[tex]2(2x + 4) + 2(x - 7) = 78[/tex]
[tex]4x + 8 + 2x - 14 = 78[/tex]
[tex](4x + 2x) + (8 - 14) = 78[/tex]
[tex]6x - 6 = 78[/tex]
[tex]6x = 78 + 6[/tex]
[tex]6x = 84[/tex]
[tex]x = \frac{84}{6} [/tex]
[tex]x = 14[/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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Translate sentence into inequality
A number c increased by 8 is greater than 30.
Step-by-step explanation:
the inequality is
[tex]c + 8 > 30[/tex]
I'm having an issue with a perpendicular line equation
Answer:
Step-by-step explanation:
y = [tex]\frac{5}{6}[/tex] x - 12
m = [tex]\frac{5}{6}[/tex]
( - 1, 2 )
y - 2 = [tex]\frac{5}{6}[/tex] ( x - ( - 1 ))
Equation of the ║ line is y = [tex]\frac{5}{6}[/tex] x + [tex]\frac{17}{6}[/tex]
Slope of the perpendicular line is ( - [tex]\frac{6}{5}[/tex] )
y - 2 = - [tex]\frac{6}{5}[/tex] ( x - ( - 1 ))
Equation of the ⊥ line is y = - [tex]\frac{6}{5}[/tex] x + [tex]\frac{4}{5}[/tex]
A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 28 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has the following gas mileages. (Round your answers to four decimal places.) (a) less than 26 mpg (b) greater than 34 mpg (c) between 22 and 34 mpg
Answer:
Step-by-step explanation:
We are finding the probability, which is a percentage, of each of these intervals on our standard bell curve. In order to find this percentage, we need to find the z-score that provides this percentage. To find the z-score:
[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex] which is the number in question minus the mean, all divided by the standard deviation. We're first looking for the probability that the gas mileage on a certain model of car is less than 26 mpg.
To find this z-score:
[tex]z=\frac{26-28}{4}=-.5[/tex] Depending upon which table you look at for the z-score determines how you will find it. The z-score that measure from the value and to the left of it is what we need. This decimal is .3085375, or 30.8538%.
Onto b., which is for the percentage of cars that have gas mileage over 34 mpg. Find the z-score, and this time, we look to the right of the value for the percentage:
[tex]z=\frac{34-28}{4}=1.5[/tex] and to the right of 1.5 standard deviations we will find .0668072, or 6.68072%
Then finally c., which wants the probability that the gas mileage on one of these cars is greater than 22 but less than 34 mpg. To do this we have to find the z-scores of each and then do some subtracting. First the z-scores:
[tex]z=\frac{22-28}{4}=-1.5[/tex] The percentage of data that lies to the right of that z-score is .9331927
The z-score for the other value, 34, was already found as 1.5, having .0668072 of the data to the right of that z-score. We subtract the smaller from the larger to determine what's left in-between:
.9331972 - .0668072 = .86639, or as a percentage, 86.639% of the cars fall into this interval for gas mileage.
What is the measure
Pls help i will give brainliest
Picture included
The distance from the plane to the building __ meters
Answer:
1200 ×90÷8 is not correct ans
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
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 = nᵃ-1/5y+7=7
What is the value of y?
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
HELP PLEASE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please?
Answer:
46%
Step-by-step explanation:
Divde the smaller # by the bigger # to get the precentage
An average San Francisco customer uses what percent of electricity used by an average Houston customer?
In other words, San Francisco is what part of Houston?
---Just like, 7 is what part of 49? These are the same questions and would be solved in the same way
San Francisco / Houston
6753 / 14542
0.4644 = 46.44%
ANSWER: 46%
Hope this helps!
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
A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius.
Each of the central angles has a measure of 40°. How many sides does the polygon have?
