Casey asks a random sample of students at his school about their natural hair and eye colors. The results of his survey are shown in
the relative frequency table below.
Black
Brown
Hair
Red
Color
Blonde
Total
Brown
0.225
0.350
0,025
0.050
0.650
Eye Color
Blue Other
0.000 0.025
0.125 0.100
0.000 0.025
0.075 0.000
0.200 0.150
Total
0.250
0.575
0.050
0.15
1.000
In the sample, there are 4 more students with brown hair and blue eyes than blond hair and blue eyes.
How many total students have black hair?
Answers
=======================================================
Explanation:
x = total number of students surveyed
According to the table, 0.075 of the students (aka 7.5%) have blond hair and blue eyes. This means 0.075x is the number of blond hair blue eye people.
Also, 0.125x is the number of brown hair blue eye people for similar reasoning as the previous paragraph.
We're told that "There are 4 more students with brown hair and blue eyes than blond hair and blue eyes"
So,
(BrownHair_BlueEyes) = (BlondHair_BlueEyes) + 4
0.125x = (0.075x) + 4
0.125x-0.075x = 4
0.05x = 4
x = 4/0.05
x = 80
There are 80 students surveyed.
Of those eighty students, 0.075x = 0.075*80 = 6 have blond hair and blue eyes; while 0.125x = 0.125*80 = 10 have brown hair and blue eyes. Notice how this is four more than the blond person count with blue eyes. This confirms we have the correct sample size.
The last step is to calculate how many of the students have black hair based on the sample size we just found.
The table shows 25% = 0.250 of the students have black hair, so 0.25x = 0.25*80 = 20 students have black hair
Related Questions
Find the product of 40 and
100.
Answers
Answer:
4000
Step-by-step explanation:
40 x 100
In ΔHIJ, \text{m}\angle H = (x-1)^{\circ}m∠H=(x−1)
∘
, \text{m}\angle I = (2x+5)^{\circ}m∠I=(2x+5)
∘
, and \text{m}\angle J = (7x+6)^{\circ}m∠J=(7x+6)
∘
. What is the value of x?x?
Answers
The measure of angle L is 52
Step-by-step explanation:
Mathematically, in a triangle, the sum of the angles equal 180
So in this case;
J + K + L = 180
So therefore;
8x + 6 + 2x + 2 + 4x + 4 = 180
8x + 2x + 4x + 6 + 2 + 4 = 180
14x + 12 = 180
14x = 180 -12
14x = 168
x = 168/14
x = 12
So to get the measure of angel L, we simply substitute the value x in the equation for L
From the question, L = 4x + 4
So therefore L = 4(12) + 4 = 48 + 4 = 52
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
If in ΔHIJ, m∠H = x - 1, m∠I = 2x + 5, and m∠J = 7x + 6.
The value of x is 17.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
Example:
Triangle ABC:
m∠A + m∠B + m∠C = 180
We have,
ΔHIJ
m∠H = x - 1
m∠I = 2x + 5
m∠J = 7x + 6
We know that,
The sum of the angles of the triangle is 180 degrees.
m∠H + m∠I + m∠J = 180
(x - 1) + (2x + 5) + (7x + 6) = 180
x - 1 + 2x + 5 + 7x + 6 = 180
10x + 10 = 180
Take 10 common.
10 (x + 1) = 180
Divide both sides by 10.
x + 1 = 180/10
x + 1 = 18
Subtract 1 on both sides.
x = 18 - 1
x = 17
Thus,
If in ΔHIJ,
m∠H = x - 1
m∠I = 2x + 5
m∠J = 7x + 6.
The value of x is 17.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ5
If you roll a 6-sided die 54 times, what is the best prediction possible for the number of times
you will roll a five?
Answers
Vivian is trying to save money for her summer vacation. She puts $40 in her lucky money jar on week 1. She will put an additional $15 in the lucky jar each week.
a. Write an explicit formula for this scenario?
b. How much money will she have saved for her vacation by week 20.
