Vince has 10 boxes into his truck
Answer:
Here, x represents the number of 20-pound boxes and y represents the number of 30 pound boxes.
Step-by-step explanation:
I think is the same question for this answer
There are 364 first-grade students in park elementary school. If there are 26 more girls than boys, how many girls are there?Use polya's strategy and make an equation.
Answer:
there are 195 girls
Step-by-step explanation:
the equation is: 364= 2x+26
subtract 26 from both sides and you get 338
338 divided by 2 is 169, therefore there are 169 boys.
169+26 more girls is 195
169+195= 364
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer.
[ 1 -2 -5 0 4 3 -3 3 0]
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer.
A. The matrix is not invertible. In the given matrix the columns do not form a linearly independent set.
B. The matrix is not invertible. the given matrix is A, the equation Ax b has no solution for at least one b in R.
C. The matrix is invertible. The given matrix is not row equivalent to the nx n identity matrix.
D. The matrix is invertible. The given matrix has 3 pivot positions.
Answer:
This shows 3 pivot position matrixes.
Step-by-step explanation:
The given matrix is:
[tex]\left[\begin{array}{ccc}1&-2&-5\\0&4&3\\-3&3&0\end{array}\right][/tex]
The option D is correct for this matrix.
The matrix is invertible and the given matrix has 3 pivot positions.
The matrix is invertible if its determinant is nonzero.
Multiply the 3rd row by 1/3.we get:
[tex]\left[\begin{array}{ccc}1&-2&-5\\0&4&3\\-1&1&0\end{array}\right][/tex]
Now, add the first row with third row:
[tex]\left[\begin{array}{ccc}0&-1&-5\\0&4&3\\-1&1&0\end{array}\right][/tex]
Replace third row by first row:
[tex]\left[\begin{array}{ccc}-1&1&0\\0&4&3\\0&-1&-5\end{array}\right][/tex]
This shows 3 pivot position matrixes.
Hence, a matrix is invertible and has 3 pivot positions.
The coordinates of three vertices of square ABCD are A(−212,112),B(−212,−3), and C(2,112).When point D is placed on this square, what will the perimeter of the square be?Enter your answer in the box.
The perimeter of a shape is the total measurement of all the edges of a shape.
Perimeter of the square is 460 unit.
Since, coordinates of three vertices of square ABCD are given as A(−212,112), B(−212,−3) and C(2,112).
If coordinate of M(a, b) and N(c, d) are given.
Then by using distance formula,
[tex]MN=\sqrt{(d-b)^{2} +(c-a)^{2} }[/tex]
Similarly, [tex]AB=\sqrt{(-3-112)^{2}+(-212+212)^{2} } \\\\AB=115[/tex]
In square, all four sides are equal.
Perimeter of Square, [tex]=4*side[/tex]
[tex]=4*115=460[/tex] unit.
Learn more:
https://brainly.com/question/13511952
In 1 year, how many more hours of sleep
does a giant armadillo get than a platypus?
Answer:
Step-by-step explanation:
If the given variables are 127 hours of sleep per week for a Giant Armadillo, and 98 hours of sleep per week for a Platypus, to determine which animal gets the most sleep, first multiply the total hours of sleep of each animal per week to the total number of weeks In a year, which is 52. Once you get the answers, which are 6,604 hours of sleep in a year for the Giant Armadillo and 5,096 hours of sleep in a year for a Platypus. You subtract 6,604 and 5,096 together to get the answer, which is 1,508. Therefore we conclude that that the Giant Armadillo has 1,508 hours more hours of sleep than a Platypus in a Year.
Answer:
1508 hour I think !!!!!!!!!!
Which statement illustrates the distributive property?
A. 9(51 - 12) = 9(51) – 121
OB. 9(5i +121) = 9(121 + 51)
OC. 9(51 – 12) = 9(51) — 9(121)
OD
9 + (51 – 12i) = (9 +51) - (9 + 121)
Answer: Choice C
9(51-12) = 9(51) - 9(12)
============================================
Explanation:
The distributive property is
a(b+c) = a*b + a*c
which can also be written as
a(b-c) = a*b + a*(-c) = a*b - a*c
In this case we're using
a(b-c) = a*b - a*c
where a = 9, b = 51, c = 12
1.5 = m ÷ 9
I am in sixth grade please help me with this
Answer:
13.5 or if in fraction 27÷2
Step-by-step explanation:
1.5 = m ÷ 9
1.5 × 9 = m (since you're finding m,shift the 9 to the left.So divide becomes multiply)
27/2 (27÷2) or 13.5 = m
Marco has a collection of 437 bottles. Each month he buys 32 bottles .
