Answer:
The probability is 0.97682
Step-by-step explanation:
We start by finding the z-values of the runner times given.
Mathematically;
z-score = (x-mean)/SD
From the question, mean = 13 seconds and SD = 0.3 seconds
So for 12.4 seconds, we have;
z = (12.4-13)/0.3 = -0.6/0.3 = -2
For 14 seconds, we have;
z = (14-13)/0.3= 1/0.3 = 3.33
So the probability we want to calculate is;
P(-2<z<3.33)
We can find this using the standard normal distribution table
Mathematically;
P(-2<z<3.33) = P(z<3.33) - P(z < -2)
Using the standard normal distribution table, the value of this is;
P(-2<z<3.33) = 0.97682
Yazmin is investigating the growth of plants under different conditions for her science class. Once the little sprouts were 1 inch tall, she found that they were growing at a steady rate of about 1/2 inch per day. Write a function that helps Yazmin to see how many days it takes for the plants to reach a given height. Let h = height of the plant (inches), and let d = number of days (days)
Answer:
0.5+d=h
Step-by-step explanation:
If a plant is growing at a steady rate of 0.5 inches (h) in 1 day (d) then after one day your equation should look like: 0.5+1 which would give you the height of the plant in inches. If this is true, then you would keep the height per day the same (0.5) substitute the 1 for d (one day); then your equation would look like this: 0.5+d which would give you the height of the plant in inches (h).
0.5+d=h
The function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.
What is a function?Functions were originally the idealization of how a varying quantity depends on another quantity.
Now it is given that,
Height of sprout = 1 inch
Growth per day = 1/2 inch
Let h = height of the plant (inches), and let d = number of days (days)
∵ Growth per day = 1/2 inch
So, Growth of plant in d days = d * 1/2 = d/2 = 0.5d
Thus, height of the plant, h = 1 + Growth of plant in d days
⇒ h = 1 + 0.5d
Thus, the function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.
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In Isosceles trapezoid ABCD, the longer base, AB, is one and one half times as long as the shorter base, CD. The other two sides, AD and BC, are both 13 cm. long. a. If the perimeter is 76 cm. find the lengths of AB and CD. b. If the height of the trapezoid is 12 cm. find its area. (Hint: Area
otal perimeter = 76cm = AB + BC + CD + AD
AD & BC = 13cm
AB = 1.5*(CD)
Solution:
Since we know AD & BC are both 13cm long, plug those numbers into the perimeter equation
76cm+=+AB+%2B+BC+%2B+CD+%2B+AD Place 13cm in for AD & BC
76cm+=+AB+%2B+13cm+%2B+CD+%2B+13cm Combine like terms
76cm+=+AB+%2B+CD+%2B+26cmSubtract 26cm from both sides
50cm+=+AB+%2B+CD Now it is time to substitute the 1.5*(CD) for AB
50cm+=+1.5%2A%28CD%29+%2B+CD rewrite the equation
50cm+=+2.5%2A%28CD%29 Divide both sides by 2.5
20cm+=+CD
To find AB, plug 20cm in for CD in the equation AB = 1.5*(CD)
AB+=+1.5%2A20cm
AB+=+30cm
What effect will replacing x with (x – 7)have on the graph of the equation y = = (x + 4)??
A. slides the graph 3 units down
B. slides the graph 3 units up
C. slides the graph 7 units right
D. slides the graph 3 units right
Answer:
D
Step-by-step explanation:
When you graph the first equation y = (x + 4) it will have a x-intercept of -4 and a y-intercept of 4.
When you replace x with (x-7) the equation will be converted into
y = ((x-7)+4)
y = x-3
When you graph this you see it has a x-intercept of 3 and a y-intercept of -3
To find the distance add the 2 x values together:
-4 + (-3) = ?
-4 -3 = ?
-7 = ?