Answers
Answer:
she saved $340 in total
Step-by-step explanation:
(15 x 20) + 40 = s
s = savings
A rectangle has a width of x centimetres and a perimeter of 8x centimetres. A square has
sides of length one fourth the length of the rectangle.
a) Determine the length of the rectangle.
b) Determine the perimeter of the square.
c) Determine how many centimetres greater the rectangle's perimeter is than the square's
perimeter if x = 4.
d) Determine how many square centimetres greater the rectangle's area is than the square's
area if x = 4.
Answers
Answer:
Part A) The length of rectangle is [tex]3x[/tex] [tex]cm[/tex]
Part B) The perimeter of the square is [tex]3x[/tex] [tex]cm[/tex]
Part C) [tex]20[/tex] [tex]cm[/tex]
Part D) [tex]39[/tex] [tex]cm^2[/tex]
Step-by-step explanation:
Part A) Find the length of the rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]P=8x[/tex] [tex]cm[/tex]
[tex]W=x[/tex] [tex]cm[/tex]
substitute and solve for L
[tex]8x=2(L+x)[/tex]
[tex]4x=(L+x)[/tex]
[tex]L=4x-x=3x[/tex] [tex]cm[/tex]
Part B) Find the perimeter of the square
we know that
The perimeter of a square is
[tex]P=4b[/tex]
we have that
[tex]b=(1/4)L[/tex]
substitute the value of L
[tex]b=(1/4)3x=(3/4)x[/tex] [tex]cm[/tex]
Find the perimeter of the square
[tex]P=4(3/4)x=3x[/tex] [tex]cm[/tex]Part C) Find how many cm greater the rectangle's perimeter than the square's perimeter if x=4
Find the value of rectangle's perimeter
[tex]P=8x[/tex] [tex]cm[/tex] ------> [tex]P=8(4)=32[/tex] [tex]cm[/tex]
Find the value of square's perimeter
[tex]P=3x[/tex] [tex]cm[/tex] ------> [tex]P=3(4)=12[/tex] [tex]cm[/tex]
Find the difference
[tex]32[/tex] [tex]cm[/tex] [tex]-12[/tex] [tex]cm[/tex] [tex]=20[/tex] [tex]cm[/tex]
Part D) Find how many square cm greater the rectangle's area is than the square's area if x=4
Find the value of rectangle's area
[tex]A=(3x)(x)=3x^2[/tex] [tex]cm^2[/tex] ------> [tex]A=3(4^2)=48[/tex] [tex]cm^2[/tex]
Find the value of square's area
[tex]A=((3/4)x)^2[/tex] [tex]cm^2[/tex] ------> [tex]A=((3/4)(4))^2 = 9[/tex] [tex]cm^2[/tex]
Find the difference
[tex]48[/tex] [tex]cm^2[/tex] [tex]-9[/tex] [tex]cm^2[/tex] [tex]=39[/tex] [tex]cm^2[/tex]There are yellow counters and black counters in a bag in the ratio 3:1
21 yellow counters are removed and the ratio becomes 5:4
Work out how many black counters there are in the bag.
Answers
Answer:
12 black countersStep-by-step explanation:
Let the yellow counters be represented by 'y' and black counters by 'b'.
Originally
y : b = 3 : 1After removing 21 counters
y - 21 : b = 5 : 4Taking the first ratio, equate it to b.
y/b = 3b = y/3Now, substitute for 'b' in the second ratio.
y - 21 / (y/3) = 5/43 (y - 21) / y = 5/412 (y - 21) = 5y12y - 252 = 5y7y = 252y = 36 yellow countersNow, to find b :
b = y/3b = 36/3b = 12 black countersAnswer:
12
Step-by-step explanation:
Given ratio
yellow : black = 3 : 1
⇒ yellow : black = [tex]3x : x[/tex]
If 21 yellow counters are removed and the ratio becomes 5 : 4
[tex]\implies \textsf{yellow - 21: black = 5 : 4}[/tex]
[tex]\implies (3x - 21):x=5:4[/tex]
[tex]\implies \dfrac{3x - 21}{x}=\dfrac54[/tex]
[tex]\implies 4(3x - 21)=5x[/tex]
[tex]\implies 12x-84=5x[/tex]
[tex]\implies7x=84[/tex]
[tex]\implies x=12[/tex]
Substituting [tex]x=12[/tex] into the original ratio:
[tex]\implies \textsf{yellow : black} =3(12) : (12)=36:12[/tex]
So the total number of black counters = 12
Linda is baking a pumpkin pie for her family and friends at Thanksgiving.
