Answer:
[tex] \frac{7 + 7 \sqrt{5} }{ - 4} [/tex]
Step-by-step explanation:
We would multiply the fraction by its conjugate
( A conjugate is a expression that has the same integer or number values but have different signs) for example
[tex]5x + 2[/tex]
and
[tex]5x - 2[/tex]
ARE Conjugates.
The conjugate of
[tex]1 - \sqrt{5} [/tex]
is
[tex]1 + \sqrt{5} [/tex]
So this means we will multiply the expression by 1 plus sqr root of 5 on the numerator and denominator.
Our new numerator will be
[tex]7 \times (1 + \sqrt{5} ) = 7 + 7 \sqrt{5} [/tex]
We can apply the difference of squares for the denominator.
[tex](x + y)(x - y) = x {}^{2} - {y}^{2} [/tex]
So our denominator will be
[tex]1 - 5 = - 4[/tex]
So our rationalized fraction will be
[tex] \frac{7 + 7 \sqrt{5} }{ - 4} [/tex]
-1/5y+7=7
What is the value of y?
Solve d – 0.31 ≥ 1.87 Question 1 options: A) d ≤ 2.18 B) d = 2.18 C) d ≥ 1.56 D) d ≥ 2.18
Answer:
D) d ≥ 2.18
Step-by-step explanation:
d – 0.31 ≥ 1.87
d >_ 1.87 + 0.31
d >_ 2.18
A 7% acid solution will be mixed with a 15% acid solution. 20 L of a 12% acid solution needs to be made.
a) Use the varialbes defined in part a to create a system of linear equations that models the given situation. SHOW YOUR WORK .
b) How many litres of each solution are needed? SHOW YOUR WORK *
c) Verify the solution. SHOW YOUR WORK *
Answer:
see below
Step-by-step explanation:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
.07r + .15 y = (r+y) .12
r+y = 20
y = 20-r
.07r + .15 (20-r) = (20) .12
0.07r+0.15(20-r)=2.4
.07r+ 3 - .15r = 2.4
-.08r = 2.4-3
-.08r = -.6
Divide by-.08
r =7.5 Liters of the 7%
y = 20-7.5
y = 12.5 L of 12%
Check
.07 *7.5 + .15 (12.5) =20*.12
.525+1.875=2.4
2.4=2.4
Find the center and radius of the circle (x + 1)^2 + y^2 = 4
Answer:
(-1,0) r=2
Step-by-step explanation:
the equation of a circle can be written as (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
Of the travelers arriving at a small airport, 60% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 50% are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.
What is the probability that the person
a. is traveling on business?
b. is traveling for business on a privately owned plane?
c. arrived on a privately owned plane, given that the person is traveling for business reasons?
d. is traveling on business, given that the person is flying on a commercially owned plane?
Answer:
a) 0.55 = 55% probability that the person is traveling on business
b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.
c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
50% of 60%(major airlines)
70% of 20%(privately owned airplanes)
80% of 100 - (60+20) = 20%(comercially owned airplanes). So
[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]
0.55 = 55% probability that the person is traveling on business.
Question b:
70% of 20%, so:
[tex]p = 0.7*0.2 = 0.14[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
Question c:
Event A: Traveling for business reasons.
Event B: Privately owned plane.
0.55 = 55% probability that the person is traveling on business.
This means that [tex]P(A) = 0.55[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
This means that [tex]P(A \cap B) = 0.14[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]
0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
Question d:
Event A: Commercially owned plane.
Event B: Business
80% of those arriving on other commercially owned planes are traveling for business reasons.
This means that:
[tex]P(B|A) = 0.2[/tex]
0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
Simplify the expression.
Please add an explanation if you understand how to do this.
