Answer:
Δf(u) /Δx = 92,8 ( razón de cambio promedio)
Step-by-step explanation:
La expresión de la utilidad de la empresa u(x) en función de la cantidad de unidades producidas "x" es:
u(x) = 0,04*x² + 44*x -4000
Entonces la razón de cambio promedio en un intervalo (a ; b) en este caso ( 620 ; 600 ) viene dada por la expresión:
Δf(x)/ Δx = [ f(b) - f(a) ]/( b - a )
en donde f(b) y f(a) se obtienen por sustitución de los valores a y b es decir 600 y 620 respectivamente en la función f(x) = u(x) entonces
Δf(u) /Δx = [ u(b) - u(a) ]/( b -a ) (1)
u(b) = 0,04*(620)² + 44*(620) - 4000
u(b) = 15376 + 27280 -4000
u(b) = 2656 unidades
u(a) = 0,04* (600)² + 44* 600 - 4000
u(a) = 14400 + 26400 - 4000
u(a) = 800
Sustituyendo esos valores en la ecuación 1
Δf(u) /Δx = 2656 - 800 / 620 - 600
Δf(u) /Δx = 92,8
Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?
Answer:
[tex]\sqrt{51}[/tex] units.
Step-by-step explanation:
Point E is inside a rectangle ABCD.
Please refer to the attached image for the given statement and dimensions.
Given that:
Sides AE = 6 units
BE = 7 units and
CE = 8 units
To find:
DE = ?
Solution:
For a point E inside the rectangle the following property hold true:
[tex]AE^2+CE^2=BE^2+DE^2[/tex]
Putting the given values to find the value of DE:
[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]
Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.
What is the length of Lisa's flower garden?
Answer:
9 m
Step-by-step explanation:
Given that
Width of rectangular flower garden, w = 4 m
Perimeter of rectangular flower garden, p = 26 m
To find:
Length of Lisa's flower garden = ?
Solution:
First of all, let us understand perimeter, length and width of a rectangle.
Let ABCD be a rectangle. Please refer to the attached image.
Opposite sides of a rectangle are equal to each other.
AB = CD = Length
Let the length be [tex]l[/tex] m.
BC = DA = Width = 4 m
Perimeter of a closed image is equal to the sum of all the sides of the image.
So, perimeter of ABCD:
[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]
[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]
PLEASE HELP ASAP WILL GIVE BRAINLIEST
A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.) from a large batch of cups. They take a random sample of 200 cups from the batch of a few thousand cups and found 18 to be defective. The goal is to perform a hypothesis test to determine if the proportion of defective cups made by this machine is more than 8%.
Required:
a. Calculate a 95% confidence interval for the true proportion of defective cups made by this machine.
b. What is the sample proportion?
c. What is the critical value for this problem?
d. What is the standard error for this problem?
Answer:
a
The 95% confidence interval is [tex]0.0503 < p < 0.1297[/tex]
b
The sample proportion is [tex]\r p = 0.09[/tex]
c
The critical value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
d
The standard error is [tex]SE =0.020[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is [tex]H_o : p = 0.08[/tex]
The alternative hypothesis is [tex]H_a : p > 0.08[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{18}{200}[/tex]
[tex]\r p = 0.09[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the standard of error is mathematically represented as
[tex]SE = \sqrt{\frac{\r p (1 - \r p)}{n} }[/tex]
substituting values
[tex]SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }[/tex]
[tex]SE =0.020[/tex]
The margin of error is
[tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]
=> [tex]E = 1.96 * 0.020[/tex]
=> [tex]E = 0.0397[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < \mu < p < \r p + E[/tex]
=> [tex]0.09 - 0.0397 < \mu < p < 0.09 + 0.0397[/tex]
=> [tex]0.0503 < p < 0.1297[/tex]
Which of the following is the graph of the quadratic parent function
This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.
how many meters are in 250 centimeters
Answer:
2.5 meters
Step-by-step explanation:
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation? 0.1 1 10
Answer:
1
Step-by-step explanation: diliation is like multiplilcation if you were to do 3*1 =3. simply congruent means all sides and angles are the same.
Given that the image and the preimage of the triangle are congruent, their
dimensions are the same.
The scale factor of dilation of an image of a triangle that is congruent to the pre-image is; 1Reasons:
Let ΔABC represent the preimage, and let ΔA'B'C' represent the image.
