Answer:
[tex]4000(1.023)^t\\\\[/tex]
Step-by-step explanation:
Using this exponential growth equation we can get an equation that models the situation.
A= Principal Amount
R= Rate of Growth
T= Amount of time
[tex]A=4000\\R=2.3/100=.023\\T= Non[/tex]
[tex]A(1+R)^t\\4000(1+0.23)^t\\4000(1.023)^t\\\\[/tex]
I need some help pls! I'm getting stuck!
Answer: 3 pounds.
Step-by-step explanation:
We have two metals:
One that contains 20% nickel, let's call it metal A.
One that contains 80% nickel, let's call it metal B.
We have 6 pounds of metal B, in those 6 punds we have:
0.80*6lb = 4.8lb of nickel.
Now, if we add X pounds of metal A, then we will have:
X + 6lb in total weight.
4.8lb + 0.2*X of nickel.
And we want to have exactly 60% of nickel, so we must have that the quotient between the amount of nickel and the total weight is equal to 0.6
(4.8lb + 0.2*X)/(6lb + X) = 0.6
now we solve it for X:
(4.8lb + 0.2*X) = 0.6*(6lb + X) = 3.6lb + 0.6*X
4.8lb - 3.6lb = 0.6*X - 0.2*X
1.2lb = 0.4*X
1.2lb/0.4 = 3lb = X
We should use 3 pounds of the metal with 20% of nickel.
Which expression is equivalent to (jk)l? A. (j + k) + l B. j(kl) C. (2jk)l D. (j + k)l
Answer:
B. j(kl)
Step-by-step explanation:
(jk)l
We can change the order we multiply and still get the same result
j(kl)
Answer:
Step-by-step explanation:
its B i did it
To the nearest tenth, what is the value of P(C|Y)? 0.4 0.5 0.7 0.8
Answer:
P(C|Y) = 0.5.
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
Now, we have to find the probability of P(C/Y).
As we know that the conditional probability formula of P(A/B) is given by;
P(A/B) = [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]
So, according to our question;
P(C/Y) = [tex]\frac{P(C \bigcap Y)}{P(Y)}[/tex]
Here, P(Y) = [tex]\frac{30}{146}[/tex] and P(C [tex]\bigcap[/tex] Y) = [tex]\frac{15}{146}[/tex] {by seeing third row and second column}
Hence, P(C/Y) = [tex]\frac{\frac{15}{146} }{\frac{30}{146} }[/tex]
= [tex]\frac{15}{30}[/tex] = 0.5.
Answer: 0.5
Step-by-step explanation:
edge
(a) A survey of the adults in a town shows that 8% have liver problems. Of these, it is also found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability that this person i. Has a liver problems?
Answer:
The probability that the selected adult has liver problems is 0.08
Step-by-step explanation:
In this question, from the data given, we want to calculate the probability that an adult selected at random has liver problems.
Let E(L) be the event that an adult has liver problems.
The probability is directly obtainable from the question and it is given as 8%
Thus, the probability that the selected adult has liver problems; P(L) = 8% = 8/100 = 0.08
How to divide using area model
Answer:
In mathematics, an area model is a rectangular diagram or model used for multiplication and division problems, in which the or the and define the length and width of the rectangle.
We can break one large of the rectangle into several smaller boxes, using number bonds, to make the calculation easier. Then we add to get the area of the whole, which is the or quotient.
To multiply two 2-digit numbers, using the area model, follow the given steps:
Write the multiplicands in expanded form as tens and ones.
For example, 27 as 20 and 7, and 35 as 30 and 5.
Draw a 2 × 2 grid, that is, a box with 2 rows and 2 columns.
Write the terms of one of the multiplicands on the top of the grid (box). One on the top of each cell.
On the left of the grid, write the terms of the other multiplicand. One on the side of each cell.
Write the product of the number on the tens in the first cell. Then write the product of the tens and ones in the second and third cell. Write the product of the ones in the fourth cell.
write the product in the cell
Finally, add all the partial products to get the final product.
Here, for example, the area model has been used to multiply 27 and 35.
area model multiplication
Let us see how to find the product of 3-digit number by a 2-digit number using the area model.
Find the Product using Area Model
Let us now use the area model for the division. Here, we divide 825 by 5.
Area Model Division 1
Area Model Division 2
Fun Facts
The area model is also known as the box model.
The area model of solving multiplication and division problems is derived from the concept of finding the area of a rectangle. Area of a rectangle = Length × Width.
Math Games for Kids
Math Games for Kids
Online Live Math Classes
SplashLearn Content
Resources
StudyPad®, Splash Math®, SplashLearn™ & Springboard™ are Trademarks of StudyPad, Inc.
