Debbie should have included 8 as a possible choice. The correct inequality is p ≤ 8.
Debbie's error is that she did not include the possibility that exactly 8 passengers could fit in the van. Therefore, the correct inequality symbol to use would be less than or equal to, represented by "<=".
The correct inequality is p <= 8. This means that the number of passengers that can fit in the van is either less than or equal to 8. So, including 8 as a possible choice is also necessary to correctly represent the situation.
Hence the correct answer is C.
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--The given question is incorrect; the correct question is
"The Martins' van can hold up to 8 passengers. Debbie writes the inequality p <8, where p is the number of passengers that can fit in the van. Select the choice that provides the best explanation for Debbie's error and the correct answer in this case.
A. Debbie should have used 8p because 8 passengers can fit in the van. The correct inequality is 8p < 1
B. Debbie should have switched the inequality symbol to greater than. The correct inequality is p > 8.
C. Debbie should have included 8 as a possible choice. The correct inequality is p ≤ 8.
D. Debbie should have used the not equals sign to compare the two sides of the inequality. The correct answer is p = 8"--
The distance between Matt’s house and his school is 3 inches on the map. The actual distance is 1.5 miles. What is the scale of the map?
Answer:
1 inch to .5 miles
Step-by-step explanation:
a teacher wants to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf. in how many ways can he do that? (all the copies of each book are identical.)
The total number of ways to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf is 35.
A permutation of a set of objects is an ordering of those objects. When some of those objects are identical, the situation is transformed into a problem about permutations with repetition. Problems of this form are quite common in practice; for instance, it may be desirable to find orderings of boys and girls, students of different grades, or cars of certain colors, without a need to distinguish between students of the same grade (or cars of the same color, or people of the same gender).
Total number of copies = 3 +4 = 7
Number of ways to arrange 7 copies together = 7!
However, there are 3 copies of introduction to geometry and 4 copies of introduction to number theory. Thus, all copies of each book are identical.
Now, the total number of ways to arrange 7 copies together
= \(\frac{7!}{3!* 4!}\)
=35
Thus, the total number of ways to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf is 35.
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Ms. Ayala had 152 pencils. She divided the numbers of pencils equally among 13 students. What is the greatest numberof pencils Ms.Ayala could have given each student
Answer:
11
Step-by-step explanation:
she divides the number of pencils equally
so the number of pencils per student is 152/13
which is 11.692...
but she can't give 0.69 of a pencil so she gives only the whole part 11
and she keeps 9 pencils
Describe the sampling distribution of p. Assume the size of the population is 30,000. n 700, p 0.388 Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The shape of the sampling distribution of p is not normal because n s0.05N and np(1-p)210. O B. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-p) <10. C. The shape of the sampling distribution of pis not normal because n s05N and np(1-p)<10 O D. The shape of the samplingdistrbution of p is approximately normal because n s0.05N and np(1 -p)210 Determine the mean of the sampling distribution of p. Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of p. Round to three decimal places as needed.)
The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:
D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
The mean of the sampling distribution of p is of:
0.388.
The standard deviation of the sampling distribution of p is of:
0.0184.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:
The mean is \(\mu = p\).The standard deviation is \(s = \sqrt{\frac{p(1 - p)}{n}}\)The shape is approximately normal.As long as these two conditions are respected:
\(n \leq 0.05N\)\(np(1 - p) > 10\)The values of the parameters in this context are given as follows:
N = 30000, n = 700, p = 0.388.
Hence the conditions are:
n/N = 700/30000 = 0.0233 < 0.05.np(1 - p) = 700 x 0.388 x 0.612 = 166 > 10.Then the shape is approximately normal and option D is correct.
The mean of the distribution is of:
\(\mu = p = 0.388\)
The standard error of the distribution is of:
\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184\)
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Use a change of variables (and the Jacobian) to find the volume of the solid region lying below the surface z = f(x,y) and above the plane region R. Picture of the solid
f(x,y) = (x+y)ex-y
R: the region of the xy-coordinate plane bounded by the square with vertices (4,0), (6,2),
(4,4), and (2,2) i need to know how to solve this problem for my test today, thaks
The volume of the solid region is approximately 10.4109 cubic units.
To find the volume of the solid region lying below the surface z = f(x,y) and above the plane region R, we can use the formula:
V = ∬R f(x,y) dA
where dA is the area element in the xy-plane and the double integral is taken over the region R.
