The probability of someone being 5 feet and 4.2 inched tall is 0.2877
Probability:
Probability means the possibility of occurring the specific even across the total number of event.
Given,
100 people where sampled and their heights were recorded, it was discovered the mean height was 5 feet and 6.3 inches with a standard deviation of 3.75 inches.
Here we need to find the the probability of someone being 5 feet and 4.2 inches tall.
From the given details, we know that,
n = 100
mean (ч) = 5 feet and 6.3 inches
standard deviation (σ) = 3.75 inches
We know that the formula to find the probability is,
P = (x - ч)/σ
But here we have used the different measurement for each. So, the first step is convert them into inches.
So,
5 feet and 6.3 inches = 60 + 6.3 inches = 66.3 inches.
Similarly 5 feet and 4.2 inches = 64.2 inches.
So, the probability is,
P (X < 64.2) = (64.2 - 66.3)/3.75
P (X < 64.2) = -0.56
Based on the standard normal table to conclude that:
P (X < 64.2) = -0.56 = 0.2877
Therefore, the probability of someone being 5 feet and 4.2 inches tall is 0.2877.
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11.) You have $49.99 to spend for a pair of jeans. The sales tax is 7%. What is the
most the jeans can cost?
A) $46.49
B) $46.72
C) $29.41
D) $45.16
Answer:
B) $46.72
Step-by-step explanation:
Let j = cost of the jeans
j * 1.07 is the cost of the jeans with tax
j * 1.07 = 49.99
Divide each side by 1.07
j * 1.07 /1.07 = 49.99 / 1.07
j =46.72
The jeans can cost no more than 46.72
Answer:
B) $46.72
Step-by-step explanation:
The problem can be expressed as an equation you solve for "y"
y + y * 0.07 = 49.99
We factor out the "y" from the equation and we get
y * (1 + 0.07) = 49.99
Which is the same as
y * 1.07 = 49.99
We can then divide by 1.07 both sides
y = 49.99 / 1.07
Which yields
y = 46.719
If rounding is allowed the answer is B, otherwise the answer is A. I'll go with the rounded one
Triangle ABC has vertices A(-4, 1), B(-1, 1), and C(-1, 3) as shown. Reflect triangle ABC twice, first across the y-axis, then across the x-axis. Graph both reflections on one coordinate plane. Then rotate triangle ABC 180° about the origin. Graph the rotation.
As per the given question;
The coordinates of the original triangle ABC with vertices is ;
A(-4, 1), B(-1, 1), and C(-1, 3)
For the first reflection along y-axis, the coordinates of y will remain same and x will reverse to positive.
Y-axis reflection: A(4, 1), B(1, 1), and C(1, 3)
Now, the triangle is again reflected along x-axis.
Thus, for the first reflection along x-axis, the coordinates of x will remain same and y will reverse to positive.
x-axis reflection: A(4, -1), B(1, -1), and C(1, -3)
Rotation: The circular motion of an item around a center is referred to as rotation.
The rotation of triangle ABC 180° about the origin.
Rule for Rotation 180° (Clockwise and Counterclockwise);
(x, y) ----- > (-x, -y)
A(4, -1) ------> A(-4, 1)
B(1, -1) ------> B(-1, 1)
C(1, -3) ------> C(-1, 3)
Rotation 180° = A(-4, 1), B(-1, 1) and C(-1, 3)
Thus, the result of the coordinates of the new triangle with vertices are found.
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Sophie has
1
2
cup of chocolate which can make
1
3
of a S’more recipe. How many cups of chocolate are needed to make one whole S’more recipe? EXTRA POINTS FOR A CORRECT ANSWER
Answer:
1 1/2 cups of chocolate
Step-by-step explanation:
Sophie has
1/2
cup of chocolate which can make
1/3
of a S’more recipe. How many cups of chocolate are needed to make one whole S’more recipe? EXTRA POINTS FOR A CORRECT ANSWER
1 1/2 cups of chocolate because 1/3 takes 3 times to get a whole so 1/2x3=
1 1/2
Find the common ratio 2,2/3,2/9,2/27,2/81
Zoe downloaded a trial game to her computer. She has at most 60 free minutes to
play the game. It takes 5 minutes to set up her character, and the instructions say
each level takes 8 minutes.