Copyright © 2020 Studypad Inc. All Rights Reserved
Let f(x) = - 4x + 5. Find and simplify f(x + 2).
Answer:
-4x - 3.
Step-by-step explanation:
f(x) = -4x + 5.
f(x + 2) = -4(x + 2) + 5
= -4x - 8 + 5
= -4x - 3.
Hope this helps!
Answer:
f(x+2)=-4x-3
Step-by-step explanation:
We are given:
[tex]f(x)= -4x+5[/tex]
and asked to find f(x+2). Therefore, we must substitute x+2 for each x in the function.
[tex]f(x+2)=-4(x+2)+5[/tex]
Now, simplify. First, distribute the -4. Multiply each term inside the parentheses by -4.
[tex]f(x+2)=(-4*x)+(-4*2)+5\\f(x+2)=-4x+(-4*2)+5\\f(x+2)=-4x-8+5[/tex]
Next, combine like terms. There are 2 constants (terms without a variable) that can be added. Add -8 and 5.
[tex]f(x+2)=-4x(-8+5)\\f(x+2)=-4x-3[/tex]
f(x+2) is -4x-3.
A rectangular paperboard measuring 29in long and 20in wide has a semicircle cut out of it, as shown below.
Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
Here, we are required to find the area of the paper board given after the semicircle is cut out of it
Area of the paper board that remains is 423 in²
Length = 29 in
Width = 20 in
Area of a rectangle = length × width
= 29 in × 20 in
= 580 in²
Area of a semi circle = πr²/2
π = 3.14
r = diameter / 2 = 20 in / 2 = 10 in
Area of a semi circle = πr²/2
= 3.14 × (10 in)² / 2
= 3.14 × 100 in² / 2
= 314 in²/2
= 157 in²
The semicircle is cut out of the rectangle
Find the area of the paper board that remains after the semicircle is cut out of it by subtracting the area of a semi circle from the area of a rectangle
Area of the paper board that remains = Area of a rectangle - Area of a semi circle
= 580 in² - 157 in²
= 423 in²
Read more:
https://brainly.com/question/16994941
In kickboxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 7 pounds of pressure to break a board that is 3 feet long, how long is a board that requires 5 pounds of pressure to break?
Answer:
4.2
Step-by-step explanation:
f varies inversly with L can be translated matimatically as:
● f = k/L
It takes 7 pounds of pressure to break a 3 feet long board.
Replace f by 7 and L by 3.
● 7 = k/3 => k=7×3=21
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's find tge length of a board that takes 5 pounds of pressure to be broken.
● 5 = k/L
● 5 = 21/L
● L = 21/5 = 4.2
So the board is 4.2 feet long
PLEASE HELP ME WITH THIS QUESTION
Answer:
y-k
x-h
Step-by-step explanation:
Given E &D, F would be at (x, k).
That means E to F would be y-k.
And F to D would be x-h.
I assume you don’t need to find E to D, since that’s just r. (You could use the Distance Formula or Pythagoreans theorem to come up with and equation, but it wouldn‘t be one of those listed.)
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
a) What is the cost of a chicken shawarma wrap?
$10.99
b) What is the cost of one order of spiced potatoes?
$4.99
c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
Step-by-step explanation:
Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,
Cost of a chicken sharwarma wrap = x
Cost of an order of spiced potatoes = y
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
Hence, the Equations needed to solve the question is:
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
We use Elimination method to solve for this.
Multiply Equation 1 by coefficient of x in Equation 2
Equation 2 by coefficient of x in Equation 1
3x + 2y = $42.95 .............Equation 1 × 5
5x + 4y = $74.91 ................Equation 2 × 3
15x + 10y = 214.75..............Equation 3
15x + 12y = 224.73..............Equation 4
Subtract Equation 3 from Equation 4
2y = 9.98
y = 9.98/2
y = 4.99
Therefore, y = Cost of an order of spiced potatoes = $4.99
Subtitute 4.99 for y in Equation 1
3x + 2y = $42.95 .............Equation 1
3x +2(4.99) = 42.95
3x + 9.98 = 42.95
3x = 42.95 - 9.98
3x = 32.97
x = 32.97/3
x = 10.99
x = Cost of a chicken sharwarma wrap = $10.99
Therefore,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
The probability that a patient recovers from a disease is 0.3.
If 6 people are known to have contacted the disease, what is the probability that at least 4 survive?
