Answer:
Step-by-step explanation:
x3−x2+5x−12
x
≥0
Let's find the critical points of the inequality.
x3−x2+5x−12
x
=0
x3−x2+5x−12=0(Multiply both sides by x)
(Use cubic formula)
x=1.836169
Check possible critical points.
x=1.836169(Works in original equation)
Critical points:
x=1.836169(Makes both sides equal)
x=0(Makes left denominator equal to 0)
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<0(Works in original inequality)
0<x≤1.836169(Doesn't work in original inequality)
x≥1.836169(Works in original inequality)
Answer:
x<0 or x≥1.836169
Simplify the given equation.
6 - (3x+10) + 4(2 - x) = 15
O 4-7 x = 15
O4 - 4 x= 15
O 12 - 7 x= 15
Answer:
-7x-11
Step-by-step explanation:
expand brackets
6-3x-10+8-4x=15
4-7x=15
move 15 to left side
-7x-11
Answer:
4-7x=15
Step-by-step explanation:
[tex]6 - (3x + 10) + 4(2 - x) = 15 \\ 6- 3x - 10 + 8 - 4x = 15 \\ - 7x = 15 + 10 - 8 - 6\\ - 7x = 11 \\ the \: same \: one \: is \\ 4 - 7x = 15[/tex]
Functions f and g are defined for all real
numbers. The function f has zeros at -2, 3, and 7:
and the function g has zeros at -3, -1, 4, and 7.
How many distinct zeros does the product
function f g have?
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Answer:
6
Step-by-step explanation:
The number of distinct zeros in the product will be the union of the sets of zeros. Duplicated values are not distinct, so show in the union of sets only once.
F = {-2, 3, 7}
G = {-3, -1, 4, 7}
F∪G = {-3, -2, -1, 3, 4, 7} . . . . . . a 6-element set
The product has 6 distinct zeros.
_____
As you may notice in the graph, the duplicated zero has a multiplicity of 2 in the product.
A toy car costs $60. It is reduced to 10% in a sale. How much does it cost in a sale ?
Answer:
$54
Step-by-step explanation:
10% of $60 is $6
$60-$6=$54
Help please this is due today
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Answer:
the correct choice is marked
Step-by-step explanation:
The end behavior matches that of an odd-degree polynomial. The only function shown that has that behavior is the one marked:
[tex]f(x)=\dfrac{x^2-36}{x-6}=\dfrac{(x+6)(x-6)}{(x-6)}=x+6\qquad x\ne6[/tex]
__
Additional comment
The other functions have horizontal (not slant) asymptotes, so do not have the described end behavior.
B: y=0
C, D: y=1
In 2018, Mike Krzyewski and John Calipari topped the list of highest paid college basketball coaches (Sports Illustrated website). The following sample shows the head basketball coach's salary for a sample of 10 schools playing NCAA Division I basketball. Salary data are in millions of dollars.
University Coach's Salary University Coach's Salary
North Carolina State 2.2 Miami (FL) 1.5
Iona 0.5 Creighton 1.3
Texas A&M 2.4 Texas Tech 1.5
Oregon 2.7 South Dakota State 0.3
Iowa State 2.0 New Mexico State 0.3
a. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division I basketball.
b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches.
c. What is the 95% confidence interval for the population variance?
d. What is the 95% confidence interval for the population standard deviation?
From the data given, we estimate the population mean and population standard deviation. Then, we use this estimate to find a 95% confidence interval for the population variance and the population standard deviation.
Sample:
Salaries in millions of dollars: 2.2, 1.5, 0.5, 1.3, 2.4, 1.5, 2.7, 0.3, 2.0, 0.3
Question a:
The mean is the sum of all values divided by the number of values. So
[tex]\overline{x} = \frac{2.2 + 1.5 + 0.5 + 1.3 + 2.4 + 1.5 + 2.7 + 0.3 + 2.0 + 0.3}{10} = 1.42[/tex]
The sample mean salary is of 1.42 million.
Question b:
The standard deviation is the square root of the difference squared between each value and the mean, divided by one less than the number of values.
So
[tex]s = \sqrt{\frac{(2.2-1.42)^2 + (1.5-1.42)^2 + (0.5-1.42)^2 + (1.3-1.42)^2 + (2.4-1.42)^2 + (1.5-1.42)^2 + (2.7-1.42)^2 + ...}{9}} = 0.8772[/tex]
Thus, the estimate for the population standard deviation is of 0.8772 million.
