Answer:
2 units I used the distance formula
An electronics store receives a shipment of 35 graphing calculators including 7 that are defective. Eight calculators are chosen at random to be sent to a local high school. 8. How many total selections can be m
Complete question :
An electronics store receives a shipment of 35 graphing calculators, including 7 that are defective. 8 of these calculators are selected for a local high school. (A) How many selections can be made? (B) How many of these selections will contain no defective calculators?
Answer:
23535820 ways
3108105 ways
Step-by-step explanation:
A.) How many selections can be made:
Number of ways of selecting 8 calculators from 35
35C8 :
Combination formula :
nCr = n! /(n-r)! r!
35C8 = 35! / (35-8)!8!
35C8 = 35! / 27! 8!
35C8 = (35*34*33*32*31*30*29*28) / (8*7*6*5*4*3*2*1)
35C8 = 948964262400 / 40320
= 23535820 ways
B.) number of non-defective calculators :
35 - 7 = 28
28C8 = n! /(n-r)! r!
28C8 = 28! / (28-8)!8!
28C8 = 28! / 20! 8!
28C8 = (28*27*26*25*24*23*22*21) / (8*7*6*5*4*3*2*1)
28C8 = 2506375872000 / 40320
= 3108105 ways
PLEASE PLEASE PLEASE HELP!!!! A lot of points! Will mark brainliest and leave thanks on all of your answers if it's correct!
The LCM(12, 15, 20, k) = 420. What is the least possible value of k?
Answer:
add them all up and subtract 420 from 15+20+12!
Step-by-step explanation:
hope this helps
I'll give you brainlist if someone can answer this question
What is the degree for this solution?
Answer:
95 degrees
Step-by-step explanation:
The was it has been rotated
American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters
Answer:
91.44
Step-by-step explanation:
Jonathan’s parents told him that for every five hours of homework or reading he completes, he would be able to play three hours of video games. His friend Lucas’ parents told their son that he could play 30 minutes for every hour of homework or reading he completes. If both boys spend the same amount of time on homework and reading this week, which boy gets more time playing video games? How do you know?
Answer:
So, to set up this equation, lets just say that Lucas did 5 hours of homework also. The ratio of Lucas's homework to video games is 60 minutes of homework/30 minutes of video games. If we converted the 5 hours into 300 minutes then you would multiply the 60 minutes by 5 and the 30 minutes by 5 also. You would get 300 minutes/150 minutes. Jonathan's ratio is every 5 hours of homework/3 hours of video games. We would convert this to minutes by taking both numbers and multiplying them by 60. We would get 300 minutes/180 minutes. Using this we know that Jonathan gets more time to play video games because every 5 hours of homework he gets 180 minutes of gaming and for Lucas, every 5 hours of homework he only gets 150 minutes of gaming. I hope that this helped you!
Step-by-step explanation:
Answer:
Jonathan gets more time to play video games
Step-by-step explanation:
Using ratios
Jonathan 5:3
Lucas 2:1
Jim earned $95 after working 4 days. At this rate how many days will it take him to earn $285?
Answer:
12 days
Step-by-step explanation:
95÷4=23.75
285÷23.75=12
Answer:
12 days
Step-by-step explanation:
multiply by 3 to get the answer
I’ll make you brainliest if you answer the question
Answer:
The first one
Step-by-step explanation:
Are the vectors 2+5x+3x2, 4+11x+6x2 and 1+2x+x2 linearly independent? choose If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0= (2+5x+3x2)+ (4+11x+6x2)+ (1+2x+x2).
Answer:
Vectors [tex]p_{1} = 2+5\cdot x + 3\cdot x^{2}[/tex], [tex]p_{2} = 4+11\cdot x +6\cdot x^{2}[/tex] and [tex]p_{3} = 1+2\cdot x +x^{2}[/tex] are linearly independent.
Step-by-step explanation:
From Linear Algebra, we must remember that a set of vectors is linearly independent if and only if coefficients of its linear combinations are all zeroes. That is:
[tex]\Sigma\limits_{i=1}^{n} \alpha_{i}\cdot p_{i}= 0[/tex], where [tex]\alpha_{i} = 0[/tex]. (Eq. 1)
Where:
[tex]p_{i}[/tex] - i-th Polynomial of the set of vectors, dimensionless.
[tex]\alpha_{i}[/tex] - i-th coefficient associated with the i-ith polynomial of the set of vectors, dimensionless.
