Answer:
B. The vectors v and w are orthogonal because their dot product is 0
Step-by-step explanation:
Given that :
v= - i - j
w= - i + j
Therefore;
vw = ( - i - j ) ( - i + j )
Taking each set of integer of the vector into consideration:
vw = ( -1 × - 1) ( -1 × 1)
vw = 1 - 1
vw = 0
Hence, we can conclude that :
The vectors v and w are orthogonal because their dot product is 0
6(x + 2) = 30Solve the following linear equation
Answer:
[tex]\huge \boxed{x=3}[/tex]
Step-by-step explanation:
[tex]6(x+2)=30[/tex]
[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]
[tex]x+2=5[/tex]
[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]
[tex]x=3[/tex]
Answer:
3
Step-by-step explanation:
30 = 6(x+2)
30/6 = 5
5 = x+2
5-2 = 3
3=x
This is a pretty simple question and I tried to make it as simple as possible when explaining it.
What is the difference between a consistent and inconsistent system of equations?
Answer:
A consistent of equations has at least one solution,and an inconsistent system has no solution, watch an example of analyzing a system to see if its consistent or inconsistent.
Answer: see below
Step-by-step explanation:
Consider the standard form of a linear equation in Slope-Intercept form:
y = mx + b where
m is the slopeb is the y-interceptA CONSISTENT system of equations is where the equations have different slopes OR the same slope and y-intercept.
This results in the lines crossing so they have at least one solution.
An INCONSISTENT system of equations is where the equations have the same slope but different y-intercepts.
This results in parallel lines so they have no solutions.
Someone help again:/
The length and width of a rectangle are measured as 58 cm and 45 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
Error in calculated area = [tex]\pm 10.3 cm^2[/tex]
Step-by-step explanation:
x = 58 cm
y = 45 cm
A = x*y
delta A
= delta (x*y)
= y delta x + x delta y (neglecting small qty delta x * delta y = 0.01)
= 45(0.1) + 58(0.1)
= 103(0.1)
= 10.3 cm^2
Solve for x: the quantity of x plus 4 over 3 = 2.
Answer:
x =2
Step-by-step explanation:
(x+4) /3 = 2
Multiply each side by 3
(x+4) /3 *3= 2*3
x+4 = 6
Subtract 4
x+4-4 = 6-4
x =2
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 2
▹ Step-by-Step Explanation
[tex]\frac{x + 4}{3} = 2\\\\3 * 2 = 6\\\\x + 4 = 6\\\\x = 2[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Using the digits 0-9, at most only one time each, fill in the boxes to
Answer:
2 * 3 + 4 * 5 = 26
5 * 7 + 1 * 8 = 43
Step-by-step explanation:
Given
_ * _ + _ * _ = _ _
Required
Fill in the boxes with digits 0 to 9
From the question we understand that the result must be two digits i.e. _ _
To solve this, we'll make use of trial by error method:
Fill the first two boxes wit 2 and 3: _ * _ becomes 2 * 3
Fill the next two boxes with 4 and 5: _ * _ becomes 4 * 5
So,we have
2 * 3 + 4 * 5
6 + 20
26
Hence, the first combination is 2 * 3 + 4 * 5 = 26
Another possible combination is:
Fill the first two boxes wit 5 and 7: _ * _ becomes 5 * 7
Fill the next two boxes with 1 and 8: _ * _ becomes 1 * 8
So,we have
5 * 7 + 1 * 8
35 + 8
43
Hence, another combination is 5 * 7 + 1 * 8 = 43
Note that; there are more possible combinations
A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. The player scored 17 times. She scored 3 more 2-point field goals than 1-point free throws. The system of equations below represents the situation, where x is the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. x + y + z = 17 x + 2y + 3z = 33 y – x = 3
Answer:
No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4
Step-by-step explanation:
Equations : x + y + z = 17 [ Total times taken to score ]
1x + 2y + 3z = 33 [ Total Score ]
Also, y = x + 3
Putting the value of 'y' in both equations :
x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14 (i)
1x + 2 (x + 3) + 3z = 33 → x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)
Solving these equations :
From (i), z = 14 - 2x
Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27
42 - 3x = 27 → 3x = 15 → x = 5
y = x + 3 = 5 + 3 → y = 8
z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4
Answer:
4
Step-by-step explanation:
I will rate you brainliest!
