Answer:
D
Step-by-step explanation:
one yard is 3 feet
100x3=300
Create a table to represent the function y=1/3x+4
Answer:
this is a linear equation. whatever value you set for x, you substitute and make a table that would probably look like this.
x | y
-------------|-----------
5 | 17/3 <------- what would y be if x is 5?
3 | 5 lets substitute x with 5
| y=1/3*5+4
| y=5/3+4
| y=17/3
Mona wants to buy carpet for a floor in her house.
The floor is rectangular with a width of 8 m and a length of 9 m.
Two shops sell carpet with the prices shown below.
How much will Mona save by going to Carpet World ?
which of these tables represents a function
Answer: choice D
Step-by-step explanation:
In order for something to be a function for every x input there must be exactly 1 y output. This means that if x is a number then y must always be 1 number and that 1 number only.
Use mathematical induction to prove the following statement:
The sum of the first n even positive integers is (n2 + n). That is, 2 4 6 8 .... 2n
Answer:
Step-by-step explanation:
To prove that the sum of the first n even +ve integers is:
[tex]\mathsf{2+4+6+8+ . . . +2n = n^2+ n }[/tex]
By using mathematical induction;
For n = 1, we get:
2n = 2 × 1 = 2
2 = 1² + 1 ----- (1)
∴ the outcome is true if n = 1
However, let assume that the result is also true for n = k
Now, [tex]\mathsf{2+4+6+8+. . .+2k = k^2 + k --- (2)}[/tex]
[tex]\mathsf{2+4+6+8+. . .+2k+2(k+1)}[/tex]
we can now say:
[tex]\mathsf{= (k^2 + k) + 2(k + 1)} \\ \\ \mathsf{= k^2 + k + 2k + 1}[/tex]
[tex]\mathsf{= (k^2 + 2k + 1) + (k + 1)}[/tex]
[tex]\mathsf{= (k + 1)^2 + (k + 1)}[/tex]
∴
[tex]\mathsf{2 + 4 + 6 + 8 + . . . + 2k + 2(k + 1) = (k + 1)^2 + (k + 1)}[/tex]
Thus, the result is true for n = m+1, hence we can posit that the result is also true for each value of n.
As such [tex]\mathsf{2+4+6+8+. . .+2n = n^2 + n }[/tex]
Graph (x-4)^2/4 + y^2/9 = 1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Compare the equation to that of an ellipse with center (h, k) and axes of lengths 2a and 2b.
((x -h)/a)^2 +((y -k)/b)^2 = 1
We see that (h, k) = (4, 0) and a=2, b=3.
This tells us the center of the ellipse is (4, 0), the major axis is parallel to the y-axis, and the minor axis is parallel to the x-axis. The ellipse extends ±2 units from its center in the x-direction and ±3 units from its center in the y-direction.
Answer:
It is graph C on edge.
Step-by-step explanation:
wHAT IS THE REFERENCE ANGLE -935°
If 80 persons can perform a piece of work in 16 days of 10 hours each, how
many men will perform a piece of work twice as great in tenth part of the time
working 8 hours a day supposing that three of the second set can do as much
work as four of the first set?
Answer:
The number of men needed to perform a piece of work twice as great in tenth part of the time working 8 hours a day supposing that three of the second set can do as much work as four of the first set is:
1200 men.Step-by-step explanation:
To find the answer, first, we're gonna find how many hours take to make the piece of work in 16 days, taking into account each day just has 10 hours:
Number of hours to make a piece of work = 16 * 10 hoursNumber of hours to make a piece of work = 160 hours.Now, we divide the total hours among the number of persons:
Equivalence of hours per person = 160 hours / 80 persons.Equivalence of hours per person = 2 hours /personThis equivalence isn't the real work of each person, we only need this value to make the next calculations. Now, we have a piece of work twice as great as the first, then, we can calculate the hours the piece of work needs to perform it (twice!):
Number of hours to make the second piece of work = 160 hours * 2Number of hours to make the second piece of work = 320 hoursWe need to make this work in tenth part of the time working 8 hours a day, it means:
Time used to the second work = 320 hours / 10Time used to the second work = 32 hours Time used to the second work = 32 hours / 8 hours (as each day has 8 hours)Time used to the second work = 4 daysNow, we know three of the second set can do as much work as four of the first set, taking into account the calculated equivalence, we have:
Work of four workers of first set = Work of three workers of second setWork of four workers of first set = Equivalence * 4 persons.Work of four workers of first set = 2 hours /person * 4 personsWork of four workers of first set = 8 hours.So, three persons of the second set can make a equivalence of 8 hours. At last, we calculate all the number of workers we need in a regular time:
Number of needed workers in a regular time = (320 hours / 8 hours) * 3 persons.Number of needed workers in a regular time = 40 * 3 personsNumber of needed workers in a regular time = 120 personsRemember we need to perform the job not in a regular time, we need to perform it in tenth part of the time, by this reason, we need 10 times the number of people:
Number of needed workers in tenth part of the time = 120 persons * 10Number of needed workers in tenth part of the time = 1200 personsWith this calculations, you can find the number of men needed to perform a piece of work twice as great in tenth part of the time working 8 hours a day supposing that three of the second set can do as much work as four of the first set is 1200 persons.