Therefore the graph will shift units right
Someone pls HELP MEEEE i’m giving the rest of my points away . i have like 20 mins to turn this in
Answer:
1) 27.89
2) 20
Step-by-step explanation:
#1)
9.5x + 75 --> 340
340 - 75 --> 265
265 / 9.5 = 27.89
#2)
120 / 6 =
20 minutes
Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest
number of possible solutions to this system?
Answer:
greatest number of solutions is 2
Step-by-step explanation:
one is a parabola, the other is a line
so it can intersect in 0, 1, 2 points
Point E is on line segment DF. Given DE
EF.
6 and DF =9, determine the length EF
Answer:
3Step-by-step explanation:
IF point E lies on the line segment DF, this means that all the points DEF are collinear and DE+EF = DF.
Given parameter
DE = 6
DF = 9
Required
EF
Substituting the given parameter into the expression above to get the required will be;
DE+EF = DF.
EF = DF-DE
EF = 9-6
EF = 3
Hence the length of EF is equivalent to 3
The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month). Water costs 0.20 dollars per liter.
Answer:
$86.40
Step-by-step explanation:
The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the
entire month). Water costs 0.20 dollars per liter.
How much did Trevor's family pay per minute on shower water
Average person=72 liters of water
6 people=72*6= 432 liters
Each person = 480 minutes
6 people=480*6= 2,880 minutes
Water=$0.20 per liter
Total cost of water= 432 * 0.20
= $86.40
Answer:
o.o3
Step-by-step explanation:
If a number is divided by 3 or 5, the remainder is 1. If it is divided by 7, there is no remainder. What number between 1 and 100 satisfies the above conditions?
Answer:
91
Step-by-step explanation:
Look at multiples of 7 and you’ll find 91.
91 dived by 3 is 30 with a remainder of 1.
91 divided by 5 is 18 with a remainder of 1.
91 divid by 7 is 13 with no remainder.
91 is the number between 1 and 100 satisfies the above conditions
What is Number system?A number system is defined as a system of writing to express numbers.
Given that a number is divided by 3 or 5, the remainder is 1.
If it is divided by 7, there is no remainder
We need to find the number between 1 and 100 which satisfies the given conditions.
Let us consider 91.
When 91 is divided by 3 we get 30 and 1 as remainder.
91 divided by 5 is 18 with a remainder of 1.
91 divided by 7 is 13 it does not have any remainder or remainder is zero.
Hence, 91 is the number between 1 and 100 satisfies the above conditions
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which whole number has a factor that is the greatest prime factor between 1 and 30?
А. 1,593
B. 1,247
C. 1,311
D. 943
Answer:
B
Step-by-step explanation:
The greatest prime factor between 1 and 30 is 29. Remember that a prime number is a number whose only 2 factors is 1 and the number itself. To find out which number is a multiple of 29, all we have to do is divide it by 29, and if the quotient is a whole number then we have found our answer.
A: 1593 / 29 ≈ 54.93
B: 1247 / 29 = 43
We don't need to check C and D because we know that B is the answer.
1247 has the greatest prime factor between 1 and 30
The factor of a number that divides another number perfectly without leaving any remainder.
For example, the factors of 12 are 1,2,3,4,6 and 12
A prime factor is a number that a prime number
A prime number is a number that can be divided only by 1 and that number
Prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
The greatest prime factor between 1 and 30 is 29
To determine which number has the greatest prime factor, divide each of the numbers in the options by 29.
1593 / 29 = 54.9 (29 is not a prime factor of 1593)
1247/29 = 43 (29 is a prime factor of 1247)
1311 / 29 = 45.2 (29 is not a prime factor of 1311)
943 / 29 = 32.5 (29 is not a prime factor of 943)
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The graph below shows the survey results for a group of students who were asked how many honors classes they have taken and how many elective classes: How many elective classes would a student likely have taken if he or she has taken 12 honors classes? 15, because y = one halfx + 9 12, because y = y = negative one halfx + 9 6, because y = one halfx + 9 3, because y = negative one halfx + 9
Answer:
3, because [tex]y=-\frac{1}{2}x+9[/tex].