Answer:
2x^31
Step-by-step explanation:
~Simplify the expression
2x^29/x^-2
~Apply quotient rule [ a^b/a^c = a^b-c ]
2x^31
Best of Luck~
Answer:
2x³¹Step-by-step explanation:
(x¹⁶ + x⁴x¹²)x⁹x⁴/x⁻² =(x¹⁶ + x¹⁶)x¹³x² = 2x¹⁶x¹⁵ =2x³¹Used identities:
nᵃnᵇ = nᵃ⁺ᵇ1/n⁻ᵃ = nᵃWhat fraction is equivalent to 0.46464646...
A)
46∕999
B)
46∕99
C)
23∕50
D)
46∕100
Answer:
Hello,
answer is B
Step-by-step explanation:
[tex]0.\overline{46}=\dfrac{46}{99}[/tex]
The answer is a fraction with numerator is the period (46) and the denominator is a number made with 9 as longer that there are digits in the periode (here 2 digits ==> 99)
The sides of a triangle are in the ratio of 4:5:7 and its perimeter is 64. Find its sides
Answer:
16,20,28
Step-by-step explanation:
64 /(4+5+7)
64/16= 4
sides of triangle=4×4 :5×4: 7×4
=16:20:28
Which of these statements is NOT true regarding a randomized block design experiment?
a.)
This design has an advantage of controlling for variables that might confound the response.
b.)
The elements are randomly allocated to treatment and control groups.
c.)
The sample is divided into participants or subjects and then grouped by a variable of interest.
d.)
Elements are randomly selected from equal-sized blocks of the total population.
The correct answer is D. Elements are randomly selected from equal-sized blocks of the total population is NOT true regarding a randomized block design experiment
From the question we are told that one statement is NOT true regarding a randomized block design experiment.
Where
A) This design has an advantage of controlling for variables that might confound the response is TRUEB)The elements are randomly allocated to treatment and control groups is TRUEC)The sample is divided into participants or subjects and then grouped by a variable of interest is TRUED) Elements are randomly selected from equal-sized blocks of the total population is Not True
In conclusion
The all other Options are true except option D which states that Elements are randomly selected from equal-sized blocks of the total population.
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On a recent trip to the convenience Store you picked up 4 gallons of milk 4 bottles of water and 5 snack size bags of chips your total was $28.35 if a bottle of water cost twice as much as a bag of chips and a gallon of milk cost $2.10 more than a bottle of water how much does each item cost
Answer:
The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each
Step-by-step explanation:
I think Im right
A random sample of bolts is taken from inventory, and their lengths are measured. The average length in the sample is 5.3 inches with a standard deviation of .2 inches. The sample size was 50. The point estimate for the mean length of all bolts in inventory is
Answer:
[tex]L_x=5.3 inches[/tex]
Step-by-step explanation:
Average length [tex]\=x =5.3 inches[/tex]
Standard deviation [tex]\sigma=0.2 inches[/tex]
Sample size [tex]n=50[/tex]
Generally The point estimate for the mean length of all bolts in inventory is
[tex]L_x= \=x[/tex]
[tex]L_x=5.3 inches[/tex]
Write an equation that expresses the following relationship.
w varies directly with u and inversely with the square of d
In your equation, use k as the constant of proportionality.
Answer:
w = [tex]\frac{ku}{d^{2} }[/tex]
Step-by-step explanation:
An equation that expresses the given relationship is ud²=1.
Given that, w varies directly with u and inversely with the square of d.
We need to write an equation that expresses the following relationship.
What is directly and inversely varies?Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant.
Now, w∝u⇒w=ku
and w∝1/d²⇒w=k/d²
⇒wd²=k
⇒w=wd²u
⇒ud²=1
Therefore, an equation that expresses the given relationship is ud²=1.
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What is the difference of the rational expressions below?
Answer:
B
Step-by-step explanation:
(3x+1)/x² - 5x
we can only simplify this by bringing both terms to the same denominator : x²
to achieve this we need to multiply 5/x by x/x (remember, to keep the value of a term unchanged, we need to multiply numerator and denominator with the same values).
so, we get
(3x+1)/x² - 5x/x² = (3x+1-5x)/x² = (-2x+1)/x²
therefore, B is correct
Read the following scenario, which is represented by a polynomial expression. Then answer the questions to interpret the parts of the expression in terms of the given context.
