Answer:
b. (10,10,0)
Step-by-step explanation:
r+v can be evaluated if the vectors/matrices have the same dimensions.
These do. They are both 1 by 3 vectors.
Just add first to first in each.
Just add second to second in each.
Just add third to third in each.
Example:
(5,-5,6)+(1,2,3)
=(5+1,-5+2,6+3)
=(6,-3,9)
Done!
In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).
r+v
=(7,3,9)+(3,7,-9)
=(7+3,3+7,9+-9)
=(10,10,0)
Done!
From 1985 to 2007, the number B B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 B(t)=-329.4t+13747 where t is the year and t=0 corresponds to 1985. How many federally insured banks were there in 1990?
Answer:
12100
Step-by-step explanation:
If the number B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 from 1985 to 2007 where t = 0 correspond to year 1985
In order to determine the amount of federally insured banks that were there in 1990, we will first calculate the year range from initial time 1985 till 1990
The amount of time during this period is 5years. Substituting t = 5 into the modeled equation will give;
B ( t ) = − 329.4 t + 13747
B(5) = -329.4(5) + 13747
B(5) = -1647+13747
B(5) = 12100
This shows that there will be 12100 federally insured banks are there in the year 1990.
Solve.
1/3-6<24
{s | s<6}
O {S | s < 10}
O {S | s < 54}
O {S | s < 90}
Answer:
The answer is:
The fourth option,
{s | s <90}
Step-by-step explanation:
yes
Answer:
[tex]\boxed{s|s<90}[/tex]
Step-by-step explanation:
1/3s-6<24
Add 6 on both sides.
1/3s<30
Multiply both sides by 3.
s<90
A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint. If a can of paint contains 75 ounces of white paint, how many ounces of blue paint are in the can?
Answer:
60 ounces
Step-by-step explanation:
A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint, that is, the white paint (w) to blue paint (b) ratio is 5:4. We can apply this ratio to different units such as ounces. This means that the mixture has 5 ounces of white paint to 4 ounces of blue paint. If a can of paint contains 75 ounces of white paint, the ounces of blue paint in the can are:
75 oz w × (4 oz b/5 oz w) = 60 oz b
Simplify the expression:
3+ – 5(4+ – 3v)
Answer:
The answer is
15v - 17Step-by-step explanation:
3+ – 5(4+ – 3v) can be written as
3 - 5( 4 - 3v)
Expand and simplify
That's
3 - 20 + 15v
15v - 17
Hope this helps you
A restaurant operator in Accra has found out that during the partial lockdown, if she sells a plate of her food for GH¢20 each, she can sell 300 plates, but for each GH¢5 she raises the price, 10 less plates are sold.
Draw a table of cost relating to number of plates using 6 values of cost and its corresponding number of plates bought.
What price in GH¢ should she sell the plates to maximize her revenue?
Answer:
Step-by-step explanation:
First, note this parameters from the question.
We let x = number of $5 increases and number of 10 decreases in plates sold.
Our Revenue equation is:
R(x) = (300-10x)(10+5x)
We expand the above equation into a quadratic equation by multiplying each bracket:
R(x) = 3000 + 1500x - 3000x - 1500x^2
R(x) = -1500x^2 - 1500x + 3000 (collect like terms)
Next we simplify, by dividing through by -1500
= 1500x^2/1500 - 1500x/1500 + 3000/1500
= X^2 - x + 2
X^2 - x + 2 = 0
Next, we find the axis of symmetry using the formula x = -b/(2*a) where b = 1, a = 1
X = - (-1)/2*1
X = 1/2
Number of $5 increases = $5x1/2 = $2.5
=$2.5 + $20 = $22.5 ticket price gives max revenue.
Which equation represents the function graphed
coordinate plane?
Answer:
b. y = |x+4| - 10
Step-by-step explanation:
When you see a v-shaped graph, it could very well relate to an absolute-value function.
The value of the absolute value function has the vertex at x= -4, meaning that it has a minimum value when x=-4, which means that the absolute value function is of the form |x+4| giving a zero when x= -4.
Also, the minimum of the function occurs at y = -10, meaning that the function has been translated by -10.