Let [tex]p_{1} = 2+5\cdot x + 3\cdot x^{2}[/tex], [tex]p_{2} = 4+11\cdot x +6\cdot x^{2}[/tex] and [tex]p_{3} = 1+2\cdot x +x^{2}[/tex] elements of the set of vectors, whose linear combination is:
[tex]\alpha_{1}\cdot p_{1}+\alpha_{2}\cdot p_{2}+\alpha_{3}\cdot p_{3}= 0[/tex]
[tex]\alpha_{1}\cdot (2+5\cdot x+3\cdot x^{2})+\alpha_{2}\cdot (4+11\cdot x +6\cdot x^{2})+\alpha_{3}\cdot (1+2\cdot x+x^{2}) = 0[/tex]
[tex](2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3})+(5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3})\cdot x+(3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3})\cdot x^{2} = 0[/tex]
Values of coefficient are contained in the following homogeneous system of linear equations:
[tex]2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3} = 0[/tex] (Eq. 2)
[tex]5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3} = 0[/tex] (Eq. 3)
[tex]3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3} = 0[/tex] (Eq. 4)
The solution of this system is:
[tex]\alpha_{1} = 0[/tex], [tex]\alpha_{2} = 0[/tex], [tex]\alpha_{3} = 0[/tex]
Which means that given set of vectors are linearly independent.
Jose borrowed $1500 from the bank at a rate of 8% simple interest per year. He paid in interest in three years.
Answer:
$1,860
Step-by-step explanation:
please hurry
Solve for t: 5t - 4 = 11
Answer:
t=3
Step-by-step explanation:
5t-4=|11
+4 |+4
5t= | 15
÷5 | ÷5
t = 3
Determine whether the data shown is DISCRETE or CONTINUOUS.
Answer:
Option (b)
Step-by-step explanation:
From the graph attached in the figure,
Graph (a) is a scatter plot of a data set.
Data in this graph is not connected. In other words, a scatter plot represents a discrete function.
Similarly, in the graph (b) there is a straight line.
All points lying on this straight line are connected and follow the same rule.
Therefore, graph (b) represents a continuous function.
Therefore, Option (b) is the correct option.
simplify a(x + y) - a(x - y)
Answer:
2ay
Step-by-step explanation:
To simplify first we expand the brackets.
ax+ay- (ax-ay)
Now collect like-terms
ax-ax= 0
ay- (-ay) = 2ay
Therefore The simplified version would be 2ay
What is the equation of the line that has a slope of -3/4 and goes through the point of (0,-5)
Answer:
Find the equation using slope-intercept form.
y=−3(0,−5)/4 x+y
Find the measure of the missing value
Answer:
x = 48, y = 70
Step-by-step explanation:
Since 2 sides are congruent, then the triangle is isosceles and the base angles are congruent, thus
x + 7 = 55 ( subtract 7 from both sides )
x = 48
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles from 180 for y, that is
y = 180 - (55 + 55) = 180 - 110 = 70
jina made $168 for 12 hours of work at the same rate, how many hours would she have to work to make $252
I really need help on this question! I’m new to Brainly, but if you can help that would be great!
Assuming there are no reflections or dilations, explain how you would write the equation of the function whose graph is sketched below. Assuming there are no reflections or dilations, explain how you would write the equation of the function whose graph is sketched below.
Answer: Start with the parent function y=1/x^2
Add 3 to x in the denominator, because the graph is shifted left 3.
Add 1 to the fraction, because the graph is shifted up 1 unit
Step-by-step explanation:
Find an equation of the plane that passes through the point (1, 2,3) and cuts off the smallest volume in the first octant. [This one is a little tricky.]
Answer and Step-by-step explanation:
Solution:
The equation is given by:
z – z0 = a(x – x0) + b(y – y0).
The point (1, 2, 3) is given , substitute them for x0, y0 and z0:
Z – 3 = a (x – 1) + b(y-2)
Both a and b should be negative, because normal vector to point in the negative x and y direction so that plane will enclose a tetrahedron with finite area in the first octant.
This will only happen if z becomes smaller as we move towards the positive x and y directions.
To find expressions for V, firstly find expression for x, y and z intercepts.
X – Intercepts (y and z = 0) : 2b +a -3 / a
y- Intercepts (x, z = 0): 2b + a- 3 / b
z – Intercepts( x, y = 0): 3 – a – 2b
The base is = (2b+a-3)2/ 2ab
Volume is 1/3 base x height, so
V (a, b) = - (2b+a-3)3 / 6ab
The gradient vector:
ΔV (a, b) = |- (3(2b+a-3)2 ab-b (2b+a-3)3)/6a2b2, (6(2b+a-3)2 ab-a(2b+a-3)3)/6a2b2| = 0
b (2b+a-3)2 [ (2b+a-3) -3a] = 0
a (ab + a-3)2 [(2b +a -3) – 6b] = 0
Where a, b not equal to 0.