The volunteers at a high school football team’s concession stand are trying to decide on the price of the hot dogs they are selling. When they charge $2 for a hot dog, they sell an average of 70 hot dogs per game. With every $1 increase in the price, the number of hot dogs sold per game decreases by 8.
The volunteers can calculate the revenue earned from selling the hot dogs at each game using the expression -8x2 + 54x + 140, where x is the number of $1 increases in price.
Part A
What is the constant term in the polynomial expression, and what does it represent?
Answer:
x is the number of $1 increase in the price.
If there is no increase, then the total money earned is
2 × 70 = 140
If there is $1 increase, then the total money earned is
(2 + 1) × [70 - 8(1)]
If there is $2 increase, then the total money earned is
(2 + 2) × [70 - 8(2)]
If we continue the pattern, for x times $1 increase, total money earned is
(2 + x)(70 - 8x) = -8x^{2} +54x+140−8x2+54x+140
If we substitute x = 0 in the above equation, we will get
the total money earned = $140.
It means if there is no increase, then the total money earned = 140.
Hence, 140 is the constant term and it represents that there is no increase in price.
Help pls and thank you
Answer pleaseeeeeeee
Answer:
17x^2-9x-9 -->B
Step-by-step explanation:
7x^2 -12x +3 +10x^2+3x-12
Hey guys not good at math please help
Answer:
3/2
Step-by-step explanation:
Recall that slope is y2 - y1 / x2 - x1.
Excellent. The question provides us with two points: (2,4) and (0,1). We can insert these two points into our equation.
Slope = (4 - 1) / (2 - 0) = 3 / 2.
Hope this helps!
Answer:
3/2
Step-by-step explanation:
(0,1) and (2,4)
(y2-y1)/(x2-x1)
= (4-1)/(2-0)
=3/2
Answered by GAUTHMATH
4 trillion = 4x 10million missing exponent
Answer:
3
Step-by-step explanation:
im pretty sure
solve the following ineuality -1+6(-1-3x) >-39-2x
Step-by-step explanation:
(=) 5 (-1-3x) >-39-2x
(=) -5-15x > -39-2x
(=) -13x > -34
=> x < 34/13
please help me out with this
Answer:
5<x<29
Step-by-step explanation:
One theorem tells us that if a triangle has two congruent sides and one of the included angle is bigger than the other, the triangle with the included angle that is bigger. has a bigger side than the other.
This is the opposite in this case. The triangles share two sides and we know that the triangle with the side length 18 has a bigger angle than the triangle with the side length 15. So this means that
[tex]48 > 2x - 10[/tex]
Let find the range of x values.
An angle cannot be negative or zero so this means that
[tex]2x - 10 > 0[/tex]
Solve for x.
[tex]2x > 10[/tex]
[tex]x > 5[/tex]
The angle cannot be bigger than 48 so
[tex]48 > 2x - 10[/tex]
Solve for x.
[tex]58 > 2x[/tex]
[tex]29 > x[/tex]
So x must be greater than 5 but less than 29.
Find the slope of the line containing the points (5, 3) and (-7, 2).
find the derivative of e power ax divide by log bx
Answer:
Step-by-step explanation:
A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)
Answer:
The answer is "-3.04"
Step-by-step explanation:
[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]
Sample distribution:
[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]
[tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]
can someone help me with this and show me how to do it?