Answer:
B
Step-by-step explanation:
X must not be equal to -6, -1, 1 or 3
15. What is the next number in this series?
6, 11, 9, 14, 12,
a. 17
b. 10
C. 18
d. 16
Answer:
a. 17
Step-by-step explanation:
The pattern is add 5 then subtract 2
What is the solution of the system of equations?
y = -3x + 7
y = 2x - 8
Answer:
x = 3, y = -2
Step-by-step explanation:
Since y=y
then, -3x +7 = 2x-8
7+8 = 3x+2x
15 = 5x
x=3
substitute
y = 2(3) - 8
y = -2
Hope that helped!!! k
Answer:
y = -2
x = 3
Step-by-step explanation:
Solve using elimination
1. Rearrange the equations to make it easier to solve
y = -3x + 7 → 3x + y = 7
y = 2x - 8 → 2x - y = 8
2. Multiply the equations to have a matching coefficient
2(3x + y = 7) = 6x + 2y = 14
3(2x - y = 8) = 6x - 3y = 24
3. Subtract
6x + 2y = 14
- 6x - 3y = 24
0 + 5y = -10
4. Solve for y
5y = -10
y = -2
5. Substitute y in any equation to solve for x
-2 = -3x + 7
-3x = -9
x = 3
What is the value of 1/3x-3/4 when x =1/4
Answer:
The value of 1/3x-3/4 when x=1/4 is 0.08333 repeated.
Step-by-step explanation:
Use technology to find the P-value for the hypothesis test described below. The claim is that for 12 AM body temperatures, the mean is F. The sample size is n and the test statistic is t.
Answer:
P value = 0.1575
Step-by-step explanation:
Data provided in the question
t = 1.021
n = 33
[tex]\mu[/tex] = 98.6° F
Based on the above information, the P-value could be determined by using the excel spreadsheet i.e. shown in the attachment
So, the P value is 0.1575
The 1.021 denotes the test statistic
32 denotes degrees of freedom
And,
1 denotes one tailed alternative hypothesis.
the formula s= I dont know how to type that but I really need helppppp
Answer:
[tex] s = \sqrt{30} - 2\sqrt{5} m [/tex]
Step-by-step explanation:
Given:
Formula for side length of cube, [tex] s = \sqrt{\frac{SA}{6} [/tex]
Where, S.A = surface area of a cube, and s = side length.
Required:
Difference in side length between a cube with S.A of 180 m² and a cube with S.A of 120 m²
Solution:
Difference = (side length of cube with 180 m² S.A) - (side length of cube with 120 m² S.A)
[tex]s = (\sqrt{\frac{180}{6}}) - (\sqrt{\frac{120}{6}})[/tex]
[tex] s = (\sqrt{30}) - (\sqrt{20}) [/tex]
[tex] s = \sqrt{30} - \sqrt{4*5} [/tex]
[tex] s = \sqrt{30} - 2\sqrt{5} m [/tex]
Line A passes through the point (-1,2). Which of the
following CANNOT be the equation of line A?
A y=1 - 2
B
y = x +1
C
X = -1
D y=x+3
Answer:
b
Step-by-step explanation:
y = x + 1
The correct answer is (B). The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the "m" in front of the "x" variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn't give us y = 2 is (B).
Option B is correct.
Given:
Line A passes through the point [tex](-1,2)[/tex].
To find:
Which of the given equations cannot be the equation of line A.
Solution:
If Line A passes through the point [tex](-1,2)[/tex], it means the equation of Line A must be satisfied by the point
In option A, consider the given equation is:
[tex]y=1-x[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=1-(-1)[/tex]
[tex]2=1+1[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=1-x[/tex] can be the equation of line A.
Similarly, check for the other options.
In option B,
[tex]y=x+1[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+1[/tex]
[tex]2=0[/tex]
This statement is false. So, [tex]y=x+1[/tex] cannot be the equation of line A.
In option C,
[tex]x=-1[/tex]
It is a vertical line and it passes through the point [tex](-1,2)[/tex] because the x-coordinate is [tex]-1[/tex]. So, [tex]x=-1[/tex] can be the equation of line A.
In option D,
[tex]y=x+3[/tex]
Substituting [tex]x=-1,y=2[/tex], we get
[tex]2=-1+3[/tex]
[tex]2=2[/tex]
This statement is true. So, [tex]y=x+3[/tex] can be the equation of line A.
Therefore, the correct option is B.
Learn more:
https://brainly.com/question/13078415
p-value problem. Suppose the director of manufacturing at a clothing factory needs to determine wheteher a new machine is producing a particulcar type of cloth according to the manufacturer s specification which indicate that the cloth should have mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds. THe p value for this hypothesis testing scenario is
Answer:
The P-Value is 0.07186
Step-by-step explanation:
GIven that :
Mean = 70
standard deviation = 3.5
sample size n = 49
sample mean = 69.1
The null hypothesis and the alternative hypothesis can be computed as follows;
[tex]H_o : \mu = 70 \\ \\ H_1 : \mu \neq 70[/tex]
The standard z score formula can be expressed as follows;
[tex]\mathtt{z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]
[tex]\mathtt{z = \dfrac{69.1 - 70}{\dfrac{3.5}{\sqrt{49}}}}[/tex]
[tex]\mathtt{z = \dfrac{-0.9}{\dfrac{3.5}{7}}}[/tex]
z = -1.8
Since the test is two tailed and using the Level of significance = 0.05
P- value = 2 × P( Z< - 1.8)
From normal tables
P- value = 2 × (0.03593)
The P-Value is 0.07186
paul worked 50 hours last week. if he earns $10 per hour plus time-and-a-half for any hours worked beyond 40 in a week, how much did he earn last week?