Answer:
0.07047
Step-by-step explanation:
at least 4 people survive is
4 people survive and 2 don't +
5 people survive and 1 doesn't +
all 6 people survive
the probability of 4 people to survive is the product of the individual probabilities :
0.3×0.3×0.3×0.3 = 0.3⁴ = 0.0081
times the probability 2 don't survive
0.7×0.7 = 0.49
0.0081×0.49 = 0.003969
now, the chance that 4 out of 6 survive is that probabilty times how many times we can select 4 out of 6.
to select 4 out of 6 is
[tex] \binom{6}{4} [/tex]
= 6! / (4! × (6-4)!) = 6! / (4! × 2!) = 6×5/2 = 30/2 = 15
so, the probability of having 4 survivors is
15×0.003969 = 0.059535
the probability of 5 people surviving is 0.3⁵ times one not
0.3⁵×0.7 = 0.001701
we have 6 over 5 combinations to pick 5 out of 6 = 6.
so, in total for 5 survivors we get
6×0.001701 = 0.010206
and the probabilty of all 6 surviving is
0.3⁶ = 0.000729
so, the probability of at least 4 out of 6 surviving is
0.059535 +
0.010206 +
0.000729
---------------
0.070470
Which Expression is equivalent to -2(x + 6) 2x + (-12) 2x + 12 2x + 6
Answer:
-2x -8
Step-by-step explanation:
Time spent using e-mail per session is normally distributed with a mean = to 8 minutes and standard deviation = 2minutes. If a random samples of 36 sessions were selected, the computed sample standard deviation would be
a. 0.25
b. 0.3333
c. 0.42
d. 0.48
Answer:
The correct option is (b) 0.3333.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].
The standard error is given as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]
Compute the standard deviation of the sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]
Thus, the standard deviation of the sample mean is 0.3333.
What is the solution for this equation?
by – 12) = 21
O {9, 33)
O {-9, 33}
O {-33, -9}
O {-33, 9}
Sol-1
[tex]\\ \sf\longmapsto |y-12|=21[/tex]
[tex]\\ \sf\longmapsto y+12=21[/tex]
[tex]\\ \sf\longmapsto y=21-12[/tex]
[tex]\\ \sf\longmapsto y=9[/tex]
Sol:-2
[tex]\\ \sf\longmapsto y-12=21[/tex]
[tex]\\ \sf\longmapsto y=21+12[/tex]
[tex]\\ \sf\longmapsto y=33[/tex]
Pedro thinks that he has a special relationship with the number 6. In particular, Pedro thinks that he would roll a 6 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pp is the true proportion of the time Pedro will roll a 6.
Required:
a. State the null and alternative hypotheses for testing Pedro's claim.
b. Now suppose Pedro makes 42 rolls, and a 6 comes up 9 times out of the 42 rolls. Determine the P-value of the test: P-value.
c. Does this sample provide evidence at the 5% level that Pedro rolls a 6 more often than you'd expect?
Answer:
Step-by-step explanation:
a) The sample space, n(S) = 6^6 = 46656
Let the number fair dice toss that show 6 = n(A)
Hence, the probability of getting, P(A) = n(A)/n(S)
b) Sample space, n(S) = 6^42
n(A) = 6^9
∴ P(A) = n(A)/n(S) = 6^9/6^42 = 1/(6^33) = 2.09 X 10^(-26)
c) No
purchased a book rs 500 sold 20%profit find its actual profit and sel
ling price
Answer:
Selling price=rs.600.
Profit of rs=100.
Step-by-step explanation:
C.P=500; profit%=20%
S.P.=100+profit%×C.P/100
S.P=120×500/100
=rs.600
S.P>C.P
Profit S.P-C.P
600-500=100
he gained for rs.100.
Two metal spheres of diameter 2.3cm and 3.86cm are melted. The molten material is used to cast equal cylindrical slabs of radius 8mm and length 70mm. If 1/2 of the metal is lost during casting. Calculate the number of complete slabs casted.
Answer:
4
Step-by-step explanation:
If 1/20 of the metal is lost during casting. Calculate the number of complete slabs casted. (4mks)
Sandy used these rules to write a 6-digit number.
• 3 in the tens place
• 6 in the hundreds place
1 in the thousands place
• 8 in the ten thousands place
4 in the ones place
• 2 in the hundred thousands place
.
What number did she write?
A. 281,634
B. 361.842
C. 681,234
D. 864,321
9514 1404 393
Answer:
A. 281,634
Step-by-step explanation:
You can identify the number after the first two "rules".
Choices A and C have 3 in the tens place.
Choice A has 6 in the hundreds place.
Determining the normal form of the equation of a line is like finding the equation of a tangent line to a circle of radius p.
