Answer:
[tex]Probability = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
Grape = 15
Cherry = 7
Lemon = 3
Strawberry = 5
Total = 30
Required
Determine the probability of picking a strawberry
The probability of drawing a strawberry is calculated by dividing the number of strawberry by the total number of fruits as follows;
[tex]Probability = \frac{Strawberry}{Total}[/tex]
Substitute 5 for Strawberry and 30 for Total
[tex]Probability = \frac{5}{30}[/tex]
Divide the numerator and denominator by 5
[tex]Probability = \frac{1}{6}[/tex]
Hence, the required probability is [tex]\frac{1}{6}[/tex]
The rate of growth of mice is inversely proportional to the square of the population:__________
Answer:
The value is [tex]y'(t) = \frac{k}{\sqrt{y(t)} }[/tex]
Step-by-step explanation:
From the question we told that are
The rate of growth of mice is inversely proportional to the square of the population
This above statement can be mathematically represented as
[tex]\frac{d y }{dt} \ \ \ \alpha \ \ \frac{1}{\sqrt{y(t)} }[/tex]
Here [tex]y(t)[/tex] is the population
=> [tex]\frac{d y }{dt} = \frac{k}{\sqrt{y(t)} }[/tex]
=> [tex]y'(t) = \frac{k}{\sqrt{y(t)} }[/tex]
Find the distance between the points (-74,-76) and (-35,4)
Answer:
The answer is
[tex]89 \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-74,-76) and (-35,4)
The distance between the points is
[tex]d = \sqrt{( { - 74 + 35})^{2} + ({ - 76 - 4})^{2} } \\ = \sqrt{ ({ - 39})^{2} +( { - 80})^{2} } \\ = \sqrt{1521 + 6400} \\ = \sqrt{7921} [/tex]We have the final answer as
[tex]89 \: \: units[/tex]Hope this helps you
What expression is equivalent to (8^2)^-4
Answer:
(64)^-4= 1/64^4= 1/16777216
Point A (2, 6) has been translated 1 left and 3 up followed by a 180 degree rotation.
What is the image of Point A?
Answer:
[tex]A(-1,-8)[/tex]
Step-by-step explanation:
Given
Point: A(2,6)
Translation: 1 left and 3 up
Rotation: 180 degrees
Required
Image of Point A
Taking the exercise one after the other
Represent the function as: (x,y)
Such that
[tex]A(x,y) = A(2,6)[/tex]
1 unit left translation means the function becomes (x - 1, y)
2 unit up translation means the function becomes (x - 1, y + 2)
Applying the above transformation
[tex]A(2,6) -> A(2-1,6+2)[/tex]
[tex]A(2,6) -> A(1,8)[/tex]
At this stage, the coordinate becomes
[tex]A(1,8)[/tex]
When a function (x,y) is rotated by 180, the new function becomes (-x,-y)
So;
The further transformation of A is
[tex]A(1,8) -> A(-1,-8)[/tex]
Hence, the new image of A is
[tex]A(-1,-8)[/tex]
Answer:
its -1,-9
Step-by-step explanation:
A 25 foot long rectangular sheet of metal, 12 inches wide, is to be made into a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many inches should be turned up to give the gutter its greatest capacity?
Answer:
The value is [tex]k = 3 \ inches[/tex]
Step-by-step explanation:
From the question we are told that
The length is [tex]l = 25 \ ft[/tex]
The width is [tex]w = 12 \ inches = \frac{12}{12} = 1\ ft[/tex]
Generally let assume that (k ft) was turned up on each side hence the remaining width is
[tex](1 - 2 k ) \ ft[/tex]
Now the capacity is also the volume it can hold which is mathematically represented as
[tex]C = 25 (1- 2k) k[/tex]
[tex]C = 25 (k- 2k^2)[/tex]
[tex]C = 25k - 50k^2[/tex]
At maximum or minimum
[tex]\frac{dC}{dk} = 0[/tex]
=> [tex]\frac{dC}{dk} = 25 - 100k = 0[/tex]
=> [tex]k = 0.25\ ft[/tex]
Now to see if the value obtained is positive or negative we differentiate a second time
So
[tex]\frac{d^2C}{dk^2} = - 100k[/tex]
at k = 0,25 ft
[tex]\frac{d^2C}{dk^2} = - 100(0.25)[/tex]
[tex]\frac{d^2C}{dk^2} = -25[/tex]
since a negative value is obtained then k is the maximum value
converting to inches
[tex]k = 0.25 * 12[/tex]
[tex]k = 3 \ inches[/tex]
Solve 6x+57=2x+315 . A. x=−911 B. x=911 C. x=119 D. x=−119
Explanation:
Remember: we have to isolate the variable x, so that means we have to get x by itself.
