Answer:
The prime factors are:
a. 5 and 5 (5 × 5 = 25)
b. 2 and 19 (2 × 19 = 38)
c. 2, 2, 3, and 3 (2 × 2 × 3 × 3 = 36)
d. 3, 5, and 19 (3 × 5× 19 = 285)
e. 2, 5, 5, and 13 (2 × 5 × 5 × 13 = 650)
f. 2, 2, 3, 5, and 29 (2 × 2 × 3 × 5 × 29 = 1,740)
Step-by-step explanation:
straight from Penn
Use cavalieri's Principle to calculate the exact of an oblique cylinder with a radius of 10 meters and a height of 11 meters.
Answer: Volume of cylinder is 1152.38 m³.
Step-by-step explanation:
Since we have given that
Radius of cylinder = 10 m
Height of cylinder = 11 m
Using Cavalieri's principle , volume of an oblique cylinder is equal to volume of cone.
So, Volume of an oblique cylinder is given by
[tex]V=\frac{1}{3}\pi r^2h\\\\V=\frac{1}{3}\frac{22}{7}\times 10\times 10\times 11\\\\V=1152.38\ m^3[/tex]
Hence, Volume of cylinder is 1152.38 m³.
Lemon drops and jelly beans are mixed to make a 100 pound mix. if the lemon drops cost $1.90 per pound and jelly beans cost $1.20 per pound, how many pounds of lemon drops are need to make the mix cost $1.48 per pound. formulate an equation and then solve it to find how many pounds of lemon drops are needed. show all of your work
L = lemon drops
J = jelly beans
L +J = 100
L=100-J
1.90L + 1.20J=1.48*100
1.90(100-j) +1.20J =148
190-1.90J+1.20J=148
190-0.7J=148
-0.7J=-42
J = 60
L=100-60 = 40
40 pounds of Lemon Drops are needed
Final answer:
40 pounds of lemon drops are needed.
Explanation:
To find out how many pounds of lemon drops are needed to make a 100-pound mix that costs $1.48 per pound, we can set up a system of equations. Let L represent the number of pounds of lemon drops and J represent the number of pounds of jelly beans.
Since the total weight of the mix is 100 pounds:
L + J = 100
Given the cost of lemon drops is $1.90 per pound and jelly beans cost $1.20 per pound, and the entire mix should cost $1.48 per pound:
1.90L + 1.20J = 100 * 1.48
We already have that L + J = 100, so J can be expressed as 100 - L. Substituting J in the second equation we get:
1.90L + 1.20(100 - L) = 148
Solving for L:
1.90L + 120 - 1.20L = 148
0.70L = 28
L = 28 / 0.70
L = 40
Therefore, 40 pounds of lemon drops are needed for the mix.
what is the measure of angle 1?
straight line = 180 degrees
180-92 = 88
so angle 1 = 88 degrees
If M9=119,what is the sum of the measures 0f 11 and 16?
238
299
122
119
find the value of x if angle x measures 102°
The value of x is 13.
The problem at hand has a quadrilateral shape. The problem depicts four angles and sides, with the only known angle being X.
The graphic depicts four sides (quad), and the stick drawn in the center of each side explains the length relationship.
One stick is equal to two sticks, and two sticks are equal to one stick.
Angles Assumed:
X=102 deg
W=(7x+4) deg
Y=(5x-4) deg
Because angle X is 102 degrees, angle Z must also be 102 degrees. A quadrilateral has a total angle of 360 degrees.
So, to find x, do the following:
102 + 102 + 7x + 4 + 5x - 4 = 360
Add the constant terms: 102 + 102 + 4 - 4 = 204
Combine x terms: 7x + 5x = 12x
Substitute the combined terms:
204 + 12x = 360
Isolate x:
12x = 360 - 204
12x = 156
x = 156 / 12
Simplify:
x = 13
Therefore, the solution is x = 13.
Which statement is true the graph of y=log(x-4) is the graph of y=log(x) translated 4 units down
The true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.
Let's analyze each statement:
1. The graph of [tex]\(y - \log(x-4)\)[/tex] is the graph of [tex]\(y - \log(x)\)[/tex] translated 4 units down.
This statement is incorrect. The function [tex]\(y - \log(x-4)\)[/tex] is the result of shifting the graph of [tex]\(y = \log(x)\) 4[/tex] units to the right, not down.
2. The graph of [tex]\(y = \log(x) - 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units down.
This statement is incorrect. The function [tex]\(y = \log(x) - 4\)[/tex] represents a vertical translation of 4 units down from the graph of [tex]\(y = \log(x)\)[/tex], not left.
