Answer:
The zeroes of f(x) = (x-7)(x+8) are 7 and -8.
Step-by-step explanation:
You have to figure out what makes each of the equal to zero.
Step 1 : Make the 2 equations both equal 0.
x-7 = 0
x+8 = 0
Step 2: Solve for x
x-7 = 0
x=7
x+8 = 0
x=-8
So 7 and -8 are both zeroes of this function.
Which of the following is the result of the equation below after completing the square and factoring? x^2-4x+2=10
A. (x-2)^2=14
B. (x-2)^2=12
C. (x+2)^2=14
D. (x+2)^2=8
9514 1404 393
Answer:
B. (x-2)^2=12
Step-by-step explanation:
The constant that completes the square is the square of half the coefficient of the x-term. That value is (-4/2)^2 = 4.
There is already a constant of 2 on the left side of the equal sign, so we need to add 2 to both sides to bring that constant value up to 4.
x^2 -4x +2 = 10 . . . . . . . given
x^2 -4x +2 +2 = 10 +2 . . . . complete the square (add 2 to both sides)
(x -2)^2 = 12 . . . . . . . . . write as a square
Can the range of a function be written like this {6,7,8,10} instead of like this [tex]6\leq x\leq 10[/tex]?
Answer:
No unless x is being used to define only elements of an integer set.
Step-by-step explanation:
No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....
Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.
{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.
If interest is 8% and it is compounded semiannually, and after one year, the total value is $10,816, what was the original investment?
For each of the following variables, identify the type of variable (categorical vs. numeric). (1) Temperature (in Fahrenheit) of an office building (11) Traffic congestion (e.g. light, medium, heavy)
1) (1) Numeric, and (II) Categorical
2) (1) Numeric, and (II) Numeric
3) (1) Categorical, and (II) Numeric
4) There is no correct match.
5) (1) Categorical, and (11) Categorical
Answer:
(a) Temperature: Numerical
(b) Traffic congestion: Categorical
Step-by-step explanation:
Required
Determine the variable type
(a) Temperature
Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.
Hence, the variable is numerical
(b) Traffic congestion
From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....
Hence, the variable is categorical
NEED HELP
The average amount of money spent for lunch per person in the college cafeteria is $6.75 and the standard deviation is $2.28. Suppose that 18 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
C. For a single randomly selected lunch patron, find the probability that this
patron's lunch cost is between $7.0039 and $7.8026.
D. For the group of 18 patrons, find the probability that the average lunch cost is between $7.0039 and $7.8026.
Answer:
C.[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)\approx 0.2942[/tex]
Step-by-step explanation:
We are given that
n=18
Mean, [tex]\mu=6.75[/tex]
Standard deviation, [tex]\sigma=2.28[/tex]
c.
[tex]P(7.0039<x<7.8026)=P(\frac{7.0039-6.75}{2.28}<\frac{x-\mu}{\sigma}<\frac{7.8026-6.75}{2.28})[/tex]
[tex]P(7.0039<x<7.8026)=P(0.11<Z<0.46)[/tex]
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
Using the formula
[tex]P(7.0039<x<7.8026)=P(Z<0.46)-P(Z<0.11)[/tex]
[tex]P(7.0039<x<7.8026)=0.67724-0.54380[/tex]
[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)=P(\frac{7.0039-6.75}{2.28/\sqrt{18}}<\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}})<\frac{7.8026-6.75}{2.28/\sqrt{18}})[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(0.47<Z<1.96)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(Z<1.96)-P(Z<0.47)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.97500-0.68082[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.29418\approx 0.2942[/tex]
A public opinion survey is administered to determine how different age groups feel about an increase in the minimum wage. Some of the results are shown in the table below.
For Against No Opinion
21-40 years 20 5
41-60 years 20 20
Over 60 years 55 15 5
The survey showed that 40% of the 21 - 40 year-olds surveyed are against an increase, and 15% of the entire sample surveyed has no opinion. How many 21 - 40 year-olds surveyed are for an increase? How many 41 - 60 year-olds are against an increase?
Answer:
25 ; 35
Step-by-step explanation:
Given :
____________For __ Against __ No Opinion
21-40 years _________20 _______5
41-60 years ___20 ______________20
Over 60 years _55____ 15________ 5
Given that :
40% of 21-40 are against
Then :
40% = 20
To a obtain 100% of 21 - 40
40% = 20
100% = x
Cross multiply
0.4x = 20
x = 20/0.4
x = 50
100% of 21 - 40 = 50 people
For = 50 - (20 + 5)
= 50 - 25
= 25
2.)
