Step-by-step explanation:
Let the smaller number be x.
So, according to Question,
the larger number will be 1+4x.
Now, sum of the numbers is 61, like this:-
[tex]1 + 4x + x = 61[/tex]
[tex]5x = 61 - 1[/tex]
[tex]5x = 60[/tex]
[tex]\tt{x = \dfrac{60}{5}}[/tex]
[tex]\boxed{\tt{x = 12}}[/tex] is the required Answer.
Hope it helps :)
An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is programmed to go on at a randomly selected time after the subject clicks "Start." The density curve models the amount of time the subject has to wait for the light to flash. a. What height must the density curve have? Justify your answer. b. About what percent of the time will the light flash more than 3.75 seconds after the subject clicks "Start"? c. Calculate and interpret the 38th percentile of this distribution.
Using the uniform distribution, it is found that:
a) The height of the density curve is of 0.25.
b) 31.25% of the time will the light flash more than 3.75 seconds after the subject clicks "Start".
c) The 38th percentile of this distribution is of 2.52 seconds. It means that 38% of the time, the light will go on in at most 2.52 seconds.
Uniform distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
In this problem, uniform between 1 and 5, hence [tex]a = 1, b = 5[/tex]
Item a:
The height of the uniform distribution is:
[tex]h = \frac{1}{b - a}[/tex]
Hence:
[tex]h = \frac{1}{5 - 1} = 0.25[/tex]
Item b:
[tex]P(X > 3.75) = \frac{5 - 3.75}{5 - 1} = 0.3125[/tex]
0.3125 x 100% = 31.25%
31.25% of the time will the light flash more than 3.75 seconds after the subject clicks "Start".
Item c:
The 38% percentile is x for which P(X < x) = 0.38, hence:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
[tex]0.38 = \frac{x - 1}{4}[/tex]
[tex]x - 1 = 4(0.38)[/tex]
[tex]x = 2.52[/tex]
The 38th percentile of this distribution is of 2.52 seconds. It means that 38% of the time, the light will go on in at most 2.52 seconds.
A similar problem is given at https://brainly.com/question/15855314
Becka borrowed $460 from her cousin at the rate of 8.5% per year. If the inflation rate was 2.7% that year, what is her cousin's actual rate of return on the loan?
Answer:4%
Step-by-step explanation:
6%-2%=4%
Whats the InversE of Y=3x+2
IF U CAN HELP ME ILL BRAINIFY U AND U GET ALL MY POINTS. IT HAS TO BE A GOOD ANSWER, AS I THINKING I GOT THE CORRECT ANSWER, SO YOU CANT FOOL ME!!
Sherie makes a canvas frame for a painting using stretcher bars. The retuangular painting will be 12 inches long and 9 inches wide. What should be the diagonal length of the painting in Sherie's question? Record your numerical response. Do not include words, units or spaces
it would be 15 in. diagonal
A cylinder has a radius of 1 inch and height of 1 inch.
What is the approximate volume of the cylinder? Round to the nearest hundredth. Use 3.14 for π.
1.05 cubic inches
1.57 cubic inches
3.14 cubic inches
6.28 cubic inches
Answer:
3.14, confirmed on Edge
Step-by-step explanation:
Since this cylinder has a radius of 1 inch, its volume is equal to 3.14 cubic inches.
Given the following data:
Radius of cylinder = 1 inch.
Height of can = 1 inch.
[tex]\pi =3.14[/tex]How to calculate the volume.Mathematically, the volume of a cylinder is given by this formula:
[tex]V = \pi r^2h[/tex]
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
[tex]V = 3.14 \times 1^2 \times 1\\\\V=3.14 \times 1[/tex]
V = 3.14 cubic inches.
Read more on cylinder here: brainly.com/question/21367171
In triangle ABC, it is given that A = 70 degree, B = 52 degree, BO and CO are the bisectors of angle B and angle C
respectively. Find angle OCB andangle BOC.