3. The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units up.
This statement is true. Adding a constant term to a function vertically shifts the graph of the function by that amount. So, adding 4 to [tex]\(y = \log(x)\)[/tex] shifts it 4 units up.
4. The graph of [tex]\(y = \log(x+4)\)[/tex] is the graph of [tex]\(y = \log_2(x)\)[/tex] translated 4 units right.
This statement is incorrect. The function [tex]\(y = \log(x+4)\)[/tex] represents a horizontal translation of 4 units to the left from the graph of [tex]\(y = \log(x)\).[/tex]
Therefore, the true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.
Question
Which statement is true?
The graph of Y - log(x-4) is the graph of y-log,(x) translated 4 units down.
The graph of Y = log: (x)-4 is the graph of y = log. (x) translated 4 units left.
The graph of y = log,(x)+4 is the graph of Y=log.(x) translated 4 units up.
The graph of y = log. (x+4) is the graph of y = log2 (x) translated 4 units right.
What is the simplified form of 15 x to the eighth power over 24 y to the fifth power divided by 4 x to the fourth power over 8 squared
A) 4 y cubed over 5 x to the fourth power
B) 4 y to the fourth power over 5 x cubed
C) 5 x to the fourth power over 4 y cubed
D) 5 x cubed over 4 y to the fourth power
Perform the indicated operation. 5/17 ∙ 3/8
Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k. k = _______ Graph of f of x and g of x. f of x equals 1 over 3 x minus 3 and g of x equals 1 over 3 x plus 1 Numerical Answers Expected!
Answer:
The value of k is 4.
Step-by-step explanation:
Given,
f of x equals 1 over 3 x minus 3,
[tex]\implies f(x)=\frac{1}{3}x-3[/tex]
Also, g of x equals 1 over 3 x plus 1,
[tex]\implies g(x)=\frac{1}{3}x+1[/tex]
Since, g(x) = f(x) + k,
By substituting the values,
[tex]\frac{1}{3}x+1=\frac{1}{3}x-3+k[/tex]
[tex]1=k-3[/tex]
[tex]\implies k = 1+3 = 4[/tex]
Hence, the value of k is 4.
How many window coverings are necessary to span 50 windows if each window covering is 15 windows long? 3 4 5 6?
To cover 50 windows with coverings that are 15 windows long, at least 4 window coverings are needed to span all the windows.
Explanation:The question asks how many window coverings are necessary to span 50 windows, given that each window covering is 15 windows long. To find out how many window coverings are required, you divide the total number of windows by the length of one window covering. So, we do 50 ÷ 15 which equals approximately 3.33. Since you can't have a fraction of a window covering, you'll need at least 4 full window coverings to span all 50 windows.
How to quickly convert degrees to radians?
for f(x)=5x-2 and g(x)=2x+1,find(f+g(x)
How tall is the tower ?
x = 50 * tan(60) = 50sqrt(3) =86.6 feet
tower is 93.6 feet tall
15. In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
Because C is the centroid, therefore:
Segments PZ = ZR;
RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer: PC = 20 PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer: ZC = 5 ZQ = 15
C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer: PQ = 40
A carnival game allows a group of players to each draw and keep a marble from a bag. The bag contains 5 gold marbles, 25 silver marbles, and 70 red marbles. A player wins a large prize for drawing a gold marble and a small prize for drawing a silver marble. There is no prize for drawing a red marble. At the start of the game, the probability of winning a large prize is 0.05 and the probability of winning a small prize is 0.25. Suppose that the first player draws a silver marble and wins a small prize. What is the probability that the second player will also win a small prize? If a group of four plays the game one at a time and everyone wins a small prize, which player had the greatest probability of winning a large prize? How could the game be made fair for each player? That is, how could you change the game so that each player has an equal chance of winning a prize?
It is given that:
The bag contains 5 gold marbles, 25 silver marbles, and 70 red marbles.
Ques 1)
We are asked to find the probability that the second player will also win a small prize given that the first player wins a small prize.
That is we need to find the conditional probability.
Let A denote the event that first player wins the small prize.
B denote the vent that the second player wins the small prize.
A∩B denote the event that both the player wins the small prize.
Let P denote the probability of an event.