How many levels L is she estimated to complete on the free trial?
Show work or explain. Write your answer as an inequality. (here are inequality symbols you can
copy and paste < > ≤ ≥)
Answer:
6 levels
Step-by-step explanation:
60 - 5 (to set up the character)
55 total minutes
8(l) = 55
L = 55/8
L = 6.875
.˙. they can finish 6 levels
During their family vacation, marcus took 18 photos on his cell phone. the ratio of the number of photos marcus took to the number of photos his sister maribel took is 3 to 4. how many photos did maribel take?
Given,
No. of photos Marcus took on his cell phone = 18
Ratio of photos took by Marcus and Maribel = 3:4
Let the no. of photos took by Maribel be [tex]x[/tex].
∴ [tex]\frac{18}{x} = \frac{3}{4}[/tex]
⇒[tex]3x = 72[/tex]
⇒ [tex]x = \frac{72}{3} = 24[/tex]
Hence, Maribel took 24 photos.
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1. Given the sequence: {5, 7, 9, 11, ...}
Which explicit formula generates this sequence?
What’s the answer
Given that each term has a common difference, this is an arithmetic sequence as per the explicit formula that generates this sequence.
Arithmetic Sequence formula.In this instance, the next word in the sequence is obtained by adding 2 to the previous term. To put it another way, a n = a 1 + d (n – 1) This is the arithmetic sequence’s formula.
How are explicit formulas handled?Firstly, we have to find the initial phrase in a given series. Thereafter we have to find the shared difference between the following phrases in the sequence. For an explicit rule, replace the general form with the first term and common difference.
What in mathematics is an arithmetic sequence?The distance between succeeding terms in an arithmetic series is always the same.
The difference between consecutive terms in the sequence 3, 5, 7, 9…, for instance, is an example of an arithmetic sequence.
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Find the equation of the line.
Use exact numbers.
Answer:
y = (1/2)x + -3
Step-by-step explanation:
Point 1: (0, -3); Point 2: (6, 0)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 0 - (-3) 0 + 3 3 1
m = ------------- = ------------ = ---------- = -------- = --------
x₂ - x₁ 6 - 0 6 6 2
y - y₁ = m(x - x₁)
y - (-3) = (1/2)(x - 0)
y + 3 = (1/2)x
- 3 -3
----------------------------------
y = (1/2)x - 3
I hope this helps!
Answer: y=0.5x-3
Step-by-step explanation:
[tex]\displaystyle\\(0,-3)\ \ \ \ (6,0)\\ \frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=0\ \ \ \ x_2=6\ \ \ \ \ y_1=-3\ \ \ \ \ y_2=0\\\\\frac{x-0}{6-0} =\frac{y-(-3)}{0-(-3)}\\\\\frac{x}{6} =\frac{y+3}{0+3} \\\\\frac{x}{6} =\frac{y+3}{3}[/tex]
Multiply both parts of the equation by 3:
[tex]\displaystyle\\\frac{x}{2} =y+3\\\\0.5x=y+3\\\\0.5x-3=y+3-3\\\\0,5x-3=y\\\\Thus,\ y=0.5x-3[/tex]
Error Analysis - Describe the error in a sentence or two. Then, solve the problem
correctly.
13. If f(x)=2x-1, then find the x-value so that f(x) = 21.
A f(21) = 2(21)-1
B
f(21) = 42 - 1
C
f(21) = 41
The error was in line A, B, or C
The correct answer is [ans]
Answer:
The error is in line A. f(x), not x, is equal to 21.
f(x) = 2x - 1 = 21
2x = 20, so x = 10.
9. A teacher assigns 4 points for a correct
answer, -1 points for an incorrect answer,
and 0 points for leaving the question
unanswered. What is the score for a
student who had 23 correct answers, 2
incorrect answers, and 1 unanswered
questions?
Answer:
90
Step-by-step explanation:
4 x 23 = 92
2 x (-1) = -2
1 x 0 = 0
92 + (-2) + 0 = 90
Consider the function that is represented by the equation y = 3x + 2. If we had an x-value of 3, what would the corresponding y-value be?