Answer: 4150
Step-by-step explanation:
You take the 50, becuse the amount earned increases once you surpass 40 you do 40 x 10 and that = 4000 then you take the remaining 10 and times that by 15 (becuse after 40 it is 1.5 of what you where earning before you hit 40 hours and half of ten is 5 so you do 10 plus 5 and times that by 10) then add both numbers together and you have 4150! Hope that helped!
Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?
Answer: There are 75 books.
Price of each book = $4.
Step-by-step explanation:
Let x = Number of books in the box.
Then as per given,
Cost of x books = $300
Cost of one book = [tex]\$(\dfrac{300}x)[/tex]
Books left after giving 15 of them = x-15
Selling price of (x-15) books= $330
Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]
Profit on each book= $1.50
Profit = selling price - cost price
[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]
[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]
Number of books cannot be negative.
So, there are 75 books.
Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]
So price of each book = $4.
What is the best way you learn math?
Answer:
to provide interest in the subject
As per my experience,I used to hate math and always scored less marks,the moment I was going to high school I realized the importance of math towards the future, see you'll find maths in nearly all subjects like the 3 sciences, economics, geography, business e.t.c
Why did you write this question at first?, just take some free time and think about it,the only best way to learn maths is to take maths positively as the best and most valuable subject,if you want to ace math you have to race it, challenge math like you'd challenge anyone to a game, practice math if it's your weakest point, practice is very much needed to skill maths and never be shy to ask your teachers whether you are studying online/offline. You'll need to get the shy behaviour out of you whether you like /don't like your teacher or your an average student.
Concentrate while learning math, whether there's noise in you background or not, Nothing can stop you in excelling math if you have full concentration, positiveness and the "will" to do so.
if you're next to your exams then just one thing, Start now!!
hope this helps!
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 6 3/4" by 4 1/2" on the drawing, how large is the bedroom? Please Help! (No other information was given.)
1 inch = four 1/4’s
1 inch = 4 feet
6 X 4 = 24 feet
3/4 inches = 3 feet.
6 3/4 inches = 27 feet
4 x 4 = 16
1/2 inch = 2 feet
4 1/2 inches = 18 feet
Room is 27 feet x 18 feet
In a genetics experiment on peas, one sample of offspring contained green peas and yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of that was expected? 350 127 3 4 The probability of getting a green pea is approximately . (Type an integer or decimal rounded to three decimal places as needed.) Is this probability reasonably close to ? Choose the correct answer below. 3 4 A. No, it is not reasonably close. B. Yes, it is reasonably close.
Complete Question
In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?
Answer:
The probability is [tex]P(g) =0.72[/tex]
Yes the result is reasonably close
Step-by-step explanation:
From the question we are told that
The number of of green peas is [tex]g = 436[/tex]
The number of yellow peas is [tex]y = 171[/tex]
The sample size is [tex]n = 171 + 436 = 607[/tex]
The probability of getting an offspring pea that is green is mathematically represented as
[tex]P(g) = \frac{g}{n}[/tex]
[tex]P(g) = \frac{436}{607}[/tex]
[tex]P(g) =0.72[/tex]
Comparing [tex]P(g) =0.72[/tex] to [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close
Hakim is making a mosaic
from square tiles. The area he
needs to fill measures 150 mm
by 180 mm. The tiles have side
lengths of 4, 6 or 8mm and are
too small to cut. Which tiles
should Hakim use?
Step-by-step explanation:
check the tile whose side length is divisible by both 150 and180 in such a way that you don't get decimal points
150÷4=37.5 so that is impossible
150÷8=18.75 so that is also impossible
150÷6=25 180÷6=30
so the six sided tile is applicable
find the total area of the prism
Answer:
63.5
Step-by-step explanation:
In the multiplication below, each of A, B and
C represents a different digit. What is ABC?
A B C
X
3
В В В
Answer:
ABC = 148, 3*148 = 444
Step-by-step explanation:
We know that 111 = 3* 37, so all numbers of the form BBB has the factor 37.
So we need a multiple of 37 such thant when multiplied, we get three digits the same as the middle digit.
