Step-by-step explanation:
so, simply, when is c = 0 ?
0 = -0.0166x² + 1.2109x + 41.708
the solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = -0.0166
b = 1.2109
c = 41.708
x = (-1.2109 ± sqrt(1.2109² - 4×-0.0166×41.708))/(2×-0.0166) =
= (-1.2109 ± sqrt(1.46627881 + 2.7694112))/-0.0332 =
= (-1.2109 ± sqrt(4.23569001)/-0.0332 =
= (-1.2109 ± 2.058079204...)/-0.0332
x1 = (-1.2109 + 2.058079204...)/-0.0332 =
= -25.5174459... years
x2 = (-1.2109 - 2.058079204...)/-0.0332 =
= 98.46322904... years
x1 represents then a calculation backwards of 1940 - 25.5 years (≈ 1914) as the estimated starting point with 0 million sold papers.
x2 is the projected year in the future with 0 million dogs papers :
1940 + 98.46322904... = 2038.463229... ≈ 2038
based on this equation it is expected that during 2038 the circulation of weekday newspapers will drop to 0 millions.
I NEED HELP PLEASE
f+3n=7n
Answer:
4n
Step-by-step explanation:
67 and 113 multiples of 3,6 and 7
The number 67 and 113 are not the multiples of 3,6 and 7.
What is defined as the multiples?Multiples are the results of multiplying one whole number from another whole number.
A multiple is a products produced by multiplying one number by another. For instance, if we say 4 5 = 20, 20 is a multiple of 4 as well as 5.Every number multiplies itself.A number's multiples are infinite.A number's multiple is equal or greater to the number on its own (except for 0).Now, for the given question;
As, 67 and 113 are not completely divisible by 3. They are not multiple of 3.
67 and 113 are not entirely divisible by 6. So, they are also not the multiple of 6.
Now, 67 and 113 are also not entirely divisible by 7. Thus, they are also not the multiple of 7.
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i need some help please help
3x + 1<10
The value of x from the inequality is x < 3
What is an inequality?An inequality is defined as a statement of an order relationship between two numbers or algebraic expressions.
Given the inequality;
3x + 1 < 10
To determine the solution, we take the followings steps;
collect like terms
3x < 10 - 1
Find the difference between the terms
3x < 9
Make 'x' the subject of formula
x < 9/ 3
x < 3
Thus, the value of x from the inequality is x < 3
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Which equation represents the graph of this function?
_
A ) f(x)= √ x −4
____
B) f(x)= √x + 4
____
C) f(x)= √x - 4
_
D) f(x)= √x + 4
Answer:
USE air math
Step-by-step explanation:
hope that helps
Students on a campus of a college in California were asked "What will most likely help you to succeed in
college?" The results of this survey are tabulated below.
Reason
have a good roommate
study hard
live on campus
supportive family
always go to class
have a goal in mind
other
(a) What is the relative frequency for the reason "study hard"? (Write your answer as a fraction.)
Answer:
Frequency
583
620
187
163
558
645
439
(b) What is the relative frequency for the reason "have a goal in mind"? (Write your answer as a fraction.)
Answer:
Answer:
(a) [tex]\frac{620}{3195}[/tex]
(b) [tex]\frac{645}{3195}[/tex]
Step-by-step explanation:
Relative frequency of an event = Event Frequency/Total Frequency
In this case the event is the number of responses for each reason and the total frequency is the sum of all responses.
Total Responses = 583 + 620 + 187 + 163 + 558 + 645 + 439 = 3195
(a) What is the relative frequency for the reason "study hard"?
= Number of responses for "study hard" / 3195
= 620/3195
==> [tex]\frac{620}{3195}[/tex] Answer to (a)
(b) What is the relative frequency for the reason "have a goal in mind"?
= Number of responses for the reason "have a goal in mind"/3195
= 645/3195
==> [tex]\frac{645}{3195}[/tex] Answer to (b)
I think it is OK to leave it as it is without reducing the fraction any further
NO LINKS!! Please help me with these problems. Part 10a1
y = √(x - 2)
Answer:
Domain: [2, ∞)Range: [0, ∞)Continuity: Function is continuous on its domain [2, ∞).Minimum point at (2, 0).Increasing function: (2, ∞)Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.Step-by-step explanation:
Given function:
[tex]y=\sqrt{x-2}[/tex]
DomainThe domain is the set of all possible input values (x-values).
As the square root of a negative number cannot be taken, the domain of the given function is restricted.
[tex]x-2\geq 0 \implies x\geq 2[/tex]
Therefore, the domain of the given function is [2, ∞).
RangeThe range is the set of all possible output values (y-values).
As the square root of a negative number cannot be taken, the range of the given function is restricted.