Step 1:
Let’s look at our equation:
[tex]6x+57=2x+315[/tex]
Let’s subtract 2x from both sides of the equation, since our goal is to isolate the variable. You could also subtract 6x from both sides, but you would end up with a negative number, and I find it easier to deal with positive numbers.
[tex]6x(-2x)+57=2x(-2x)+315\\4x+57=315[/tex]
Step 2:
Now, let’s subtract 57 from both sides of our equation.
[tex]4x+57(-57)=315(-57)\\4x=258[/tex]
Step 3:
Since we have to isolate x, let’s divide both sides of the equation by 4.
[tex]4x/4=x\\258/4=64.5[/tex]
Our final answer: x = 64.5
None of your options is the correct answer. Notify your teacher, tutor, etc. since there none of the options are correct.
A group of 8 children and 8 adults are going to a movie. Child tickets cost $2, and adult tickets cost $6. How much will the movie tickets cost in all? ANSWER PLEASE LOTS LOTS OF POINTS.
Answer:
64 dollars
Step-by-step explanation:
8 children and 8 adults
2 dollars for a child and 6 dollars for an adult
cost for children
8 children * 2 dollars each = 16
cost for adults
8 adults * 6 dollars each = 48
Add the two costs together
16+48 =64
Answer:
8×2=16
8×6=48
48+16=64
Please help me with the question below
Answer:
1/8x + 1/2 y
Step-by-step explanation:
Charlotte gets 1/4x from dayna
Charlotte now has
1/4x+y
She lends 1/2 of this
1/2 ( 1/4x +y)
1/8x + 1/2 y
A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.84mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.24mm. Would this outcome warrant a refund (meaning that it would be unusual)?
Answer:
4.32%; no
Step-by-step explanation:
The value of 0.24 differs from the mean by 0.84 -0.24 = 0.60. 2 standard deviations from the mean would be a difference of 2×0.35 = 0.70.
A statistical calculator says the probability of a depth less than 0.24 mm for the given distribution is about 4.32%.
The value differs from the mean by less than 2 standard deviations, so is not considered unusual.
ID: A
17. N.Q.1-2 ULHS has a student that can run 100 yds in 15 seconds. Mrs. Duke's class converted his speed to
miles per hour below and determined he can run 4.55 miles per hour. Is the conversion correct? If not, explain
what the class did wrong and then work it out using dimensional analysis. You MUST Show all work.
100 yds
60 sec
60 min 1 mile
= 4.55 mph
15 sec
1 min 1 hr 5280 yds
its hard to explain and show work but so you know the answer is no and its because they converted yards to miles and did the formula for ft to miles instead of yd to miles they did 5280 ft per mile and not 1760 yd per miles
Answer:
13.63 miles per hour
Step-by-step explanation:
100 yards / 15 sec converted to miles per hour
100 yards x 60 sec x 60 min x 1 mile = 13.63 miles/hr
15 sec 1 min 1 hr 1760 yards
the mistake on Mrs Dukes is the conversion from miles to yards.
1 mile = 1760 yards NOT 5280 yards
If x is 2+ root 3 then find (x^2+1/x^2) (x^2-1/x^2)
Answer:
Here x=2−3–√ ................…………………………………….....(1)
Hence 12−3√=12−3√⋅2+3√2+3√=2+3–√ .....................(2)
From (1) and (2) we get x+1x=4 .......……………………………....(3)
and x−1x=−23–√ ...............…………………….………....(4)
From (3) and (4) we get x2−1x2=(x+1x).(x−1x)=−83–√.
Hoped I helped
determine whether the variable is qualitive or quantitive nation of origin
It does not deal with numeric values, but rather we're talking about names or labels when we are talking about nations of origin. This variable is categorical and nominal. It is not ordinal as we cannot order the nations in any way. You could argue about alphabetical ordering of course, but that won't apply here because you could do that about any set of labels (eg: colors red,green,blue can be ordered alphabetically but intrinsically it doesn't make sense to sort colors).