Therefore the function is
y = |x+4| - 10
Answer:
B
Step-by-step explanation:
EDGE unit review
Find the midpoint of the segment between the points (17,−11) and (−14,−16)
Answer:
(1.5, -13.5)
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
Simply plug in our coordinates into the formula:
x = (17 - 14)/2
x = 3/2
y = (-11 - 16)/2
y = -27/2
Answer:
(-1.5, -13.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
( 17+-14)/2 = 3/2 =1.5
To find the y coordinate of the midpoint, add the x coordinates and divide by 2
( -11+-16)/2 = -27/2= - 13.5
Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 25% of the passengers are on business while on ordinary jets 30% of the passengers are on business. Of Global's air fleet, 40% of its capacity is provided on jumbo jets. (Hint: The 25% and 30% values are conditional probabilities stated as percentages.) What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
Answer:
Answer:
The probability is [tex]P(J|B) = 0.36[/tex]
Step-by-step explanation:
B =business
J=jumbo
Or =ordinary
From the question we are told that
The proportion of the passenger on business in the ordinary jet is [tex]P(B| Or) = 0.25[/tex]
The proportion of the passenger on business in the jumbo jet is [tex]P(B|J) = 0.30[/tex]
The proportion of the passenger on jumbo jets is [tex]P(j) = 0.40[/tex]
The proportion of the passenger on ordinary jets is evaluated as
[tex]1 - P(J) = 1- 0.40 = 0.60[/tex]
According to Bayer's theorem the probability a randomly chosen business customer flying with Global is on a jumbo jet is mathematically represented as
[tex]P(J|B) = \frac{P(J) * P(B|J)}{P(J ) * P(B|J) + P(Or ) * P(B|Or)}[/tex]
substituting values
[tex]P(J|B) = \frac{ 0.4 * 0.25}{0.4 * 0.25 + 0.6 * 0.3}[/tex]
[tex]P(J|B) = 0.36[/tex]
Step-by-step explanation:
The letters G, E, N, I, D, S are placed in a bag. What is the probability that the letters are randomly pulled from the bag in the order that spells DESIGN?
Answer as a fraction = 1/5040
Answer in decimal form (approximate) = 0.000198
Answer in percentage form (approximate) = 0.0198%
=========================================================
Explanation:
There is only one ordering of the letters to get DESIGN out of 5040 different permutations. The 5040 comes from the fact that 7*6*5*4*3*2*1 = 5040. In shorthand notation, use factorials to say 7! = 5040. Notice how we started with 7 and counted down until reaching 1, multiplying all along the way. You could use the nPr permutation formula to get the same result of 5040 (use n = 7 and r = 7).
So because we have 1 way to order the letters (getting DESIGN) out of 5040 ways total, this means the probability is the fraction 1/5040. Use your calculator to find that 1/5040 = 0.000198 approximately. Move the decimal over 2 spots to the right to convert 0.000198 to 0.0198%
Can Someone plz help me with the question??
Answer:
[tex]\boxed{x^2+y^2 = 49}[/tex]
Step-by-step explanation:
First, we'll find the length of the radius using distance formula and the coordinates (0,0) and (7,0)
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
R = [tex]\sqrt{(7-0)^2+(0-0)^2}[/tex]
R = [tex]\sqrt{7^2}[/tex]
Radius = 7 units
Now, Equation of circle:
[tex](x-a)^2+(y-b)^2 = R^2[/tex]
Where (a,b) = (0,0) So, a = 0, b = 0 and R = 7 units
=> [tex](x-0)^2+(y-0)^2 = (7)^2[/tex]
=> [tex]x^2+y^2 = 49[/tex]
This is the required equation of the circle.
Answer:
x^2 + y^2 = 49
Step-by-step explanation:
We can write the equation of a circle as
( x-h) ^2 + ( y-k) ^2 = r^2
where ( h,k) is the center and r is the radius
The radius is the distance from the center to a point on the circle
(0,0) to (7,0) is 7 units
so the the radius is 7
( x-0) ^2 + ( y-0) ^2 = 7^2
x^2 + y^2 = 49
Please help ASAP!!! Thank you so much!!! Just want confirm my answer it is y=150x-50. A concession stand at a football game took in $100 after being open for 1 hour. After 3 hours, the stand had taken in $400. Assuming a linear function, write an equation in the form y=mx+b that shows the revenue earned from being opened for x hours.
Answer: You have the correct answer. It is y = 150x-50
Nice work on getting the correct answer. For anyone curious, the explanation is below.