Given that the image and the preimage are congruent, we have;
AB ≅ A'B'
BC ≅ B'C'
AC ≅ A'C'
By definition of congruency, we have;
AB = A'B'
BC = B'C'
AC = A'C'
The scale factor of dilation is given as follows;
[tex]\displaystyle Scale \ factor = \mathbf{ \frac{A'B'}{AB}} = \frac{AB}{AB} = 1[/tex]Therefore;
If the image is congruent to the pre-image, the scale factor of dilation is; 1Learn more about dilation transformation here:
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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 9 hours of burning, a candle has a height of 25.4 centimeters. After 23 hours of burning, its height is 19.8 centimeters. What is the height of the candle after 22 hours?
Answer:
Suppose that the height (in centimeters) of a candle is a linear function of
the amount of time (in hours) it has been burning.
After 11 hours of burning, a candle has a height of 23.4 centimeters.
After 30 hours of burning, its height is 12 centimeters.
What is the height of the candle after 13 hours?
:
Assign the given values as follows:
x1 = 11; y1 = 23.4
x2 = 30; y2 = 12
:
Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29
m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19
:
Find the equation using the point/slope formula: y - y1 = m(x - x1)
y - 23.4 = -11.4%2F19(x - 11)
y - 23.4 = -11.4%2F19x + 125.4%2F19
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19
y = -11.4%2F19x + 570%2F19
y = -11.4%2F19x + 30, is the equation
:
What is the height of the candle after 13 hours?
x = 13
y = -11.4%2F19(13) + 30
y = -148.2%2F19 + 30
y = -7.8 + 30
y = 22.2 cm after 13 hrs
The graph of the function f(x) = (x − 3)(x + 1) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answer:
x < -1
Step-by-step explanation:
Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.
all real values of x where x < -1
Given the graph, find an equation for the parabola.
Answer:
[tex]\Large \boxed{\sf \bf \ \ y=\dfrac{1}{16}(a-3)^2-2 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
When the parabola equation is like
[tex]y=a(x-h)^2+k[/tex]
The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))
As the vertex is (3,-2) we can say that h = 3 and k = -2.
We need to find a.
The focus is (3,2) so we can say.
[tex]2=-2+\dfrac{1}{4a}\\\\\text{*** We add 2. ***}\\\\\dfrac{1}{4a}=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=\dfrac{1}{16}[/tex]
So an equation for the parabola is.
[tex]\large \boxed{\sf y=\dfrac{1}{16}(a-3)^2-2 }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
In designing an experiment involving a treatment applied to 4 test subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the question below.
What is the probability of each simple random sample in thiscase?
Answer:
The probability is [tex]p(n ) = 3.18*10^{-5}[/tex]
Step-by-step explanation:
From the question we are told that
The population size is N = 31
The sample size n = 4
Generally the number of way by which the n can be selected from N is mathematically represented as
[tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]
The number of ways of selecting a particular sample size is is [tex]k = 1[/tex]
Therefore the probability of each simple random sample in this case is mathematically evaluated as
[tex]p(n ) = \frac{1}{31465}[/tex]
[tex]p(n ) = 3.18*10^{-5}[/tex]
If the area of the square is A(s) = s², find the formula for the area as a function of time, and then determine A(s(3)).
A(t) = 100t^2 + 500t + 625
3,025 square pixels
Answer:
A(t) equals 100t²+ 500t + 625.
The area of the square image after 3 seconds is 3,025 square pixels.
Cases Prudence has a special (cubic) die. The values on its face are the integers from 1 to 6, but they are not arranged ae in a normal die. When Prudence first tosses the die, the sum of the values on the four side faces is 15. In her second toss, the sum of these values is 12. Find what value appears in the face opposite 6 on Prudence’s special die. (Hint: what are possible values for the top and bottom face when the sum of the side faces is 12).
Answer: 3
Step-by-step explanation:
first, we know that:
1 + 2 + 3 + 4 +5 +6 = 21
Now, which two numbers we should take out in order to have 15?
we can remove the 2 and the 4, or the 1 and the 5.
so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)
in the other arrange, we have that removing two numbers we should get 12.
in order to reach 12, we should remove two numbers that add 9 together.
those can be 4 and 5, or 6 and 3.
Now, notice that in the first restriction we have that:
Or 2 and 4 are opposite,
or 1 and 5 are opposite.