Answer:
what is the question
Step-by-step explanation:
Plz help me with this
Answer:
63°
Step-by-step explanation:
Hi there !
ABCD parallelogram => ∡A = ∡C
13x - 41 = 6x + 15
13x - 6x = 15 + 41
7x = 56
x = 56 : 7
x = 8
∡C = 6×8 + 15 = 48 + 15 = 63°
Good luck !
F(x)=-(2x-1)^2-2. What is the value of f(-3)
Work Shown:
f(x) = -(2x-1)^2 - 2
f(-3) = -(2*(-3)-1)^2 - 2 ... replace every x with -3
f(-3) = -(-6-1)^2 - 2
f(-3) = -(-7)^2 - 2
f(-3) = -49 - 2
f(-3) = -51
what i the scientific notation of 13400000
correct answer only
Answer:
1.34 x 10^7
Step-by-step explanation:
I hope this helped!
2w − w = 15
explain if possible, please
Answer:
2w - w = 15You subtract w from 2w and u remain with w.w = 15What is 15:2=n:8
Solve for n
Answer:
2+|3x|=2+3
in(x)+2=5
x-4>7
Right triangle A has a base of 2 inches and a height of 7 inches. Right triangle B has a base of 10 inches and a height of 35 inches. Enter the scale factor applied to Right triangle A to produce Right triangle B.
Given:
Right triangle A: Base = 2 inches and Height = 7 inches.
Right triangle B: Base = 10 inches and Height = 35 inches.
To find:
The scale factor applied to Right triangle A to produce Right triangle B.
Solution:
We have,
Base of right triangle A = 2 inches
Base of right triangle B = 10 inches
Now,
[tex]\text{Scale factor}=\dfrac{\text{Side of right triangle B}}{\text{Corresponding side of right triangle A }}[/tex]
[tex]Scale\text{Scale factor}=\dfrac{\text{Base of right triangle B}}{\text{Base of right triangle A }}[/tex]
[tex]\text{Scale factor}=\dfrac{10}{2}[/tex]
[tex]\text{Scale factor}=5[/tex]
Therefore, the scale factor of 5 applied to Right triangle A to produce Right triangle B.
If f(x) = -3x - 5 and g(x) = 4x-2, find (f -g)(x).
Answer:
(f - g)(x) = -7x - 3
Step-by-step explanation:
Step 1: Define
f(x) = -3x - 5
g(x) = 4x - 2
Step 2: Find (f - g)(x)
(f - g)(x) = -3x - 5 - (4x - 2)
(f - g)(x) = -3x - 5 - 4x + 2
(f - g)(x) = -7x - 3
a car has a 45% mark up. the wholesale cost is 9,000. what is the selling price
Answer:
I would think that would be $200
2x + 5 = 2x - 3 please help
Answer:
X=0
Step-by-step explanation:
most likely it's zero i also double checked it too so I think,you should be good.
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10. Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Answer:
First, let's find the equations for our lines:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
f(x) passes through (5,0) and (10, 10), then the slope is:
a = (10 - 0)/(10 - 5) = 10/5 = 2.
then we have:
y = 2*x + b
And when x = 5, we have y = 0.
0 = 2*5 + b
0 = 10 + b
b = -10
Then the equation for f(x) is:
y = f(x) = 2*x - 10.
Now for g(x) we have the points:
(3, 0) and (2, 10)
a = (10 - 0)/(2 - 3) = -10
y = -10*x + b
0 = -10*3 + b
b = 30.
y = g(x) = -10*x + 30.
A) Ok, the transformations:
Transformation 1 or T1.
f(x) = 2*x - 10
g(x) = -10*x + 30.
Then, we start with f(x):
First, we can move f(x) up 4 units and get:
f'(x) = 2*X - 6
Now we can dilate f(x) with a scale factor of -5 from the origin, now we get:
f''(x) = -5*f'(x) = -10*x + 30.
And this is g(x).
Transformation 2 or T2.
Move f(x) up 10 units, so now we have:
f'(x) = 2*x
Do a reflection over the x-axis, so the sign of y changes, and now we get:
f''(x) = -2*x
Do a dilation of scale factor 5
f'''(x) = 5*-2*x = -10*x
Now do a vertical translation of 30 units up.
f''''(x) = -10*x + 30 = g(x).
These are two transformations that start with f(x) and end with g(x).
B) Ok, as i was writting the transformations i already solved them, so this part is already done.
C) the equation for the transformations are:
T1) g(x) = -5*(f(x) + 4)
T2) g(x) = -(f(x) + 10)*5 + 30
Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel). Hotel occupancy data for February in two consecutive years are as follows.
