Answer:
a. 3/4
Step-by-step explanation:
The expected value is the sum of each outcome times its probability.
If n is the total number of marbles, then the expected value is:
E = (3/8) (n) + (3/8) (n)
E = 3/4 n
sorry wrong question-
How old am I if 500 reduced by 3 times my age is 278?
Let your age = X
Now you have 500 - 3x = 278
Subtract 500 from each side:
-3x = -222
Divide both sides by -3:
x = -222 / -3
x = 74
You are 74 years old.
The age of an old man is 74 years old.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Let the age of an old man be x.
500 reduced by 3 times my age is 278 can be expressed as
⇒ [tex]500-3x=278[/tex]
⇒ [tex]500-278=3x[/tex]
⇒ [tex]222=3x[/tex]
⇒ [tex]x=\frac{222}{3}[/tex]
⇒ [tex]x=74[/tex]
Hence we can conclude that the age of an old man is 74 years old.
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I need help with this problem please ! Evaluate 3/7r + 5/8s when r=14 and s=8.
Answer:
11
Step-by-step explanation:
It is given that:
r = 14 & s = 8
Plug in the corresponding numbers to the corresponding variables:
(3/7)(14) + (5/8)(8)
Solve. Remember to simplify. Do multiplication & division first, then add:
(3/7)(14) + (5/8)(8)
(3 * 14)/7 + (5 * 8)/8
(3 * 2) + 5
(6) + 5
11
11 is your answer.
~
How does the graph of f(x) = 5
cos 1/2 X
Answer:
The graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] is a vertical stretch of 5 units and a horizontal stretch by 2 units of the parent graph
Step-by-step explanation:
We want to find out how the graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] compare with the graph of the parent function [tex]g(x)=\cos (x)[/tex].
We can observe that the transformation applied to the basic cosine function is of the form:
[tex]y=A \cos Bx[/tex]
The [tex]A=5[/tex] is a vertical stretch by a factor of 5 units.
[tex]B=\frac{1}{2}[/tex] is a horizontal stretch by a factor of 2 units.
Therefore the graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] will stretch vertically by a factor of 5 units and stretch horizontally by a factor of 2 units as compared to [tex]g(x)=\cos (x)[/tex].
See attachment
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answer:
All real numbers
Step-by-step explanation:
we have
f(x) = 3x +9
The linear function has a range of all real numbers -------> (-∞, ∞)
f(x) can take any real value.
Please see attached image below, for more information
Answer:
I think its B because K is = to Y
So if K is 9 then the asymptote would be 9
Limiting the Y to the to be only greater than 9
Step-by-step explanation:
Type the expression as radicals.
Y3/5
Answer:
[tex]\sqrt[5]{y^{3} }[/tex]
Step-by-step explanation:
[tex]y^{\frac{3}{5} } = y^{\frac{1}{5} * 3}[/tex] = [tex]\sqrt[5]{y^{3} }[/tex]
This is true because of the fractional exponent rule.
Answer:
Step-by-step explanation:If
n
is a positive integer that is greater than
x
and
a
is a real number or a factor, then
a
x
n
=
n
√
a
x
.
a
x
n
=
n
√
a
x
Use the rule to convert
y
3
5
to a radical, where
a
=
,
x
=
, and
n
=
.
5
√
y
3
Someone please help me with this question. I would greatly appreciate it. Please and thank you.
[tex]\dfrac{15(15-1)}{2}=\dfrac{15\cdot14}{2}=15\cdot7=105[/tex]
if 8 markers cost $20 what is the cost of 12 markers
Answer:
$30
Step-by-step explanation:
Find the cost per marker.
Given: 8 markers = $20
Divide 8 from both sides.
Let x = amount of markers.
(8x)/8 = (20)/8
x = 2.5
Each marker costs $2.50
Now, multiply 12 with $2.50
2.50 x 12 = 30
$30 is the cost of 12 markers.