Step-by-step explanation:
Looking at this graph, we can start to determine the equation for it.
The y-intercept of this graph is 9, therefore there will be a constant of 9.
We can find the slope by looking at rise over run. It vertically travels -1 for every 2 horizontally. So the slope is [tex]-\frac{1}{2}[/tex].
Making this into an equation gets us [tex]y=-\frac{1}{2}x+9[/tex].
Now we can substitute 12 into this equation as x.
[tex]y=-\frac{1}{2}(12)+9\\ y=-6+9\\y=3[/tex]
Hope this helped!
Answer:
the other person is correct! C:
Step-by-step explanation:
Jerry wants to gravel an area represented by a square with side lengths of 3/4ft. What is the area he needs to fill.
Answer:
0.5625 ft^2
Step-by-step explanation:
area of square = side * side
A = s^2
A = (0.75 ft)^2 = (0.75 ft)(0.75 ft) = 0.5625 ft^2
I really need help Please help me please
What angle does an arc 6.6cm in length subtends at the centre of a circle of radius 14cm. Use π = 22/7)
Answer:
STEP 1: Find the circumference:
Circumference = 2πr
Circumference = 2π(14) = 28π cm
............................................................................................
STEP 2: Find the length of the arc:
Length of the arc = 36/360 x 28π
Length of the arc = 8.8 cm
.............................................................................................
Answer: The length of the arc is 8.8 cm
............................................................................................
hope it helpssss
Mark it as brilliant answer plzzz
ФωФ
Answer:
27°
Step-by-step explanation:
arc length = circumference × fraction of circle
let x be the central angle, then
2πr × [tex]\frac{x}{360}[/tex] = 6.6
2 × [tex]\frac{22}{7}[/tex] × 14 × [tex]\frac{x}{360}[/tex] = 6.6
88 ×[tex]\frac{x}{360}[/tex] = 6.6 ( multiply both sides by 360 )
88x = 2376 ( divide both sides by 88 )
x = 27
Thus central angle is 27°
The midpoint (x, y) and the end point (x2, y2) are known. Find (x1, Y1) using the midpoint formula.
a. (x1,y1) = (2x + x2, 2y+y2)
b. (x1,y1) = (2x - x2, 2y - y2)
c. (x1,y1) = (x + x2, y + y2)
d. (x1,y1) = (x - x2, y - y2)
Answer:
(x1,y1) = (2x - x2, 2y - y2)
Step-by-step explanation:
Given:
Midpoint = (x , y)
End point = (x2, y2)
Find:
(x1, y1)
Computation:
Mid-point formula
x = (x1 + x2) / 2 , y = (y1 + y2) / 2
So,
2x = x1 + x2 , 2y = y1 + y2
x1 = 2x - x2 , y1 = 2y - y2
So,
(x1,y1) = (2x - x2, 2y - y2)
Match the graph with the correct equation.
Answer:
work shown and pictured
What are the vertical and horizontal asymptotes for the function f(x)=
3x2/x2-4
Answer: f(x) will have vertical asymptotes at x=-2 and x=2 and horizontal asymptote at y=3.
Step-by-step explanation:
Given function: [tex]f(x)=\dfrac{3x^2}{x^2-4}[/tex]
The vertical asymptote occurs for those values of x which make function indeterminate or denominator 0.
i.e. [tex]x^2-4=0\Rightarrow\ x^2=4\Rightarrow\ x=\pm2[/tex]
Hence, f(x) will have vertical asymptotes at x=-2 and x=2.
To find the horizontal asymptote , we can see that the degree of numerator and denominator is same i.e. 2.