So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.
Then we can affirm that the value that appears in the face opposite to the 6, is the 3.
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently conducted a survey to gauge support for each of the two candidates. The results of the poll are shown in the two-way frequency table below.
Answer:
3 only
Step-by-step explanation:
Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.
Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.
Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.
Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.
Therefore, the true statement is III only.
More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Data given in the table shows the data of elections between two candidates among the different cities.
What is Statistic?
Statistics is the study of mathematics that deals with relations between comprehensive data.
I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.
II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false
III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.
IV. Overall, more residents support candidate A than candidate B. it is also false.
Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Learn more about Statistics here:
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What is the correct alternate hypothesis if the pilots' average gain score due to alcohol is indicated in the hypothesis statement by
Answer:
Ha : Pilots average gain score not due to alcohol.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. Here the null hypothesis is that pilots average gain due to alcohol. Then if there is no alcohol what is pilots average gain. This thing will be tested as alternative hypothesis.
i need help asap please
Answer:
[tex]x = -\frac{3}{2}[/tex] or [tex]x = 1[/tex]
Step-by-step explanation:
Using the zero product property, first step is to set the given equation, [tex] 2x^2 + x - 1 = 2 [/tex] , to zero. Then factorise the left side.
Thus,
[tex] 2x^2 + x - 1 = 2 [/tex]
Subtract 2 from both sides
[tex] 2x^2 + x - 1 - 2 = 2 - 2 [/tex]
[tex] 2x^2 + x - 3 = 0 [/tex]
Factorise the left side
[tex] 2x^2 + 3x - 2x - 3 = 0 [/tex]
[tex] x(2x + 3) - 1(2x + 3) = 0 [/tex]
[tex] (x - 1)(2x + 3) = 0 [/tex]
Find the solution
[tex] x - 1 = 0 [/tex]
Or
[tex]2x + 3 = 0[/tex]
[tex] x = 1 [/tex]
Or
[tex]2x + 3 = 0[/tex]
[tex]2x = -3[/tex]
[tex]x = -\frac{3}{2}[/tex]
The answer is: [tex] x = 1 [/tex] or [tex]x = -\frac{3}{2}[/tex]
Please help me with this question
Answer:
0 ≤ x ≤ 10
Step-by-step explanation:
The domain of f(x) is the set of values of x for which the function is defined. Here, the square root function is only defined for non-negative arguments, so we require ...
-x^2 +10x ≥ 0
x(10 -x) ≥ 0
The two factors in this product will both be positive only for values ...
0 ≤ x ≤ 10 . . . . the domain of f(x)
Complete parts (a) through (c) below.
(a) Determine the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.
(b) Determine the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 level of significance based on a sample size of n = 20.
(c) Determine the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.
Answer:
(a) 1.341
(b) -2.539
(c) -2.160 and 2.160
Step-by-step explanation:
(a) We have to find the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 15 and the level of significance for a right-tailed test is 0.10, i.e. P = 10%
Now, looking in the t table with P = 10% and [tex]\nu[/tex] = 15, we get the critical value of 1.341.
(b) We have to find the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 based on a sample size of n = 20.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 20 - 1 = 19 and the level of significance for a left-tailed test is 0.01, i.e. P = 1%
Now, looking in the t table with P = 1% and [tex]\nu[/tex] = 19, we get the critical value of 2.539. But since it is a left-tailed test, so the critical value will be -2.539.
(c) We have to find the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 14 - 1 = 13 and the level of significance for a two-tailed test is [tex]\frac{0.05}{2}[/tex] is 0.025, i.e. P = 2.5%.
Now, looking in the t table with P = 2.5% and [tex]\nu[/tex] = 13, we get the critical value of -2.160 and 2.160 for a two-tailed test.
the angle theta is in the second quadrant and cos theta = -2/√29 determine possible coordinates for point P on the terminal arm of theta a. (2,5) b. (-2,√29) c. (-5,2) d. (-2,5)
[tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex] and $\theta$ lies in $2^{\text{th}}$ quadrant.
where, $x-$ coordinate is negative, and $y-$ coordinate is positive
so it can't a.
now, cosine means, side adjacent over the hypotenuse, in Cartesian plane, that will be $x-$ coordinate over the distance from origin.