~
14 points!!
Is this shape a polygon?
Answer:
TRUEStep-by-step explanation:
A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit.
rectangle ABCD is shown on the coordinate grid below. which of the following graphs represent the translation of rectangle ABCD over the following: (x, y) —> (x + 1, y-2)?
Answer:
the answer is c glad i could help
Can somebody help thanks if you do
Answer:
It is A i believe.
Step-by-step explanation:
Because, 15/100 = 0.15 and y is your regular price so;
y - 0.15
Sorry had to rewrite what i did, but i hope my answer has helped you.
If s(x) = x-7 and f(x) = 4x? – X+3, which expression is equivalent to (tos)(x)?
04(x-7)2 – X-7 + 3
0 4(x-7)2 – (x-7) + 3
(4x2 - x + 3)-7
0 (4x2 – x+3)(x-7)
Answer:
4(x-7)^2-(x-7)+3 (Assuming t is f)
Step-by-step explanation:
Let s(x)=x-7 and t(x)=4x^2-x+3 .
(t o s)(x)=t(s(x))=t(x-7)
Before I continue this means replace the orginal x in t with x-7.
This will then give you
4(x-7)^2-(x-7)+3
Find the standard equation and graph of a parabola that matches the given set of characteristics. vertex (0, 0) focus (-2, 0)
The standard equation of a parabola with vertex (0, 0) and focus (-2, 0) is y^2 = -8x. It opens to the left with the directrix x = 2.
To find the standard equation of a parabola with vertex (0, 0) and focus (-2, 0), we can use the definition of a parabola as the set of all points equidistant from a point (the focus) and a line (the directrix).
Since the focus is at (-2, 0), the directrix is a vertical line equidistant from the vertex on the opposite side of the focus, which is x = 2. The distance between the vertex and the focus (or the vertex and the directrix) is 2 units, so q = 2. This means that the parabola opens to the left.
The standard equation for a parabola that opens horizontally is of the form (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus. Here, p = -2 because the parabola opens to the left.
Therefore, the standard equation for the given parabola is y^2 = -4(2)x or y^2 = -8x.
(4.0 •10^6) divided by (5.0•10^9) in scientific notation
Answer: [tex]8.0*10^{-4}[/tex]
Step-by-step explanation:
You need to remember the Quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
Then, given the expression:
[tex]\frac{(4.0*10^6)}{(5.0*10^9)}[/tex]
You must divide the coefficients and subtract the exponents. Then:
[tex]=0.8*10^{-3}[/tex]
In order to write this result in Scientific notation form, you need to move the decimal point one place to the right. Therefore, you get:
[tex]=8.0*10^{-4}[/tex]
in a gymnastics competition an athletes final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score all scores are out of 10 and one gymnast has a 7.6 average technical score what artistic score does the gymnast need to have a final score of at least 8.0
Answer:
x ≥ 9.2
Step-by-step explanation:
If in a gymnastics competition an athletes final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score all scores are out of 10 and one gymnast has a 7.6 average technical score, the gymnast needs x ≥ 9.2 to have a final score of at least 8.0.
7.6 x 75 / 100 = 5.7
Final answer:
The gymnast requires an artistic score of at least 9.2 to achieve a final score of at least 8.0, calculated by taking 75% of their average technical score and adding 25% of their artistic score.
Explanation:
To find out what artistic score the gymnast needs to achieve a final score of at least 8.0, we use the given information that the final score is composed of 75% of the average technical score plus 25% of the artistic score. Let's represent the artistic score as A.
First, calculate 75% of the average technical score:
0.75 × 7.6 = 5.7
Now, set up the equation using the required final score (8.0) and the known technical score (5.7):
5.7 + 0.25A ≥ 8.0
To find the minimum artistic score (A), we subtract 5.7 from both sides of the equation:
0.25A ≥ 8.0 - 5.7
0.25A ≥ 2.3
Finally, divide by 0.25 to solve for A:
A ≥ ÷ 0.25
A ≥ 9.2
So, the gymnast would need an artistic score of at least 9.2 to achieve a final score of at least 8.0.
