Which function has exactly one real solution? A. f(x) = -4x2 + 9x B. f(x) = 2x2 + 4x – 5 C. f(x) = 6x2 + 11 D. f(x) = -3x2 + 30x – 75
Answer:
A.
[tex]{ \tt{f(x) = - 4 {x}^{2} + 9x }}[/tex]
Step-by-step explanation:
[tex]{ \tt{f(x) = x( - 4x + 9)}}[/tex]
The edge roughness of slit paper products increases as knife blades wear. Only 2% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 4% of products slit with worn blades exhibit roughness. If 25% of the blades in the manufacturing are new, 60% are of average sharpness, and 15% are worn, what is the proportion of products that exhibit edge roughness
Answer:
The proportion of products that exhibit edge roughness is 0.029 = 2.9%.
Step-by-step explanation:
Proportion of products that exhibit edge roughness:
2% of 25%(new blades).
3% of 60%(average sharpness).
4% of 15%(worn). So
[tex]p = 0.02*0.25 + 0.03*0.6 + 0.04*0.15 = 0.029[/tex]
The proportion of products that exhibit edge roughness is 0.029 = 2.9%.
A plane traveled 4425 miles with the wind in 7.5 hours and 3675 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is
Answer:
540 miles per hour and 50 miles per hour respectively.
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50
The auto parts department of an automotive dealership sends out a mean of 6.3 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3
Answer:
0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3
Step-by-step explanation:
We have the mean, which means that the poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The auto parts department of an automotive dealership sends out a mean of 6.3 special orders daily.
This means that [tex]\mu = 6.3[/tex]
What is the probability that, for any day, the number of special orders sent out will be exactly 3?
This is P(X = 3). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-6.3}*6.3^{3}}{(3)!} = 0.0765[/tex]
0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3
Jan gives Ted a loan at 4% effective to be repaid by 10 annual payments of 100, followed by 5 annual payments of 200. Just after Ted makes the 5th payment, Jly and Ted discover that each of the 15 payments should have been 10% higher than they were originally scheduled. They agree that Ted will make increased payments of K in the 6th through 10th years to adjust for the error. The payments of 200 in the 11th through 15th years will not change. Determine K.
a. 129
b. 113
c. 145
d. 139
e. 149
Answer:
139 ( D )
Step-by-step explanation:
Interest rate on loan = 4% = 0.04
Number of payments = 15
First 10 payments = 100 each
last 5 payments = 200 each
Calculating the value of K
K = [ ( 100 / 0.04 * ( 1-1 / 1.04^10 ) + 200/0.04 * ( 1-1 / (1 +0.04)^5)* 1 /1.04^10)
* 1.1 - 100 / 0.04 * ( 1-1 / (1+0.04)^5 ) - 200/0.04 * (1-1 /1.04^5) * 1/1.04^10)*0.04 / ( 1-1 / 1.04^5) * (1 + 0.04)^5
= 138.6051 ≈ 139
4) A box has dimensions of 14 inches long, 1.4 feet wide,
and 9 inches high. What is the volume of the box?
The formula for the volume is V=1.w.h.
Answer:
2116.8 in^3
Step-by-step explanation:
V = l*w*h
All the units need to be the same
Convert 1.4 ft to inches
1.4 ft * 12 inches/ ft = 16.8 inches
V = 14 * 16.8 * 9
= 2116.8 in^3
dilan bought a table for Rs 3600. He sells it to Kirtim at a profit of Rs 205. Kritim sells it at Rs 4968 to Aayush. Find the percentage profit of Kritim.
Answer:
30.57%
Step-by-step explanation:
Dylan bought it for 3600.
Kirtim bought it from Dylan for 3600+205 = 3805
Aayush bought it from Kirtim for 4968.
that difference (profit for Kirtim) = 4968 - 3805 = 1163
Kirtim's initial 100% = 3805
1% = 100%/100 = 3805/100 = 38.05
now we want to know how many % in relation to his buying cost this 1163 selling profit is.
that means we need to see how often 1% fits into that amount.
%profit = profit / 1% cost = 1163 / 38.05 = 30.57%
=>
Kirtim made a profit of 30.57%.