We are asked to find:
P(B|A)
[tex]P(B|A)=\dfrac{P(B\bigcap A)}{P(A)}[/tex]
Now we know that:
[tex]P(A)=\dfrac{25}{100}[/tex]
( Since out of 100 marbles 25 are silver)
Also,
[tex]P(A\bigcap B)=\dfrac{25_C_2}{100_C_2}\\\\\\P(A\bigcap B)=\dfrac{25\times 24}{100\times 99}[/tex]
Hence,
[tex]P(B|A)=\dfrac{24}{99}[/tex]
Hence, the probability that the second player will also win a small prize is:
0.242424
Ques 2)
The probability that the first player will win a large prize is:
5/100
( But the first player draws a silver marble and wins)
The probability that the second player will win a large prize is:
5/99
( Since one marble has been taken out by the first player so the second player is left with 99 choices and here also the second player draws a silver and wins the game)
Similarly,
The probability that the third player will win a large prize is:
5/98
( Since one more marble has been taken out by the second player so the third player is left with 98 choices and here also the third player draws a silver and wins the game)
The probability that the fourth player will win a large prize is:
5/97
Hence, the greatest probability of winning a gold marble is by:
Player 4. ( Since, 5/97 is greater than the rest three probabilities)
Ques 3)
The game can be made fair for each player if all have the equal choices of drawing a marble and this can be done by replacing the marbles that have been drawn out by the previous player.
Sally Leadfoot was pulled over on her way from Syracuse to Ithaca by an officer claiming she was speeding. The speed limit is 65 mph and Sally has traveled 97 km in 102 minutes. How fast was Sally's average speed in mph? In a complete sentence, explain whether or not Sally deserves a ticket?
Answer:
35.5 mph
Step-by-step explanation:
We are given that Sally Leadfoot was pulled over on her way from Syracuse to Ithaca by an officer claiming she was speeding.
Speed limit =65 mph
Sally traveled distance 97 km in 102 minutes
We have to find the Sally's average speed in mph
Time =102 minutes
We know that 1 hour =60 minutes
[tex]102 minutes=\frac{102}{60}=1.7 [/tex]hours
We know that 1 km=0.621371
97 km=[tex]0.621371 \times 97=60.272987[/tex]miles
Average speed =[tex]\frac{60.272987}{1.7}=35.45 mph[/tex]
Average speed of Sally's =35.5 mph
Hence, average speed of Sally is less than 65 mph .Therefore, she was not fast speeding and she deserves a ticket.
Solve this inequality: 8z + 3 – 2z < 51
Consider the function given by the graph.
What are these values?
f(–2 ) =__
f(0) = __
f(4) = __
Answer:
f(-2 ) =2
f(0) = 3
f(4) = -1
Step-by-step explanation:
Clearly by looking at the graph of the given function f(x) we could observe that the function f(x) is increasing in the interval (-∞,0] and then decreasing in the interval (0,∞).
Also, the function is discontinuous at x=0.
( Since, there is a break in a graph and also the left and right hand limit of the function are not equal at x=0)
Hence, from the graph we could directly say that:
f(-2 ) =2
f(0) = 3
f(4) = -1
The values of the function values are:
f(-2 ) =2, f(0) = 3 and f(4) = -1
The value of f(-2)On the graph, the value of the function when x = -2 is 2
Hence, the value of f(-2) is 2
The value of f(0)On the graph, the values of the function when x = 0 are 1 and 3.
However, the line that has a closed circle (i.e f(0) = 3) will take precedence over the line that has an open circle (i.e f(0) = 1)
Hence, the value of f(0) is 3
The value of f(4)On the graph, the value of the function when x = 4 is -1
Hence, the value of f(4) is -1
Read more about functions and graphs at:
https://brainly.com/question/13136492
The sum of four consecutive odd integers is -72. write an equation to model this situation. find the value of the four integers
Find the slope and the y- intercept then rewrite the equation in slope intercept form 2x+3y=6
The perimeter of a square is 56 cm what is the approximate length of its diagonal
perimeter = 4s
56=4s
s=56/4 = 14
diagonal = sqrt (s^2 x 2)= sqrt(14^2 x 2) = sqrt(392) = 19.7989 cm
round answer as needed
Answer:
The approximate length of diagonal is:
19.796 cm.
Step-by-step explanation:
We are given the perimeter of a square as 56 cm.
Let 's' be the side of the square.
We know that the perimeter of square is given as:
[tex]Perimeter=4\times s\\\\56=4s\\\\s=\dfrac{56}{4}\\\\s=14[/tex]
Hence, the side of square is 14 cm.