can you find the limits of this
Answer:
[tex]\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{-3}{8}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Constant]: [tex]\displaystyle \lim_{x \to c} b = b[/tex]
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
L'Hopital's Rule
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
We are given the following limit:
[tex]\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16}[/tex]
Let's substitute in x = -2 using the limit rule:
[tex]\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{(-2)^3 + 8}{(-2)^4 - 16}[/tex]
Evaluating this, we arrive at an indeterminate form:
[tex]\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{0}{0}[/tex]
Since we have an indeterminate form, let's use L'Hopital's Rule. Differentiate both the numerator and denominator respectively:
[tex]\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \lim_{x \to -2} \frac{3x^2}{4x^3}[/tex]
Substitute in x = -2 using the limit rule:
[tex]\displaystyle \lim_{x \to -2} \frac{3x^2}{4x^3} = \frac{3(-2)^2}{4(-2)^3}[/tex]
Evaluating this, we get:
[tex]\displaystyle \lim_{x \to -2} \frac{3x^2}{4x^3} = \frac{-3}{8}[/tex]
And we have our answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Question 7 of 21
Which of the following expressions is equivalent to the one shown below?
(-5. 43
A. –158.12
B. (-5)9.4
C.-15.12
D. -8.7
SUBMIT
Answer:
C-15.12. That is the most suitable answer
There are 90 girls in fourth form 25 of whom study biology what percentage of fourth form girl study biology?
Csikszentmihalyi & Figurski (1982) conducted a study to determine the degree to which people find out about themselves through the process of introspection (thinking about themselves). They gave people beepers and asked them to write down what they were thinking about when the beepers went off randomly throughout the day. The results indicated that:
Answer:
We think about ourselves way less than we think 8% of the time.
Step-by-step explanation:
In a self-awareness: introspection research study conducted by Mihaly Csikszentmihalyi and Thomas Figurski in 1982, to determine the degree to which people find out about themselves through the process of introspection (thinking about themselves).
The research involved an arrangement where participants were given beepers and asked to write down what they were thinking about when the beepers went off randomly throughout the day. The results indicated that "We think about ourselves way less than we think 8% of the time."
Cells use the hydrolysis of adenosine triphosphate, abbreviated as ATP, as a source of energy. Symbolically, this reaction can be written asATP(aq)+H2O(l)⟶ADP(aq)+H2PO−4 (aq)where ADP represents adenosine diphosphate. For this reaction, ΔG∘=−30.5kJ/mol.a. Calculate K at 25∘C .b. If all the free energy from the metabolism of glucoseC6H12O6(s)+6O2(g)⟶6CO2(g)+6H2O(l)goes into forming ATP from ADP, how many ATP molecules can be produced for every molecule of glucose?
Answer:
Step-by-step explanation:
From the given information:
ΔG° = -30.5 kJ/mol
By applying the following equation to calculate the value of K.