Since "nation of origin" involves categories or labels representing different countries, it is considered a qualitative variable.
We have,
Qualitative variables, also known as categorical variables, represent characteristics or qualities that cannot be measured numerically.
These variables typically involve categories or labels that describe different groups or attributes.
In the case of "nation of origin," it refers to the country from which someone originates.
This variable is qualitative because it involves different categories or labels representing different nations or countries.
Examples of possible categories for nation of origin include "United States," "Canada," "France," "China," and so on.
Therefore,
Since "nation of origin" involves categories or labels representing different countries, it is considered a qualitative variable.
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The radius of the wheel on a bike is 21 inches. If the wheel is revolving at 154 revolutions per minute, what is the linear speed of the bike, in miles per hour
Answer:
The linear speed of the bike is 19.242 miles per hour.
Step-by-step explanation:
If sliding between the bottom of the wheel and ground can be neglected, the motion of the wheel can be well described by rolling, which is a superposition of coplanar pure rotation and translation, The speed of the bike occurs at the center of the wheel, where resulting instantaneous motion is pure translation parallel to ground orientation. The magnitude of the speed of bike ([tex]v_{B}[/tex]), measured in inches per second, is:
[tex]v_{B} = R\cdot \omega[/tex]
Where:
[tex]R[/tex] - Radius, measured in inches.
[tex]\omega[/tex] - Angular speed, measured in radians per second.
Now, the angular speed must be converted from revolutions per minute into radians per second:
[tex]\omega = \left(154\,\frac{rev}{min} \right)\cdot \left(2\pi\,\frac{rad}{rev} \right)\cdot \left(\frac{1}{60}\,\frac{min}{s} \right)[/tex]
[tex]\omega \approx 16.127\,\frac{rad}{s}[/tex]
The speed of the bike is: ([tex]R = 21\,in[/tex] and [tex]\omega \approx 16.127\,\frac{rad}{s}[/tex])
[tex]v_{B} = (21\,in)\cdot \left(16.127\,\frac{rad}{s} \right)[/tex]
[tex]v_{B} = 338.667\,\frac{in}{s}[/tex]
Lastly, the outcome is converted into miles per hour:
[tex]v_{B} = (338.667\,\frac{in}{s} )\cdot \left(3600\,\frac{s}{h} \right)\cdot \left(\frac{1}{63360}\,\frac{mi}{in} \right)[/tex]
[tex]v_{B} = 19.242\,\frac{mi}{h}[/tex]
The linear speed of the bike is 19.242 miles per hour.
how do you simplify 15/40
Answer:3/8
Step-by-step explanation:
The simplest form of
15 /40 is 3 /8 .
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 15 and 40 is 5
Divide both the numerator and denominator by the GCD
15 ÷ 5
40 ÷ 5
Reduced fraction:
3 /8
Therefore, 15/40 simplified to lowest terms is 3/8.
There are 30 people at a meeting, They each shake hands with everyone. How many
handshakes were there? Hint: Think "The number of combinations of 30 people at a
meeting giving handshakes to each other 2 at a time."
Step-by-step explanation:
435 handshakes
hope this would be the right answer....
The total hands shake will be 435 hands shakes.
What is permutation and combination?The combination will apply when order dose not matter and when order matter permutation will apply.
the permutation and combination rule.
nCr=n!/r!(n−r)!
here. we have,
To find the total number of hands shakes we have to apply the permutation and combination rule.
nCr=n!/r!(n−r)!
Given:
There are 30 people in meeting.
In the given question order not does not matter so combination will applicable.
Calculate the number of hands shakes
C(30,2) = 30!/ 2! (30-2)!
=435
Thus, the total hands shake will be 435 hands shakes.