Question c:
The sample size is [tex]n = 10[/tex]
The significance level is [tex]\alpha = 1 - 0.05 = 0.95[/tex]
The estimate, which is the sample standard deviation, is of [tex]s = 0.8772[/tex].
Now, we have to find the critical values for the Pearson distribution. They are:
[tex]\chi^2_{\frac{\alpha}{2},n-1} = \chi^2_{0.025,9} = 19.0228[/tex]
[tex]\chi^2_{1-\frac{\alpha}{2},n-1} = \chi^2_{0.975,9} = 2.7004[/tex]
The confidence interval for the population variance is:
[tex]\frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2},n-1}} < \sigma^2 < \frac{(n-1)s^2}{\chi^2_{1-\frac{\alpha}{2},n-1}}[/tex]
[tex]\frac{9*0.8772^2}{19.0228} < \sigma^2 < \frac{9*0.8772^2}{2.7004}[/tex]
[tex]0.3641 < \sigma^2 < 2.5646[/tex]
Thus, the 95% confidence interval for the population variance is (0.3641, 2.5646)
Question d:
Standard deviation is the square root of variance, so:
[tex]\sqrt{0.3641} = 0.6034[/tex]
[tex]\sqrt{2.5646} = 1.6014[/tex]
The 95% confidence interval for the population standard deviation is (0.6034, 1.6014).
For more on confidence intervals for population mean/standard deviation, you can check https://brainly.com/question/13807706
A movie theater has a seating capacity of 187. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1338, How many children, students, and adults attended?
___ children attended.
___ students attended.
___ adults attended.
Answer:
A) children attended=98 b) students attended=60 c)adults attended=49
Step-by-step explanation:
system%28a%2Bc%2Bx=207%2Cc%2Fa=2%2C5c%2B7x%2B12a=1498%29
Simplify and solve the system.
-
a%2B2a%2Bx=207
3a%2Bx=207
x=207-3aandc=2a
-
The revenue equation can be written in terms of just one variable, a.
10a%2B7%28207-3a%29%2B12a=1498
Solve for a;
use it to find x and c.
FURTHER STEPS
-
10a%2B1449-21a%2B12a=1498
a%2B1449=1498
a=98-49
highlight%28a=49 -------adults
-
c=2a
c=2%2A49
highlight%28c=98 -------children
-
x=207-a-c
x=207-49-98
highlight%28x=60 ---------students
7. Solve -4(6x + 3) = -12(x + 10).
Tìm diện tích của mặt. Phần mặt x2+y2+z2=9 nằm bên trên mặt phẳng z=1.
If you're familiar with surface integrals, start by parameterizing the surface by the vector-valued function,
r(u, v) = 3 cos(u) sin(v) i + 3 sin(u) sin(v) j + 3 cos(v) k
with 0 ≤ u ≤ 2π and 0 ≤ v ≤ arccos(1/√8).
Then the area of the surface (I denote it by S) is
[tex]\displaystyle\iint_S\mathrm dA = \int_0^{2\pi}\int_0^{\arccos\left(1/\sqrt8\right)}\left\|\dfrac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm dv\,\mathrm du \\\\ = \int_0^{2\pi}\int_0^{\arccos\left(1/\sqrt8\right)}9\sin(v)\,\mathrm dv\,\mathrm du \\\\ =18\pi \int_0^{\arccos\left(1/\sqrt8\right)}\sin(v)\,\mathrm dv = \boxed{\frac{9(4-\sqrt2)\pi}2}[/tex]
what is the volume of the solid?
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Answer:
(9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Step-by-step explanation:
The area of the hexagon is given by the formula ...
A = (3/2)√3·s^2 . . . . for side length s
The area of the hexagonal face of this solid is ...
A = (3/2)√3·(2 ft)^2 = 6√3 ft^2
__
The area of the circular hole in the hexagonal face is ...
A = πr^2
The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.
A = π(1 ft)^2 = π ft^2
Then the area of the "solid" part of the face of the figure is ...
A = (6√3 -π) ft^2
__
The volume is ...
V = Bh . . . . . where B is the area of the base of the prism, and h is its height
V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Given the triangle below, what is the length of the third side, rounded to the nearest whole number?