She is baking the pie in a 10 inch pie plate. What is the area of her pie?
Answers
Answer:
about 78in^2
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex]
A = [tex]\pi 5^{2}[/tex]
A = [tex]\pi * 25[/tex]
A = 3.14 * 25
A ≈ 78[tex]in^{2}[/tex]
NO LINKS!!!
Movies generally lose 23% of it's audience for each week in the theatre. A movie STARTED with an audience of 196 people per viewing.
Answers
Answers:
a) The equation is [tex]y = 196(0.77)^x[/tex]
b) See image attachment below
c) See image attachment below
d) Week 10
=======================================================
Explanation:
a)
One common template for an exponential equation is [tex]y = a*b^x[/tex] where 'a' is the starting amount and b is the growth or decay factor.
a = 196 is the starting amount of people who saw the movie per showtime
b = 1-0.23 = 0.77 is the decay factor. If the view count goes down by 23%, then we keep the remaining 77%
Therefore we go from [tex]y = a*b^x[/tex] to [tex]y = 196(0.77)^x[/tex]
x = number of weeks
y = number of people, per viewing, who saw the movie for the particular week
--------------------
b)
Plug in x = 0 to find that y = 196
Plug in x = 1 to get y = 150.92 which rounds to y = 151 since we're talking about the number of people
Repeat for x = 2 all the way up to x = 9 to account for the first ten weeks. We stop at 9 instead of 10 because we started at x = 0.
The table is shown in the attachment below next to the graph.
I'm not sure why your teacher put a dollar sign over the second column of the table when it should be the number of people. It might be a typo. If they meant to do it, then there's missing information about ticket prices.
--------------------
c)
The graph is shown below. You can plot each (x,y) point on the same grid and then draw a curve through them. A much quicker way is to use software like GeoGebra (which is what I used) or Desmos or a pocket calculator. There are tons of many options to pick from. Feel free to choose your favorite.
The blue dashed segments on the graph visually help verify the result of part (d). We have y = 20 lead to an x value somewhere between x = 8 and x = 9. When submitting the graph to your teacher, you'll leave out the blue dashed segments.
--------------------
d)
Refer to the table we made in part (b). We have x = 9 lead to y = 19 approximately which is when y is below 20 people. Recall that x = 0 refers to week 1, so x = 9 refers to week 9+1 = 10. Week ten is where the view count drops below 20 people per showing.
If you wanted to use the graph in part (c), then you'd follow the blue dashed line mentioned earlier. Start at the y axis at y = 20. Trace the blue dashed line until reaching the curve. Then drop straight down to arrive somewhere between x = 8 and x = 9. Round up to x = 9. Then make the adjustment to go from x = 9 to week ten.
If you want an algebraic method, then follow the steps below.
Plug in y = 20 and solve for x. We'll need to involve logarithms to isolate the exponent.
[tex]y = 196(0.77)^x\\\\20 = 196(0.77)^x\\\\20/196 = (0.77)^x\\\\0.1020408 \approx (0.77)^x\\\\(0.77)^x \approx 0.1020408\\\\\text{Log}\left((0.77)^x\right) \approx \text{Log}(0.1020408) \\\\x*\text{Log}\left(0.77\right) \approx \text{Log}(0.1020408) \\\\x \approx \text{Log}(0.1020408)/\text{Log}\left(0.77\right) \\\\x \approx 8.7325564 \\\\[/tex]
This rounds up to x = 9 leading to week ten as the answer.