Answer:
Angle OCB= 35 degrees and Angle BOC= 119
Step-by-step explanation:
ANGLE OCB= 1/2 C (Construction of bisector)
= 1/2 70
= 35
ANGLE OBC= 1/2 B (Construction of bisector)
= 1/2 52
= 26
Therefore, in triangle BOC,
180 degree= ANGLE OBC+ANGLE BOC+ANGLE OCB
180= 35+26+ANGLE BOC
180= 61+ANGLE BOC
ANGLE BOC= 180-61
ANGLE BOC= 119
Answer:
angle ocb=58°
angleboc=96°
Step-by-step explanation:
first get the measure of angle acb which is 58°
this is becoz the total angles in a triangle add up to 180°
angle cbo =26° and angle bco=58°
therefore to get the remaining angle boc ,u add 58 &26 ,then minus from 180
the answer is 96°
Help me ASAP!!pls I don’t get it:(
What is the expression -7(3z + 5t - 3g) in simplest form?
Answer:
-3z-5t+3g
Step-by-step explanation:
-7(3z+5t-3g)
= -7×3z +( -7×5t)( -7×-3g)
= -21z-35t+21g
divide all elements by 7
= -21÷7 -35÷7+21÷7
= -3z-5t+3g
What is the Vertex of the Absolute Value parent function?
(1,1)
[0,0)
(0,0)
0 (-00,00)
Answer:
Step-by-step explanation:
(0,0)
:I
image 1
image 2
image 3
none
Answer:
Image 1
Step-by-step explanation:
It has a varitiy of differnt circles, while the others only have one kind of circle.
T-shirts
$7.50
Shorts
$9.00
Windbreakers
$12.25
If she will buy 35 T-shirts, 45 pairs of shorts, and 25 windbreakers, what will be her total cost?
$958.75
$973.75
$1,021.25
$1,038.75
Answer:
$973.75
Step-by-step explanation:
7.50x35=262.5
45x9.00=405
25x12.25=306.25
If you add all the sums together you would get $973.75
If there are 90 calories in Three-fourths cup of yogurt, how many calories are in 3 cups of yogurt?
Answer:
360 calories
Step-by-step explanation:
If you look at the ammount of Calories per 3/4 you will quickly find that 3/4 ths of a cup is 1/4 of your goal so multiply the amount of calories by 4 and you will get your awnser.
Can anyone help with these? I appreciate and I will award 5 stars and brainliest
Graph 1
coordinates : (0,-5) (-6,-2)
m = (y2-y1)/(x2-x1)
m = (-2-(-5))/(-6-0)
m = 3/-6 = -1/2
Substitute the values,
y = mx + c
-2 = (-1/2)(-6) + c
-2 = 3 + c
c = -5
Thus, equation is y = -1/2x -5
Graph 2
coordinates : ( 4,-2) (-5,3)
m = (y2-y1)/(x2-x1)
m = (3-(-2))/(-5-4)
m = 5/-9
Substitute the values,
y = mx + c
-2 = (-5/9)(4) + c
-2 = -20/9 + c
c = 2/9
Thus, the equation is y = -5/9 + (2/9)
Hope it helps :)
Classify the following triangle. Check all that apply.
Answer: A.) obtuse & F.) isosceles
Explanation:
Obtuse because the large angle is greater than 90°
isosceles because two of the sides are equal length
Would someone help me to understand this math. Thank you
LINES & LINE SEGMENTS ASSIGNMENT
Plot the following points on the number line below:
A: -25 B: -17 C: -13
D: -1 E: 4 F: 11
G: 16 H: 23 I: 25
Using the points and number line from the problem above, find each of the following. The first one is done for you.
a) BD = | -17 – (-1) | = | -17 + 1 | = | -16 | = 16
b) AE
c) EF
d) GI
e) CH
f) BG
g) CF
h) AC
Answer:
16, 29, 7, 9, 36, 33, 24, 12
Step-by-step explanation:
The distance between two points on a number line is the magnitude of the difference between their coordinates. In general, that means you can subtract the coordinate of the left point from the coordinate of the right point to find the distance.
Here, the points are in alphabetical order on the number line, left-to-right, as are the letters in the segment names. So you subtract the coordinate of the first point of the name from the coordinate of the last point in the name.
