[tex]\frac{5}{2}x-7=\frac{3}{4}x+14[/tex]
[tex]\frac{5x}{2}-7=\frac{3}{4}x+14\\\\\frac{5x}{2}-7=\frac{3x}{4}+14[/tex]
10x−28=3x+56
10x=3x+56+28
10x=3x+84
10x−3x=84
7x=84
[tex]x=\frac{84}{7}[/tex]
x=12
Hope this helps, have a blessed and wonderful day!
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 !
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
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.
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
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.
2w − w = 15
explain if possible, please
Answer:
2w - w = 15You subtract w from 2w and u remain with w.w = 15A 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.
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:
Marco has a collection of 437 bottles. Each month he buys 32 bottles .
Answer:
what is the question
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...
what i the scientific notation of 13400000
correct answer only
Answer:
1.34 x 10^7
Step-by-step explanation:
I hope this helped!
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.
what is the quotient of4/6and2/9
Answer:
3
Step-by-step explanation:
Trust meh
What is the probability of a sample mean being greater than a z-value of -0.79?
Select one:
a. 0.7852
b. 0.4500
c. 0.2148
d. 0.2852
Step-by-step explanation:
d uahsizagxuxbsixvaixbx akbxoa soxnaox aoxk. is. os xia xida
What is the approximate distance between the points (-6, 8) and (4, 13)?
A.3.87
B.125
C.21.10
D. 11.18
do u have a diagram for this?
(3х + 4)°
(8х +11)°
Answer:
11x+15
Step-by-step explanation:
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
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.
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
*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.
The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week. Assume that a sample of 420 accidents provided the following data.
Sunday 66
Monday 50
Tuesday 53
Wednesday 47
Thursday 55
Friday 69
Saturday 80
A) Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. What is the P-Value? Use a 0.05 level of significance, what is your conclusion?
B) Compute the percentage of traffic accidents occuring on each day of the week. What day has the highest percentage of traffic accidents? Does this seem reasonable? Explain.
Answer:
(A) There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.
(B) Saturday has the highest percentage of traffic accidents.
Step-by-step explanation:
(A)
The Chi-square goodness of fit test would be used to determine if the proportion of traffic accidents is the same for each day of the week.
The hypothesis for the test can be defined as follows:
H₀: The proportion of traffic accidents is the same for each day of the week.
Hₐ: The proportion of traffic accidents is not same for each day of the week.
Assume that the significance level of the test is, α = 0.05.
The Chi-square test statistic is given by:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
Compute the values in Excel.
The expected frequency for all the days is 60.
The Chi-square test statistic value is, 14.333.
Compute the p-value using the Excel function "=CHISQ.DIST.RT(14.33,6)".
p-value = 0.0262
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
The p-value is less than 0.05.
The null hypothesis will be rejected.
Conclusion:
There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.
(B)
Compute the percentage of traffic accidents occurring on each day of the week as follows:
[tex]\text{Sunday}=\frac{66}{420}\times 100\approx 16\%\\\\\text{Monday}=\frac{50}{420}\times 100\approx 12\%\\\\\text{Tuesday}=\frac{53}{420}\times 100\approx 13\%\\\\\text{Wednesday}=\frac{47}{420}\times 100\approx 11\%\\\\\text{Thursday}=\frac{55}{420}\times 100\approx 13\%\\\\\text{Friday}=\frac{69}{420}\times 100\approx 16\%\\\\\text{Saturday}=\frac{80}{420}\times 100\approx 19\%[/tex]
Saturday has the highest percentage of traffic accidents.
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]
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:
Find the sum of the first 25 terms of the arithmetic sequnce 17,22,27,32.37
Answer:
Step-by-step explanation:
This sequence is adding 5 so
17 22 27 32 37 42 47 52 57 62 67 72 77 82 87 92 97 102 107 112 117 122 127 132 137 = 1925
Answer: The sum of the first 25 terms of this arithmetic sequence is 1925.
Explanation: This sequence, beginning at 17, increases by 5 per term. By simply adding 5 to the preceding term in the sequence, you can find the next term. The first term is 17, and the last term is 137. This means the list of terms is 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, and 137. The sum of these terms is 1925.
Select 3 ratios that are equivalent to 4 : 3
Answer:
3 ratios that are equivelent to 4 : 3
8 : 6
20 : 15
and 12 : 9
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!
Evaluate the expression.
(-4)2
Answer:
-8
Step-by-step explanation:
4x2=8
change to negative since a negative times a positive is a negative
-8
Answer: -8
Step-by-step explanation: -4* 2= -8
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
2 3/4 subtracted from 11 is equal to 8 1/4
Answer: 2/3
i think 3 divided by 2/3
Step-by-step explanation:
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 !!!!!!!!!!