As confirmation
[tex]y = 196(0.77)^x = 196(0.77)^8 \approx 24.22 \approx 24\\\\y = 196(0.77)^x = 196(0.77)^9 \approx 18.65 \approx 19\\\\[/tex]
Answer:
Part (a)We can model this as an exponential equation.
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is the initial valueb is growth factorx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
As the movie theatre lost 23% of its audience each week, the growth (decay) factor will be 100% - 23% = 77% → 0.77
Given:
a = 196b = 0.77x = times (in weeks)y = audience (in number of people)Substitute the given values into the formula to create the exponential equation:
[tex]y=196(0.77)^x[/tex]
Part (b)[tex]\begin{tabular}{| c | r |}\cline{1-2} \bf weeks & \bf audience \\\cline{1-2} 1 & 150.92\\\cline{1-2} 2 & 116.21\\\cline{1-2} 3 & 89.48\\\cline{1-2} 4 & 68.90\\\cline{1-2} 5 & 53.05\\\cline{1-2} 6 & 40.85\\\cline{1-2} 7 & 31.46\\\cline{1-2} 8 & 24.22\\\cline{1-2} 9 & 18.65\\\cline{1-2} 10 & 14.36\\\cline{1-2}\end{tabular}[/tex]
**all values rounded to 2 dp**
Part (c)see attached for graph
Part (d)Set y < 20 and solve for x:
[tex]\begin{aligned}196(0.77)^x & < 20\\\\(0.77)^x & < \dfrac{5}{40}\\\\\ln (0.77)^x & < \ln\left(\dfrac{5}{49}\right)\\\\x\ln (0.77) & < \ln\left(\dfrac{5}{49}\right)\\\\x & > \dfrac{\ln\left(\dfrac{5}{49}\right)}{\ln (0.77)}\\\\x & > 8.732555795\end{aligned}[/tex]
Therefore, the movie audience will fall below 20 people per viewing during the 9th week.
Easy math help picture below problem 4
Answers
Answer: is 126 degrees
Step-by-step explanation:
9. The price of one gallon of heating oil is $2.689.Which is this number rounded
to the nearest penny?
A $2.68
B $2.69
C $2.70
D $3.00
Answers
kawika is a woodworker and he carves a block in the shape of a right triangular prism. what is the total surface area of the block
Answers
Answer:The answer is D
Step-by-step explanation:
I know this because all the area of each face is equal to 10+10+52+32+40 and that is equal to 144in. squared
Answer:
D :)
Step-by-step explanation:
wait, have you smiled today? its very important:)
The following chart shows a company's sales records of four employees over the past year,
Sales by Month
50
45
40
Sales 61000)
35
Ben
Marcel
30
25
Rebecca
20
2
8 9 10 11 12
Month
Based on this graph, which employee is likely to have the greatest sales next month?
a Ben
b Marcel
c Kim
d. Rebecca
Save and Exit
Next
Sul
Mark this and return
Answers
Answer:
The answer is C
Step-by-step explanation:
URGENT PLS HELP 20 POINTS
Answers
Step-by-step explanation:
The radius,r is 1 unit
The sum of angles is = π + π/4
5π/4
The length of the arc = (5π/4)/2π • 2πr
= 5π/4 units
Can someone please help me with this? Thank you. No links!
Answers
Answer: 2(mJKL)=mJL
Step-by-step explanation: The arc angle is double the inscribed angle
John made a lump sum deposit of $ 7,800 in an account that pays 5.5% per year. Find
the value (maturity value) of his account after 3 years. How much is the interest ?
Answers
Maturity Value: 9,159.08
Interest: 1,359.08
Apr 13, 11:50:23
A group of friends wants to go to the amusement park. They have no more than $90
to spend on parking and admission. Parking is $16.50, and tickets cost $10.50 per
person, including tax. Use the drop-down menu below to write an inequality
representing p, the number of people who can go to the amusement park.
