answer: It is perpendicular because it makes a 90-degree angles
Step-by-step explanation: A perpendicular is when it makes a 90-degree angle or has the same length!
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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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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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:
On a math fact tet Paul got 1/8 of the quetion incorrect in percent and fraction form how many quetion did Paul get wrong
Fraction form 12.5% question did Paul get wrong .
What do math fractions mean?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided.
Both are integers in a simple fraction. In the numerator or denominator of a complex fraction is a fraction. A proper fraction has a numerator that is lower than its denominator.
Fraction of incorrect question = 1/8
Present of incorrect question
Computation:
Present of incorrect question = (Fraction of incorrect question)(100)
Present of incorrect question = (1/8)(100)
Present of incorrect question = 12.5%
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a boat leave a dock and sails 8 km north and then 13 km east how far is the boat from the dock
There were 234 roses growing in the back garden. If 50% of the roses were red. How many were not red?
Answer:
C)117
Step-by-step explanation:
50%=1/2
If you want to figure out how much is left of a half all you do is have to divide the total number of whatever it is, in this case, its roses, by 2.
So now that we know that, let's get started.
234/2=117
Which we know is correct because it's one of your answer choices.
So 117 roses are not red. The other half was.
I hope this helps!!!
A knife cot 3 time the cot of a poon. 9 poon and 12knive cot 82. 80
How much doe one knife cot
One knief costs 5.52 dollars
Let the cost of knief be x dollars and the cost of spoon be y dollars.
A knife costs 3 times the cost of a spoon.
So, we get an equation,
x = 3y ..............(1)
9 spoons and 12 knives cost $82.80
So, we get an equation,
12x + 9y = 82.80 .........(2)
Substitute above value of x in equation (2),
12(3y) + 9y = 82.80
45y = 82.8
y = 1.84
Subatitute above value of y in equation (1),
x = 5.52
Therefore, the cost of knief is 5.52 dollars
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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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HELP ASAP PLS!!!
Zachary purchased a computer for $1,400 on a payment plan. Two months after he purchased the computer his balance was $1,100. Four months after he purchased the computer, his balance was $800. What is an equation that models the balance y after x months?
The equation
models the balance y after x months:
Answer:
Zachary pays $150 per month for his computer
Step-by-step explanation:
after 2 months:
2x + 1100y = 1400..... equation 1
after 4 months:
4x + 800y = 1400...... equation 2
we can either multiply equation 1 by 2 or we can divide equation 2 by 2, the purpose is simply to get the x values equal so it can be eliminated from the equation.
dividing equation 2 by 2:
2x + 400y = 700 ...... equation 3
Now equation 1 minus equation 3:
0x + 700y = 700
700y = 700
y = 700/700
y = 1
substituting y=1 into equation 3
2x + 400(1) = 700
2x = 700 - 400
2x = 300
x = 300/2
x= 150
Therefore it is concluded that Zachary has a payment plan where he pays $150 each month for the computer
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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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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if
[tex]a \sqrt{2 } + b \sqrt{5 } = 3(2 \sqrt{2} - 3 \sqrt{ {5} } ) \: find \: the \: value \: of \: a[/tex]
please tell the
answer
Answer:
see attached
Step-by-step explanation:
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).
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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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 inequality does not belong with the other three? Explain your reasoning
The inequality does not belong with the other three is - 1 ≤ x/1.25.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given,
1. 4x ≥ 12 ⇒ x ≥ 3.
2. - 1 ≤ x/5 ⇒ - 5 ≤ x.
3. 12 > x/1.25 ⇒ x < 15.
4. 2.5x > - 6.4 ⇒ x > - 2.56.
x ≥ 3 and x < 15 is, 3 ≤ x < 15.
- 5 ≤ x and x > - 2.56 here one common region is x > - 2.56 so - 5 ≤ x does not fit.
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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
What is the equation of a line that is perpendicular to y-3x-2 and passes
through the point (6, 8)?
A. y=-x+10
OB. y--x+8
OC. y-x+6
OD. --x+4
The perpendicular equation is y = -1/3x + 10 Option A
How to find perpendicular of an equation?You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 3 we flip it and make it a negative and the new slope is -1/3.
Now we can use that and the point to get the y intercept using slope intercept form.
y = mx + c
m = gradient of the line
c = y -intercept
8 = (-1/3)(6) + c
8 = -2 + c
10 = c
And now we can use our new slope and new intercept to model the equation. y = -1/3x + 10
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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:
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
Can anyone help solve for x
Answer:
X = 33.19
Step-by-step explanation:
You're welcome.
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