Total who have no opinion :
(5 + 20 + 5) = 30
30 = 15%
Total number surveyed will be , x :
30 = 15%
x = 100%
Cross multiply :
0.15x = 30
x = 30/0.15
x = 200
Number of 41 - 60 against an increase, y:
(25 + 20 + 5 + 20 + y + 20 + 55 + 15 + 5) = 200
165 + y = 200
y = 200 - 165
y = 35
There are four different colored balls in a bag. There is equal probability of selecting the red, black, green, or blue ball.What is the expected value of getting a green ball out of 20 experiments with replacement?
Answer:
The expected value is of 5 green balls.
Step-by-step explanation:
For each experiment, there are only two possible outcomes. Either it is a green ball, or it is not. Since there is replacement, the probability of a green ball being taken in an experiment is independent of any other experiments, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
20 experiments
This means that [tex]n = 20[/tex]
There is equal probability of selecting the red, black, green, or blue ball.
This means that 1 in 4 are green, so [tex]p = \frac{1}{4} = 0.25[/tex]
What is the expected value of getting a green ball out of 20 experiments with replacement?
[tex]E(X) = np = 20*0.25 = 5[/tex]
The expected value is of 5 green balls.
The expected value of getting a green ball out of 20 experiments with replacement is 5.
What is a binomial distribution?The binomial probability distribution of the number of successes in a sequence of n independent experiments is the binomial distribution with parameters n and p.
As it is given that the probability of all the balls coming out of the bag is equal. Therefore, the probability of a green ball coming can be written as,
[tex]\text{Probability of Green Ball} = 0.25[/tex]
Also, we can write the probability of not getting a green ball can also be written as,
[tex]\rm Probability(\text{Not coming Green Ball}) = P(Red\ ball)+P(Black\ ball)+P(Blue\ ball)[/tex]
[tex]=0.25+0.25+0.25\\\\=0.75[/tex]
Now, as there are only two outcomes possible, therefore, the distribution of the probability is a binomial distribution. And we know that the expected value of a binomial distribution is given as,
[tex]\rm Expected\ Value, E(x) = np[/tex]
where n is the number of trials while p represents the probability.
Now, substituting the values, we will get the expected value,
[tex]\rm Expected\ Value, E(Green\ ball) = 20 \times 0.25 = 5[/tex]
Hence, the expected value of getting a green ball out of 20 experiments with replacement is 5.
Learn more about Binomial Distribution:
https://brainly.com/question/12734585
Use reduction of order to find a second linearly independent solution
(2x+5)y′′−4(x+3)y′+4y=0,x>−52,y1=e2x
Given that exp(2x) is a solution, we assume another solution of the form
y(x) = v(x) exp(2x) = v exp(2x)
with derivatives
y' = v' exp(2x) + 2v exp(2x)
y'' = v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)
Substitute these into the equation:
(2x + 5) (v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)) - 4 (x + 3) (v' exp(2x) + 2v exp(2x)) + 4v exp(2x) = 0
Each term contains a factor of exp(2x) that can be divided out:
(2x + 5) (v'' + 4v' + 4v) - 4 (x + 3) (v' + 2v) + 4v = 0
Expanding and simplifying eliminates the v term:
(2x + 5) v'' + (4x + 8) v' = 0
Substitute w(x) = v'(x) to reduce the order of the equation, and you're left with a linear ODE:
(2x + 5) w' + (4x + 8) w = 0
w' + (4x + 8)/(2x + 5) w = 0
I'll use the integrating factor method. The IF is
µ(x) = exp( ∫ (4x + 8)/(2x + 5) dx ) = exp(2x - log|2x + 5|) = exp(2x)/(2x + 5)
Multiply through the ODE in w by µ :
µw' + µ (4x + 8)/(2x + 5) w = 0
The left side is the derivative of a product:
[µw]' = 0
Integrate both sides:
∫ [µw]' dx = ∫ 0 dx
µw = C
Replace w with v', then integrate to solve for v :
exp(2x)/(2x + 5) v' = C
v' = C (2x + 5) exp(-2x)
∫ v' dx = ∫ C (2x + 5) exp(-2x) dx
v = C₁ (x + 3) exp(-2x) + C₂
Replace v with y exp(-2x) and solve for y :
y exp(-2x) = C₁ (x + 3) exp(-2x) + C₂
y = C₁ (x + 3) + C₂ exp(2x)
It follows that the second fundamental solution is y = x + 3. (The exp(2x) here is already accounted for as the first solution.)