We cannot solve for 2b +a-3 = 0 because, that will lead to V = 0, which is impossible.
Therefore, we only solve for second halves equations, which are system of linear equations:
-2a + 2b = 3 and a – 4b = 3
Which gives a = -3 and b = -3/2
Put in equation:
Z – 3 = -3 (x-1) – 3/2 (y-2)
3x +3/2 y +z = 9
Multiplying by 2:
6x + 3y + 2z = 18.
Problem 9-8 (modified). The height of adult males in a particular city is normally distributed, with mean 69.5 in. and standard deviation 2.65 in. When a random sample is taken of size 20, find (1) the standard error of Xbar
Complete Question
Problem 9-8 (modified). The height of adult males in a particular city is normally distributed, with mean 69.5 in. and standard deviation 2.65 in.
When a random sample is taken of size 20, find (1) the standard error of Xbar
(2) the probability that Xbar falls within .5 in. of the true mean
Probability=
Answer:
1
[tex]\sigma_{\= x} = 0.5926[/tex]
2
[tex]P( 69 < \= X < 70) = 0.60134[/tex]
Step-by-step explanation:
From the question we are told that
The true mean is [tex]\mu = 69.5 \ in[/tex]
The standard deviation is [tex]\sigma = 2.65 \ in[/tex]
The sample size is n = 20
Generally the standard error of Xbar[tex](\= x)[/tex] is mathematically represented as
[tex]\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x} = \frac{ 2.65 }{\sqrt{ 20 } }[/tex]
=> [tex]\sigma_{\= x} = 0.5926[/tex]
Generally for [tex]\= x[/tex] to fall within 0.5 of the true mean the [tex]\= x[/tex] must be within
[tex]a = \mu + 0.5[/tex]
=> [tex]a = 69.5 + 0.5[/tex]
=> [tex]a = 70[/tex]
or [tex]b = \mu -0.5[/tex]
=> [tex]b = 69.5 -0.5[/tex]
=> [tex]b = 69[/tex]
Generally the probability that [tex]\= x[/tex] fall with 0.5 of the true mean is mathematically represented as
[tex]P( 69 < \= X < 70) = P(\frac{69 - 69.5 }{ 0.5926} < \frac{\= X - \mu }{ \sigma_{\= x} } <\frac{70- 69.5 }{ 0.5926})[/tex]
=> [tex]P( 69 < \= X < 70) = P(-0.844 < Z < 0.844)[/tex]
=> [tex]P( 69 < \= X < 70) = P( Z < 0.844) - P( < -0.844)[/tex]
From the z table the probability of ( Z < 0.844) and ( Z < -0.844) is
[tex]P( Z < 0.844) = 0.80067[/tex]
and
[tex]P( Z < - 0.844) = 0.19933[/tex]
So
[tex]P( 69 < \= X < 70) = 0.80067 - 0.19933[/tex]
=> [tex]P( 69 < \= X < 70) = 0.60134[/tex]
The standard error of the given data comes to be 0.593.
It is given that
mean [tex]\mu[/tex] = 69.5 inch
Standard deviation [tex]\sigma[/tex] = 2.65 inch
Sample size n =20
What is the standard error?The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.
The standard error is given by:
[tex]SE =\frac{\sigma}{\sqrt{n} }[/tex]
[tex]SE =\frac{2.65}{\sqrt{20} }[/tex]
[tex]SE=0.593[/tex]
Hence, the standard error of the given data comes to be 0.593.
To get more about standard errors visit:
https://brainly.com/question/1191244
x + 2x - 1 = -8 + 3x + 7
Answer:
All real numbers are solutions.
0=0
Step-by-step explanation:
Let's solve your equation step-by-step.
x+2x−1=−8+3x+7
Step 1: Simplify both sides of the equation.
x+2x−1=−8+3x+7
x+2x+−1=−8+3x+7
(x+2x)+(−1)=(3x)+(−8+7)(Combine Like Terms)
3x+−1=3x+−1
3x−1=3x−1
Step 2: Subtract 3x from both sides.
3x−1−3x=3x−1−3x
−1=−1
Step 3: Add 1 to both sides.
−1+1=−1+1
0=0
Answer:
All real numbers are solutions.
Twice a increased by the cube of a equals b.