When we have an x-value of 3 the corresponding y-value in the equation is 11.
How to compute the equation?It should be noted that an equation simply shows the relationship between the expression that's illustrated.
In this case, the function that is represented by the equation function that is represented by the equation y = 3x + 2. and we have an x-value of 3,
Therefore, the value of y will be:
y = 3x + 2.
y = 3(3) + 2
y = 9 + 2
y = 11
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A construction crew is lengthening a road. The road started with a length of 53 miles, and the crew is adding 4 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked.
Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 36 days.
Answer:
L = 4D + 53
After 36 days of work, the road will be 197 miles long.
Step-by-step explanation:
This question requests that an equation is found to represent the relationship between the length of a road and the days that the workers spend working on the road.
We are given that the road is 53 miles long prior to the work done by the construction crew. This means that this will be added in addition to what we will find.
L represents the length of the road after D days. Since the road is lengthened by 4 miles each day, this could be represented by 4 * D, or simply 4D.
Therefore, the equation we find can be written as L = 4D + 53.
Since we need to find how many miles the road will be after 36 days of work, substitute 36 days as D and solve for L:
L = 4(36) + 53
L = 144 + 53
L = 197
Therefore, the road will be 197 miles long after 36 days of construction.
Write as
a Ratio : 18:11
Answer:
This is all ready written as a ratio. You could also write it as 11:18, but other than that, your good!
Step-by-step explanation:
Hope it helps! =D
Solve the equation for y. Then find the value of y for each value of x. y + 2x = 5; x = -2, 0, 4
please help me
Answer: y=9 when x=-2
y=5 when x=0
y=-3 when x=4
Step-by-step explanation:
y+2x=5
y=5-2x
y=5-2(-2)
y=5-(-4)
y=5+4
y=9 when x=-2
y=5-2(0)
y=5 when x=0
y=5-2(4)
y=5-8
y=-3 when x=4
Write an equation for the line parallel to the given line that contains C.
8
C(-1,8); y=8/9x-7
y=
The equation for the line parallel to given line containing C:
y = 8/9x + 64 / 9
What is Parallel line ?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Given that a line's equation is,
y = 8 / 9x - 7
If we contrast this equation with a line's slope-intercept,
this line's slope = 8/9
Since every line parallel to this one will have a same slope,
The parallel line's slope is equal to
The symbol for the line with the slope 'm' and the coordinates (x', y') is
y - y' = m(x - x')
As a result, the equation of the line through (-1, 8) with a slope will be,
y - 8 = 8/9 (x-1)
y =8/9x - 8/9 - 8
y = 8/9x + 64 / 9
Hence, The equation for the line parallel to given line containing C is
y = 8/9x + 64 / 9
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Write a rule to describe the transformation.
E(-1-3), F(0,1), G(3,-2)
E'(-1.5,-4.5), F'(0,1.5), G' (4.5.-3)
Answer:
x= x1.5 y = x1.5
E' = E dilated by 1.5
Step-by-step explanation:
-1 x 1.5 =-1.5 -3 x 1.5 = -4.5 (-1.5,-4.5)
0 x 1.5 =0 1 x 1.5 = 1.5 (0,1.5)
3 x 1.5 = 4.5 -2 x 1.5 =-2 (4.5.-3)
please help. urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
From the given linear equation graph, we can tell that the equation of the line in slope intercept form is; y = 1.2x + 3
How to Interpret Linear Equation Graph?
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
From the given graph, we see that;
y - intercept = 3
x - intercept = -2.5
Now, we can find the slope by taking two coordinates;
(-2.5, 0) and (0, 3)
Slope = (3 - 0)/(0 - (-2.5))
Slope = 3/2.5
Slope = 1.2
Thus, the equation of the line is;
y = 1.2x + 3
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Multiply −14y(7y − 5).
−98y2 + 70y
−98y2 + 70
−98y2 − 5
98y2 − 70y
Answer:
[tex]-98y^2+70y[/tex]
Step-by-step explanation:
Expand the equation [tex]-14y(7y-5)[/tex], we get
[tex](-14y*7)-(-14y*5)[/tex]
Which is equal t0:o
[tex]-98y^2+70y[/tex]
The product of given monomial by binomial is -98y²+70y.