ΔG° =-RT㏑K
making ㏑ K the subject of the formula:
[tex]\mathtt{ In \ K} = \dfrac{\Delta G^0}{-RT}[/tex]
where;
Temperature at 25° C = (25 + 273)K
= 298K
R = 8.3145 J/mol.K (gas cosntant)
[tex]\mathtt{ In \ K} = \dfrac{-30.5 \times 10^{3}\ J /mol} {-(8.3145 \ J/mol. K \times 298 \ K}[/tex]
[tex]\mathtt{ In \ K} = \dfrac{-30.5 \times 10^{3}\ J /mol} {-2477.721 J/mol }[/tex]
㏑K = 12.309
[tex]K = e^{12.309}[/tex]
K = 221682.17
K = 2.22 × 10⁵
b) The reaction for the metabolism of glucose is given as:
[tex]C_6H_{12} O_6 + 6O_{2(g)} \to + 6CO_{2(g)} + 6H_2O_{(l)}[/tex]
From the above expression, let calculate the Gibbs free energy by using the formula:
[tex]\Delta G^0_{rx n }= \Delta G^0_{product}- \Delta G^0_{reactant}[/tex]
[tex]\Delta G^0_{rx n }= [6 \times \Delta G^0_{f}(CO_2) + 6 \times \Delta G^0_{f}(H_2O)] - [1 \times \Delta G^0_{f}(C_6H_{12}O_6) + 6 \times \Delta G^0_{f}(O_2)][/tex]
At standard conditions;
The values of corresponding compounds are substituted into the equation above:
Thus,
[tex]\Delta G^0_{rx n }= [6 \times (-394) + 6 \times (-237)] - [1 \times (-911) + 6 \times (0)] \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= [-2364-1422] - [-911+0] \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -3786 +911 \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -2875 \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -2875000 \ J/mol[/tex]
Now, the no of ATP molecules generated = [tex]\dfrac{\Delta G^0 \text{of metabolism for glucose}}{\Delta G^0 \text{of hydrolysis for ATP}}[/tex]
= (-2875000 J/mol ) / -30500 J/mol
= 94.26
≅ 94 ATP molecules generated
Is w = 8 a solution to the equation 5 + w = 58? Explain
No.
Since w = 8, you must replace the variable with the number associated to it.
So, it would be 5 + 8 = 58
5 + 8 is not equal to 58, it is equal to 13.
If you wanted to find out what w was, simply subtract 5 on both sides.
w = 58 - 5
Find the area of the circle. Round your answer to the nearest tenth.
Answer:
254.47 mm
Step-by-step explanation:
Nevaeh is going to drive from her house to City A without stopping. Let DD represent Nevaeh's distance from City A tt hours after leaving her house. The table below has select values showing the linear relationship between tt and D.D. Determine the distance from Nevaeh's house to City A, in miles.
t d
1 195
2 130
2.5 97.5
Answer:
Step-by-step explanation:
Answer:
260
Step-by-step explanation:
What is the answer for this question?
Answer:
The answer is A 1 4/5
Work:
7 1/5- 6 2/5
turn 7 1/5 into 6 6/5 and now subtract the two fractions
6/5-2/5= 4/5
now subtract the whole numbers:
6-6=1
So, your answer should be 4/5 (A)
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 175, 125, 180, 220, 240, and 245. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 99% confidence interval for the average number of customers served on weekdays.
Answer:
(121.576 ; 273.424)
Step-by-step explanation:
Given the data:
175, 125, 180, 220, 240, 245
We can calculate the mean and standard deviation
Mean = Σx/ n = 1185 / 6 = 197.5
Standard deviation = 46.125 (calculator)
The confidence interval :
Mean ± margin of error
Margin of Error = Tcritical * s/sqrt(n)
Tcritical at 99%, df = n - 1 ; 6 - 1 = 5
Tcritical = 4.032
Margin of Error = 4.032 * 46.125/√6
Margin of error = 75.924
Confidence interval :
197.5 ± 75.924
Lower boundary = 197.5 - 75.924 = 121.576
Upper boundary = 197.5 + 75.924 = 273.424
(121.576 ; 273.424)
Classify the quadrilateral.
Answer:
Trapezoid
Step-by-step explanation:
It has two opposite parallel lines and the other two are not parallel
You damage your car and it will cost $7,200 to repair. You have a $1,000 deductible. How much will the insurance company pay?
Answer:
Amount paid by insurance company = $6,200
Step-by-step explanation:
Given:
Total cost of car damage = $7,200
Amount deductible = $1,000
Find:
Amount paid by insurance company for total damage
Computation:
Amount paid by insurance company = Total cost of car damage - Amount deductible
Amount paid by insurance company = $7,200 - $1,000
Amount paid by insurance company for total damage = $6,200
What is the measure of n?
Answer:
n = √108 or 6√3
Step-by-step explanation:
n is the altitude of the right triangle
Based on the right triangle altitude theorem, we would have:
h = √(xy)
Where,
h = n
x = 18
y = 6
Substitute
n = √(18*6)
n = √108
Or
n = 6√3
Find the volume of the prism.