I dentify the domain and range and sketch the graph
[tex] y = sqrt { - x - 3 - 3} [/tex]
Answer:
Step-by-step explanation:
y=√(-x-3) - 3
y exisit : - x -3 ≥ 0
- x ≥ 3
x ≤ - 3 the domain is : D=] -∞,-3 ]
y=√(-x-3) - 3
y + 3 = √(-x-3)
x exisit : y + 3 ≥ 0 ; y ≥ -3
the range is : w = [- 3,+ ∞ [
look the graph
Lightning travels much faster than thunder so lightning is seen before thunder is heard. Using inductive reasoning and graph if you count 45 s between the lightning and thunder how far away is the storm?
Answer:
9 seconds.
Step-by-step explanation:
On your graph, use a ruler and your eye to get the best fitting line.
Then find the time in seconds (45) which is between 40 and 50 on the x axis.
Go across to the y axis. You will find it is about 9 seconds.
Based on the information depicted by the graph, the distance of the storm 45 seconds between Lightning and Thunder will be 9 miles
From the graph, we can create a proportional relationship thus :
Distance from storm = Seconds between Thunder
4 miles = 20 seconds
Let the miles traveled by Storm between 45 seconds = s
Hence, we have ;
4 miles = 20 seconds
s miles = 45 seconds
Cross multiply :
20s = 45 × 4
20s = 180
Divide both sides by 20
s = 180 / 20
s = 9 miles
Therefore, the storm will be 9 miles away.
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What is the solution to this equation?
x- 12 = 9
Answer:
x = 21
Step-by-step explanation:
x- 12 = 9
Add 12 to each side
x- 12+12 = 9+12
x = 21
Answer:
[tex]\huge \boxed{x=21}[/tex]
Step-by-step explanation:
[tex]\Huge\textnormal{Add 12 from both sides of the equation.}[/tex]
[tex]\displaystyle x-12+12=9+12[/tex]
[tex]\Huge \textnormal{Simplify and solve to find the answer.}[/tex]
[tex]\displaystyle 9+12=21[/tex]
[tex]\huge \boxed{x=21}[/tex], which is our answer.
Whatis the domain and range of f(x)=2[x-4]
Answer:
Domain: All Real Numbers
Range: All real numbers
Step-by-step explanation:
The given function is:
[tex]f(x) = 2(x-4)[/tex]
Domain:
The given function will not be undefined on any value of x as there is no denominator involved in the function.
So, the domain of the function is all real numbers
Range:
Similarly the range of the function is also all real numbers.
Which is the best definition of a scalene triangle?
Answer:
B A triangle in which no two sides are congruent is scalene
Step-by-step explanation:
A triangle that has 3 congruent sides is an equilateral triangle
A triangle in which no two sides are congruent ( no sides are the same) is a scalene triangle
A triangle that has at least two congruent sides is an isosceles triangle
Answer:
a triangle in which no two sides are congruent
Step-by-step explanation:
The temperature is 50°F The temperature will decrease by 4°F each hour. Let
h be the number of hours,
When will the temperature be below 32°F?
Write an inequality for this problem,
A. 50 - 4h: 32
B. 50 - 4h32
c. 50 + 4h3 32
D. 50 + 4h+ 32
Answer:
50-4h<32
Step-by-step explanation:
If the temperature starts at 50 and the temperature is decreased by 4 per each hour, then:
1) after the first hour, the temperature is 50-4 or 46
1) after the second hour, the temperature is 46-4 or (50-4)-4 or 50-4(2).
So what I'm trying to show you that if I continue this pattern our equation for what happens h hours later is: 50-4h.
We want to know when is the temperature below 32 so less than 32.
Temperature<32
Put in our variable expression for temperature.