To evaluate this integral, we first need to perform a change of variables. Let u = x + y and v = x - y. Then the inverse transformations are x = (u + v)/2 and y = (u - v)/2. The Jacobian of this transformation is:
J = ∂(x,y) / ∂(u,v) = 1/2
Next, we need to express the surface z = f(x,y) in terms of u and v. Using the substitutions x = (u + v)/2 and y = (u - v)/2, we get:
f(x,y) = (x+y)ex-y = [(u+v)/2 + (u-v)/2]e(u-v)/2 = ueu/2
So the volume of the solid is:
V = ∬R f(x,y) dA
= ∬R ueu/2 dA
= ∫₂⁴ ∫₂⁶ (u/2)e^(u/2) du dv (using the limits of integration for R in terms of u and v)
= ∫₂⁶ [e^(u/2)u²/4] from 2 to 4 dv
= ∫₂⁴ [e^(u/2)u²/4] from u-2 to 6 du
= 16(e^3 - e^2)/3
Therefore, the volume of the solid region is approximately 10.4109 cubic units.
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X - 3.5 > 6.9
Pls what is the solution to the inequality
Answer:
x > 10.4
Step-by-step explanation:
Isolate X by adding 3.5 to each side of the inequality
That leaves you with x > 6.9 + 3.5
what is 2.8 repeating as adecimal
Given Q= [2 3]
[1 -2] prove that (3Q)^(t) = 3Q^(t)
(3Q)^(t) = 3Q^(t) this expression can be concluded as true.
The given matrix is Q = [2 3][1 -2]
To prove that (3Q)^(t) = 3Q^(t),
we need to calculate the transpose of both sides of the equation.
Let's solve it step by step as follows:
(3Q)^(t)
First, we will calculate 3Q which is;
3Q = 3[2 3][1 -2]= [6 9][-3 6]
Then we will calculate the transpose of 3Q as follows;
(3Q)^(t) = [6 9][-3 6]^(t)= [6 9][-3 6]= [6 -3][9 6]Q^(t)
Now we will calculate Q^(t) which is;
Q = [2 3][1 -2]
So,
Q^(t) = [2 1][3 -2]
Therefore, we can conclude that (3Q)^(t) = 3Q^(t) is true.
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Use the values representing g(x) to find each value.
a) g(-6) = __
b) g(4) = __
c) Find x when (x) =0
x =___
X | Y
——-
(-8,4)
(-5,0)
(-3,-2)
(0,-4)
(2,-5)
(4,-6)
a) To find g(-6), we can estimate the value of g(-6) by finding the equation of the line that passes through the points (-5,0) and (-3,-2). To do this, we can use the slope-intercept formula:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the points on the line.
m = (y2 - y1) / (x2 - x1) = (-2 - 0) / (-3 - (-5)) = -1/2
Using the point-slope formula with (x1, y1) = (-5, 0), we get:
y - 0 = (-1/2)(x - (-5))
y = (-1/2)x + 5/2
Therefore, g(-6) is approximately equal to g(-5), which we can find by substituting x = -5 into the equation:
g(-5) = (-1/2)(-5) + 5/2 = 5/2
So, g(-6) is approximately equal to 5/2.
b) To find g(4), we look for the value of y when x is 4. From the table, we can see that when x is 4, g(x) is equal to -6. Therefore, g(4) = -6.
c) To find the value of x when g(x) is 0, we look for the row where g(x) is 0. From the table, we can see that when x is -5, g(x) is equal to 0. Therefore, x = -5 when g(x) = 0.
HELP FAST!!!! A parking garage charges $5 for the first hour, $10 for up to two hours, and $12 for the entire day. Let G be the dollar cost of parking for t hours. Is t a function of G? Explain your reasoning.
Answer:
27
Step-by-step explanation:
just do 5+10+12
HELP!!!plzzzzzzzzzzz!!!!!!!!!!!!!!
Answer:
m∠2 = 47°
Step-by-step explanation:
m∠1 + m∠2 = 90°
3x + 13 + 5x - 3 = 90
8x + 10 = 90 ⇒ x = 10
m∠2 = 47°
Which relation is a function?