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Calculate the first, second, and third quartiles of the following sample. 5 8 2 9 5 3 7 4 2 7 4 10 4 3 5
Answer:
3 ; 4.5 ; 7.25
Step-by-step explanation:
Given the sample :
8 2 9 5 3 7 4 2 7 4 10 4 3 5
Calculate, the first, second, and third quartiles
Arranging the data in ascending order :
2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 7, 8, 9, 10
First quartile :
Q1 = [(n + 1) /4]th value
n = 14
Q1 = [(14 + 1) /4]th = (15/4)th = 3.75 value
Taking the average of the 3rs and 4th observation:
(3 +3) / 2 = 3
Second quartile :
Q2 = [2(n + 1) /4]th value
Q2 = 2(15)/4 = (30/4)th value
Q2 = 7.5 ; taking the 7th and 8th value
Q2 = (4 +5) /2 = 9/2 = 4.5
Q3 = [3(n + 1) /4]th value
Q2 = 3(15)/4 = (45/4)th value
Q2 = 11.25 ; taking the 11th
Q2 = 7 + 0.25 = 7.25
What are the degrees of freedom for Student's t distribution when the sample size is 16? d.f. = Use the Student's t distribution to find tc for a 0.95 confidence level when the sample is 16. (Round your answer to three decimal places.) A button hyperlink to the SALT program that reads: Use SALT.
Answer:
degrees of freedom = 15
tc= 1.746
Step-by-step explanation:
The degrees of freedom is given by n-1 where n is the sample size .
so the degrees of freedom for a t distribution is 16-1= 15
Now we have to find tc for 95% confidence interval. For this we look at the t- table under the 1-0.95= 0.05 for alpha for 15 degrees of freedom and the value is 1.746
This area is to the right side under the t distribution with the given degrees of freedom for the given alpha.
It can also be found out by other calculators such as graphing calculator.
Using the degree of freedom formula and the Tcritical distribution, the degree of freedom and Tcritical value are 15 and 2.131 respectively
Given that :
Sample size, n = 16The degree of freedom , df = n - 1Hence, the degree of freedom, df = 16 - 1 = 15
The t critical value :
Confidence level, α/2 = 0.05Tcritical = [tex]t_{\frac{0.05}{2}}, 15 = 2.131 [/tex]
Hence, the Tcritical value is 2.131.
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In 2 1/4 hours, Nick wrote 36 text messages what’s was his unit rate during the time?
A.14 messages per hour
B.16 messages per hour
C.34 messages per hour
D.81 messages per hour
Answer:
A. 224 messages per hour
B. 256 messages per hour
C. 544 messages per hour
D. 1296 messages per hour
Step-by-step explanation:
First you need to figure out how many messages Nick wrote in 1 hour
36 messages ÷ 2.25
2.25 hours ÷ 2.25
=
16 messages
1 hour
=
16 messages
hour
Then you multiply how ever many hours by 16 because Nick can write 16 messages in 1 hour.
A box is 15cm long, 4cm wide and 8cm high. Another box is 10cm long, 9cm wide and 4cm high. which box has a larger volume? what is the difference in volume between the two boxes
Answer:
Differences=
[tex] {120cm}^{3} [/tex]
Step-by-step explanation:
Volume of first box=15cm×4cm×8cm
[tex]480 {cm}^{3} [/tex]
Volume of second box=10cm×9cm×4cm
[tex] {360cm}^{3} [/tex]
Part B
Write an expression that represents the net change in Rylee's bank account balance after paying for fuel at the gas station.
Answer:
Rylee spent $25 for fuel at the gas station. This money is leaving her bank account, so represent the amount with a negative sign: -$25.
Step-by-step explanation:
None. the expression explains it.
solve for P in the scientific formula PV = nRT
[tex]PV=nRT\implies P=V^{-1}nRT[/tex].
Hope this helps.
The first Ferris wheel took 9 minutes to make a complete revolution. How fast was the wheel moving?
M=undefined, x-int=(3,0)
Answer:
x = 3
Step-by-step explanation:
Maybe you want the equation of the line.
__
A vertical line has undefined slope. Its equation is of the form ...
x = constant
In order for the line to go through a point with an x-coordinate of 3, the constant must be 3.
x = 3 . . . . equation of the line
Identify the opposite of each integer: a. 4 b. −2 c. +125 d. 1,348 e. −27 f. −398
a. −4
b. 2
c. −125
d. −1,348
e. 27
f. 398
Find the difference between the cash price and the payment plan and calculate the interest rate for the following questions.
1. A food processor for $149.50 cash, or $5.00 down and $10.00 per month for 15 months
2. A television for $675.00 cash, or $52.00 down and $120.00 per month for 6 months
3. A smartphone for $150.00 cash, or $25.00 down and $12.00 per month for 11 months
4. Bedroom furniture for $1,985.00 cash, or $400 down and $74.00 per month for 24 months
5. A jacket for $75.00 cash, or $25.00 down and $4.75 per week for 11 weeks
6. The Smiths bought new furniture that cost $3,298.00. The store offered them an option of putting $600 down and making equal payments of $300 a month for 10 months. Use the Federal Reserve System formula to find the APR the Smiths will pay for taking this plan.