=============================================
x = number of hours the stand is open
y = amount earned
(1,100) is from the fact the stand is open 1 hour and earns $100
(3,400) is due to the stand earning $400 after 3 hours.
Slope Formula
m = (y2 - y1)/(x2 - x1)
m = (400-100)/(3-1)
m = 300/2
m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.
Use m = 150 and (x,y) = (1,100) to find the value of b as shown below
y = mx+b
100 = 150(1) + b
100 = 150 + b
100-150 = b
-50 = b
b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.
So we have m = 150 as the slope and b = -50 as the y intercept.
Therefore, y = mx+b turns into y = 150x-50.
-------
As a check, plugging in x = 1 should lead to y = 100
y = 150x-50
y = 150(1)-50
y = 150-50
y = 100 and indeed it does
The same should be the case with (3,400). Plug in x = 3 and we should get y = 400
y = 150x-50
y = 150(3)-50
y = 450-50
y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).
The equation for revenue earned from being opened for x hours will be y=150x-50 so it is absolutely correct.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given,
$100 for 1 hour
So,
x = 1 and y = 100
And,
$400 for 3 hour
So,
x = 3 and y = 400
Now the slope of the linear equation is given by
m = difference in ys coordinate / difference in xs coordinate
m = (400 - 300)/(3-1) = 150
So equation become
y = 150x + b
Now put (3,400) to find out b
400 = 150(3) + b
b = -50
So, equation
y = 150x - 50
Hence " The equation for revenue earned from being opened for x hours will be y=150x-50".
For more about the equation,
https://brainly.com/question/10413253
#SPJ2
Find the volume of the region enclosed by the cylinder x squared plus y squared equals 36 and the planes z equals 0 and y plus z equals 36.
Answer:
[tex]\mathbf{V = 1296 \pi }[/tex]
Step-by-step explanation:
Given that :
Find the volume of the region enclosed by the cylinder [tex]x^2 + y^2 =36[/tex] and the plane z = 0 and y + z = 36
From y + z = 36
z = 36 - y
The volume of the region can be represented by the equation:
[tex]V = \int\limits \int\limits_D(36-y)dA[/tex]
In this case;
D is the region given by [tex]x^2 + y^2 = 36[/tex]
Relating this to polar coordinates
x = rcosθ y = rsinθ
x² + y² = r²
x² + y² = 36
r² = 36
r = [tex]\sqrt{36}[/tex]
r = 6
dA = rdrdθ
r → 0 to 6
θ to 0 to 2π
Therefore:
[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r sin \theta ) (rdrd \theta)[/tex]
[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r^2 sin \theta ) drd \theta[/tex]
[tex]V = \int\limits^{2 \pi} _0 [\dfrac{36r^2}{2}- \dfrac{r^3}{3}sin \theta]^6_0 \ d\theta[/tex]
[tex]V = \int\limits^{2 \pi} _0 [648- \dfrac{216}{3}sin \theta]d\theta[/tex]
[tex]V = \int\limits^{2 \pi} _0 [648+\dfrac{216}{3}cos \theta]d\theta[/tex]
[tex]V = [648+\dfrac{216}{3}cos \theta]^{2 \pi}_0[/tex]
[tex]V = [648(2 \pi -0)+\dfrac{216}{3}(1-1)][/tex]
[tex]V = [648(2 \pi )+\dfrac{216}{3}(0)][/tex]
[tex]V = 648(2 \pi )[/tex]
[tex]\mathbf{V = 1296 \pi }[/tex]
Please help. I’ll mark you as brainliest if correct
Answer:
1,-1,3,4
1,6,-2,-4
-4,6,-6,6
Step-by-step explanation:
I believe you just put in the values into the box. Watch the video to see how they did it to make sure it looks like how I did it.
Find the least common multiple of $6!$ and $(4!)^2.$
Answer:
The least common multiple of $6!$ and $(4!)^2.$
is 6×4! or 144
Find the unknown side length x write your answer in simplest radical form
A.24
B.4squareroot37
C.2squareroot154
D.5squareroot117
Answer:
(B)[tex]4\sqrt{37}[/tex]
Step-by-step explanation:
First, we determine the height of the triangle which we label as y.
Using Pythagoras Theorem.