14. Divide and write the fraction or mixed number in its simplest form:1/4÷3/8
Answer:
1/4 ÷ 3/8 = 2/3
Step-by-step explanation:
When dividing fractions, you have to take the reciprocal of the second fraction, then multiply from there. The reciprocal of a fraction is basically flipped. So then, 1/4 ÷ 3/8 becomes 1/4 x 3/8. Multiplying fractions should be pretty straight forward as you just need to multiply numerator (top number of a fraction) with numerator and vice versa for the denominators (bottom number of a fraction).
So then you get: (1 x 8)/(3 x 4) = 8/12. Then you just simplify it by dividing the numerator and denominator by their greatest possible factor, which in this case is 4. So then, (8 ÷ 4)/(12 ÷ 4) = 2/3.
Dan's car depreciates at a rate of 6% per year. By what percentage has Dan's car depreciated after 4 years? Give your answer to the nearest percent
Answer:
it's easy you need to do 6%×4 it's 24%
Select all that apply.
Given the points (5, 10) and (-4,-8), which of the following are true about the line passing through these points?
The line has a slope of 1/2
The line represents a direct variation function
The point (6.3) is also on the line
The line has a slope of 2
Cos(x)=0.35 all solutions
Step-by-step explanation:
you have to type shift an cos button together at one time and then write 0.35 youwill get answer
What is 5 (x-4) + 3x - 9x + 7?
Answer:
-x - 13
Step-by-step explanation:
5(x-4) + 3x - 9x + 7
First we use the distributive property to remove the parenthesis
5x -20 + 3x - 9x + 7
then we combine the like terms
-x - 13
Which formula can be used to describe the sequence?
Answer:
B could be used to show the formula to describe the sentence
find the area of the circle whose equation is x2+y2=6x-8y
Answer:
Given that the equation of a circle is :
[tex] \green{ \boxed{\boxed{\begin{array}{cc} {x}^{2} + {y}^{2} = 6x - 8y \\ = > {x}^{2} + {y}^{2} - 6x + 8y = 0 \\ = > {x}^{2} + {y}^{2} + 2 \times ( - 3) \times x + 2 \times 4 \times y = 0 \\ \\ \sf \: standard \: equation \: o f \: circle \: is : \\ {x}^{2} + {x}^{2} + 2gx + 2fy + c = 0 \\ \\ \sf \: by \: comparing \\ \\ g = - 3 \\ f = 4 \\ c = 0 \\ \\ \sf \: radius \: \: r = \sqrt{ {g}^{2} + {f}^{2} - c } \\ = \sqrt{ {( - 3)}^{2} + {4}^{2} - 0 } \\ = \sqrt{9 + 16} \\ = \sqrt{25} \\ = 5 \: unit \\ \\ \bf \: area \: = \pi {r}^{2} \\ = \pi \times {5}^{2} \\ =\pink{ 25\pi \: { unit }^{2} }\end{array}}}}[/tex]
HELP PLEASE I CANNOT FAIL PLEASE!!!!!!!
Which statement correctly compares the two functions?
A.
They have the same y-intercept and the same end behavior as x approaches ∞.
B.
They have the same x- and y-intercepts.
C.
They have the same x-intercept but different end behavior as x approaches ∞.
D.
They have different x- and y-intercepts but the same end behavior as x approaches ∞.
Answer:
B
Step-by-step explanation:
they have the same intercepts
Jason collects baseball cards. He bought one card for $25. Its current value is represented by the expression 25(1.02)t, where t is the number of years Jason has owned the card. Is Jason’s baseball card going up or down in value?
A grocery store recently sold a bag of peanuts for $0.76 and a bag of pistachios for $3.68. At the end of that day, 50 bags of peanuts and pistachios were sold for a total of $128.52. How many bags of each were sold?
Answer:
19 bags of peanuts and 31 bags of pistachios
The sum of three consecutive integers if the first is n +2
Answer:
Step-by-step explanation:
The three consecutive integers are
(n+2), (n+3), (n+4).
