Answer:
15(2a - 2)= 5(a2 - 1)
The simplified form of the given equation is 5a²-30a-31=0.
The given equation is 15/(a²-1)=5/(2a-2).
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
By cross-multiplying we get,
15/(a²-1)=5/(2a-2)
⇒ 15(2a-2)=5(a²-1)
⇒ 30a-30=5a²-1
⇒ 5a²-30a-31=0
Therefore, the simplified form of the given equation is 5a²-30a-31=0.
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s) An e-mail lter is planned to separate valid e-mails from spam. The word free occurs in 50% of the spam messages and only 3% of the valid messages. Also, 20% of the messages are spam. Determine the following probabilities: (a) The message contains the word free. (b) The message is spam given that it contains free. (c) The message is valid given that it does not contain free.
Answer:
A) P(F) = 0.124
B) P(S|F) = 0.8065
C) P(V|F^(c)) = 0.886
Step-by-step explanation:
Let us denote as follows;
F = Message contains word free
S = message is spam
V = message is valid
From the question, we are given that;
The probability that word free occurs in spam messages;P(F|S) = 50% = 0.5
The probability of the valid messages that contain free; P(F|V) = 3% = 0.03
Spam messages; P(S) = 20% = 0.2
Valid messages; P(V) = 1 - 0.2 = 0.8
A) From rule of total probability ;
probability that the message contains the word free is given as;
P(F) = P(F|S)•P(S) + P(F|V)•P(V)
P(F) = (0.5 x 0.2) + (0.03 x 0.8)
P(F) = 0.124
B) From Baye's theorem;
probability that the message is spam given that it contains free is given as;
P(S|F) = P(F|S)•P(S)/P(F)
P(S|F) = (0.5 x 0.2)/0.124
P(S|F) = 0.8065
C) From combination of complement rule and Baye's theorem;
probability that the message is valid given that it does not contain free is given as;
P(V|F^(c)) = P(F^(c)|V)•P(V)/P(F^(c))
Thus,
P(V|F^(c)) = [(1 - P(F|V))•P(V)]/(1 - P(F))
P(V|F^(c)) = ((1 - 0.03)•0.8)/(1 - 0.124)
P(V|F^(c)) = 0.776/0.876
P(V|F^(c)) = 0.886
Write an equation to find the amount of money in Pertro’s account if the total of all their accounts is $148.
Answer:
P = 2(21 + 3)
= 2(24)
=$48
Step-by-step explanation:
Add them all up.
s + 2(s+3) + 4s-5 = 148
s + 2s + 6 + 4s - 5 = 148
Group all s together and all numbers together 7s + 1 = 148
7s = 147
Divide by 7
s = 21
Plug s=21 back in for Petro
To find the amount of money in Pertro's account, use the equation x = 148 - (y + z), where y and z represent the amounts in the other two accounts.
Explanation:The equation to find the amount of money in Pertro's account can be written as:
x + y + z = 148
where x, y, and z represent the amounts in different accounts. To find the amount in Pertro's account, we need to set up another equation using the information given. If we know that the total of all accounts is $148 and we want to find the amount in Pertro's account (x), we can write:
x = 148 - (y + z)
where y and z represent the amounts in the other two accounts.
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The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x + 1 On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1.75, 6.75), and goes through (1, 5).
f(x) = x2 – 3x – 3 On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (1.75, 5), and goes through (5, 7).
f(x) = x2 + 6x + 3 On a coordinate plane, a parabola opens up. It goes through (negative 6, 3), has a vertex at (negative 3, negative 6), and goes through (0, 3).
f(x) = x2 – 6x – 1 On a coordinate plane, a parabola opens up. It goes through (0, negative 1), has a vertex at (3, negative 10), and goes through (6, 0).
Answer: fax 2 F (y axis) +4.5 =23x2=46
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
Idk how to do this!!
Answer:
2 : 5
Step-by-step explanation:
Given 2 similar figures with ratio of sides = a : b, then
ratio of areas = a² : b²
Given ratio of areas = 4 : 25, then
ratio of sides = [tex]\sqrt{4}[/tex] : [tex]\sqrt{25}[/tex] = 2 : 5
5 A pile driver drives a post 9 ft into the ground on its first hit. Each additional hit
drives the post the distance of the previous hit. Find the total distance the post has been driven after 6 hits.
Final answer:
The total distance the post is driven into the ground after 6 hits of the pile driver, each hit driving the post 9 ft, is 54 ft.
Explanation:
The problem given can be solved using the concept of arithmetic sequences since each hit of the pile driver drives the post the same distance as the previous hit.