[tex]25^2=7^2+y^2\\y^2=25^2-7^2\\y^2=576\\y=\sqrt{576}\\y=24[/tex]
In the smaller right triangle with hypotenuse, x
Base = 7-3 =4 Units
Height, y= 24 Units
Therefore, applying Pythagoras Theorem.:
[tex]x^2=24^2+4^2\\x^2=592\\x=\sqrt{592}\\ x=4\sqrt{37}[/tex]
Which of the following lines are parallel to 2Y - 3X = 4?
A. Y = 2/3 X + 4
B. Y = 6/4 X
C. 2Y=8-3X
Answer:
B. Y = 6/4 X
Step-by-step explanation:
Well to find its parallel line we need to put,
2y - 3x = 4 into slope-intercept.
+3x to both sides
2y = 3x + 4
Now we divide everything by 2,
y = 3/2x + 2
So a line that is parallel to the given line will have the same slope but different y intercept, meaning we can cross out choices A and C.
To check look at the image below ↓
Thus,
answer choice B. Y = 6/4 X is correct.
Hope this helps :)
Find the average rate of change of the function f(x), represented by the graph, over the interval [-4, -1]. Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula . The value of f(-1) is . The value of f(-4) is . The average rate of change of f(x) over the interval [-4, -1] is .
Answer:
2
Step-by-step explanation:
We are given that a graph which represents f(x).
Interval:[-4,-1]
We have to find the average rate of change of the function f(x).
From the graph we can see that
f(-4)=-3
f(-1)=3
We know that the average rate of change of the function
Average rate =[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using the formula
Average rate of change of f=[tex]\frac{3-(-3)}{-1-(-4)}[/tex]
Average rate of change of f=[tex]\frac{6}{3}=2[/tex]
A salesperson earns 6% commission on $25.000. How much
commission was earned?
The commission earned was $
Answer: $1500
Step-by-step explanation:
6% commission on $25,000
= 25000 x .06
= 1500
Help thx!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Answer E
Step-by-step explanation:
If you think about it, the origin is just (0,0). Now, think which one is the closest to that. (0,1/2), or answer E, should be your assumption.
A school has 39 vacancies for teachers.out of which 22 are for English language,21 are for mathematics and 17 are for fine arts.of these vacancies 11 are for both English language and mathematics,8 for mathematics and fine arts and 7 for both English and fine arts.calculate the number of teachers who must be able to teach all subjects and fine arts only
Answer:
12
Step-by-step explanation:
let
x= no. for English
y= no. for maths
z= no. for fine arts
a= no. for all subjects
x= 22
y= 21
z= 17
x+y+z= 39
x intersect y= 11
y intersect z= 8
x intersect z= 7
(4+a)+ (11-a)+ (7-a)+ (8-a)+ (2+a)+ (2+a)+ a= 39
34+a =39
a= 5
no.of teachers who teaches all & fine art only
= a + (2+a)
= 5+7
= 12
For the functions f(x)=2x−5 and g(x)=3x2−x, find (f∘g)(x) and (g∘f)(x).
Hi,
f°g means : apply first g then f . so calculate "g" and then use result as "x" in f.
g°f means : you apply first f then g
so : f°g = 2(3x²-x) -5 = 6x²-2x- 5
To improve in math, you need practice. have a try with g°f :)
give the answer in comments, and I will tell you if you are correct.
good luck.
The temperature is 58° F. It gets warmer by h degrees and reaches to 65° F. Find h.
Answer:
h = 7 degrees
Step-by-step explanation:
To find h, we know that it is positive because it increases in value, not decreases:
h = 65 - 58
h = 7
Answer:
h = 7°F
Step-by-step explanation:
58 + h = 65
h = 65 - 58
h = 7
Check:
68 + 7 = 65
For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, is the level of significance, p is the sample proportion, and n is the sample size.
Claim: p >=0.28; α:0.08. Sample statistics: p=0.20, n= 180
Required:
If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision.
Answer:
The Central Limit Theorem says that if the sample size is more than 30, the data follows a normal sampling distribution. Since the sample size is 180, and that is more than 30, a Normal sampling distribution can be used.
Since a normal sampling distribution can be used, we should FAIL TO REJECT the null hypothesis because p = 0.20, which is more than the significance level of α = 0.08. There is NOT sufficient evidence to suggest that the alternative hypothesis is true.