So, the graph will horizontal asymptote at [tex]y=\dfrac{\text{Coefficient of }x^2\text{ in numerator}}{\text{Coefficient of }x^2\text{ in denominator}}[/tex]
i.e. [tex]y=\dfrac{3}{1}=3[/tex]
Hence, f(x) will have horizontal asymptote at y=3.
reduce to simplest form -7/12+3/8 =_____
Answer:
-5/24
Step-by-step explanation:
make the denominators the same!
please help me on this
Answer:
YZ = 8.5
Step-by-step explanation:
Since RY is an angle bisector then the ratio of the sides of the triangle are equal to the corresponding ratio of the base, that is
[tex]\frac{YX}{YZ}[/tex] = [tex]\frac{XR}{ZR}[/tex] , substitute values
[tex]\frac{11.9}{YZ}[/tex] = [tex]\frac{7}{5}[/tex] ( cross- multiply )
7YZ = 59.5 ( divide both sides by 7 )
YZ = 8.5
What is the sign of -xy? Will give the brainlest to who ever answers it
Answer:
positive
Step-by-step explanation:
X is positive since it is to the right of zero
Y is negative since it is to the left of zero
-xy
- ( +) ( -)
negative times positive times negative
negative times negative
positive
Find the distance across the lake. Assume the triangles are similar.
80 m
х
у
20 m
60 m
Answer:
A. L = 240 m
Step-by-step explanation:
use similar triangle
L / 60 = 80 / 20
L = (80 * 60) / 20
L = 240 m
The required distance across the lake is 240 m. Hence correct option is A.
Similar triangles, are those triangles which have similar properties i.e. angles and proportionality of sides.
Since, triangles are similar.
The ratio of their sides are also equal
60/20= L/80
L=80 x 3
L = 240 m
Thus, the required distance across the lake is 240 m.
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what is the value of digit 9 in 3.45×0.27×0.3 ?
Answer:
[tex]\boxed{\pink{0.27945}}[/tex]
Step-by-step explanation:
[tex]3.45 \times 0.27 \\ = 0.9315 \times 0.3 \\ = 0.27945[/tex]
Answer: thousandths place
Step-by-step explanation:
↓
3.45 x 0.27 x 0.3 = 0.27945
The place values to the right of the decimal point are:
one to the right (2): tenths
two to the right (7): hundredths
three to the right (9): thousandths
four to the right (4): ten thousandths
five to the right (5): hundred thousandths
what is y ? x=1 y=? y=3x-7
Answer:
-4.
Step-by-step explanation:
y = 3x - 7; x = 1.
y = 3(1) - 7
= 3 - 7
= -4
Hope this helps!
Answer:
y = - 4
Step-by-step explanation:
y=3x-7
Let x =1
y = 3*1 -7
y = 3-7
y = - 4
Help please will give brainiest if correct
Answer:
(x + 1)^2 + (y - 1)^2 = (8.5)^2
Step-by-step explanation:
Consider the general equation of a circle:
(x - h)^2 + (y - k)^2 = (r)^2
Where (h,k) represent the center point of the circle, and r represents the radius of the circle.
For this circle, our center point appears to be at (-1,1) and the circle has a radius of 8.5.
Using this information, we simply plug these values into the general equation to get the following:
(x + 1)^2 + (y - 1)^2 = (8.5)^2
Cheers.
which graph represents (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis-pairs that make the equation y = 0.5x+5y=0.5x+5y, equals, 0, point, 5, x, plus, 5 true?