Assuming that the first hit drives the post 9 ft into the ground. Each subsequent hit will also drive it 9 ft further. To find the total distance after 6 hits, we simply multiply the distance per hit by the number of hits:
Total Distance Driven = Distance per Hit × Number of Hits
Total Distance Driven = 9 ft × 6 = 54 ft.
The total distance the post has been driven into the ground after 6 hits is therefore 54 feet.
Mica is solving for the zeros of a quadratic function by
completing the square. Her work is shown. What error
did Mica make?
-Mica should have set each x = 0 instead of f(x).
-Mica should have added 2 to 3 instead of 1.
-Mica should have multiplied both sides by 2 instead
of dividing
-Mica should have subtracted 1 from both sides
instead of adding.
Answer: b. micah should have added 2 to 3 instead of 1
Answer:
B. on edge
Step-by-step explanation:
The archway to the entrance of an art gallery can be model by y= -1/3(x-5)(x+5) where x and y are measured in feet. The x-axis represents the floor. Find the width of the arch at floor level.
Answer:
x=5 feet
Step-by-step explanation:
At floor level y=0
If the expression is:
[tex]0=1/3(x-5)(x+5)\\0=1/3(x^2-25)\\0=1/3x^2-25/3\\25/3=1/3x^2\\25=x^2\\x=5[/tex]
But, with the negative sign, the answer is x= 5i (where i is imaginary)
Final answer:
The width of the arch at floor level is found by determining the points where the parabola intersects the x-axis, which are at x = 5 and x = -5. The width is the distance between these points, which is 10 feet.
Explanation:
To find the width of the arch at floor level, we need to determine the distance between the two points where the parabola represented by the equation y = -1/3(x-5)(x+5) intersects the x-axis. The x-axis represents the floor, and the points of intersection occur where y is equal to 0.
Setting the equation to 0 gives:
0 = -1/3(x-5)(x+5)
By solving for x, we get x = 5 and x = -5, which are the points where the parabola intersects the x-axis. The distance between -5 and 5 on the x-axis is 10 feet, so the width of the arch at floor level is 10 feet.
PLEASE HELP IT IS VERY URGENT!!
Please help to find (b) (c) (d)
(b) is in the picture
(c) Given that the ratio of PL to LF is 2 : 3, find the ratio of the area of triangle PLM to the area of triangle PFG.
(d) A circle is drawn by using FG as the diameter. Explain if the point M lies on the circumference of this circle.
Step-by-step explanation:
(c)
[tex] In\: \triangle PLM \: \&\: \triangle PLM\\
\angle PLM \cong\triangle PFG.. (corresponding \:\angle s) \\
\angle LPM \cong \angle FPG.. (common \: \angle s) \\
\therefore \triangle PLM\sim\triangle PFG.. (by\: AA\:Postulate) \\
PF = PL + LF = 2 + 3 = 5[/tex]
By area of similar triangle theorem:
[tex] \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{PL^2}{PF^2}\\
\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{2^2}{5^2}\\
\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{4}{25}\\
A(\triangle PLM)\: :\: A(\triangle PFG) = 4 \: :\: 25
[/tex]
Landons car used 10 gallons of gas to drive 220miles. At what rate does his car use gas in gallons per mile
Answer:
1/22 gallons per mile
Step-by-step explanation:
We want to find gallons per mile, so we take the gallons and divide by the mile
10gallon/ 220 mile
1/22 gallons per mile
Answer:
1/22 gallons per mile
Step-by-step explanation:
GEOMETRY! Show your work, please.
Answer:
54°
Step-by-step explanation:
[tex]m\angle CDE = \frac{1}{2} \{237 \degree - (360 \degree -237 \degree ) \} \\ \\ = \frac{1}{2} \times \{237 \degree - 123 \degree \} \\ \\ = \frac{1}{2} \times 114 \degree \\ \\ = 54 \degree \\ \\ \huge \red{ \boxed{ \therefore \: m\angle CDE =54 \degree}}[/tex]
Troy says that 0.9>0.90 because tenths are greater than hundredths.Keith says that 0.9<0.90 bra side 90 is greater than 9. Is either Troy or Keith correct?Explain
Answer:
Neither Troy nor Keith is correct.
Step-by-step explanation:
Neither Troy nor Keith is correct.
The value 0.9 is the same as the value 0.90.
The zeros after a decimal point are always insignificant unless they are followed by a number different from zero.
0.90 = 0.900 = 0.9000 = 0.90000 = ... = 0.9000000000
and all these can be easily written as 0.9, as the zeros after the decimal point do not change the value.
But 0.901, 0.9000004, 0.90002, and so on are all different, and the zeros are relevant, as they are followed by numbers different from zero.