Answers
Answer:
16.50 + 10.50p ≤ 90
Step-by-step explanation:
add the parking amount and the ticket cause per person (p) to make it less than or equal to $90 since that’s the only amount of money that could be used
Andrew can paint a painting 2 times faster than Ethan can. When they work together on a painting it takes them 9 hours to paint. How long would it take Ethan to paint the painting by himself?
Answers
Answer:
13.5
Step-by-step explanation:
it rlly easy
Hey who knows how to copy and paste please wyd
Answers
Answer:
CTRL C to copy and CTRL V to paste
Step-by-step explanation:
please mark brainliest and btw if you dont want to get plagarized use quillbot
6 increased by 14 divided by 7
Answers
Answer:
2
Step-by-step explanation:
I think it's 2 if it is wrong pls correct me
Please help me outttt
Answers
Answer:
2 + [tex]\sqrt{3}[/tex]
Step-by-step explanation:
In decimal form, it is also 3.73205080...
hope this helps :)
I WILL GIVE YOU 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
119
Step-by-step explanation:
all angles in a triangle add up to 180
180-61-58=61
so missing inner angle is 61
then to solve 1:
180-61=119
I am a teacher and need to proofread my student's work. But it makes it quite hard when I need to watch a 30-second ad to make sure their answers are right. Is there any way I can bypass this without having to pay because this is a huge inconvenience?
Answers
Answer:i dont think so..
Step-by-step explanation:
Help Me on this!!
[tex] \\ \\ [/tex]
Answers
So here we are given that a || b and c || d, so the quadrilateral formed by the intersection of the four lines is just a parallelogram, so recall the property of parallelogram that parallelogram's opposite angles are always equal and the interior angles on the same side add up to 180°, and the property of angles that the alternate angles are always equal (that's angles Like in the Shape Z) and vertically opposite angles are equal (like in shape of X) and the property of linear pair i.e the sum of all angles on a plane line is 180°.
Now, as angles 3 and 7 are on a line d, so their sum will just be 180°, by property of linear pair
[tex]{:\implies \quad \sf m\angle 3+m\angle 7=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf m\angle 7+74^{\circ}=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf m\angle 7=180^{\circ}-74^{\circ}}[/tex]
[tex]{:\implies \quad \boxed{\bf{m\angle 7=106^{\circ}}}}[/tex]
Also, as angles 8 and 3 are vertically opposite angles, so they will be same, so we have
[tex]{:\implies \quad \boxed{\bf{m\angle 8=74^{\circ}}}}[/tex]
Now also, angle 7 and angle 11 are opposite angles of the parallelogram, so they will be equal, so we have :
[tex]{:\implies \quad \boxed{\bf{m\angle 11=106^{\circ}}}}[/tex]
Also, the interior angles on same side of Parallelogram add upto 180°, so we can have ;
[tex]{:\implies \quad \sf m\angle 11+m\angle 13=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf m\angle 13+106^{\circ}=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf m\angle 13=180^{\circ}-106^{\circ}}[/tex]
[tex]{:\implies \quad \boxed{\bf{m\angle 13=74^{\circ}}}}[/tex]
Also, Opposite angles of Parallelogram are equal, so angle 6 will be equal to angle 13, so angle 6 will be 74° and we also know the Vertically Opposite angles are equal. So, for angle 1 we have
[tex]{:\implies \quad \boxed{\bf{m\angle 1=74^{\circ}}}}[/tex]
Now, we are end with the conclusion :
[tex]{\bf{m\angle 1=74^{\circ}}}[/tex][tex]{\bf{m\angle 7=106^{\circ}}}[/tex][tex]{\bf{m\angle 8=74^{\circ}}}[/tex][tex]{\bf{m\angle 11=106^{\circ}}}[/tex][tex]{\bf{m\angle 13=74^{\circ}}}[/tex][tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Measure of Angle 3 is given, that is : Angle 3 = 74°
And the lines a and b are parallel, similarly line c and d are parallel to each other as well.