Given that, -14y(7y - 5).
What is product of polynomials?To multiply two polynomials: multiply each term in one polynomial by each term in the other polynomial. Add those answers together, and simplify if needed.
Using distributive property, multiply given monomial by binomial. That is,
-14y(7y - 5)=-14y×7y - (-14y)(5)
= -98y²+70y
Therefore, the product of given monomial by binomial is -98y²+70y.
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In the circle below, P is the center. If < APB measures 56 °, find the measure of < ACB.
Given the shown figure
since
The Central Angle Is Twice The Inscribed Angle
where
a= mACB
2a = mAPB=56
then
[tex]2a=56[/tex][tex]a=\frac{56}{2}[/tex][tex]a=28[/tex]a= mACB=28
Correct answer
option b
28
7. You bought a Gatorade and 4 bags of apples for $5.50. Write the equation that determines how much
each bag of apples was if the Gatorade cost $2.50.
Answer: (5.50-2.50)/4 = 0.75. each bag of apples is $0.75
Step-by-step explanation:
first, you subtract $5.50 by $2.50 to get $3, the cost of the 4 bags of apples altogether ($5.50 - $2.50 = $3)
then you divide $3 by 4 to get the cost of each bag of apples. (3/4 = 75)
so each bag of apples is $0.75
i hope this helps!
Using the graph as your guide, complete the following statement.The discriminant of the function is _____.
A.zero
B.positive
C.negative
The discriminant of the function will be negative.
Option C is true.
What is mean by Discriminant?
The discriminant of the function describe the roots of the function.
Which is defined as for a quadratic equation ax² + bx + c = 0;
D = b² - 4ac
Given that;
The graph of the function is shown in attached figure.
Now,
When the graph has any x - intercepts then the function has a real roots, so the discriminant must be positive.
Here, From the given graph of the function,
We have the function which have no any x - intercept, that is do not cross the x - axis at any point.
Hence, The graph of the function has no real roots.
Thus, We can say that;
The discriminant must be negative.
Therefore, The discriminant of the function is negative.
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Grand canyon tours offers air and ground scenic tours of the grand canyon. tickets for the 7-1/2 hr tour cost $169 for an adult and $129 for a child, and each tour group is limited to 19 people. on three recent fully booked tours, total receipts were $2931 for the first tour, $3011 for the second tour, and $2771 for the third tour. determine how many adults and how many children were in each tour. hint: use method of question 2 to find the number of adults and children in each tour (3 tours).
Using a system of equations, the number of people on each tour is given as follows:
First tour: 12 adults and 7 children.Second tour: 14 adults and 5 children.Third tour: 8 adults, 11 children.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the given problem.
For this problem, the variables are described as follows:
Variable x: number of adults in the tour.Variable y: number of children in the tour.All the tours were fully booked, hence the following equation is used in all cases:
x + y = 19.
Four the first tour, considering the values of the ticket and the total receipts, the following equation is built:
169x + 129y = 2931.
Using a calculator, the solution is:
x = 12, y = 7 -> 12 adults and 7 children.
For the second tour, the equation is:
169x + 129y = 3011.
Hence:
x = 14, y = 5 -> 14 adults and 5 children.
For the third tour, the equation is:
169x + 129y = 2771.
The solution is:
x = 8, y = 11 -> 8 adults, 11 children.
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line m can be represented by the equation 3x-6y=18. Write an equation of the line perpendicular to line m that passes through the point (-4,1)
Step-by-step explanation:
the perpendicular line can be represented by bx-ay+k=0 ,So the second step Is Written
since the line passes through point (-4,1) ,the value of x and y is Substitute as written in answer
Answer:
y=-2x-7
Step-by-step explanation:
3x-6y=18 also equals 3x-18=6y
divide both sides by 3 to get x-6=2y or y=x/2-3 as same line then, to find inverse switch x and y, x=(y/2)=3 and solve for y, y-6=2x, -y=2x+6 is the inverse then to make it pass thru (-4,1) change b value, y=-2x-7
which formula defines the sequence f(1)=2, f(2)=4, f(3)=8, f(4)=16, f(5)=32
please help !!