Answer:
None of them is correct
0.9=0.90
Step-by-step explanation:
0.9>0.90 (not valid)
0.9<0.90 (not valid)
1. when dealing with decimals, the digits on the left hand side of the decimal point is a whole number.
The digits at the right hand side are considered individually.
2. the place value of the first digit is tenth, next is hundredth
3. if the last digits at the right hand side of the decimal point are zeros, then they are insignificant having no place value.
Hence, 0.9 is not greater 0.90
0.9 is not also less than 0.90,
because, the '0' at the right hand side of the decimal point, immediately after 9 is insignificant.
Therefore, 0.9=0.90
What is the area of the following figure?
Answer:
16.56
Step-by-step explanation:
The area of the square is 2 × 2
The area of the circle is-
A=πr²
A=3.14 × 2²
A=3.14 × 4
A=12.56
You don't need to divide it by half because there are two half circles so it would be a whole circle
12.56 + 4 = 16.56
Sorry if it is wrong
Answer:
Area of square =side( square)
(2) square
4
diameter= 2
radius=2/2
= 1
Area of circle=πrsquare
22/7×1×1
3.14
Area of figure= Area of square+area of circle
4+3.14
7.14
i need the steps for 37
The football team needs to raise at least $7,000 for new football uniforms. An anonymous donor gave the team $1,250 toward their goal. Each player is also able to raise $100 by selling candy. Write an inequality to show how many players need to raise $100 to meet their goal.
Answer: There are 58 players to raise $100 to meet their goal.
Step-by-step explanation:
Since we have given that
Amount to raise = $7000
Amount given the team by the donor = $1250
Amount each player is able to raise = $100
Let the number of player be 'x'.
According to question, we get that
[tex]1250+100x\geq 7000[/tex]
So, the required number of players would be :
[tex]100x\geq 7000-1250\\\\100x\geq 5750\\\\x\geq \dfrac{5750}{100}\\\\x\geq 57.5[/tex]
Hence, there are 58 players to raise $100 to meet their goal.
Given f(x)=4x2−5 and g(x)=x+3 .
What is (fg)(x) ?
−4x2+x+8
4x3−15
4x3+12x2−5x−15
4x2−x−8
Final answer:
To find (fg)(x), multiply f(x) and g(x) by substituting g(x) into f(x) and simplifying the expression.
Explanation:
To find (fg)(x), we need to multiply f(x) and g(x). This can be done by substituting g(x) into f(x) and simplifying the expression.
f(x) = 4x² - 5
g(x) = x + 3
(fg)(x) = f(x) * g(x) = (4x² - 5) * (x + 3) = 4x³ + 12x² - 5x - 15
Therefore, the expression (fg)(x) simplifies to 4x^3 + 12x² - 5x - 15.
What is the surface area of the cube shown?
6.5 lenthe 6.5 hieght
Answer:A=253.5
Step-by-step explanation:
In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.
Answer:
253.5
Step-by-step explanation:
if the side lengths of the cube is 6.5 then the surface area of one side is 42.25. Since the 6 sides of the cube are all the same you can multiply this by 6 to get 253.5
8. The mean of the winning scores of a bowling tournament over the last 10 years was 279, with a standard deviation of 3. Considering that the scores were in a normal
distribution, how many scores were below 282?
For a normal distribution with a mean of 279 and a standard deviation of 3, 50% of the scores are below 282, given that 282 is one standard deviation above the mean.
Explanation:In a normal distribution, 68.2% of values fall within one standard deviation of the mean,
95.4% fall within two standard deviations, and 99.7% fall within three standard deviations. Given that the bowling scores have a mean of 279 and a standard deviation of 3, a score of 282 will fall one standard deviation above the mean.
Since 68.2% of scores fall within one standard deviation around the mean, half the scores will fall below the mean and the other half will fall above it. Thus, 50% of the scores will fall below 282. In case of a normal distribution that has no skew, the mean, median, and mode are equal, which implies that half the values fall below the mean and half the values fall above it.
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Solve the proportion. Round your answer to 1 decimal if needed:
x/4 = 6/20
what is it?
Answer:
x=6/5
Step-by-step explanation:
times both sides by 10:
5x/2=3
then times 2:
5x=6
divide it by 5:
5x/5=6/5
x=6/5
original price? percent of discount: 80% sales price: $90
Answer:
18.00 dollars
Step-by-step explanation:
message me if you need help. Or this was not the answer you were looking for.