Hope this helps!
a student showed the steps below while solving the equation 14=log5(2x-3) by graphing. which step did the student make the 1sr error
Answer:
[tex]x= \frac{5^{14}+3}{2}[/tex]
Step-by-step explanation:
The correct steps to solve the equation are:
[tex]14=log_5(2x-5)[/tex]
[tex]5^{14}=5^{log_5(2x-3)}[/tex]
Because [tex]a^{log_am}=m[/tex]
So, solving we get:
[tex]5^{14}=2x-3[/tex]
Sum 3 on every side:
[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]
Dividing by 2 into both sides:
[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]
So, the answer is [tex]x= \frac{5^{14}+3}{2}[/tex]
Answer: Step 2
Step-by-step explanation:
This is correct according to Edge 2021
According to the World Health Organization (WHO) Child Growth Standards, the head circumference for boys at birth is normally distributed with a mean of 34.5cm and a standard deviation of 1.3cm. What is the probability that a boy has a head circumference greater than 36.32cm at birth
Answer:
0.081
Step-by-step explanation:
To solve this question, we would use the z score formula
z score = (x-μ)/σ, where
x is the raw score = 36.32cm
μ is the population mean = 34.5 cm
σ is the population standard deviation = 1.3cm
z score = (36.32cm - 34.5cm)/1.3cm
z = 1.4
Using the normal distribution to find the z score for 1.4
P(z = 1.4) = 0.91924
Therefore, the probability that a boy has a head circumference greater than 36.32cm at birth is
P(x>36.32) = 1 - P(z = 1.4)
= 1 - 0.91924
= 0.080757
Approximately ≈ 0.081
For the population {0, 1, 2, 3, 5, 7},
(a) List all the simple random samples of size 5.
(b) Give an example of a systematic sample of size 3 where the elements are listed
in the order : 0, 1, 2, 3, 5, 7.
(c) Give an example of a proportional stratified sample of size 3 where the strata are
{0, 1, 2, 3}, {5, 7}.
(d) Give an example of a cluster sample size of 2 where the clusters are {0, 1}, {2,3},
{5, 7}.
Of 10 girls in a class, three have blue eyes. Two of the girls are chosen at random. Find the probability that: (a) both have blue eyes; (c) at least one has blue eyes; (b) neither has blue eyes; (d) exactly one has blue eyes.
Answer:
C.
Step-by-step explanation:
It's the most reasonable answer.
What is the difference of the rational expressions below?
6/x - 5x/x+2
A.
5x + 6
2
O
B. 5x + 6x +12
** + 2x
O
c.
5x6
2x+2
D. 5x' +6x +12
2x + 2
The difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).
Thus, the correct option would be:
C. (x + 12)/(x(x+2))
To find the difference of the rational expressions, we need to subtract the second expression from the first expression.
Let's simplify the expressions first:
The first expression is 6/x - 5x/(x+2).
To combine the terms, we need a common denominator, which is (x)(x+2).
Converting the first term, 6/x, to have a denominator of (x)(x+2), we get (6(x+2))/(x(x+2)).
Now, we can combine the terms:
[(6(x+2))/(x(x+2))] - [5x/(x+2)]
To subtract the fractions, we need to have a common denominator, which is (x)(x+2).
Expanding the numerators, we get:
[(6x + 12)/(x(x+2))] - [5x/(x+2)]
Now, we can subtract the fractions:
[(6x + 12 - 5x)/(x(x+2))]
Simplifying the numerator, we have:
(6x - 5x + 12)/(x(x+2))
Combining like terms, we get:
(x + 12)/(x(x+2))
Therefore, the difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).
Thus, the correct option would be:
C. (x + 12)/(x(x+2))
For similar question on rational expressions.
https://brainly.com/question/29061047
#SPJ8
Mike can stitch 7 shirts in 42 hours
He can stitch 1 shirt in hours, and in 1 hour he can stitch of a shirt
Answer:
He stitched 1 shirt in 6 hours.
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Given Mike can stitch 7 shirts in 42 hours
No. of shirt stitch in one hour = total no of shirt stitch/total time taken
No. of shirt stitch in one hour = 7/42 = 1/6
Thus, he can stitch 1/6 of a shirt in one hour
Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7) = 42/6 = 6 hours.
Thus, he stitched 1 shirt in 6 hours.
Answer:
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Because he stitched 7 shirts in 42 hours
42/7 = 6
so 6 hours per shirt
In one hour:
1/6
The question is with the image.
Answer:
A
Step-by-step explanation:
the graph of x'3 is B
the graph of x'(-1/3) is C