Answer:
Step-by-step explanation:
You need the Law of Cosines for this, namely:
[tex]x^2=21^2+14^2-2(21)(14)cos58[/tex] where x is the missing side.
[tex]x^2=441+196-311.5925[/tex] and
[tex]x^2=325.4075[/tex] so
x = 18.0 or just 18
1. Đường kính của một loại trục máy là một đại lượng ngẫu nhiên có phân phối chuẩn N (μ = 250mm, σ2 = 25mm2). Trục máy được gọi là hợp quy cách nếu đường kính từ 245mm đến 255mm. Cho máy sản xuất 100 trục. Tính xác suất để:
a. Có 50 trục hợp quy cách.
b. Có không quá 80 trục hợp quy cách
Answer:
please ask in English
Step-by-step explanation:
then I can help
A math class consists of 25 students, 15 male and 10 female. Three students
are selected at random to participate in a probability experiment. Compute the
probability that
a. a male is selected, then two females.
b. a female is selected, then two males.
c. two females are selected, then one male.
d. three males are selected.
e. three females are selected.
Answer:
a) 675 b) 1050 c) 675 d)455 e) 120
Step-by-step explanation:
Answer:a, 0,293
Step-by-step explanatThe number of ways to get any 3 students from 25 given students is :
25C3 = 2300
Let A be the event that has 1 Male and 2 Female
15C1*10C2=675
The probability of having 1 Male and 2 Female is
675/2300=0.293 ion:
can earn 5 coins In my town, gas prices are always listed to the thousandths place. Since the smallest coin we have is the penny, we have to round them to the hundredths place. If the price of gas is $3.545, what will the price be when we round it to the hundredths place?
Answer:
$3.55
Step-by-step explanation:
1st number after 0 is tenths, 2nd is hundredths.
since the number after is 5, we round up
Which ratio is equal to 27 : 81?
Answer:
1:3
Step-by-step explanation:
27 : 81
Divide each side by 27
27/27 : 81/27
1:3
find the equation for the parabola that has its vertex at the origin and has directrix at x =1/34
Answer:
Focus is at the origin, so (0,0)
directrix at x=1/34
the equation of the parabola is,
[tex]x = \frac{1}{68} - 17 {y}^{2} [/tex]
(abc - 4d) + (abc + 4d)
Can you solve it please?
Answer:
2abc
Step-by-step explanation:
●●●●○○○○□□□□■■■■
Answer:
=> 2abc
Step-by-step explanation:
=> (abc - 4d) + (abc + 4d)
=> abc - 4d + abc + 4d
=> abc + abc
=> 2 abc
ou invested 7000 between two accounts paying 4% and 9% annual interest, respectively. If the total interest earned for the year was $430 how much was invested at each rate? $ nothing was invested at and $ nothing was invested at
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Answer:
$3000 at 9%$4000 at 4%Step-by-step explanation:
Let x represent the amount invested at 9%. Then 7000-x was invested at 4% and the interest earned was ...
9%·x +4%(7000-x) = 430
5%·x +280 = 430 . . . . . . . . . simplify
0.05x = 150 . . . . . . . . . . . subtract 280
x = 3000 . . . . . . . . . . divide by 0.05
$3000 was invested at 9%; $4000 was invested at 4%.
Express -6 as the sum of a negative integer and a whole number
What is the completely factored form of this polynomial? x3 + 3x2 - 6x – 18
A. (x - 2)(x - 3)(x + 3)
B. (x2 - 6)(x + 3)
C. (x2 + 3)(x-6)
D. (x + 6)(x - 1)(x + 3)
Answer:
(x+3) ( x^2 -6)
Step-by-step explanation:
x^3 + 3x^2 - 6x – 18
Factor by grouping
x^3 + 3x^2 - 6x – 18
Factor x^2 out of the first group and -6 out of the second group
x^2( x+3) -6(x+3)
Factor out x+3
(x+3) ( x^2 -6)
Give the degree of the polynomial. -5-5x2wy4-y4x2-4w3
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Answer:
7
Step-by-step explanation:
The degree of each term is the sum of the degrees of the variables in it.
Term, Degrees
-5, 0
-5x^2wy^4, x:2, w:1, y:4 -- term degree = 2+1+4 = 7
-y^4x^2, y:4, x:2 -- term degree = 4+2 = 6
-4w^3, w:3 -- term degree = 3
The highest of these is 7, so the degree of this polynomial is 7.