Current Year Previous Year
Occupied Rooms 1,470 1,458
Total Rooms 1,750 1,800
Required:
a. Formulate the hypothesis test that can be used to determine if there has been an increase in the proportion of rooms occupied over the one-year period.
b. What is the estimated proportion of hotel rooms occupied each year?
c. Calculate the test statistic.
d. What is the p-value?
Answer:
Explained below.
Step-by-step explanation:
In this case we need to determine if there has been an increase in the proportion of rooms occupied over the one-year period.
(a)
The hypothesis can be defined as follows:
H₀: The proportion of rooms occupied over the one-year period has not increased, i.e. p₁ - p₂ ≤ 0.
Hₐ: The proportion of rooms occupied over the one-year period has increased, i.e. p₁ - p₂ > 0.
(b)
The information provided is:
n₁ = 1750
n₂ = 1800
X₁ = 1470
X₂ = 1458
Compute the sample proportions and total proportions as follows:
[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{1470}{1750}=0.84\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{1458}{1800}=0.81\\\\\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{1470+1458}{1750+1800}=0.825[/tex]
(c)
Compute the test statistic value as follows:
[tex]Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p(1-\hat p)\times [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.84-0.81}{\sqrt{0.825(1-0.825)\times [\frac{1}{1750}+\frac{1}{1800}]}}\\\\=2.352[/tex]
The test statistic value is 2.352.
(d)
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=P(Z>2.352)=1-P(Z<2.352)=1-0.99061=0.00939[/tex]
The p-value of the test is very small. The null hypothesis will be rejected at any significance level.
Thus, there enough evidence suggesting that there has been an increase in the proportion of rooms occupied over the one-year period.
Factor the expression using the GCF: 12x + 36 *
2(6x + 18)
314x + 12)
4(3x + 9)
12(x + 3)
The answer fam is.........12(x + 3)
*Which
.............
Answer:
If the first one is a, next is b, ect., then answer is C
Step-by-step explanation:
Just take the first thing. Distributive property and it goes to 9x. From there only one choice has 9x, so ez.
Solve the following word problem. A man travels from town X to town Y at an average rate of 60 mph and returns at an average speed of 50 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 55 mph. What is the distance from town X to Y?
___ miles
Answer:
d = 1650 milesStep-by-step explanation:
Let the distance be d
Then the time in travel is
d/60 one way, d/50 on returnThe round trip would take 1/2 hours longer if the average speed was 55 mph
d/60 + d/50 = 2d/55 + 1/2d/60 + d/50 - 2d/55 = 1/2LCM(60,50,55) = 11*12*5*5 = 3300
55d/3300 + 66d/3300 - 120d/3300 = 1/2d/3300= 1/2d = 1650 milesAnswer:
d= 1650 miles
Step-by-step explanation:
Isaac's hair was 12 centimeters long after his last haircut, and it grows 8 centimeters every year. Isaac last got his hair cut 8 years ago. How long is it now? Write and solve an equation to find the answer.
Answer:
76
Step-by-step explanation:
1.) 8 x 8 =64
2.) 12 + 64 =76
Answer: it is 76 cm long and the equation is 8x8+12= length of hair after 8 years.
Step-by-step explanation:
The hair grows 8 cm a year and it has been 8 years so we get 8x8. Then the last time he cut his hair it was 12 inches so we have to add that and yeah...
In Chicago, the temperature at noon was 11.4°F. By midnight, the temperature had decreased by 15.7 degrees. What was the temperature at midnight?
The use of mathematical methods to study the spread of contagious diseases goes back at least to some work by Daniel Bernoulli in 1760 on smallpox. In more recent years many mathematical models have been proposed and studied for many different diseases. The following problem deals with a few of the simpler models and the conclusions that can be drawn from them. Similar models have also been used to describe the spread of rumors and of consumer products. Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit the disease but who exhibit no overt symptoms. Let x and y denote the proportions of susceptibles and carriers, respectively, in the population. Suppose that carriers are identified and removed from the population at a rate β, so dy/dt = −βy.
(i) Suppose also that the disease spreads at a rate proportional to the product of x and y; thus dx/dt = −αxy.
(ii)
(a) Determine y at any time t by solving Eq. (i) subject to the initial condition y(0) = y0.
y(t) =
(b) Use the result of part (a) to find x at any time t by solving Eq. (ii) subject to the initial condition x(0) = x0.
x(t) =
(c) Find the proportion of the population that escapes the epidemic by finding the limiting value of x as t → [infinity].