Now, let's just use property of angles on parallel lines to find measure of each angle we have been asked.
[tex]\qquad \tt \dashrightarrow \: \angle1 = \angle3 = 74 \degree[/tex]
[ By Corresponding Angle pair ]
・ ．━━━━━━━†━━━━━━━━━．・
[tex]\qquad \tt \dashrightarrow \: \angle7 + \angle3 = 180 \degree[/tex]
[ By Linear Pair ]
[tex]\qquad \tt \dashrightarrow \: \angle7 = 180 - \angle3 [/tex]
[tex]\qquad \tt \dashrightarrow \: \angle7 = 180 - 74[/tex]
[tex]\qquad \tt \dashrightarrow \: \angle7 = 106 \degree[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
[tex]\qquad \tt \dashrightarrow \: \angle8 = \angle3 = 74 \degree[/tex]
[ By Vertical opposite angle pair ]
・ ．━━━━━━━†━━━━━━━━━．・
[tex]\qquad \tt \dashrightarrow \: \angle7 = \angle11 = 106 \degree[/tex]
[ opposite angles of a Parallelogram ]
・ ．━━━━━━━†━━━━━━━━━．・
[tex]\qquad \tt \dashrightarrow \: \angle13= \angle3 = 74 \degree[/tex]
[ by Corresponding Angle pair ]
A pizza was divided into fourths. Jack ate 1/2 of one of the fourths. What part of the pizza de he eat?
Answers
1/2 x 1/4 = 1/8
f(n)=−48⋅(-¼)^n. Complete the recursive formula of f(n)
f(1)=
f(n)=f(n-1)⋅
Answers
The function f(n)=−48⋅(-¼)^n is a geometric sequence
The recursive definition of f(n) is f(1) = 12; f(n) = f(n - 1) . -¼
How to determine the recursive formula of f(n)The function is given as:
f(n)=−48⋅(-¼)^n
Calculate f(1)
f(1)=−48⋅(-¼)^1
This gives
f(1) = 12
Calculate f(2)
f(2)=−48⋅(-¼)^2
This gives
f(2) = -3
Calculate the common ratio (r)
r = f(2)/f(1)
So, we have:
f = -3/12
Simplify
r = -1/4
Recall that: r = f(2)/f(1)
This gives
-1/4 = f(2)/f(1)
Make f(2) the subject
f(2) = -1/4* f(1)
Express 1 as 2 - 1
f(2) = -1/4* f(2 - 1)
Substitute 2 for n
f(n) = -1/4* f(n - 1)
Rewrite as:
f(n) = f(n - 1) . -¼
Hence, the recursive definition of f(n) is f(1) = 12; f(n) = f(n - 1) . -¼
Read more about sequence at:
https://brainly.com/question/7882626
Please help now
Pic below
Answers
12) In two successive years, the population of a town is increased by 15% and 20%. What
percent of the population is increased after two years?
A. 32%
B. 35%
C. 38%
D. 68%
Answers
Which number best represents the slope of the graphed line?
Y410
-10
10
10
Answers
Answer:
1/2
Step-by-step explanation:
I took the test and rise/run is being asked
Help picture below problem 15
Answers
If it says the triangles are =~ to each other then they are exactly the same thing.
bob has 12 red cards and 20 green cards. what is the ratio of bobs red cards to his green card
Answers
Answer:
3:5
If Bob has 12 red cards and 20 green cards, all we have to do is write the two numbers seperated by a colon.[tex]12~to~20 -- > 12:20[/tex]
How did we get 3:5 then, you may be asking? It is just a few simple steps. All you need to do is find the divisor. How do we find the divisor? Find the lowest or highest number that both parameters are divisible by.[tex]\frac{12 / 4}{20 / 4} = \frac{3}{5} -- > 3:5[/tex]
________________________________________________________
The problem is now complete, time to go over what we just learned while reading this.
________________________________________________________
What did we learn?We learned how to find and simplify ratios in a story problem.
Related questions? Ask me in the comments box.