Please select the best answer from the choices provided
True
False
Answer:
True
Step-by-step explanation:
The normal form of equation of a line is the radius of p. Tangent to a circle is the line that touches one point on the circle. The radius is the circumference of the circle. The tangent line on the circle is always perpendicular to the radius. The statement is correct.
[tex]f(x) = sqr root x+3 ; g(x) = 8x - 7[/tex]
Find (f(g(x))
[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]
Greatest to least just need some help will help ty(please don’t give wrong answer)
Answer:
try 91.78, 91.58, 91.26, 363.4
Step-by-step explanation:
What should be subtracted from 13/(-56) to get 11/28
Answer:
-5/8
Step-by-step explanation:
13/ -56 -x = 11/28
Add 13/56 to each side
13/ -56 + 13/56 -x = 11/28+ 13/56
-x = 11/28 + 13/56
Get a common denominator
-x = 11/28 *2/2 +13/56
-x = 22/56 + 13/56
-x = 35/56
Divide top and bottom by 7
-x = 5/8
Multiply both side by -1
x = -5/8
Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-floor manufacturing company. Accordingly, engineers at Lumberworks are investigating a potential new cutting method involving lateral sawing that may reduce the scrap rate. To examine its viability, two independent, random, representative samples of planks were examined. One sample contained 200 planks which were sawed using the old method. The other sample contained 400 planks which were sawed using the new method. Sixty-two of the 200 planks were scrapped under the old method of sawing, whereas 36 of the 400 planks were scrapped under the new method.
Required:
a. Construct the 90% confidence interval for the difference between the population scrap rates between the old and new methods, respectively.
b. Write the null and alternative hypotheses to test for differences in the population scrap rates between the old and new cutting methods, respectively.
c. Using the part a results, can we conclude at the 10% significance level that the scrap rate of the new method is different than the old method?
Answer:
The critical value for two tailed test at alpha=0.1 is ± 1.645
The calculated z= 9.406
Step-by-step explanation:
Formulate the hypotheses as
H0: p1= p2 there is no difference between the population scrap rates between the old and new cutting methods
Ha : p1≠ p2
Choose the significance level ∝= 0.1
The critical value for two tailed test at alpha=0.1 is ± 1.645
The test statistic is
Z = [tex]\frac{p_1- p_2}\sqrt pq(\frac{1}{n_1} + \frac{1}{n_2})[/tex]
p1= scrap rate of old method = 62/200=0.31
p2= scrap rate of new method = 36/400= 0.09
p = an estimate of the common scrap rate on the assumption that the two rates are same.
p = n1p1+ n2p2/ n1 + n2
p =200 (0.31) + 400 (0.09) / 600
p= 62+ 36/600= 98/600 =0.1633
now q = 1-p= 1- 0.1633= 0.8367
Thus
z= 0.31- 0.09/ √0.1633*0.8367( 1/200 + 1/400)
z= 0.301/√ 0.13663( 3/400)
z= 0.301/0.0320
z= 9.406
The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that the 10% significance level that the scrap rate of the new method is different from the old method.
Use Green’s theorem to evaluate line integral along curve C ∮_c〖( 3ydx+2xdy )〗, C : The boundary of 0≤x≤π,0≤y≤sin x
Answer:
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = \boxed{\bold{2}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Rule [Basic Power Rule]:
Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Multivariable Calculus
Partial Derivatives
Vector Calculus
Circulation Density:
[tex]\displaystyle F = M \hat{\i} + N \hat{\j} \rightarrow \text{curl} \ \bold{F} \cdot \bold{k} = \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}[/tex]
Green's Theorem [Circulation Curl/Tangential Form]:
[tex]\displaystyle \oint_C {F \cdot T} \, ds = \oint_C {M \, dx + N \, dy} = \iint_R {\bigg( \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} \bigg)} \, dx \, dy[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy}[/tex]
[tex]\displaystyle \text{Region:} \ \left \{ {{0 \leq x \leq \pi} \atop {0 \leq y \leq \sin x}} \right.[/tex]
Step 2: Integrate Pt. 1
Define vector functions M and N:Step 3: Integrate Pt. 2
We can evaluate the Green's Theorem double integral we found using basic integration techniques listed above:
[tex]\displaystyle \begin{aligned}\oint_C {3y \, dx + 2x \, dy} & = - \int\limits^{\pi}_0 \int\limits^{\sin x}_0 {} \, dy \, dx \\& = - \int\limits^{\pi}_0 {y \bigg| \limits^{y = \sin x}_{y = 0}} \, dx \\& = - \int\limits^{\pi}_0 {\sin x} \, dx \\& = \cos x \bigg| \limits^{x = \pi}_{x = 0} \\& = \boxed{\bold{2}}\end{aligned}[/tex]
∴ we have evaluated the line integral using Green's Theorem.