50-4h<32
The question is about using algebra to solve a real-life problem of temperature decrease. The correct inequality for the given problem is '50 - 4h < 32', which shows the number of hours it takes for the temperature (50 and decreasing 4 every hour) to be less than 32 degrees.
Explanation:The subject matter of this question is mathematics, specifically algebra and inequalities. The question provides that the temperature in degrees Fahrenheit is reducing by 4 each hour from a starting point of 50°F and seeks to find the number of hours (h) it takes for the temperature to decrease below 32°F.
We can represent this situation as an inequality: 50 - 4h < 32. In English, this states that the temperature (50, decreasing by 4 each hour) should be less than 32 degrees. So, to answer your question, option B with '50 - 4h < 32' is the correct inequality for this problem.
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In the diagram below, what is the length of ST?
Check the picture below.
If sides SX=5,SY=10,XU=4,YT=x then the length of ST=18.
What is triangle?A triangle is a two dimensional figure having three sides, three angles, three vertex. Th sum of all the angles is equal to 180°.
How to find length?We have been given SX=5, XU=4,SY=10 and we are required to find the length of ST. We can write the sides as under:
SX/SU=SY/T
SX=5,SU=5+4=9,SY=10,ST=10+x
5/9=10/(10+x)
Solving this for the value of x.
5(10+x)=10*9
50+5x=90
5x=90-50
x=40/5
x=8
We know that ST=10+x.
We have to put the value of x in ST.
ST=10+8
=18
Hence if sides are SX=5,SY=10,XU=4,YT=x then the length of ST=18.
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What is the value of x?
2
3
6
7
Answer:
2
Step-by-step explanation:
So we are going to do
(sum of parts of the secant)(part on outside)=(sum of parts of the secant)(part on outside) .
This is what you get from doing that:
(1+x+4)(x+4)=(11+x+1)(x+1)
Simplifying:
(x+5)(x+4)=(x+12)(x+1)
We could see which value of x makes both side the same.
Choice 1: Plug in 2 for x:
(2+5)(2+4)=(2+12)(2+1)
(7 )(6 )=( 14 )(3)
42 = 42
This equation is true.
Choice 2: Plug in 3 for x:
(3+5)(3+4)=(3+12)(3+1)
( 8)( 7)=( 15)( 4)
56 = 60
This equation is not true.
Choice 3: Plug in 6 for x:
(6+5)(6+4)=(6+12)(6+1)
( 11 )( 10 )=( 18 )(7 )
110 = 126
This equation is not true.
Choice 4: Plug in 7 for x:
(7+5)(7+4)=(7+12)(7+1)
(12 )( 11 )=( 19 )(8)
132 =152
This equation is not true.
Answer:
The answer is A or "2"
Step-by-step explanation:
help pls ;-;
What is the perimeter of the figure?
a. 180 in.
b. 64 in.
c. 65 in.
d. 72 in.
Answer:
180 in
Step-by-step explanation:
The perimeter is just the sum of the lengths of the sides of the shape.
So all we need to do here is:
40+10+(40-18)+(50-10)+18+50.
I got (40-18) for the bottom of the top rectangle, the part that is poking out.
I got (50-10) for the right side of the rectangle that is poking out towards the bottom.
40+10+(40-18)+(50-10)+18+50
40+10+22 +40 +18+50
50 +62 +68
50+62+68
112+68
180
180 in
I'm going to post a drawing here to show the lengths I was talking about:
please help i'd really appreciate it.
Answer:
y = [tex]\frac{1}{4}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x + 3 ← is in slope- intercept form
with slope m = - 4
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (8, 1 ) into the partial equation
1 = 2 + c ⇒ c = 1 - 2 = - 1
y = [tex]\frac{1}{4}[/tex] x - 1 ← equation of perpendicular line
Find the inverse of the following function f(x)= cubed root of x+12
Answer:
[tex]x^{3} -12[/tex]
Step-by-step explanation:
[tex]y=\sqrt[3]{x+12}[/tex]
Replace x with y to get
[tex]x=\sqrt[3]{y+12}[/tex]
Cube both side
[tex]x^{3}=y+12[/tex]
Subract 12 from both sides
[tex]x^3-12=y[/tex]
For O D, find mCBE.