A:{(1, 1), (2, 4), (4,8), (8, 16),
(8,32)}
B: (8, -2) , ( 9, -2) , (10, -2) (11, -2), (12,3)
C: (2,-3), (2,-2), (2,-1), (2,0), (2,1)
D: (9,3) , (9,-3), (16,-4), (25,-5)
Answer:
1,2,4,8,16,32,36,40,48
find the value of k by
quardractic equation two real and equal roots
5x - 2kx +20=0
Answer:
k = +10 or -10
Step-by-step explanation:
It's given in the question that the roots of the eqn. are real and equal. So , the discriminant of the eqn. should be equal to 0.
\( = > {b}^{2} - 4ac = 0\)
\( = > {( - 2k)}^{2} - 4 \times 5 \times 20 = 0\)
\( = > 4 {k}^{2} - 400 = 0\)
\( = > 4( {k}^{2} - 100) = 0\)
\( = > {k}^{2} - 100 = 0\)
\( = > k = \sqrt{100} = + 10 \: or \: - 10\)
Step-by-step explanation:
Given Equation
5x-2kx+20=0
If it has real and equal roots then\(\boxed{\sf \longrightarrow D=0 }\)
Substitute the values\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow b^2-4ac=0 \)
\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow (-2k)^2-4\times 5\times 20=0 \)
\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-20\times 20=0 \)
\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-400=0\)
\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2=400 \)
\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=\dfrac {400}{4}\)
\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=100 \)
\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=\sqrt{100}\)
\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=10 \)
\(\therefore\sf k=10 \)
Ariana solved the equation as shown. Explain her error and correct the solution.
9x² - 144= 0
9x² = 144
x² = 16
√ x² = √ 16
x=+8
Arrange in ascending order 19,654 67,923 67,397 91,945
Answer:
19654,67397,67923,91945
Step-by-step explanation:
Ascending order mean arrange the number from smaller value to bigger value
Answer:
19654,67397,67923,91945
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Find the ellipse centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1). write your equation in the form ax2 bxy cy2 = 1.
The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as
-0.3523x^2 0.5284xy 15.9268y^2 = 1.
Find the ellipse centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1).?Generally, the equation for three points is mathematically given as
a+2b+4c=1.....1 for the variable (1, 2)
4a+4b+4c=1.....2 for the variable (2, 2)
9a+3b+c=1.....3 for the variable (3, 1)
Step 1
Here we solve equations 1 and 2 simultaneously to find the value of b
Therefore
equ 2-equ1
3a+2b=0
b=-1.5a....4
Step 2
We solve equations 1 and 3 simultaneously to find the value of c
Where
9*equ1-equ3 gives
-15b-35c=-8
c=8-15b
subbing equ 4 we have
c=8+22.5a ....5
Step 3
Put values of b and c in equation 2, and we have
4a-6a+32+90a=1
a=-31/88
a=-0.3523
The value of b will be
b=-1.5*a
b=0.5284
The value of b will be
c=8-22.5*a
c=15.9268
Step 4
In conclusion, the equation is given as
By substituting the values of a b and c into the general formula we have
-0.3523x^2 0.5284xy 15.9268y^2 = 1.
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If you invest $550.00 at a 4% interest rate, what will be the interest
Step-by-step explanation:
First, look at the amount of money. It's $550 so write that down on a piece of paper or something like that.The interest rate is 4%, so you have to times 1% 4 times to get the answer. Write it down.First, let's find 1% of 550.
---------------------------------------------
HOW TO FIND 1% OF 550:
Try to find the decimal point of 550. Since it's a full number, it'll be at the back. It looks like this: 550.00(see the point?)
Since behind the point there are 2 0's, round it back 2 times.It looks like this: 5.50(see it?)
---------------------------------------------
Now, let's multiply the "new" number amount we have. ($5.50)
5.50x 4-------------
22(yeah, I don't think I need to explain this but I did lol)
YAY!You got the answer! Congrats!
-eliana44ever
A pair of equations is shown below.
x + y = 2
y = one-half.gifx + 5
If the two equations are graphed, at what point do the lines representing the two equations intersect? (4 points)
a
(4, −2)
b
(−2, 4)
c
(2, 5)
d
(5, −2)
In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student chosen randomly from the class passed the test?
Completed the homework
Did not complete the homework
Passed the test Failed the test
12
2
4
3
Answer:
20/27
Step-by-step explanation:
Please help me with my question!!
Answer:
D
Step-by-step explanation:
Since the y-intercept is 6, there must be a +6.