An angle, Theta. is in standard position. The terminal side of the angle passes through the point (6.-5).
Find sin Theta
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Answer:
sin(θ) = (-5√61)/61
Step-by-step explanation:
The distance from the origin to the given point is ...
d = √(6² +(-5)²) = √61
The sine of the angle is the ratio ...
sin(θ) = y/d = -5/√61
Rationalizing the denominator gives us ...
sin(θ) = (-5√61)/61
Choose the best answer from the choices below:
If a radius of a circle bisects a chord which is not a diameter, then ____.
Answer: the radius is perpendicular to the chord.
If a radius of a circle bisects a chord which is not diameter, then the radius is perpendicular to the chord.
Answered by Gauthmath must click thanks and mark brainliest
The radius is perpendicular to the chord.
Does the radius of the circle bisect the string?If the radius of the circle is perpendicular to the chord of the circle, the radius bisects the chord. The two strings are congruent only if they are equidistant from the center of the circle.
No, not all strings in a circle are diameters because the diameter passes through the center of the circle. Therefore, all the diameters of a circle are also strings, not all the strings of a circle.
Learn more about chord at
https://brainly.com/question/1869643
#SPJ2
there were 578 tickets sold for a basket all game. the activity cardholder's tickets cost $1.25 and the non-cardholders' tickets cost $2.00. the total amount of money collected was $880.00. how many of each kind of ticket were sold?
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Answer:
non-cardholder: 210cardholder: 368Step-by-step explanation:
Let n represent the number of non-cardholder tickets sold. Then total revenue is ...
2.00n +1.25(578 -n) = 880.00
0.75n + 722.50 = 880.00
0.75n = 157.50 . . . . . . . . . . . subtract 722.50
n = 210 . . . . . . . . . . . . . . . divide by 0.75. Number of non-cardholder tickets
578 -n = 368 . . . . . number of cardholder tickets
368 cardholder and 210 non-cardholder tickets were sold.
11. What is the reciprocal of 6/5?
OA. 12/20
OB.11/5
OC.1
OD.576
Answer: The answer is D, 5/6.
Step-by-step explanation: The reciprocal of a fraction is that fraction but the numerator and denominater swapped places.
Answer:
5/6
Step-by-step explanation:
The reciprocal is where you flip the fraction
6/5 -> reciprocal -> 5/6
I'm not sure about your answer choices tho, sorry
If Victoria's rent is $400 per month, and she pays an additional $150 for utilities and $35 for advertising each month, what is her cost function using the additional data from previous problem? Use C to denote cost and n for number of collars she makes.
Answer:
[tex]C(n) = 435n + 150[/tex]
Step-by-step explanation:
Given
[tex]Base = 400[/tex] -- Base charge per month
[tex]Utilities = 150[/tex]
[tex]Adverts = 35[/tex] per month
Required
The cost function
To do this, we multiply the rates by the number of months.
So, we have:
[tex]C(n) = Base * n + Adverts * n + Utilities[/tex]
So, we have:
[tex]C(n) = 400 * n + 35 * n + 150[/tex]
[tex]C(n) = 400n + 35n + 150[/tex]
[tex]C(n) = 435n + 150[/tex]
If contribution margin is $70000, sales is $120000, and net income is $50000, then variable and fixed expenses are
Variable Fixed
a) $190000 $70000
b) $50000 $20000
c) $50000 $70000
d) $20000 $50000
Answer:
c) $50000 $70000
Step-by-step explanation:
!!!!!!!
i need the answer to this help PLEASE
Answer:
B
Step-by-step explanation:
At 5 hours the distance traveled is 200 miles. 9 hours is less than double 5 hours so it is 360 miles.
The difference of two numbers is 8. If the sum of the smaller number and the square of the larger number is 148, what is the smaller number?
Answer:
C
Step-by-step explanation:
Which of the following shows the extraneous solution to the logarithmic equation below?
2 log Subscript 5 Baseline (x + 1) = 2
Answer:
x=4
Step-by-step explanation:
log5(x+1)=1, (x+1)=5, x=4
Answer:
x= -6
Step-by-step explanation:
i got it wrong and the answer is -6
what is the perfect square of 96
Step-by-step explanation:
We determined above that the greatest perfect square from the list of all factors of 96 is 16.