This is 8 simple subtraction problems.
a) D - B = -1 -(-17) = 16
b) E - A = 4 -(-25) = 29
c) F - E = 11 -4 = 7
d) I - G = 25 -16 = 9
e) H - C = 23 -(-13) = 36
f) G - B = 16 -(-17) = 33
g) F - C = 11 -(-13) = 24
h) C - A = -13 -(-25) = 12
_____
If you think of it as mileposts on a highway, it should be no surprise that the distance between milepost 4 and milepost 11 is 11 - 4 = 7 miles.
IF YOU CAN HELP ME I WILL LITERALLY BE SO HAPPY AND ILL FAV U TO GET SO MANY POINTS
THE WATER COMPANY INSTALLED A 40 YARD DIAGONAL BRACE ON A WATER TOWER BETWEEN TWO VERTICAL BEAMS THAT ARE 12 YARDS APART. DETERMINE THE HEIGHT OF EACH VERTICAL BEAM.
Answer:
120 yatds
Step-by-step explanation:
The height of each vertical beam is approximately 38.16 yards.
The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' (Trans. Amer. Fisheries Soc. (1991: 405-420)) gave the accompanying data on
y= maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and
x= squawfish length, both in mm.
Use the following statistics to give the equation of the least squares regression line.
x=524.880,
y=413.975,sx=12.251,sy=12.300,
r=0.9562
options:
a) ^y=0.960xâ89.910
b) ^y=0.960x+89.910
c) ^y=â89.910x+0.960
d) ^y=0.952x+89.910
e) ^y=0.952xâ89.910
f) None of the above
Answer:
the correct answer is not there. here it is:
^y = 0.960x - 89.910
Step-by-step explanation:
we have regression line equation as:
^y = a+bx
we have the following details available
x = 524.88
y = 413.975
Sx = 12.251
Sy = 12.300
r = 0.9562
we have to find values of a and b
b = rSy/Sx
= 0.9562(12.3)/12.251
= 11.76126/12.251
= 0.960
a = y - intercept
= 413.975-0.96(524.88)
= 413.975-503.8848
= - 89.9098
a = -89.910
putting these values into the equation, we have:
^y = -89.910 + 0.9600x
which is also
^y = 0.960x - 89.910
(1/5) ^ 3 * (1/5) ^ 4 * (1/5) =
9514 1404 393
Answer:
(1/5)^8
Step-by-step explanation:
The applicable rules of exponents are ...
a = a^1
(a^b)(a^c) = a^(b+c)
__
(1/5)^3 · (1/5)^4 · (1/5) = (1/5)^(3+4+1) = (1/5)^8
= 1/390625
I need help solving...
Answer:
x = 4
Step-by-step explanation:
Because we know both figures have the same perimeter, we can set them equal to each other.
3x + 4 + 5x + 1 + 2x + 5 = x + 13 + x + 13 + 2x + 2x
10x + 10 = 6x + 26 (Added like terms.)
4x + 10 = 26 (Subtracted 6x on both sides.)
4x = 16 (Subtracted 10 on both sides.)
x = 4 (Divided 4 on both sides.)
Mrs. Davis earns $100 per week plus 6% commission on all of her sales. If she sells a house this month worth $120,000, what is her total income for the month (Assume 4 weeks = 1 month)?
Answer:
$7600
Step-by-step explanation:
total income = 120,000(.06)+100(4)
total income= 7200+400
total income = 7600
.
Evaluate the expression when x = 12 and y = 2.
x above 3y
38
2
125
8
Grayson wrote 1.47 divided by 7 = 2.1.
Why is his thinking incorrect?
Answer: he needs to put the decimal in front of the 2 so it can be 0.21
Step-by-step explanation:
Answer:
he has to put the decimal point in front of the 2
hope this helps
9x-(-2y)-8x-(-12y) simplify
Answer:
x+14y
Step-by-step explanation:
9x+2y-8x+12y
x+14y
determine which of the following sets of ordered pairs represents a function
Answer:
B.
Step-by-step explanation:
Every answer besides B. has an input that repeats. A function contains inputs that have exactly one output. This means x values cannot have more than one y value.
Which of the following is a valid conclusion based on the Venn diagram?
A.