Assume the triangle , with base $2$ units and hypotenuse $\sqrt{29}$ and it's in second quadrant. (so [tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex])
now, the leftmost point on $x-$ axis is , obviously $(-2,0)$
and by Pythagoras theorem, we can find the perpendicular side, that will be $y^2=(\sqrt{29})^2-(2)^2\implies y=5$
so the coordinates of the upper vertex is $(-2,5)$, each point lying on this "ray" should have equal ratio of respective coordinates. i.e. $\frac25=\left|\frac xy\right| $
and it should lie on second quadrant, so $x<0 \, y>0$
Option d satisfies this.
Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?
0riginal break even point:
285000/ 60/35 = $166,250
New break even point = new fixed costs / ( selling price - variable cost/ selling price)
New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60
300,900 / 60-30.50/60 = $612,000
The new break even point increases.
Evaluate the expresión 6c-d when c=2 and d=10 I need help?
Answer:
the answer is 18
Step-by-step explanation:
8 is the answer
How many pepperoni pizzas did they buy if they bought 6 cheese pizzas
Answer:
Question is incomplete but use below
Step-by-step explanation:
you can do total = (price of cheese pizza) ( amount of cheese pizzas bought)+(price of pepperoni pizza) ( amount of pepperoni pizzas bought)
Quadrilateral RSTV is dilated with respect to the origin by a scale factor of 1.5 to produce quadrilateral R'S'T'V' . Vertex R is located at (6, -9). Which ordered pair represents R' after the dilation?
Answer:
(9, -13.5)
Step-by-step explanation:
It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.
Rule for dilation is,
(x, y) → (kx, ky)
where 'k' is the scale factor.
If vertex R of the quadrilateral is (6, -9),
By the given rule of dilation,
R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]
→ R'(9, -13.5)
Therefore, Option given in bottom right (9, -13.5) will be the answer.
Billy has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny has 8 fewer than Billy c) Eric has three times as many as Billy
Answer:
Charlie: 5 + xDanny: x - 8Eric: x × 3Please help me understand this question!
Answer:
C
Step-by-step explanation:
The first sentence basically sets up the equation which is given, so we can read it for knowledge but it is not crucial to solve the problem.
We start here:
we are given: $120 - 0.2($120)
= 120 - (0.2)(120) (factoring out 120)
= 120 (1 - 0.2)
= 120 (0.8)
= 0.8 (120) (answer c)
PLS HELP !!
Define two terms, each containing the variables x and y, with exponents on each. (For Example : 10x³y–⁵)Find the quotient of the two terms. Explain step-by-step how you found the quotient
Answer:
Step-by-step explanation:
Two such terms are 7x^3*y^9 and -3x*y^5
Their quotient is
7x^3*y^9
--------------
-3x*y^5
This can be simplified as follows:
The numerical coefficients become -7/3.
x^3/x = x^3*x^1 = x^(3 - 1) = x^2 (we subtract the exponent of x in the denominator from the exponent of x in the numerator).
Next, y^9*y^5 = y^4.
The quotient in final reduced form is then (-7/3)x^2*y^4
I NEED HELP WITH THESE 4 ASAP
Answer:
I'm confused by this. What do they mean by prove?
Step-by-step explanation:
The sum of two positive number is 6 times their difference. what is the reciprocal of the ratio of the larger number to the smaller?
let the numbers be a and b, a>b
a+b=6(a-b)
we need to find reciprocal of ratio of larger to smaller , which will be same as ratio of smaller to larger or b/a, let's call it x
divide the equation by a.
1+x=6(1-x)
on solving, x=5/7
THE PRICE OF AN ITEM FROM $10 TO $17. WHAT WAS THE PERCENT INCREASE IN THE PRICE OF THE ITEM?
Answer:
70%
Step-by-step explanation:
The method to find out percentage increase is by subtracting the original price from the increased price and making it into a fractional form with the denominator as 10 (out of 100%). So it results to this.
(original price - increased price) / 10
(17 - 10) / 10 = 7/10
7/10 can be converted from its fractional form to 70% i.e.its percentage.
Hope this helps and please mark as the brainliest.
What is the 50th term of the arithmetic sequence having u(subscript)1 = -2 and d = 5
Answer:
243
Step-by-step explanation:
The general term for this arithmetic sequence is:
a(n) = -2 + 5(n - 1).
Then a(50) = -2 + 5(49) = 243