Answer:
2a +a^3 =b
Step-by-step explanation:
What is the image point of (0,-5) after translation right 5 units and up 2 units
Answer:
(5, -3)
Step-by-step explanation:
translation rule: (x+5, y+2)
(0+5, -5+2)
(5, -3)
3x + 2y = 8 ( in y=mx+b form $
Answer:
y =-3/2x+4
Step-by-step explanation:
simple
(c) Archimedes was particularly pleased when he determined the ratio of the volumes of a sphere and cylinder. Determine the ratio of the volume of a sphere to the volume of a cylinder having the same radius, and having height the same as the diameter of the sphere:
The volume of the sphere and the volume of the cylinder can be
expressed in terms of their radius.
Correct response:
The ratio of the volume of the sphere to the volume of the cylinder is 2 : 3Methods by which the ratio of the volumes is calculatedThe given parameters are;
Radius of the sphere = Radius of the cylinder
Height of the cylinder = Diameter of the sphere
Required:
The ratio of the volume of a sphere to the volume of a cylinder.
Solution:
Let r represent the radius of the sphere, we have;
The diameter of the sphere, D = 2·r
Therefore, the height of the cylinder, h = D = 2·r
The volume of the cylinder is; [tex]V_{cylinder}[/tex] = π·r²·h
[tex]\mathrm{The \ volume \ of \ a \ sphere\ is} \ V_{sphere} = \mathbf{ \dfrac{4}{3} \cdot \pi \cdot r^3}[/tex]
Therefore;
[tex]\mathbf{\dfrac{V_{sphere}}{V_{cylinder}}} = \dfrac{\dfrac{4}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 \cdot h} = \dfrac{\dfrac{4}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 \times 2 \cdot r} = \dfrac{\dfrac{4}{3} }{2} =\dfrac{4}{6} = \dfrac{2}{3}[/tex]
[tex]\dfrac{2}{3} \ expressed as \ a \ ratio \ is \ 2:3[/tex]
The ratio of the volume of a sphere to the volume of a cylinder having the same radius, and having a height the same as the diameter of the sphere is 2:3Learn more about the volumes of solids here:
https://brainly.com/question/3376338
Calculate and express your answer in decimal form
Need help asap
(1.) 20.4
(2.) 150
(3) 8
(4.) 15
Solve the inequality.
7x + 4 − 11x ≥ −4x + 7
find the mean of the following : 158, 213, 107, 213, ,213, if needed round to the nearest tenth.
A 181
B 180.8
C 107
D 213
Answer:
the correct answer is 180.8. i saw that other ppl had this answer on brianly but had 0 star ratings even though they were correct.
Step-by-step explanation: i just took this test and trusted the person who ansered and got it wrong.
Suppose toms car can travel 72 miles on 3 gallons of gas . How many miles can toms car travel on 12 gallons
Answer:
288
Step-by-step explanation:
The ratio of gas to miles is 3:72. That is a proportion. 3:72 is the same as 12:288. (multiply both by 4)
pls help
8th grade math
anf i dunno anything
Answer:
The y-intercept is 0
Step-by-step explanation:
Answer:
-6, -3, 0, 3
Step-by-step explanation:
order 1/2, 1/3 and 5/6 from least to greatest?
Let us first change these fractions into each other's equivalent fractions , so that we can order them from the smallest to the largest .
[tex] (i) \: \frac{1}{2} = \frac{(1 \times 3)}{6} [/tex]
[tex]\implies \color{olive} \frac{1}{2} = \color{hotpink} \frac{3}{6}[/tex]
[tex](ii) \: \frac{1}{3} = \frac{(1 \times 2)}{6} [/tex]
[tex]\implies\color{olive} \frac{1}{3} = \color{hotpink} \frac{2}{6} [/tex]
[tex](iii) \: \frac{5}{6} = \frac{(5 \times 1)}{6} [/tex]
[tex]\implies\color{olive} \frac{5}{6} = \color{hotpink} \frac{5}{6} [/tex]
Therefore, the fractions arranged in order from the least to the greatest :-
[tex] \bold\color{hotpink} { \color{olive} = \color{hotpink} \frac{1}{3}
,
\color{olive} \frac{1}{2}
,
\color{hotpink} \frac{5}{6} }[/tex]
Kate and Isabelle do some fundraising for their sporting team. Together they raised $600. Kate raised $272 more than Isabelle.
1. Write an equation to represent the total amount of money the girls raised. Do not include any spaces when typing your equation.
Answer:
x + x - 272 = 600
Step-by-step explanation:
Let the amount raised by Kate by x and let the amount raised by Isabelle be y.
Now, we are told that Kate raised $272 more than Isabelle.
Thus, since amount raised by Kate is x, then amount raised by Isabelle is x - 272. We are told that together they raised $600.
Thus;
x + x - 272 = 600
Thus;
equation to represent the total amount of money the girls raised is;
x + x - 272 = 600