Ans: The formula that defines the sequence is Tn = 4n - 2
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Find the distance between points S(-2,4) and T(3,9). Round your answer to the nearest tenth.
Answer:
d^2=(x2-x1)^2+(y2-y1)^2
d^2=[3-(-2)]^2+(9-4)^2
d^2=(5)^2+(5)^2
d^2=25+25
d^2=50
d= [tex]\sqrt{50}[/tex]
d=7.07 units
SOLVE ASAP PLEASE!!!!
===================================
Explanation:
Recall that [tex]i = \sqrt{-1}[/tex]
Square both sides to get [tex]i^2 = -1[/tex]
So,
[tex](i\sqrt{5})^2 = i^2*(\sqrt{5})^2 = -1*5 = -5[/tex]
10 oranges and 20 grapefruits weigh 35 pounds total. 16 oranges and 10grapefruits weigh 23 pounds total. How much would 13 oranges and 15grapefruits weigh?A 28 poundsB 29 poundsC 30 poundsD 58 pounds20 Illuminate Education, Inc.
First, we will find the weight of each oranges and grape fruit
Let x be the unit weight of orange
Let y be the unit weight of grape fruit
If "10 oranges and 20 grapefruits weigh 35 pounds total"
Then this implies;
10x + 20 y = 35 -----------------(1)
And
If " 16 oranges and 10 grapefruits weigh 23 pounds total"
This implies;
16x + 10y = 23 ---------------------(2)
We can solve the two equations simultaneously.
Using elimination method;
we eliminate y and to do that, the y variables in the two equations must be same, Hence we can achieve that by multiply equation (1) by 10 and then multiply equation (2) by 20
100x + 200y = 350 ----------------------------(3)
320x + 200y = 460 ------------------------------(4)
subtract equation (3) from equation (4)
220x = 110
divide both-side of the equation by 220
x = 0.5
substitute x=0.5 into equation(1) and then solve for y
10(0.5) + 20y = 35
5 + 20y = 35
subtract 20 from both-side of the equation
20y = 35 - 5
20y = 30
divide both-side of the equation by 20
y = 1.5
"13 oranges and 15 grape fruits" = 13 x + 15y
substituting x = 0.5 and y= 1.5 in the above;
13(0.5) + 15(1.5)
=6.5 + 22.5
=29
Hence;
13 oranges and 15 grapefruits will weigh 29 pounds
Divide -2 1/8÷6 4/5 . Explain each step you used to find the quotient.
Answer: -85/272
Step-by-step explanation:
-17/8 divided by 34/5
then opposite reciprical
-17/8 x 5/34
-85/272 (check if you can simplify)
Use an integer or a fraction to describe the slope of a line perpendicular to this line please!!!
A line with slope m then the slope of a line perpendicular to it is ;M = -2/3
What is the slope of a straight line?A straight line of the form y = mx + c has its slope as 'm'
It is constant for a line. The more the slope is, the steeper the line is.
Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.
To find the slope m of the given line using the slope formula
[tex]m = \dfrac{y-q}{x-p}[/tex]
with (p, q ) = (1, 0) and (x₂, y₂ ) = (x, y) 2 points on the line
m = (3 -0)/(3-1)
m = 3/2
ALso it is given that a line with slope m then the slope of a line perpendicular to it is ;
M = -2/3
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Suppose that you decide to buy a car for $27,635, including taxes and license fees. you saved $5000 for a down payment and can get a three-year car loan at 6.36%. Find the monthly payment and the total interest for the loan
the monthly payment of $ 668.75 will be paid for the loan for the car.
Total payment for the car = $ 27,635
Money for down payment = $ 5000
Interest for 3 year loan = 6.36 %
Amount on which this interest will be applied = $ 27,635 - $ 5000
Amount = $ 22,635
Interest = 6.36 % of $ 22,635
Interest = 6.36 / 100 × $ 22,635
Interest = 1440 (approx.)
Total amount of loan = $ 22,635 + $ 1440
= $ 24075
Number of months = 3 × 12 = 36 months
So, monthly payment = $ 24075 / 36
= $ 668.75
Therefore, we get that, the monthly payment of $ 668.75 will be paid for the loan for the car.
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