9514 1404 393
Answer:
5i) f(x) = 3·13^x +5
5ii) f(x) = -6·(1/2)^x +5
6) f(x) = 3·8^x -1
9a) (1, 0), (0, -3)
9b) (2, 0), (0, 8)
Step-by-step explanation:
5. The horizontal asymptote is y = c. To meet the requirements of the problem, you must choose c=5 and any other (non-zero) numbers for 'a' and 'b'. (You probably want 'b' to be positive, so as to avoid complex numbers.)
i) f(x) = 3·13^x +5
ii) f(x) = -6·(1/2)^x +5
__
6. You already know c=-1, so put x=0 in the equation and solve for 'a'. As in problem 5, 'b' can be any positive value.
f(0) = 2 = a·b^0 -1
3 = a
One possible function is ...
f(x) = 3·8^x -1
__
9. The x-intercept is the value of x that makes y=0. We can solve for the general case:
0 = a·b^x +c
-c = a·b^x
-c/a = b^x
Taking logarithms, we have ...
log(-c/a) = x·log(b)
[tex]\displaystyle x=\frac{\log\left(-\dfrac{c}{a}\right)}{\log(b)}=\log_b\left(-\dfrac{c}{a}\right)[/tex]
Of course, the y-intercept is (a+c), since the b-factor is 1 when x=0.
a) x-intercept: log2(6/3) = log2(2) = 1, or point (1, 0)
y-intercept: 3-6 = -3, or point (0, -3)
b) x-intercept: log3(9/1) = log3(3^2) = 2, or point (2, 0)
y-intercept: -1 +9 = 8, or point (0, 8)
_____
Additional comment
It is nice to be comfortable with logarithms. It can be helpful to remember that a logarithm is an exponent. Even so, you can solve the x-intercepts of problem 9 using the expression we had just before taking logarithms.
a) 6/3 = 2^x ⇒ 2^1 = 2^x ⇒ x=1
b) -9/-1 = 3^x ⇒ 3^2 = 3^x ⇒ x=2
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. Area of larger triangle = 165 ft^2 Thank you!!
9514 1404 393
Answer:
73 ft²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)
smaller area = 73 1/3 ft² ≈ 73 ft²
Answer:
Area of the smaller triangle = 73 square feet
Step-by-step explanation:
Area of the larger triangle = 165 square feet
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]
[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]
Height = 22 ft
Since, both the triangles are similar.
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
Let the height of smaller triangle = h ft
Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]
h = [tex]\frac{22\times 10}{15}[/tex]
h = 14.67 ft
Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]
= 73.33
≈ 73 square feet
Power Function:
Analyze and model the power function: Exercise 1
(Correctly identify the function and later use it to answer the questions asked, including the development and the answer)
Answer:
The function is:
f(x) = axⁿAccording to data in the table we have:
f(1) = 3 ⇒ a(1)ⁿ = 3 ⇒ a*1 = 3 ⇒ a = 3f(2) = 12 ⇒ 3*2ⁿ = 12 ⇒ 2ⁿ = 4 ⇒ n = 2Since we found the values of a and n, the function becomes:
f(x) = 3x²The number of infected to the tenth day:
f(10) = 3*10² = 300Choose the number that belongs to the set described
Answer:
Natural numbers,integers, rational numbers, irrational numbers.
Compare –3.5 and . Use <, >, or =.
–3.5 >
–3.5 <
–3.5 =
Answer:
-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5Step-by-step explanation:
Give any integer that suits the expression:-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5• The farther a negative integer from 0, the smaller its value.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Solve four and two fifths plus two and two thirds
PLEASE HELP ASAP, I WILL GIVE BRAINLIEST!
9. What is another name for BD?
10. What is another name for AC?
11. What is another name for ray AÉ?
12. Name all rays with endpoint E.
13. Name two pairs of opposite rays.
14. Name one pair of rays that are not opposite rays.
Answer:
#9. Segment DB
#10 Segment CA
#11. Ray EA
#12. Ray EB, Ray EC, Ray ED, Ray EA
#13 Ray EA & Ray EC
#14. Ray EB and Ray EC
Step-by-step explanation:
For future reference, if you are asked to give another name for a segment, just flip the letters around (same for rays.).
Opposite Rays are rays that share 1 common endpoint, but extend in opposite directions ( together they make a 180 degree angle). Ray EB & EC share an endpoint, but they do not extend in opposite directions.
Hope this helps!