Next if the x intercept is -2, then 6+n*(-2) = 0
so n = 3
So the equation is y = 3x + 6
Answer:
y=3x+6
Step-by-step explanation:
Equation for line is in the form y=mx+b. B is 6 since that is given. Plug x into the equation: 0=-2m+6 so m=3. Final equation- y=3x+6
sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. to test if 68% also represents california's percent for full-time faculty teaching the online classes, long beach city college (lbcc) in california was randomly selected for comparison. in the same year, 34 of the 44 online courses lbcc offered were taught by full-time faculty. conduct a hypothesis test at the 5% level to determine if 68% represents california. note: for more accurate results, use more california community colleges and this past year's data
The Confidence Interval for the hypothesis test at the 5% level to determine if 68% represents California is 0.65, 0.90.
First, we need to find H₀ and Hₐ. In this case, we want to check whether California community colleges take 68% of the online classes thought by full-time faculties, or not.
H₀ : p = 0.68; Hₐ : p ≠ 0.68
Second, we need to determine the distribution needed. State what our random variable P’ represents.
Normal: N
Test Statistic : z = 0.1873
Third, we have to calculate he p-value using the normal distribution for proportions.
p-value = 0.1873
If the null hypothesis is true (the proportion is 0.68), thus there is a 0.1873 probability which the estimated proportion is 0.773 or more.
Fourth, we need to compare \(\alpha\) and the p-value, then indicate the correct decision (reject or do not reject the null hypothesis).
\(\alpha\) = 0.05
Decision : Do not reject the null hypothesis
Reason for decision : p-value > 0.05
At the 5% level, the data do not provide statistically significant evidence that the true proportion of online courses taught by full-time faculty is not 68%.
Last, define the confidence interval. The confidence interval is (0.6275, 0.8725) = (0.65, 0.90).
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HELP ASAP PLEASE
(3^2)^4
Answer:
6561
Step-by-step explanation:
3^2= 3*3=9 9^4= 9*9*9*9= 6561
Answer:
\(((3)^2)^4 = (9)^4 = 6561\\\\\\OR\\\\\\(3)^2)^4= 3^8 = 6561\)
what's the rate of change for y = 500(1-0.2)^t
To find the rate of change of y with respect to time t, we need to take the derivative of the function y = 500(1-0.2)^t with respect to t:
dy/dt = 500*(-0.2)*(1-0.2)^(t-1)
Simplifying this expression, we get:
dy/dt = -100(0.8)^t
Therefore, the rate of change of y with respect to t is given by -100(0.8)^t. This means that the rate of change of y decreases exponentially over time, and approaches zero as t becomes large.
simplify
-15a^6 divided by -3a^6
Answer:
5
Step-by-step explanation:
divide -15 by -3 to get 5
a^6/a^6 = a^0 = 1
Answer:
i think 5
Step-by-step explanation:
If x+4/4 = y+7/7 then x/4 =___.
(Number 9 is the one I need an answer for)
Answer:
4th answer is correct
Step-by-step explanation:
First, let us make x the subject.
\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)
Use cross multiplication.
\(\sf 7(x+4)=4(y+7)\)
Solve the brackets.
\(\sf 7x+28=4y+28\)
Subtract 28 from both sides.
\(\sf 7x=4y+28-28\\\\\sf7x=4y\)
Divide both sides by 7.
\(\sf x=\frac{4y}{7}\)
Now let us find the value of x/4.
To find that, replace x with (4y/7).
Let us find it now.
\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)
An analyst for FoodMax estimates that the demand for its "Brand X" potato chips is given by: In Qyd = 10.34 – 3.2 In Px+4Py+ 1.5 In Ax = where Qx and Px are the respective quantity and price of a four-ounce bag of Brand X potato chips, Pyis the price of a six-ounce bag sold by its only competitor, and Axis FoodMax's level of advertising on brand X potato chips. Last year, FoodMax sold 5 million bags of Brand X chips and spent $0.25 million on advertising. Its plant lease is $2.5 million (this annual contract includes utilities) and its depreciation charge for capital equipment was $2.5 million; payments to employees (all of whom earn annual salaries) were $0.5 million. The only other costs associated with manufacturing and distributing Brand X chips are the costs of raw potatoes, peanut oil, and bags; last year FoodMax spent $2.5 million on these items, which were purchased in competitive input markets. Based on this information, what is the profit-maximizing price for a bag of Brand X potato chips? Instructions: Enter your response rounded to the nearest penny (two decimal places). $
The profit-maximizing price for a bag of Brand X potato chips is approximately $3.35.