(n+2)+(n+3)+(n+4) = 3n+9
Geo-net, a cellular phone company, has collected the following frequency distribution for the length of calls outside its normal customer roaming area: Length (min.) Frequency 0<5 260<5 75 5<10 13910<15 10515<20 3720<25 1825+ 400 The sample mean(x) for this distribution is 14.3 minutes, and the sample standard deviation is 3.7 minutes. Determine whether these data are normally distributed (a = .05).
Answer:
Reject H0 ; and conclude that call length does not follow a normal distribution.
Step-by-step explanation:
Given :
The hypothesis :
H0: Call lengths outside normal customer roaming areas follows normal distribution
H1: Call lengths outside normal customer roaming areas do not follows normal distribution
Mean, μ = 14.3
Standard deviation, σ = 3.7
From the frequencies Given :
Expected values can be calculated :
Observed values :
16, 75, 139, 105, 37, 18 ; Total = 400
P(Z < (x - μ) / σ)) * total frequency
x = frequency
For x = 5 ;
P(Z < (5 - 14.3) / 3.7)) * 400 = 2.391
For x = 10;
P(Z < (10 - 14.3) / 3.7)) * 400 = 46.644
For x = 15;
P(Z < (15 - 14.3) / 3.7)) * 400 = 180.960
For x = 20;
P(Z < (20 - 14.3) / 3.7)) * 400 = 145.32
For x = 25;
P(Z < (25 - 14.3) / 3.7)) * 400 = 23.92
For x = 30;
P(Z < (30 - 14.3) / 3.7)) * 400 = 0.766
χ² = Σ(O - E)²/E
O = observed values
E = Expected values
χ² = (26-2.391)^2 / 2.391 + (75-46.644)^2 / 46.644 + (139-180.96)^2 / 180.96 + (105-145.32)^2 / 145.32 + (37-23.92)^2 / 23.92 + (18-0.766)^2 / 0.766 = 666.17
χ² = 666.17
The critical value "; df = n - 1= 6-1 = 5
α = 0.05
χ²critical(0.05 ; 5) = 11.07
χ²statistic > χ²critical ; Reject the Null, H0 ; and conclude that call length does not follow a normal distribution.
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.954 grams and a standard deviation of 0.292 grams. Find the probability of randomly selecting a cigarette with 0.37 grams of nicotine or less. Round your answer to four decima
Let X be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.
P(X ≤ 0.37) = P((X - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(Z ≤ -2)
where Z follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform X to Z using the rule Z = (X - mean(X))/sd(X).)
Given the required precision for this probability, you should consult a calculator or appropriate z-score table. You would find that
P(Z ≤ -2) ≈ 0.0228
You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,
P(-2 ≤ Z ≤ 2) ≈ 0.95
which means
P(Z ≤ -2 or Z ≥ 2) ≈ 1 - 0.95 = 0.05
The normal distribution is symmetric, so this means
P(Z ≤ -2) ≈ 1/2 × 0.05 = 0.025
which is indeed pretty close to what we found earlier.
Given:
HI and JK intersect at point O.
m KOH = 110
Colleen was asked to find the measure of x and explain her reasoning
Line geometry are caused from the intersection of two line. The measure of angle x from the diagram is 110degrees
Linear geometryLine geometry are caused from the intersection of two lines. From the given figures, you can see that <KOH and <IOK forms a linear pair, hence;
<KOH + <IOK = 180
110 + <IOK = 180
<IOK = 180 - 110
<IOK = 70 degrees
Similarly <x and MIOK are linear pair pair such that <x + 1<IOK = 180
<x + 70 =180
<x = 180 - 70
<x = 110degrees
Hence the measure of angle x from the diagram is 110degrees
Learn more on line geometry here: https://brainly.com/question/7098341
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Answer:
<IOK = 70 degrees
<x and <IOK form a linear pair, so m<x is = 110
Step-by-step explanation:
i did it on khan and got it right, i hope your day goes well and you get all your other questions right :)
Suppose a classmate got 12+ 2x as
the answer for Example D instead of
2x + 12. Did your classmate give a
correct answer? Explain.
Answer:
Yes
Step-by-step explanation:
Using the commutative property (a + b = b + a), we can easily calculate that 12 + 2x is equal to 2x + 12.