7n=30 what is the n
Answer:
n=4.28571429
Step-by-step explanation:
Solve for n by isolating it
7n=30
Divide both sides by 7 to "reverse" the multiplication being done to n
n=4.28571429
Answer "n" is 4 and 2 sevenths
Step-by-step explanation:
7n = 30 get "n" alone
7n / 7 = 30 / 7
n = 4 and 2/7
(5 x 5) + (6 × 7) - 50 =?
Answer:
17
Step-by-step explanation:
5 x 5 is 25
6 x 7 42
25 + 42 is 67
67 - 50 = 17
17 is your answer :)
Simplify:
7a² + ab - 4a² + 2a + 8ba + 4a
Group terms
= (7a² - ?a²) + (ab + 8ba) + ( ? + 4a)
Answer:
simplify question is 3a^2 +6a+9ab
Step-by-step explanation:
Which is the probability that a 1-6 number cube lands on a number less than 2?
A 0.67 C 0.33
B 0.50 D 0.17
Answer:
D 0.17
Step-by-step explanation:
p = 1/6×100 = 100/6 = 16.(6)% ≈ 17% = 0.17
Final answer:
The probability of rolling a number less than 2 on a 1-6 number cube is 0.17.
Explanation:
Probability Calculation:
There are 6 possible outcomes when rolling a number cube (1-6).
Only 1 outcome is less than 2 (rolling a 1).
Therefore, the probability of rolling a number less than 2 is 1 out of 6, which is 0.17.
Jamie can work no more than 20 hours a week this summer. She needs to earn at least $256 a week to save enough
Which angle does not terminate in Quadrant IV when drawn on a unit circle in standard position?
1. -300°
2. -50°
3. 280°
4. 1030°
The answer is -300
I found the answer on a regents
The angle that does not terminate when drawn on a unit circle in a standard position is -300°.
What is the position of the 4th quadrant on a unit circle?The 4th quadrant is located on the upper left side of a unit circle. In a unit circle, the angle between 270° - 360° is Quadrant IV. Others include:
Angles in Quadarant I = 0 - 90°Angles in Quadrant II = 90 - 180°Angles in Quadrant III = 180 - 270°The angle that does not terminate(i.e. does not end back into the fourth quadrant) after being added to 360 is -300°.
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Hi guys!
Im having trouble on the working out for this question could you please explain how to work it out?
Two-thirds of the jelly beans in a jar are black. There are 96 jelly beans in the jar. How many of them are black?
Thanks! Have an awesome day!
Answer:
64
Step-by-step explanation:
The first thing I would do is break down the question and put it into number form. 2/3 of the jelly beans are black. You want to find out the number of jelly beans out of 96 are black. I can try my best to explain how to do this.
Divide the number of jelly beans (96) by the denominator (3) to find out how many jelly beans would be 1/3. This is 32. To find out how many are 2/3 you would multiply the 1/3 (32) by 2 to find that it is 64.
To check your work simplify this. 64/96 and it should equal 1/3. Or put it in your calculator to find that it equals .667 which is the decimal form of 2/3.
Is 7, 20, 25 a right triangle?
Answer:
The answer to your question is below
Step-by-step explanation:
Process
To answer if they are right triangles or not use the Pythagorean theorem which states that the square of the hypotenuse equals the sum of the square of the legs.
a) 25² = 20² + 7²
625 = 400 + 49
625 ≠ 449 It is not a right triangle
b) 26² = 24² + 10²
676 = 576 + 100
676 = 676 it is a right triangle
c) 13² = 8² + (√10)²
169 = 64 + 10
169 ≠ 74 it is not a right triangle
d) 52² = 48² + 20²
2704 = 2304 + 400
2704 = 2704 it is a right triangle
The green turtle, Monique, traveled 250 centimeters in 8.7 minutes. The calculation that will give you the speed as a unit rate is The green turtle’s speed as a unit rate is centimeters per minute if the answer is rounded to the nearest tenth
Answer:
About 28.74 centimeters per minute
Step-by-step explanation:
250 centimeters / 8.7 minutes = ~28.74 centimeters per minute
Answer:
the correct answer for the first question is: 250 divided by 8.7
The second one is: 28.7 cm/min
Step-by-step explanation:
I did edgenuity
Volume with cubes with fraction lengths
How many cubes with side lengths of
cm does it take to fill the prism?
Answer:
You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.
use the protractor to measure this angle
To measure an angle using a protractor, follow these steps: Place the center point of the protractor at the vertex, align the base line with one side, and read the measure where the other side intersects the scale.
Explanation:To measure an angle using a protractor, follow these steps:
Place the center point of the protractor at the vertex of the angle.Align the base line of the protractor with one of the sides of the angle.Read the measure on the protractor where the other side of the angle intersects the measure scale.For example, if the measure reads 45 degrees, then the angle is 45 degrees.
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