Therefore, the range of the given function is [0, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Therefore, the function is continuous on its domain [2, ∞).
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}[/tex]
Therefore, there are no stationary points.
As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}[/tex]
Therefore:
The function is increasing in the interval (2, ∞).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.
Answer:
Domain: [2, ∞)
Range: [0, ∞)
Continuity: Function is continuous on its domain [2, ∞).
Minimum point at (2, 0).
Increasing function: (2, ∞)
Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.
Sue has a 8 cups of flour and needs to fill it equally in containers that hold 3/4 of a cup each. How many containers can she fill?
Answer: 10
Step-by-step explanation: First you decide that each container can fill 3/4 of a cup. You have 8 cups so you need to divide 8 by 3/4 which will give you the answer of 10.666 repeating so the answer is you can only fill up 10 containers.
Market research was undertaken to determine whether an ad campaign was successful for the software company. 15 men and 75 women were asked if they had seen the company’s latest TV advertisement. Altogether, 2 5 of the people said ‘yes’. 6 15 of the men said ‘yes’. What percentage of women said ‘no’ out of the total survey population?
50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Market research was undertaken to determine whether an ad campaign was successful for the software company.
Total number of people = 15 + 75 = 90
The number of people who said yes = (2/5)90 = 36
The number of people who said no = 90 - 36 = 54
The number of men said yes = (6/15)x15 = 6
The number of men said No = 15 - 6 = 9
The number of women who said no = 54 - 9 = 45
Percentage = (45/90)x100
The percentage of women who said ‘no’ out of the total survey population:
= 50%
Thus, 50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.
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Mathematical connection A lighthouse casts a revolving beam of light as far as the pier
The light's coverage area is given mathematically as i.e. Area=[tex]\pi d^{2}[/tex]
Given that a lighthouse casts a revolving beam of light as far as they peir and asked the area is covered.
The revolving beam of light covers the whole space i.e entirely 360°
I.e. it forms a circle-like region
Area of circle = [tex]\pi r^{2}[/tex]{ where r is the radius of circle}
Let's assume the distance traveled by light as "d"
as it forms a circular region, it forms a circle of radius "d"
Mathematical connection i.e. area of the region
⇒area of circular region=[tex]\pi d^{2}[/tex] {where d is the radius of region}
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how does this trick work? why does it always give the correct date of birthday?
The expression can be simplified to:
x + y/100
Where x is the month and y the day. This is why it always works.
Why does the trick always work?Let's define the two variables x and y as the month of your birth and the day of your birth respectively.
Now let's write the expression by following the steps, you should get:
((((7*x - 1)*13 + y + 3)*11 - x - y)/10 + 11)/100
Now let's simplify the expression we will get:
((((7*x - 1)*13 + y + 3)*11 - x - y)/10 + 11)/100
(((91x - 13 + y + 3)*11 - x - y)/10 + 11)/100
(((91x - 10 + y)*11 - x - y)/10 + 11)/100
((1001x - 110 + 11y - x - y)/10 + 11)/100
(( 1000x - 110 + 10y)/10 + 11)/100
You already can see what will happen here:
(( 1000x - 110 + 10y)/10 + 11)/100
(100x - 11 + y + 11)/100
(100x + y)/100 = x + y/100
So the expression will do the exact same thing for every values of x and y that you decide to use, it does not depend on your exact date of birthday.
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12x + 36 -14 -8x +5 =
Answer:
4x + 27
Step-by-step explanation:
12x + 36 - 14 - 8x + 5 Combine like terms (36, -14, 5)
12x + 27 - 8x Combine like terms (12x, -8x)
Solve for x on the triangle
The value of x in given diagram is x=3;
The entire area filled by a triangle's three sides on a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 b h, where b and h are the product of the triangle's base and height. All triangle shapes, including scalene, isosceles, and equilateral triangles, may be calculated using this formula. It is important to keep in mind that a triangle's base and height are perpendicular to one another.
Area of triangle SXY = 1/2 × SX × (x-2);
Area of triangle STR = 1/2 × ST × (x+3);
Area of trapezium XTRY = 1/2 × (x+3+x-2) × XT;
Area of triangle SXY = Area of triangle STR - Area of trapezium XTRY;
SX × (x-2) = ST × (x+3) - (2x + 1) × XT;
As; SX = TX = ST/2;
(x-2)/2 = (x+3) - (2x+1)/2;
x - 2 = 2x + 6 -2x -1
x = 3;
A triangle is a closed figure that has three vertices, three sides, and three angles. It is one of the most fundamental geometric forms, and it is represented by the symbol△. Triangles in mathematics can be categorized according to their sides and angles into many categories.