Try 4*37 = 148, 148*3 = 444, bingo, we got the right combination.
So ABC is 148.
The radius of a sphere is measured as 7 centimeters, with a possible error of 0.025 centimeter.
Required:
a. Use differentials to approximate the possible propagated error, in cm3, in computing the volume of the sphere.
b. Use differentials to approximate the possible propagated error in computing the surface area of the sphere.
c. Approximate the percent errors in parts (a) and (b).
Answer:
a) dV(s) = 15,386 cm³
b) dS(s) = 4,396 cm²
c) dV(s)/V(s) = 1,07 % and dS(s)/ S(s) = 0,71 %
Step-by-step explanation:
a) The volume of the sphere is
V(s) = (4/3)*π*x³ where x is the radius
Taking derivatives on both sides of the equation we get:
dV(s)/ dr = 4*π*x² or
dV(s) = 4*π*x² *dr
the possible propagated error in cm³ in computing the volume of the sphere is:
dV(s) = 4*3,14*(7)²*(0,025)
dV(s) = 15,386 cm³
b) Surface area of the sphere is:
V(s) = (4/3)*π*x³
dV(s) /dx = S(s) = 4*π*x³
And
dS(s) /dx = 8*π*x
dS(s) = 8*π*x*dx
dS(s) = 8*3,14*7*(0,025)
dS(s) = 4,396 cm²
c) The approximates errors in a and b are:
V(s) = (4/3)*π*x³ then
V(s) = (4/3)*3,14*(7)³
V(s) = 1436,03 cm³
And the possible propagated error in volume is from a) is
dV(s) = 15,386 cm³
dV(s)/V(s) = [15,386 cm³/1436,03 cm³]* 100
dV(s)/V(s) = 1,07 %
And for case b)
dS(s) = 4,396 cm²
And the surface area of the sphere is:
S(s) = 4*π*x³ ⇒ S(s) = 4*3,14*(7)² ⇒ S(s) = 615,44 cm²
dS(s) = 4,396 cm²
dS(s)/ S(s) = [ 4,396 cm²/615,44 cm² ] * 100
dS(s)/ S(s) = 0,71
How do u solve A/B + C/D = E
Suppose a triangle has two sides of length 33 amd 37, and that the angle between these two sides is 120°. What is the length of the third side of the triangle
Answer:
c = 60.65 cm
Step-by-step explanation:
Given that,
The two sides of a triangle are 33 cm and 37 cm.
The angle between these two sides is 120°.
We need to find the length of the third side of the triangle. Let c is the third side. Using cosine rule,
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
a = 33 cm, b = 37 cm and C is 120°
So,
[tex]c^2=(33)^2+(37)^2-2\times 33\times 37\cos (120)\\\\c=60.65\ cm[/tex]
So, the length of the third side of the triangle is 60.65 cm.
If the item regularly cost d dollars and is discounted 12percent which of the following represents discount price dollar
Answer:
-12
Step-by-step explanation:
4. Identify the means and the extremes in each of the following proportions.
a. 4 : 24 = 2 : 12
b. 24/6 = 164
c. 4:8 = 8:16
d. 650 = 3/25
Answer:
a) Means: 24 and 2; Extremes: 4 and 12
b) Means: 6 and 16; Extremes: 24 and 4
c) Means: 8 and 8; Extremes: 4 and 16
d) Means: 50 and 3; Extremes: 6 and 25
Step-by-step explanation:
The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:
a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.
The Means are the values that appear in the middle of the one line expression, that is: b and c.
Recall as well that the proportion can also be written with fractions:
a : b = c : d is the same as: a / b = c / d
so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$450 and $500.
Answer:
13.59%
Step-by-step explanation:
Calculate the z-scores.
z = (x − μ) / σ
z₁ = (450 − 400) / 50
z₁ = 1
z₂ = (500 − 400) / 50
z₂ = 2
Use a chart or calculator to find the probability.
P(1 < Z < 2)
= P(Z < 2) − P(Z < 1)
= 0.9772 − 0.8413
= 0.1359
Answer:
13.5
Step-by-step explanation:
Acellus sux
Last year, Leila had $30,000 to invest. She invested some of it in an account that paid 6% simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of $1580 in interest. How much did she invest in each account?
Answer:
6%: $8,0005%: $22,000Step-by-step explanation:
Let x represent the amount invested at 6%. Then 30000-x is the amount invested at 5%. Leila's total earnings for the year are ...
0.06x +0.05(30000-x) = 1580
0.01x +1500 = 1580 . . . . . . . . . . . . simplify
0.01x = 80 . . . . . . . . . . . subtract 1500
x = 8000 . . . . . . . . . . . . multiply by 100
Leila invested $8000 at 6% and $22000 at 5%.