Now, the length of a diagonal(D) is given as:[tex]D=\sqrt{2}s[/tex]
( Since it could be proved with the help of Pythagorean Theorem )
Hence, as s=14 cm
Hence, the length of diagonal is:
[tex]D=\sqrt{2}\times 12\\\\D=1.414\times 14\\\\D=19.796\ cm[/tex]
Hence, the approximate length of diagonal is:
19.796 cm.
In a race in which five automobiles are entered and tehre are no ties, in how many ways can the first three finishers come in/
there are 5 ways for 1st place, then there would be 4 ways for 2nd place, then 3 ways for third
5*4*3 = 60 different ways
Answer: The required number of ways is 60.
Step-by-step explanation: Given that there are five automobiles entered in a race and there are no ties.
We are to find the number of ways in which the first three finishers come in.
Since there are 5 automobiles entered in the race, so the number of ways in which first finisher come in is 5.
Now, there are no ties, so the number of ways in which second and third finisher come in are 4 and 3 respectively.
Therefore, the total number of ways in which the first three finishers come in is
[tex]n=5\times4\times3=60.[/tex]
Thus, the required number of ways is 60.
4 (x+2)=2 (x+3)+2 (x-1) answer?
[tex]4(x+2)=2(x+3)+2(x-1)\\\\use\ the\ distributive\ property:\ a(b\pm c)=ab\pm ac\\\\(4)(x)+(4)(2)=(2)(x)+(2)(3)+(2)(x)-(2)(1)\\\\4x+8=2x+6+2x-2\ \ \ \ |simplify\\\\4x+8=(2x+2x)+(6-2)\\\\4x+8=4x+4\ \ \ \ |-4x\\\\8=4\ FALSE!!!\\\\Answer:\ NO\ SOLUTION\ (x\in\O)[/tex]
How do you know when the function is in simplified form?
Final answer:
A function is in simplified form when all unnecessary terms have been eliminated, subscripts are used appropriately, and it uses the most compact and standard notation possible. Always verify the reasonableness of the simplified function.
Explanation:
To determine when a function is in simplified form, several steps should be followed:
Eliminate terms wherever possible to simplify the algebra.Use the simplified subscript in the final formula.Do not write the subscript if it is one, as it is understood to be implied.Condense constant quantities within parentheses, replacing them with a single symbol, for example, 'a', to make the equation look simpler.When an equation contains more than one unknown, use an additional equation to solve the problem.In cases where several unknowns must be determined, keep physical principles in mind and possibly use multiple equations to find the required variable.Condense formulas for chemical structures by using subscripts to denote multiple identical elements, making notation more compact.When you have eliminated all unnecessary terms and used standard conventions for simplification mentioned above, the function is considered to be in its simplest form. It is always good practice to check the answer to see if it is reasonable and does not violate any known principles or constraints.
You record a temperature of 0.75 °C. Is this a positive or negative temperature?
Which function represents transforming f(x)=3^x with a reflection over the x-axis and a vertical shift of 4 units? 3^x+ 4, -3^x+ 4, 3^x-4, -3^x+4
Answer: [tex]-3^x +4[/tex]
Step-by-step explanation:
The equation for the vertical reflection of a function f(x) across the x-axis is given by :-
[tex]y=-f(x) [/tex]
The vertical shift of 'k' units of a function g(x) is given by :-
[tex]y=g(x)+k [/tex]
Now, the equation for the vertical reflection of a function [tex]f(x)=3^x[/tex] across the x-axis is given by :-
[tex]-f(x)=-3^x [/tex]
Then , the equation for the vertical shift of 4 units of function [tex]-3^x[/tex] is given by :-
[tex]y=-3^x +4[/tex]
Hence, the function represents transforming [tex]f(x)=3^x[/tex] with a reflection over the x-axis and a vertical shift of 4 units
[tex]y=-3^x +4[/tex]
David is selling floral arrangements. Each arrangement uses 1 vase and 12 roses. Each vase costs David $2.00. Let C be the total cost of the arrangement and r be the cost of 1 rose. Which equation should David use to find the total cost of each arrangement?
Which of the following is a like radical to
From the table below, determine whether the data shows an exponential function. Explain why or why not.
x: 3, 1, -1, -3
y: 1, 2, 3, 4
(A) No; the domain values are at regular intervals and the range values have a common sum 1.
(B) No; the domain values are not at regular intervals.
(C) Yes; the domain values are at regular intervals and the range values have a common factor 2.
(D) Yes; the domain values are at regular intervals and the range values have a common sum 1.
Answer:
a
Step-by-step explanation:
What is the slope of the line shown below?