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Please solve this. it is due TODAY. no explain needed.
1 N b In Fig. R49 b, PT is a tangent at T to circle LMNT such that PT || LN. i Show that ANTL is isosceles. ii Find NTM. T M 498 L 36° P
Answer:
don't know that i'm looking for that to
Joe's employer will reimburse him $0.07 per mile driven. If Joe drives 253.63 miles on a business trip, what
is his mileage reimbursement?
Answer:
17.75
Step-by-step explanation:
253.63 ×0.07=17.7541
Which graph represents the function h(x)=−x√+2?
Of like f(x)= - √x+2
A b c d
Answer:
use air math
Step-by-step explanation:
hope that helps
Betsy, a recent retiree, requires $5000 per year in extra income. She has $60000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 5% per year. How much money should be invested in each to realize exactly $5000 in interest per year?
Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and $28,000 in the certificate of deposit paying 3% interest.
Interest is calculated by multiplying the rate with the principal.
Let x = the amount Betsy will invest in the B-rated bonds paying 13% per annum. The remaining amount, $60,000-x , she will invest in the certificate of deposit paying 3% per annum.
We can express the earnings on these two investments, after converting the percentages to their decimal equivalents, as: 0.13x+0.03(60000-x) and this is to earn a total of $5,000
Now we can write the necessary equation to solve for x.
or, 0.13x+0.03(60000-x) = 5000
or, 0.13x+1800-0.03x = 5000
or, 0.1x+1800 = 5000
or, 0.1x = 3200
or, x = 32000
So Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and the remainder ($60,000-$32,000 = $28,000) in the certificate of deposit paying 3% interest to obtain $5,000 in interest per annum.
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A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $1,900 per month for the next three years and then $3,800 per month for two years after that. If the bank is charging customers 9.75 percent APR, how much would it be willing to lend the business owner?
The amount will be $141647.55.
we need to use the present value of an annuity formula:
the formula used to determine the present value factor of an annuity is:
present value annuity factor = [1 - 1/(1 + i)ⁿ ] / i
we must divide this into 2 parts:
the first part will deal with the $19,00 monthly payment
the second part deals with the $38,000 monthly payment
i = 9.75% / 12 = 0.8125%
n (first part) = 36
n (second part) = 24
the PV annuity factor for first part = [1 - 1/(1 + 0.8125%)³⁶ ] / 0.8125% = 31.1043
the PV annuity factor for second part = [1 - 1/(1 + 0.8125%)²⁴ ] / 0.8125% = 21.7251
loan = ($219,00 x 31.1043) + ($38,00 x 21.7251)//(1 + 0.8125%)³⁶ = $59092.17 + $82555.38 = $141647.55
hence we get the amount as $141647.55
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A student is given this proof.
Given: AOM DON
Prove: CON~ BOM
ZAOM ZDON
given
ZBOM DON
vertical angles
theorem
ZAOM ZBOM
transitive
property of
congruence
ZAOM ZCON
vertical angles
theorem
ZCON BOM
transitive
property of
congruence
The student says that the proof shows that AOM BOM because they
are vertical angles.
Which statement best corrects the student's interpretation?
From the steps below, it has been proved that by transitive property of congruence, we can say that; ∠CON ≅ ∠BOM
How to prove congruent angles?
We are given;
∠AOM ≅ ∠DON
To prove that;
∠CON ≅ ∠BOM
Now, from the image attached, we can say that;
∠BOM ≅ ∠DON because of vertical angles theorem
Similarly, we can say that ∠AOM ≅ ∠BOM due to transitive property of congruence.
Also, we can say that from vertical angles theorem, ∠AOM ≅ ∠CON
Finally, since ∠AOM ≅ ∠BOM, then by transitive property of congruence, we can say that;∠CON ≅ ∠BOM
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What is the perimeter of a rectangle that has a length of 40 Ft and a width of 17 ft?
Answer:
i think 114ft
Step-by-step explanation:
Answer:
114 FT
Step-by-step explanation:
Perimeter formula: P = 2 (l + w)
P = 2 (40 + 17)
Use distributive property or PEMDAS
Distributive property: P = 80 + 34
P = 114
PEMDAS: P = 2(57)
P = 114
You get 114 either way
Find a pair of real number whose sum and product are both 12
The real number whose sum and product are both 12 area 1.101 and 11.899
A quadratic formula that provides the solutions of the final equation ax2 + bx + c = zero which is typically written within the form x = (-b ± √(b2 − 4ac))/(2a) ...(1)Let first number be " x "
Let other number be " 12 - x "
According to the question the product of two numbers is 12 which is given by x(12 - x) = 12
12x - x² = 12
x²- 12x + 12 = 0
Using quadratic formula , we get
Put a = 1 , b = -12 , c = 12 in equation (1) , we get
[tex]\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(12)} }{2(1)} \\\\\frac{12\pm\sqrt{144-48} }{2} \\\\\frac{12\pm\sqrt{96} }{2} \\\\\frac{12\pm9.79 }{2} \\\\[/tex]
Two numbers are 12 + 9.79 / 2 = 1.10 and 12 - 9.79/2 = 10.89
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2/3, ¹/3 =I need to find a LCD less common denominator for this question
In order to answer this issue, I need to identify an LCD, or least common denominator—something that unites all of the group members. We had all previously worked for the same employer, so that was our common denominator.
