Answer:
18 paperclips are in the pile!
Step-by-step explanation:
We know that a dozen paperclips are equal to 9.6g, so we are going to divide 9.6 by 12 to figure out how much each paperclip weighs (0.8g). So we then divide 14.4 by 0.8 to figure out how many paperclips are in the pile! Hope this helps!
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.
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.
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:
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]
1 +1 +1+1+1+46×7×7×7×75×8×56+4+6+8
Answer:
11,524,869
Step-by-step explanation:
Answer:
530140823Step-by-step explanation:
[tex]1+1+1+1+1+46\times \:7\times \:7\times \:7\times \:75\times \:8\times \:56+4+6+8\\\\\mathrm{Multiply\:the\:numbers:}\:46\times \:7\times \:7\times \:7\times \\\:75\times \:8\times \:56\\\\\\=530140800\\\\=1+1+1+1+1+530140800+4+6+8\\\mathrm{Add\:the\:numbers:}\:1+1+1+1+1+530140800+4+6+8\\=530140823[/tex]
Tanaka Madison has part time job. $15.32 per hour. She works 20 hours each week. What is her straight time pay for a week
Answer:
$306.40
Step-by-step explanation:
Multiply 15.32 by 20
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.
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
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
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.
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 expression is equivalent to (8^2)^-4
Answer:
(64)^-4= 1/64^4= 1/16777216
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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If an angle’s measure is between 0 and 90° then it is said to be a _____angle...
Answer:
acute
Step-by-step explanation:
An acute angle measures less than 90°.
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
carli bought a new pair of jean for $60 if the tax if the tax rate is 8.25% how much will carli have to pay for the jeans including tax
Answer:
2.5075
Step-by-step explanation:
If the sales tax rate is 7.375% in New York State then how much sales tax would you pay in Albany for a $34 pair of pants
Sales Tax. If the sales tax rate is 7.375% in New York State, then how much sales tax would you pay in Albany for a $34 pair of pants? 34.00 x 0.07375 = 2.5075.
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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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]
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
Mary leaves her house to take a walk. The graph shows the distance, d, in feet from her house that Mary is at any given time, t, in minutes. How many minutes has Mary walked when she reaches the farthest point from her house?
Answer:
It would be option A. 10 Minutes.
Step-by-step explanation:
If you look at the graph, the farthest point, and the time of 10 minutes meet at the point (10, 2,500)
(Really hoping this helps <3)
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
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
Shelley compared the number of oak trees to the number of maple trees as part of a study about hardwood trees in a woodlot. She counted 9 maple trees to every 5 oak trees. Later in the year there was a bug problem, and many trees died. New trees were planted to make sure there were the same number of trees as before the bug problem. The new ratio of the number of maple trees to the number of oak trees is 3:11. After planting new trees, there were 132 oak trees. How many more maple trees were in the woodlot before the bug problem than after the bug problem?
Answer:
72
Step-by-step explanation:
Initial ratio of maple trees to oak trees
9:5New ratio of maple trees to oak trees
3:11Number of oak trees = 132
Number of maple trees
132*3/11 = 36Total number of trees
132+36 = 168Initial number of maple trees
168*9/14 = 108The difference in the number of maple trees:
108 - 36 = 72Answer:
72 more trees before the bug problem
Step-by-step explanation:
The ratio was 9:5 before the bug problem and 3:11 after.
After the bug problem there were 132 oak trees,
m : 132 = 3 : 11
Then we know
m/132 = 3/11
Multiplying both sides by 132 cancels on the left
132 × (m/132) = (3/11) × 132
m = (3/11) × 132
Then solving for m
m = 132 × (3/11)
m = 36 This gives us the number of trees after the bug problem.
This would give us 168 trees in total, 132 oak, and 36 maple.
Since there is the same number of trees as before we calculate the number of maple and oak previously.
If Shelley counted 9 maple for every 5 oak we know that 9 out of 14 trees are maple and 5 out of 14 trees are oak.
9/14 = .6428 which is the percentage of maple trees before the bug problem.
We multiply .6428 x 168 (the total number of trees) and we get 108.
if there are 108 maple trees then 168-108 = 60 oak trees.
Further proof:
9:5 or 9/5 = 1.8 108/60 = 1.8
108 maple trees and 60 oak before the bug problem.
So 108 (maple before bug problem) and 36 maple trees after:
108 - 36 = 72 more trees before the bug problem
PLSSSSS HELP MARKING BRAINLIST PLS I THINK NO ONE WILL HELP ME :(
Step-by-step explanation:
sorry jesica I don't know the answer
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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PLS HELP ASAP GUYS! 50 POINTS!! Match the verbal expression to its correct algebraic expression.
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.
What’s the slope of these points (-8,3) and (-8,2)
Answer:
donkeey kongy
Step-by-step explanation:
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
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%