If a pet is not a dog, then it is a beagle.
B.
If a pet is a dog, then it is a beagle.
C.
If a pet is a beagle, then it is a dog.
D.
If a pet is a dog, then it is not a beagle.
Answer:
C
Step-by-step explanation:
A beagle is a dog but not all dogs are beagles.
Let f(x)=10x. Which function represents a transformation of f(x) by a vertical stretch with factor 1.25? g(x)=101.25x g(x)=0.8⋅10x g(x)=1.25⋅10x g(x)=100.8x
Answer:
g(x) = 1.25 x 10^x
Answer:
g(x)=1.25 ₓ 10ˣ
Step-by-step explanation:
Find the sigma notation of the following sum:
[tex][(\frac{2}{n})^3-\frac{2}{n} ](\frac{2}{n} )+...+[(\frac{2n}{n} )^3-\frac{2n}{n} ](\frac{2}{n} )[/tex]
Answer:
[tex]\displaystyle \frac{2}{n} \sum_{i = 1}^{n} \left(\left(\frac{2i}{n}\right)^3 - \frac{2i}{n}\right)[/tex]
Step-by-step explanation:
We have the sum:
[tex]\displaystyle \left[\left(\frac{2}{n}\right)}^3-\frac{2}{n}\right]\left(\frac{2}{n}\right)+...+\left[ \left(\frac{2n}{n}\right)^3-\frac{2n}{n}\right]\left(\frac{2}{n}\right)[/tex]
And we want to find the sigma notation that represents the sum.
Note that the leftmost term is the first term while the rightmost term is the last term.
n is the number of terms. Therefore, (2 / n) will stay constant. Hence, we can factor it out of the series:
[tex]\displaystyle =\frac{2}{n}\left(\left[\left(\frac{2}{n}\right)^3-\frac{2}{n}\right]+...+\left[\left(\frac{2n}{n}\right)^3-\frac{2n}{n}\right]\right)[/tex]
Notice the differences between the first term and the last term. The first term is given by [tex]\displaystyle \left(\frac{2}{n}\right)^3- \frac{2}{n}[/tex]. The last term is given by [tex]\displaystyle \left(\frac{2n}{n}\right)^3- \frac{2n}{n}[/tex]. Because at the last term, our initial term i is equal to n, we can replace the extra n with i for our summation.
Therefore, we can write the following summation:
[tex]=\displaystyle \sum_{i=1}^{n} \frac{2}{n}\left(\left[\left(\frac{2i}{n}\right)^3-\frac{2i}{n}\right]\right)[/tex]
And since (2 / n) is constant:
[tex]\displaystyle = \frac{2}{n} \sum_{i = 1}^{n} \left(\left(\frac{2i}{n}\right)^3 - \frac{2i}{n}\right)[/tex]
Sketch 9 red counters and 4 yellow counters. How many zero pairs can you make ? How many counters do you have after you remobe the zero pira ? What do they represent ?
Answer:
You have 5 yellow counters left because you can make 4 zero pairs, the zero pairs represent the even amount that when they get added together they cancel out
Step-by-step explanation:
Yellow-1,2,3,4,
Red-1,2,3,4,5,6,7,8,9
Cancel out-1,2,3,4
Left with-5,6,7,8,9
Of the 1,400 students enrolled at Berkmar Middle School, 40% of students enrolled are in the 6th grade. How many students are enrolled in 6th grade? Show your work.
ASAP
Answer:
3500
Step-by-step explanation:
1400 divided by 40% = 3500
If Isaac uses a coupon entitling him to a 25% discount off the purchase price before tax, how much will his bill be? Assume that a 7% sales tax is applied to the discounted price. Using words, explain how you found the discounted price.
Answer:
hope it helps...
Step-by-step explanation:
25/100 x 79
= 19.75
= 79 - 19.75
= $59.25 (before tax)
7/100 x 59.25
= 414.75/100
= 4.15
= 59.25 + 4.15
= $63.4 (after adding tax)
First we have to take out the percentage of discount and minus it from the total cost . To find the discounted price with tax, we have to take out the percentage of the tax from the discounted amount and add it to the discounted amount to get the total cost.