If four pounds of potatoes cost $6.00, how much would 10 pounds of potatoes cost.
SHOW ALL YOUR WORK!!!!!
Answer:
10 pounds of potatoes would cost $15.
Step-by-step explanation:
Set up proportion.
4/6=10/x
simplify 4/6 into 2/3,
2/3=10/x
cross product,
2*x=3*10
2x=30
x=30/2
x=15
lemme just add some to the great reply above,
[tex]\begin{array}{ccll} lbs&\$\\ \cline{1-2} 4&6\\ 10&x \end{array}\implies \cfrac{4}{10}=\cfrac{6}{x}\implies 4x = 60\implies x = \cfrac{60}{4}\implies x = 15[/tex]
16. Risa wants to order business cards. A print-
ing company determines the cost (C) to
the customer using the following function,
where b the number of boxes of cards and
n= the number of ink colors.
C= $25.60b + $14.00b(n - 1)
If Risa orders 4 boxes of cards printed in 3
colors, how much will the cards cost?
OA. $214.40
OB. $168.00
C. $144.40
OD. $102.40
Answer:
A - $214.40
Step-by-step explanation:
Since b is the number of boxes of cards and n is the number of ink colors, and we're given the number of boxes of cards, and number of ink colors, we plug in:
4= b
and
3 = n
into the given equation to solve for C.
Using the order of operations we start inside our parentheses and work from there:
C= $25.60*4 + $14.00*4(3 - 1)
C= $25.60*4 + $14.00*4(2)
C= $102.40 + $112
C= $214.40
Find the value of x in the kite below.
60°
O
x = [?]
Answer:
30
Step-by-step explanation:
The given is right triangle with angle measure 90-60 and 30 degrees as we can see on the image.
Answer the following.
(a) Find an angle between and that is coterminal with .
(b) Find an angle between and that is coterminal with . Give exact values for your answers.
I believe this is your question:
A.) find an angle between 0 degrees and 360 degrees that is coterminal with 570 degrees.
Answer:
210 degrees
Explanation:
Coterminal angles begin on the same initial side and end or terminate on the same side as an angle. Example 45 degrees and 405 degrees are coterminal angles because they both begin and end on the same side.
To find an angle between 0 and 360 that is coterminal with 570 degrees, w simply subtract 360 degrees from 570, hence:
570-360=210 degrees
570 degrees is coterminal with 210 degrees
AB is a diameter of Circle O. Find the measure of BCA
Answer:
∠ BCA = 90°
Step-by-step explanation:
∠ BCA is an angle in the semicircle and equals 90°
which statements are true for the functions g(x)=x^2 and h(x)=-x^2? Check all that apply
Answer:
if x=0 then they have same value
1 and 2 options are out
for x=-1
g(-1)=1
h(-1)=-1
3 is true
4th
FALSE
for all values except 0, g(x)>h(x)
correct ones are
g(x) > h(x) for x = -1.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Step-by-step explanation:
If 3 3/4m of cloth was used for one suit, how many suits can be made with 30m cloth
Answer:
8 suits
Step-by-step explanation:
Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then
30 ÷ 3.75 = 8
Then 8 suits can be made from 30 m of cloth
Suppose the sales (1000s of $) of a fast food restaurant are a linear function of the number of competing outlets within a 5 mile radius and the population (1000s of people) within a 1 mile radius. The regression equation quantifying this relation is (sales)
Answer:
[tex]Sales = 86.749[/tex]
Step-by-step explanation:
Given
[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]
[tex]Competitors = 4[/tex]
[tex]Population = 12000[/tex]
See comment for complete question
Required
The sales
We have:
[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]
Substitute values for competitors and population
[tex]Sales = 0.845*4 + 5.79*12 + 13.889[/tex]
[tex]Sales = 3.38 + 69.48 + 13.889[/tex]
[tex]Sales = 86.749[/tex]
What is the measure of angle b
Answer:
51 ?
Step-by-step explanation:
90-39= 51. I hope its correct
Answer:
51 degrees
Step-by-step explanation:
Well if you look at the picture angle b and the 39 degrees angle together must make a 90 degree angle
90-39 is 51 so therefor angle b must be 51 degrees
Describe how the graph of y = |x - 2| - 5 is a transformation of the graph of y = |x|. Use terms such as "shifted", "reflected", "stretched", or "compressed".
Answer:
The original graph was shifted 2 units to the left and 5 units down.