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
Step-by-step explanation:
Given the exponential function g(x)= 1∕2(2)^x, evaluate ƒ(1), ƒ(3), and ƒ(6).
A) ƒ(1) = 1, ƒ(3) = 4, ƒ(6) = 32
B) ƒ(1) = 2, ƒ(3) = 9, ƒ(6) = 64
C) ƒ(1) = 1, ƒ(3) = 2, ƒ(6) = 8
D) ƒ(1) = 4, ƒ(3) = 16, ƒ(6) = 128
Answer:
A) ƒ(1) = 1, ƒ(3) = 4, ƒ(6) = 32
Step-by-step explanation:
f(x)= 1∕2(2)^x,
Let x = 1
f(1)= 1∕2(2)^1 = 1/2 ( 2) = 1
Let x = 3
f(3)= 1∕2(2)^3 = 1/2 ( 8) = 4
Let x = 1
f(6)= 1∕2(2)^6 = 1/2 ( 64) = 32
Answer:
A) ƒ(1) = 1, ƒ(3) = 4, ƒ(6) = 32
Step-by-step explanation: I took the test
If f(x)=5(x+3)^3-2. What does f^-1(x) equal?
9514 1404 393
Answer:
C ∛((x+2)/5) -3
Step-by-step explanation:
To find the inverse function, solve for y:
x = f(y)
x = 5(y +3)³ -2 . . . . . . substitute f(y)
x +2 = 5(y +3)³ . . . . . add 2 -- already you know C is the answer
(x +2)/5 = (y +3)³ . . . . divide by 5
∛((x +2)/5) = y +3 . . . . take the cube root
∛((x +2)/5) -3 = y . . . . subtract 3
f^-1(x) = ∛((x +2)/5) -3 . . . . matches expression C
Which of the following is the graph of
(x - 1)^2 + (y + 2)^2 = 4 ?
Answer:
a
Step-by-step explanation:
The correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given equation is ( x-1 )² + ( y + 2 )² = 4
The graph of the equation is attached with the answer below when we plot the graph we will get the circle that is lying in the third and the fourth quadrant.
Therefore the correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.
To know more about graphs follow
https://brainly.com/question/25020119
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find the area of this unusual shape
Answer:
38 ft²
Step-by-step explanation:
The shape consists of a rectangle and two triangles.
Area of the shape = area of rectangle + area of the two triangles
✔️Area if the rectangle = L × W
L = 8 + 2 = 10 ft
W = 3 ft
Area of rectangle = 10 × 3 = 30 ft²
✔️Area of the large triangle = ½ × bh
b = 4 ft
h = 3 ft
Area of large triangle = ½ × 4 × 3 = 6 ft²
✔️Area of the small triangle = ½ × bh
b = 2 ft
h = 2 ft
Area of large triangle = ½ × 2 × 2 = 2 ft²
✅Area of the shape = 30 + 6 + 2 = 38 ft²
I really need help please
what is this?
Answer:
431.2
Step-by-step explanation:
Area of a regular polygon = # of sides * side length of 1 side * apothem
We want to find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length with 7.7 meters
So # of sides = 7
apothem = 8
side length = 7.7
so the area would equal 7 * 8 * 7.7 = 431.2
It says to round to the nearest tenth however 431.2 is already rounded to the nearest tenth
Answer:
That answer ^ is incorrect. The correct answer ( in acellus that is ) is 2
15.6
Step-by-step explanation:
Quick can someone plot these in a scatter plot
(9.2,2.33)
(19.5,3.77)
(15.5,3.92)
(0.7,1.11)
(21.9,3.69)
(0.7,1.11)
(16.7,3.5)
(0.7,1.11)
(18,4)
(18,3.17)
The scatterplot is below.
I used GeoGebra to make the scatterplot. Though you could use other tools such as Excel or Desmos, or lots of other choices.
Side note: I'm not sure why, but you repeated the point (0.7,1.11) three times.
What is the axis of symmetry of the
parabola graphed below?
O x=4
Oy=2
Oy=4
Ox=2
Other:
Answer:
A
Step-by-step explanation:
i think so..sorry if im wrong