---
Learn more about multivariable calculus: https://brainly.com/question/14502499
---
Topic: Multivariable Calculus
Unit: Green's Theorem and Surfaces
You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.
Answer:
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Solution Set : { x = 123, y = 246, z = 11 }
Step-by-step explanation:
Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,
x + y + z = 380,
And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.
5x + 3y + 10z = 1460
The silly string tickets were sold for twice as much as the car wash tickets.
y = 2x
Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.
System of Equations :
[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,
[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three
And we can continue, canceling the leading co - efficient in each row until this matrix remains,
[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]
x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold
A circle is centered at (7, 8) and has a radius of 11. Which of the following is the equation for this circle? (x − 7)2 + (y − 8)2 = 121 (x − 7)2 + (y − 8)2 = 11 (x + 7)2 + (y + 8)2 = 121 (x + 7)2 + (y + 8)2 = 11
Answer:
(x − 7)2 + (y − 8)2 = 11
Step-by-step explanation:
I took the test
The equation of the circle with center at (7, 8) and radius of 11 is
(x - 7)² + (y - 8)² =121
The equation of a circle with center at (a, b) and radius of r is:
(x - a)² + (y - b)² = r²
The center of the circle, (a, b) = (7, 8)
That is, a = 7, b = 8
The radius, r = 11
Substitute a = 7, b = 8, and r = 11 into the equation (x - a)² + (y - b)² = r²:
(x - 7)² + (y - 8)² = 11²
(x - 7)² + (y - 8)² = 121
Therefore, the equation of the circle with center at (7, 8) and radius of 11 is
(x - 7)² + (y - 8)² =121
Learn more here: https://brainly.com/question/23226948
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
Y=-3x+1
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Answer:
y = 1 m = -3 b = 1
Step-by-step explanation:
y = mx + b y = -3x + 1
y = 1
m = -3
b = 1
3(2+7) - 9 x 7 = 3+8 x 2 x 2 - 4 = 16 ÷ 2 x 5 x 3 ÷ 6 = Please answer! ✨✨
Answer:
At first, we have 3 expressions that are equal.
[tex]3(2+7) - 9 \cdot 7= 3+8 \cdot 2 \cdot 2 - 4[/tex]
[tex]6+21 - 63= 3+32 - 4[/tex]
[tex]-36=31[/tex]
[tex]-36\neq 31[/tex]
This is not true.
x/5=-2 . And how did you get it?
[tex]\dfrac{x}{5}=-2\\\\x=-10[/tex]
Answer:
[tex]\huge \boxed{{x=-10}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{x}{5} =-2[/tex]
We need the x variable to be isolated on one side of the equation, so we can find the value of x.
Multiply both sides of the equation by 5.
[tex]\displaystyle \frac{x}{5}(5) =-2(5)[/tex]
Simplify the equation.
[tex]x=-10[/tex]
The value of x that makes the equation true is -10.
A regression analysis between sales (y in $1000) and advertising (x.in dollars) resulted in the following equation: ỹ= 30,000 + 4x
The above equation implies that an:________
a. increase of $l in advertising is associated with an increase of $4 in sales.
b. increase of $4 in advertising is associated with an increase of $4000 in sales.
c. increase of $1 in advertising is associated with an increase of $34,000 in sales.
d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Answer:
Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Step-by-step explanation:
Given the equation of regression analysis is given as:
[tex]y= 30,000 + 4x[/tex]
where [tex]x[/tex] is the cost on advertising in Dollars.
and [tex]y[/tex] is the sales in Thousand Dollars.
To find:
The correct increase in sales when there is increase in the advertising cost.
Solution:
Suppose there is an increase of [tex]\$1[/tex] in the advertising cost.
Let the initial cost be [tex]x[/tex] then the cost will be [tex](x+1)[/tex].
Initial sales
[tex]y= 30,000 + 4x[/tex] ....... (1)
After increase of $1 in advertising cost, final cost:
[tex]y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)[/tex]
Subtracting (2) from (1) to find the increase in the sales:
[tex]y'-y=30004+4x-30000-4x = 4[/tex]
The units of sales is Thousand Dollars ($1000).
So, increase in sales = [tex]4 \times1000 = \bold{\$4000}[/tex]
So, correct answer is:
d. increase of $1 in advertising is associated with an increase of $4000 in sales.