A. 311.1°
B. 311.20
C.352 29
D. 332.19
Check the picture below.
Answer:
i think its d
Step-by-step explanation:
P(A) = 0.60, P(B) = 0.20, and P(A and B) = 0.15. What is P(A or B)?
Answer:
P(A or B) = 0.65
Step-by-step explanation:
Given that P(A) = 0.60, P(B) = 0.20, and P(A and B) = 0.15
We have to find P(A or B)
Apply the formula:
P(A or B) = P(A)+P(B)- P(A and B)
Now substitute the values in the formula:
P(A or B) = 0.60 + 0.20 - 0.15
P(A or B) = 0.80 - 0.15
P(A or B) = 0.65
Thus P(A or B) = 0.65 ....
Answer:
0.65 ~apex
Step-by-step explanation:
Use the diagram to find the measure of the given angle.
Given angle: PRQ
Answer:
∠PRQ = 85°
Step-by-step explanation:
∠PRS and ∠TRQ are vertical angles and congruent, thus
4x + 15 = 3x + 35 ( subtract 3x from both sides )
x + 15 = 35 ( subtract 15 from both sides )
x = 20
Hence ∠PRS = (3 × 20) + 35 = 60 + 35 = 95°
∠PRQ and ∠PRS form a straight angle and are supplementary, hence
∠PRQ = 180° - 95° = 85°
Answer:
Angle QRP = 85
Step-by-step explanation:
Hopefully you can see QRS and TRP both equal 180 degrees, we will use this.
QRS is the same as QRP and PRS added together. Just like TRP is TRQ and QRP. We will call QRP R for simplicities sake, and we are given a formula for PRS and TRQ. PRS = 3x+35 and TRQ = 4x+15.
So now we have two equations.
180 = QRP + PRS = R + 3x + 35
180 = TRQ + QRP = 4x + 15 + R
So it's basically a system of equations.
180 = 35 + R + 3x
145 = R + 3x
R = 145 - 3x
180 = 4x + 15 + R
Replace R with what we found in the last equation
180 = 4x + 15 + 145 - 3x
180 = x +160
x = 20
Now go back to the first equation and plug 20 in for x
R = 145 - 3x
R = 145 -3(20)
R = 145 - 60
R = 85
So Angle QRP = 85
Let em know if something doesn't make sense.
Find the average rate of change of f(x) = 2x2 – 7x from x = 2 to x=6.
Simplify your answer as much as possible.
Answer:
-6Step-by-step explanation:
[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}\\\\f(x)=2x^2-7x\\\\\text{Put the values of x = 2 and x = 6 to the equation of the function:}\\\\f(2)=2(2^2)-7(2)=2(4)-14=8-14=-6\\f(6)=2(6^2)-7(6)=2(36)-42=72-42=-30\\\\\dfrac{f(6)-f(2)}{6-2}=\dfrac{-30-(-6)}{4}=\dfrac{-24}{4}=-6[/tex]
There are 12 girls and 10 boys in the student council. What is the ratio of the number of girls to the total number of members? F. 6:5. G. 5 to 6. H. 6 to 11. I. 1 to 2.
Answer:
i think the answer is choice H
Step-by-step explanation:
the number of girls to total number of members is 12:22, if you simplify this it's 6:11
Answer:
6:11
Step-by-step explanation:
There are 12 girls.
There are 12+10 member in all.
That means there are 22 members in all.
So the ratio of girls to total members is 12 to 22 or 12:22. To reduce this, look for a common factor. 12 and 22 both share 2 as a common factor so divide both by 2 gives you 6:11.