THE
9
Answer: 90 sides
Step-by-step explanation:
Let's say the circle has a center at A and B and C are at the vertices of a polygon. Since this figure is inscribed in a circle, we can draw two radii through the vertices. Because all radii are congruent, we know segment BA is congruent to Segment CA. If a triangle has at least 2 congruent sides, we can identify the triangle as an isosceles triangle. With this we can conclude <ACB is congruent to <ABC. By the definition of congruent angles, m<ACB = M<ABC. Let's say m<ACB = x. By the Triangle Sum Theorem, 40 + x + m<ABC = 180. By substitution, 40 + x + x = 180. When we solve we get x =70. Since radii bisect interior angles we know that each interior angle of this polygon is 140 degrees. If we plug in 140 to our equation, [tex]\frac{(n-2)180}{n}[/tex] where n is the number of sides, we get n = 90. So we can conclude this polygon has 90 sides
how do I do this?????????????????????????????
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
Divide p(x)=x^3-4x^2+x+6 by (x-3). Find the remainder and the quotient.
Answer:
Quotient is x² - x - 2
Remainder is 0
3a + 2b = 9
and
8x + y = 60
(i) What is the value of 9a + 6b?
(ii) What is the value of 4x + 3y?
Answer:
i dont kbow lol gggggggggg
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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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]
A line is perpendicular to the line y = 4x - 3 and has x-intercept (2,0). Which of the following is an equation of the line?
Answer:
y = -1/4x+1/2
Step-by-step explanation:
y = 4x - 3
This is in slope intercept form, y = mx+b where the slope is m
The slope is 4
Perpendicular lines have slopes that are negative reciprocals
-1/4 is the slope of the perpendicular line
y = -1/4x+b
Using the point (2,0)
0 = -1/4(2)+b
0 = -1/2+b
b = 1/2
y = -1/4x+1/2
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
What is the distance between the following points?
y
+
+++ 3
1 2 3 4 5 6 7 8 9
.
-27
-3+
-4
-5+
-6
-7
-8
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
Answer:
8.49 or 6√2
Step-by-step explanation:
Use the distance formula to calculate the distance between the two points. The distance formula is √(x1-x2)^2+(y1-y2)^2 plug in (2,-3) and (8,-9) to get the solution of √72 or 8.49
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
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
2/5 + 1/10= In simplest form
A. 3/15
B. 5/10
C. 1/4
D. 1/2
Answer:
1/2
Step-by-step explanation:
2/5 + 1/10
Get a common denominator of 10
2/5 * 2/2 + 1/10
4/10 + 1/10
5/10
simplify
Divide the top and bottom by 5
1/2
Answer:
[tex] \frac{1}{2} [/tex]
Answer D is correctStep-by-step explanation:
[tex] \frac{2}{5} + \frac{1}{10} \\ \frac{2 \times 2}{5 \times 2} + \frac{1}{10} \\ \frac{4}{10} + \frac{1}{10} \\ \frac{5}{10} \\ \frac{5 \div 5}{10 \div 5} \\ = \frac{1}{2} [/tex]
Ram and his sister Kalpana win a prize of Rs 2000. They decide to share the prize in the ratio of their ages. Ram is 15 years old and Kalpana is 10 years old. How much do each of them receive
9514 1404 393
Answer:
Ram -- ₹1200Kalpana -- ₹800Step-by-step explanation:
Their age total is 15+10=25, so Ram will get 15/25 = 0.6 of the total. Kalpana will get the remaining 0.4 of the total.
Ram receives 0.6 × ₹2000 = ₹1200
Kalpana receives 0.4 × ₹2000 = ₹800
tính công thức Taylo đến x^13
Answer:
أنت مجنون ، هل تعرف ذلك؟
Step-by-step explanation:
بنسلفانيا
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 = 300Ray’s weight increased by 11% in the last two years. If he gained 16.5 pounds, what was his weight two years ago?
Answer:
Ray weighed 150 pounds two years ago.
Step-by-step explanation:
11/100 = 16.5/x
11x = 16.5(100)
11x = 1,650
(11x)/11 = (1,650)/11
x = 150
About time that he should start going to the gym!
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.