To determine the profit-maximizing price, we need to find the price that maximizes the profit function. The profit function can be expressed as follows:
Profit = Total Revenue - Total Cost
Total Revenue (TR) is calculated by multiplying the quantity sold (Qx) by the price (Px):
TR = Qx * Px
Total Cost (TC) includes the costs of advertising, plant lease, depreciation, employee payments, and the costs of raw materials:
TC = Advertising Cost + Plant Lease + Depreciation + Employee Payments + Raw Material Costs
Given the information provided, last year FoodMax sold 5 million bags of Brand X chips, spent $0.25 million on advertising, and incurred costs of $2.5 million for raw materials.
To find the profit-maximizing price, we differentiate the profit function with respect to Px and set it equal to zero:
d(Profit)/d(Px) = d(TR)/d(Px) - d(TC)/d(Px) = 0
The derivative of the total revenue with respect to the price is simply the quantity sold:
d(TR)/d(Px) = Qx
The derivative of the total cost with respect to the price is found by substituting the given demand equation into the cost equation and differentiating:
d(TC)/d(Px) = -3.2 * Qx
Setting these two derivatives equal to each other:
Qx = -3.2 * Qx
Simplifying the equation:
4.2 * Qx = 0
Since the quantity sold cannot be zero, we solve for Qx:
Qx = 0
This implies that the quantity sold, Qx, is zero when the price is zero. However, a price of zero would not maximize profit.
To find the profit-maximizing price, we substitute the given values into the demand equation:
5 million = 10.34 - 3.2 * Px + 4 * Py + 1.5 * 0.25
Simplifying the equation:
5 million = 10.34 - 3.2 * Px + 4 * Py + 0.375
Rearranging terms:
3.2 * Px = 14.34 - 4 * Py
Substituting the given value of Py as 0 (since no information is provided about the competitor's price):
3.2 * Px = 14.34 - 4 * 0
Simplifying:
3.2 * Px = 14.34
Dividing both sides by 3.2:
Px = 4.48
Thus, the profit-maximizing price for a bag of Brand X potato chips is approximately $4.48. However, since the price is limited to the nearest penny, the profit-maximizing price would be approximately $4.48 rounded to $4.47.
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Solve for f.
4f = -2 + 5f
Answer:
f=2
Step-by-step explanation:
First, you move the variables to the left side of the equation and change its sign.
After doing so, you have 4f -5f =2.
Now, combine like terms. 4f-5f = -f, or -1f. Either way is fine.
Your equation looks like this now: -f = -2
Now remove the negative symbols due to their being one on both side.
f=2
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what are the greatest common divisors of the following pairs of integers? (a) and answer = (b) and answer = (c) and answer =
The greatest common divisor (GCD) of 24 and 16 is 8. (A)
The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. One way to find the GCD of two numbers is to factor both numbers into their prime factors and then find the product of the common prime factors.
In this case, 24 can be factored as 2³ * 3 and 16 can be factored as 2⁴. The largest power of 2 that divides both 24 and 16 is 2³, so the GCD of 24 and 16 is 2³ = 8.
Another way to find the GCD is to use the Euclidean algorithm, which involves repeatedly dividing the larger number by the smaller number and taking the GCD of the smaller number and the remainder until the remainder is 0.
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Complete question:
what are the greatest common divisors of 24,16
A) 8
B) 4
C) 2
D) 1
in a convex quadrilateral, the measure of the largest angle is twice the measure of the smallest angle, and the other two angles are both right angles. how many degrees are in the largest angle?
Answer: 90 degrees.
Step-by-step explanation:
Step 1: The smallest angle must be 90/2 = 45 degrees.
Step 2: The largest angle is twice the size of the smallest angle, so it is 90 degrees.
What are the first 3 terms of the sequence represented by the expression n(n – 2) – 4 ?
The first 3 terms of the sequence using the expression are -5, -4 and -1
Calculating the first 3 terms of the sequence using the expressionFrom the question, we have the following sequence that can be used in our computation:
n(n – 2) – 4
This means that
T(n) = n(n – 2) – 4
Set n = 1, 2 and 3
So, we have
T(1) = 1 * (1 – 2) – 4 = -5
T(2) = 2 * (2 – 2) – 4 = -4
T(3) = 3 * (3 – 2) – 4 = -1
Hence, the first 3 terms of the sequence using the expression are -5, -4 and -1
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