Step-by-step explanation:
y = |x|
From this, we go to: y = |x - 2|.
When we want to shift a function f(x) a units to the left, we find f(x - a). So first, the graph was shifted 2 units to the left.
y = |x - 2|.
From this, we go to: y = |x - 2| - 5.
Shifting a function f(x) down b units is the same as finding f(x) - b, so the second transformation was shifting the graph 5 units down.
Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.
Answer:
The sum is 2275
Step-by-step explanation:
Given
[tex]75,76,77....99,100[/tex]
Required
The sum
Using arithmetic progression, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where:
[tex]T_1 = 75[/tex] --- first term
[tex]T_n = 100[/tex] --- last term
[tex]n = T_n - T_1 + 1[/tex]
[tex]n = 100 - 75 + 1 = 26[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]
[tex]S_n = 13*175[/tex]
[tex]S_n = 2275[/tex]
An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the same rate of speed?
Answer:
262.5 miles
Step-by-step explanation:
Correct me if I am wrong
At what x value does the function given below have a hole?
f(x)=x+3/x2−9
Answer:
hole at x=-3
Step-by-step explanation:
The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)
The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.
So anyways we have (x+3)/(x^2-9)
= (x+3)/((x-3)(x+3))
Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.
can anyone help with this please !!!!
Answer:
"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
Step-by-step explanation:
Let be the following system of linear equations:
[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)
[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)
[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)
1) We eliminate [tex]y[/tex] by adding (1) and (2):
[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]
[tex]6\cdot x +2\cdot z = 24[/tex] (4)
2) We eliminate [tex]y[/tex] by adding (1) and (3):
[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]
[tex]9\cdot x -4\cdot z = 36[/tex] (5)
Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
. A small home business is set up with an investment of Birr 1,000,000 for equipment. The business manufactures a product at a cost of Birr 60 per unit. If the product sells for Birr 140, how many units must be sold before the business breaks even?
Answer:
12,500
Step-by-step explanation:
P = R-E
b.e.p : P=0
R=E
140x = 1000000 + 60 x
80x = 1000000
x=12,500
one strip is cut into 9 equal bars shade 1/3:of strip
hiiksbsjxbxjsoahwjsissnsks
What is the next three-term of the geometric sequence? 60, 30, 15...?
Answer:
7.5
Step-by-step explanation:
it is feometeic progression
r=0.5
if x+y=12 and xy =27,then find the value of x^2+y^2
PLEASE HELP !
Answer:
90
Step-by-step explanation:
=> x + y = 12
=> x² + y² + 2xy = 144
=> x² + y² + 2 * 27 = 144
=> x² + y² = 144 - 54
=> x² + y² = 90
Peter is 8 years younger than Alex. In 9 years time, the sum of their ages will be 76 . How old is Alex now?
Answer:
Peter is a-8 in 9 years, (a-8)+ 9+ a+ 9= 76
Answer:
P = 25
A = 33
Step-by-step explanation:
P + 8 = A
P + 9 + A + 9 = 76
P + A = 58
~~~~~~~~~~~~~~
P = 58 - A
P = 58 - P - 8
2 P = 50
P = 25
A = 33
What is the inverse of function f? f(x)=10/9+11
Answer:
Option D is answer.
Step-by-step explanation:
Hey there!
Given;
f(x) = 10/9 X + 11
Let f(X) be "y".
y = (10/9) X + 11
Interchange "X" and "y".
x = (10/9) y + 11
or, 9x = 10y + 99
or, y = (9x-99)/10
Therefore, f'(X) = (9x-99)/10.
Hope it helps!
Exercise 2.2.3: The cardinality of a power set. (a) What is the cardinality of P({1, 2, 3, 4, 5, 6})
Answer:
Cardinality of the power set of the given set = [tex]2^6=64[/tex]
Step-by-step explanation:
Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.
Example set:
{1,2,3}
All the possible subsets of this set:
{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}
The power set of the above set is written as:
P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })
Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.
Cardinality of the power set of a given set is expressed by a formula: [tex]2^n[/tex]
where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.
Hence in the given case, we have n = 6.
if TS is a midsegment of PQR find TS
Answer:
B. 7
Step-by-step explanation:
Recall: according to thee Mid-segment Theorem of a triangle, the Mid-segment of a triangle is half the length of the base of the triangle
Base length of the traingle, RQ = 14 (given)
Mid-segment = TS
Therefore,
TS = ½(RQ)
Plug in the value
TS = ½(14)
TS = 7