Answer:
a
[tex]y(t) = y_o e^{\beta t}[/tex]
b
[tex]x(t) = x_o e^{\frac{-\alpha y_o }{\beta }[e^{-\beta t} - 1] }[/tex]
c
[tex]\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }[/tex]
Step-by-step explanation:
From the question we are told that
[tex]\frac{dy}{y} = -\beta dt[/tex]
Now integrating both sides
[tex]ln y = \beta t + c[/tex]
Now taking the exponent of both sides
[tex]y(t) = e^{\beta t + c}[/tex]
=> [tex]y(t) = e^{\beta t} e^c[/tex]
Let [tex]e^c = C[/tex]
So
[tex]y(t) = C e^{\beta t}[/tex]
Now from the question we are told that
[tex]y(0) = y_o[/tex]
Hence
[tex]y(0) = y_o = Ce^{\beta * 0}[/tex]
=> [tex]y_o = C[/tex]
So
[tex]y(t) = y_o e^{\beta t}[/tex]
From the question we are told that
[tex]\frac{dx}{dt} = -\alpha xy[/tex]
substituting for y
[tex]\frac{dx}{dt} = - \alpha x(y_o e^{-\beta t })[/tex]
=> [tex]\frac{dx}{x} = -\alpha y_oe^{-\beta t} dt[/tex]
Now integrating both sides
[tex]lnx = \alpha \frac{y_o}{\beta } e^{-\beta t} + c[/tex]
Now taking the exponent of both sides
[tex]x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} + c}[/tex]
=> [tex]x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} } e^c[/tex]
Let [tex]e^c = A[/tex]
=> [tex]x(t) =K e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }[/tex]
Now from the question we are told that
[tex]x(0) = x_o[/tex]
So
[tex]x(0)=x_o =K e^{\alpha \frac{y_o}{\beta } e^{-\beta * 0} }[/tex]
=> [tex]x_o = K e^{\frac {\alpha y_o }{\beta } }[/tex]
divide both side by [tex] (K * x_o)[/tex]
=> [tex]K = x_o e^{\frac {\alpha y_o }{\beta } }[/tex]
So
[tex]x(t) =x_o e^{\frac {-\alpha y_o }{\beta } } * e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }[/tex]
=> [tex]x(t)= x_o e^{\frac{-\alpha * y_o }{\beta} + \frac{\alpha y_o}{\beta } e^{-\beta t} }[/tex]
=> [tex]x(t) = x_o e^{\frac{\alpha y_o }{\beta }[e^{-\beta t} - 1] }[/tex]
Generally as t tends to infinity , [tex]e^{- \beta t}[/tex] tends to zero
so
[tex]\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }[/tex]
Anthony's father wants a quick way to estimate the amount of fencing needed. Mr. Chen asked Anthony to help him. Anthony realizes that this is just a perimeter question. He starts his task by analyzing the relationship between the length of the side of a square flower bed and the perimeter of the flower bed. This will tell him the amount of fence needed to enclose the flower bed. Anthony realizes that lengths of sides of flower beds are not always whole numbers, but he decides to use square tiles to build models of flower beds of various sizes to help him find a pattern. In his models, 1 tile represents 1 square foot.
Answer:
it is just length plus width times two.
Step-by-step explanation:
Lisa and two friends shop at a bookstore. They each choose a book and share the cost equally among the 3 of them.
The total cost of the books is $27.00.
A. Create an equation that models the situation, using c to represent how much, in dollars, each person pays.
B. How much does each person pay?
Answer:
A: 27 divided by 3 B. $9.00
Step-by-step explanation:
-26 times a number minus 22 is equal to 90 less than the number.
Answer:
[tex]x = \frac{68}{27}[/tex]
Step-by-step explanation:
Let x be the number
Write it out: -26x - 22 = x - 90Combine like terms: -27x + 68 = 0Subtract 68 from each side, so it now looks like this: -27x = -68Divide each side by -27 to cancel out the -27 next to x. It should now look like this: [tex]x = \frac{68}{27}[/tex]I hope this helps!
A square picture frame encloses a picture with area 65in2. Use the formula s=A‾‾√ to find the length of one side of the picture. Round your answer to the nearest tenth of a inch.
PLEASE HELP AS SOON AS YOU CAN
Answer:
FOR QUESTION 2
1. Segment addition postulate
2. Substitution
3. Substitution
4. Addition property of equality
5. Division property of equality
6 symmetric property
FOR QUESTION 3
1. given
2. Definition of complementary angles (complementary angles add upto 90)
3. Substitution
4. Subtraction property of equality
FOR QUESTION 4
1. Given
2. Definition of supplementary angles (supplementary angles add upto 180)
3. Definition of supplementary angles
4. Substitution
5. Subtraction property if equality
6. Definition of congruent angles (congruent angles are equal)
Step-by-step explanation:
Answer:
I not understand your questions