The volume of the prism is (B) 864 mm3
Circle the answer choice below that does not equal the following:
– 80/10
1) - 8
2) 80/-10
3) - (80/10)
4) 8
Answer: 4) 8
Step-by-step explanation:
-80/10=-8
-8 = - 8. - No
80/-10= - 8. - 8=-8 - No
-(80/10)=-(8)=-8. - 8=-8 - No
8 - Yes.
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer: yes yes no yes yes no
Step-by-step explanation:
14+6×(9-6)
please answer
Answer:
32
Step-by-step explanation:
14+6(9-6)
[9-6=3]
14+6x3
[6x3=18]
14+18
32
---
hope it helps
Answer:
14+6×(9-6)=32
Find the value of x in the given figure
Answer:
20 degrees
Step-by-step explanation:
Angles on a line equal 180 degrees.
180–140=40
40=2x
x=20
20 degrees
What is the area??!??
Answer:
142.7 m²
Step-by-step explanation:
but sure, what you know about triangles and trigonometry (simplified, the relationship of angles and sides of shapes based on circles enclosing them)
so, here a quick summary of important facts and angle/side relationships in triangles :
the sum of all angles in a triangle is always and for every triangle 180 degrees.
sin(angle) is vertically up or down from the horizontal diameter of the encircling circle to the point on the circle hit by a line from the center of the circle with the described angle from the horizontal diameter.
cos(angle) is horizontally left or right from the center of the encircling circle to the point, where the sine-line hits the horizontal diameter.
the sides are named in relation to their opposing corners and their angles. so, for example, side a is opposing the corner point A and the angle at this point (also called A).
here it is also important to know :
a/sin(A) = b/sin(B) = c/sin(C)
and the area of a general triangle is
area = 1/2 × b × c × sin(A) or
1/2 × a × c × sin(B) or
1/2 × a × b × sin(C)
so, if we want to use the first option, we need to calculate b first. for this we use
b/sin(B) = c/sin(C)
b = (c × sin(B)) / sin(C)
for this we need to calculate C first. and we use
A + B + C = 180
C = 180 - A - B = 180 - 54.3 - 30.4 = 95.3 degrees
=>
b = (26.3 × sin(30.4)) / sin(95.3) = 13.36583...
=> area = 1/2 × 13.36583... × 26.3 × sin(54.3) = 142.7324...
= 142.7 (rounded)
Some help figuring out the answer?? Also explain a little how you got there
9514 1404 393
Answer:
x = 10·cos(θ) -4·cot(θ)
Step-by-step explanation:
Apparently, we are to assume that the horizontal lines are parallel to each other.
The relevant trig relations are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
If the junction point in the middle of AB is labeled X, then we have ...
sin(θ) = 4/BX ⇒ BX = 4/sin(θ)
cos(θ) = x/XA ⇒ XA = x/cos(θ)
Then ...
BX +XA = AB = 10
Substituting for BX and XA using the above relations, we get
4/sin(θ) +x/cos(θ) = 10
Solving for x gives ...
x = (10 -4/sin(θ))·cos(θ)
x = 10·cos(θ) -4·cot(θ) . . . . . simplify
_____
We used the identity ...
cot(θ) = cos(θ)/sin(θ)
bill took a nap for 1 1/4 hour on friday and then took a nap for 3/4 hour on tuesday. how much longer was Bill's nap on friday?
Which set of values could be the side lengths of a 30-60-90 triangle? A. {5, 10, 10-2} B. {5,5,12,10) O C. {5,5,5, 10) D. {5, 10, 10.5)
Answer:
The hypotenuse is twice the length of the shortest side so;
A could be the answer as when 5 is shortest and 10 is hypotenuse we get 5√3 for the other side which = 8.6
It cannot be B, C or D as the numbers cannot be 2 values same as hypotenuse (the longer length) as 5 + 5 = 10 and we cant use 4 lengths in one triangle and either of 3 out of 4 values do not show ratio of lowest side any value middle value = LV +√3 and hyp LV(2)
so A is the answer.
Step-by-step explanation:
11-11×11+11 =?????
Answer:
-99
Step-by-step explanation:
Answer:
- 99
Step-by-step explanation:
11 - 11 × 11 + 11
➛ 0 × 11 + 11
➛ - 110 + 11
➛ - 99