Answer:
1).
Difference = $6
Interest rate= 4.03%
2).diffrence = $97
Interest rate = 14.37%
3). Difference = $7
Interest rate= 4.67%
4). difference= 191
Interest rate= 9.6%
5). Difference= 2.25
Interest rate= 3%
6). Difference=$ 302
Interest rate=9.12%
Step-by-step explanation:
1).$10 per months for 15 months
= 10*15=$150
PLus a down payment of $5= $155
Interest = 155-149= $6
Interest rate = 6/149*100= 4.03%
2.)$120.00 per month for 6 months
= 120*6=$ 720
Plus a down payment of $52=$772
Interest= 772-675= $97
Interest rate = 97/675 *100= 14.37%
3). $12.00 per month for 11 months
= 12*11= 132 plus down payment of $25
= $157
Interest= 157-150= $7
Interest rate=7/150 *100= 4.67%
4).$74.00 per month for 24 months
= 74*24=$1776
Plus a down payment of $400=$ 2176
Interest= 2176-1985= 191
Interest rate= 191/1985*100= 9.6%
5).$4.75 per week for 11 weeks
= 4.75*11=$52.25
Plus a down payment if $25
= 25+52.25=$ 77.25
Interest= 77.25-75= 2.25
Interest rate= 2.25/75 *100= 3%
6).$300 a month for 10 months
= 300*10= $3000
Plus a down payment of $600
= $3600
Interest=3600-3298= 302
Interest rate= 302/3298 *100=9.12%
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 56.6 degrees. Low Temperature (◦F) 40−44 45−49 50−54 55−59 60−64 Frequency 2 7 9 5 2 The mean of the frequency distribution is nothing degrees.
Answer:
Computed mean = 51.6
Actual mean > computed mean
Step-by-step explanation:
Low temp. - - Freq(f) - - midpoint(x) - - fx
40−44 - - - - - 2 - - - - - - - 42 - - - - - - 84
45−49 - - - - - 7 - - - - - - - 47 - - - - - - 329
50−54 - - - - - 9 - - - - - - - 52 - - - - - - 468
55−59 - - - - - 5 - - - - - - - 57 - - - - - - 285
60−64 - - - - - 2 - - - - - - - 62 - - - - - - 124
Mean (m) = Σ(fx) / Σ(f)
Σ(fx) = 84 + 329 + 468 + 285 + 124 = 1290
Σ(f) = 2 + 7 + 9 + 5 + 2 = 25
Mean (m) = 1290 / 25
Computed mean (m) = 51.6
Actual mean = 56.6
Actual mean > computed mean
56.6 > 51.6
For what values of b are the vectors ⟨−39,b,3⟩ and ⟨b,b2,b⟩ orthogonal?
Answer:
b = 0, -6 and 6Step-by-step explanation:
Given the vectors ⟨−39,b,3⟩ and ⟨b,b²,b⟩, for the vectors to be orthogonal, the dot product of both vectors must be equal to zero.
Taking the dot product of both vectors and equating it t zero we will have;
⟨−39,b,3⟩*⟨b,b²,b⟩ = -39(b)+ b(b²)+3(b)
(Note that when multiplying, we multiply component wise and take the sum of the product if each component)
Since the vectors are orthogonal, then -39(b)+ b(b²)+3(b) = 0
open the parenthesis
-39b+b³+3b = 0
on rearranging
b³+3b-39b= 0
b³-36b= 0
factor out b from the equation
b(b²-36) = 0
b = 0 and b²-36 = 0
from b²-36 = 0
add 36 to both sides of the equation
b²-36+36= 0+36
b² = 36
take the square root of both sides
√b² = ±√36
b = ±6
Hence the values of b for the vectors to be orthogonal are 0, -6 and 6.
PLS HELP ASAP GUYS! 50 POINTS!! Match the verbal expression to its correct algebraic expression.
Percy spent money on new shirts for the summer each shirt cost $7 he spent $42 all together how many shirts did Percy buy
PLSSSSS HELP MARKING BRAINLIST PLS I THINK NO ONE WILL HELP ME :(
Step-by-step explanation:
sorry jesica I don't know the answer