The graph of [tex]\mathbf{y = 0.5x + 5}[/tex] has a slope of 0.5, and a y-intercept of 5
The equation is given as:
[tex]\mathbf{y = 0.5x + 5}[/tex]
A linear equation is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where m represents the slope, and c represents the y-intercept
So, by comparison:
m = 0.5
c = 5
This means that:
The slope is 0.5, and the y-intercept is 5
Hence, the graph of [tex]\mathbf{y = 0.5x + 5}[/tex] has a slope of 0.5, and a y-intercept of 5
See attachment for the graph of [tex]\mathbf{y = 0.5x + 5}[/tex]
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3rd one i just did it on edge :P
Simplify 27^(-2/3) x 25^(1/2) x 5^0 9 5 9/5 5/9
Answer:
[tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Using the rules of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex] , [tex]a^{0}[/tex] = 1
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
Given
[tex]27^{-\frac{2}{3} }[/tex] × [tex]25^{\frac{1}{2} }[/tex] × [tex]5^{0}[/tex]
= [tex]\frac{1}{27^{\frac{2}{3} } }[/tex] × [tex]\sqrt{25}[/tex] × 1
= [tex]\frac{1}{9}[/tex] × 5 × 1
=[tex]\frac{5}{9}[/tex]
Shawn wanted to model the number 13,450 using 13,450 using base-ten blocks how many large cubes, flats, and longs does he need to model the number
Answer:
See attached
Step-by-step explanation:
13450 = 13000 + 400 + 50
13*1000 = 13 large cubes4*100 = 4 flats5*10 = 5 longsI need Helpppp quick!!!!
Answer:
G
Step-by-step explanation:
let his fixed price be x and his hourly fee be y;
270 = 4y + x
420 = 7y + x
x is common in both equations
equate the two;
x = 270-4y and x = 420-7y
270-4y = 420-7y
3y = 150
y = 50
x = 270-4*50
x = 70
Let P (2,-3), Q (-2, 1) be the vertices of the triangle PQR. If the centroid of ΔPQR lies on the line 2x +3y = 1, then the locus of R is a. 2x + 3y = 9 b. 2x - 3y = 9 c. 3x + 2y = 5 d. 3x - 2y = 5
Answer:
Correct answer is a. 2x + 3 y = 9.
Step-by-step explanation:
Let the coordinates of centroid be (h,k)
{h/3 , (-2+k)/3}
h = (2 – 2 + a)/3 = a/3 ---eqn 1
k= ( - 3+ 1 + b )/3 = (-2 + b)/3 -----eqn 2
Where (x,y) are any point on the line 2x+3y=1
3h = a and 3k + 2 = b
From 2x +3y = 1,
Then, 2h +3k = 1, 3k = 1 - 2h -----eqn 3
b = 1 - 2h + 2 = 3 - 2h
also b = 3 - 2a/3
b = (9 -2a)/3
3b = 9 - 2a
3b + 2a = 9
Now (x,y) satisfy the point on the line 2x+3y=9
So the locus is 2x + 3 y = 9.
Possible Points: 100 One January day, the low temperature in Fargo, ND was -8 degrees. Over a period of six hours, the temperature rose 4 degrees per hour. After si hours, what was the temperature?
Plz help ASAP assignment due today !!!
Write the Properties of at least 5 different types of polygons of your choice and the properties of a circle.
Square - a rectangle (4 sided shape) whose sides are equal length
Rectangle - a polygon that has 4 sides and 4 right angles - two pairs of parallel lines
Triangle: a polygon with 3 sides and 3 angles. The angles add up to a total of 180 degrees. There are 3 kinds of triangles
Parallelogram - a polygon with 4 sides, 2 pair of parallel lines, 2 obtuse angles and 2 acute angles.
Trapezoid - a polygon with 4 sides and only 1 pair of parallel lines
Circle: a shape with no sides, angles, or parallel lines. Any point in the circumference to the center of the circle is the same length.
Happy to help!
Answer:
1). Triangle - Has 3 equal sides and angles of 60°.
2). Square - A quadrilateral with 4 equal sides and angles (all the angles are right angles).
3). Rectangle - A quadrilateral with 2 equal parallel sides horizontal and vertical. All the angles are equal because they are right angles.
4). Pentagon - It has 5 equal sides with equal angles of 108°.
5). Hexagon - It has 6 equal sides with equal angles of 120°.
PROPERTIES OF A CIRCLE:
It has no sides with no angles. The radius in any direction from the point are of the same length.