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.
Prime number seven.
7*8 = 56
56 is the lowest common factor.
3/7 * 8/8 = 24/56
5/8*7/7 = 35/56
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In a bag there are 72 candy bars. 40 of them are snickers, 24 of them are milky ways, the rest are Kit Kats.
Answer: 8 kitkats
Step-by-step explanation:
40+24= 64
72-64=8
Answer:
Total candy bars to snickers = 72:40 or simplified 9:5
Ratio of kit kats to milky ways = 8:24 or simplified 1:3
Ratio for kit kats to total candy bars = 8:72 or simplified 1:9
Step-by-step explanation:
72 = 40 + 24 + x
x = 8
Estimate actual problem by rounding all the way and do actual division: LU 1-1(2), LU 1-3(2)
Actual. Estimate
695)8,950
The actual problem will be 9000 % 700, with the remainder 600 and quotient 12.
Since we are with the actual problem, which is 8,950 % 695, here the dividend is 8950 and the divisor is 695, the actual division we come up with the 12 as quotient and remainder 620. Now making the expression simple using the round-off rule, here in the dividend 8950, the last two digits are 50, so we can round off it to 9000 and in the divisor 695, the last digit is 5, so we add 1 in the preceding number converting it to 700, after the actual division of the estimated expression, the quotient we come up with is 12, and the remainder is 600.
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In Ms. Block's class 8 students share a box of cherries equally. Each of them receives 9 cherries. There are
then 6 cherries left over. How many cherries were there altogether in the box?
Answer: 78
Step-by-step explanation:
first, you multiply 8 by 9 then you get 72, and then you can add the leftover cherries with 72 so 72 + 6 = 78
Answer:
Step-by-step explanation:
78
Find the dimensions of a rectangle given that its perimeter is 80 cm and its length is 1 cm more than twice its width.
Set up your solution using the variables L for the length, W for the width, and P for the perimeter.
Part a: Using the definition of perimeter, write an equation for P in terms of L and W .
Part b: Using the relationship given in the problem statement, write an equation for L in terms of W .
Solve the equations from parts a and b.
Answer:
The length should equal 27.
The width should equal 13.
A: P= 2L+ 2W
B: L=2W+1
Step-by-step explanation:
Perimeter is always equal to all of the sides added up.
You can find out the width and length by subsititution.
80=2(2W+1) +2W
80=4W+2+2W
80=6W+2
78=6W
W=13
L=(13*2)+1
L=27
What is the midpoint of the line segment from p1 to p2 is (-4,1). If P1 =(-4,5) what is p2??
A shipment of 480 bags of coffee beans contains an equal number of 0.75-pound bags,
1.5-pound bags, and 2-pound bags. What is the total weight of the shipment?
A 520 pounds
B 608 pounds
C 680 pounds
D 720 pounds
Answer:680
Step-by-step explanation:
160x.75=120
160x1.5=240
160x2=320
Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.
The number of weeks that it takes to empty the lake is; 350/11 weeks
How to solve fraction problems?We are told that Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.
Let w = number of weeks required to empty the lake
let the completed job = 1 (an empty lake)
Thus;
w/14 - w/25 = 1
Multiply through by 350 to get;
25w - 14w = 350
11w = 350
w = 350/11 weeks
Thus, the number of weeks that it takes to empty the lake is; 350/11 weeks
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Consider the following equation.
6x - 4y = 9
Step 1 of 2: Determine the missing coordinate in the ordered pair (-4, ?) so that it will satisfy the given equation.
The missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is -33/4.
Let the missing ccordinate of the ordered pair be m.
According to the given question.
We have an equation 6x - 4y = 9.
Here, we have given a ordered pair (-4, ?) which satisfy the given equation 6x - 4y = 9.
Therefore, the missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is given by
6x - 4y = 9
⇒ 6(-4) - 4(m) = 9
⇒ -24 - 4m = 9
⇒ -4m = 9 + 24
⇒ -4m = 33
⇒ m = -33/4
Hence, the missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is -33/4.
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