After simplification,
(2x + 1)/2(x^2)
Given,
(x/4)+(1/8)/(x^2/4)
Simplifying,
Firstly take LCM of 4 and 8,
LCM of 4 and 8 will be 8.
Then,
(2x +1) /(8) / x^2 /4
Further,
Take reciprocal of the denominator,
(2x +1) /(8) (4/x^2)
(2x + 1)/2(x^2)
Hence after simplification the expression becomes (2x + 1)/2(x^2).
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equivalent value of the equation is 18x-9=72 and x=4.5
Given data ,
Let the equation be represented as A
Now , the value of A is
(3/5)(30x-15)=72
On simplifying the equation , we get
3(6x-3)=72
On further simplification , we get
18x-9=72
x=81/18
x=4.5
Hence , the equation is 18x-9=72
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Which statement describes the relationship between the x- and y-values shown in the graph?
A coordinate plane has x-axis and y-axis with values ranging from negative 6 to 10. A positive slope passes through the points (negative 4, negative 6), (negative 2, negative 4), (2, 0), (4, 2), and (6, 4).
In this example, a positive relationship between the x- and y-values is demonstrated. This basically demonstrates that when one value increases, the other typically does too, and vice versa when one value decreases in the graph.
An x and y coordinate plane with values between -6 and +10 is displayed on the graph.
The points (2, 0), (4, 2), (6, 4), (negative 2, negative 4), and (negative 4, negative 6) are all connected by a line. The y values rise in proportion to the x values because the line has a positive slope.
In this example, a positive relationship between the x- and y-values is demonstrated. This basically demonstrates that when one value increases, the other typically does too, and vice versa when one value decreases.
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The complete question is-
Which statement describes the relationship between the x- and y-values shown in the graph?
A coordinate plane has x-axis and y-axis with values ranging from negative 6 to 10. A positive slope passes through the points (negative 4, negative 6), (negative 2, negative 4), (2, 0), (4, 2), and (6, 4).
-4 is less than w, and 0 is greater than w
Answer:
-3,-2,-1 is less than -4 and not greater than
Step-by-step explanation:
A right rectangular prism measures 8 inches long, 12 inches high, and 6 inches deep. A half-sphere with a diameter of 2 inches is carved out of the prism. What is the approximate volume of the resulting composite figure?
Answer:
[tex]573.9 \text{ in}^3[/tex]
Step-by-step explanation:
First, we can find the volume of the rectangular prism using the formula:
[tex]V_\square = l \cdot w \cdot d[/tex]
where [tex]l[/tex] is the prism's length, [tex]w[/tex] is its width, and [tex]d[/tex] is its depth.
Plugging the given dimensions into the formula:
[tex]V_\square = 8 \cdot 12 \cdot 6[/tex]
[tex]V _\square= 96 \cdot 6[/tex]
[tex]\boxed{V_\square = 576 \text{ in}^3}[/tex]
Next, we can find the volume of the half-sphere using the formula:
[tex]V_\circ = \dfrac{2}{3} \pi r^3[/tex]
where [tex]r[/tex] (or [tex]d/2[/tex]) is the half-sphere's radius.
Plugging the given diameter value into the formula:
[tex]V_\circ = \dfrac{2}{3} \pi (2/2)^3[/tex]
[tex]V_\circ = \dfrac{2}{3} \pi (1)^3[/tex]
[tex]\boxed{V_\circ=\dfrac{2}{3}\pi \text{ in}^3}[/tex]
Finally, we can find the volume of the composite figure by subtracting the volume of the half-sphere from the volume of the rectangular prism.
[tex]V = V_\square - V_\circ[/tex]
[tex]V = 576 \text{ in}^3 - \dfrac{2}{3}\pi \text{ in}^3[/tex]
We can evaluate this using a calculator.
[tex]\boxed{V\approx 573.9 \text{ in}^3}[/tex]
Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. What is the shape of distribution:
A.skewed right
B. skewed left
C. uniform
D. symmetric
Solve the following equation. 25 + 2 � = 3 ( 4 � + 3 ) 25+2x=3(4x+3)
The solution to the equation is x = 1.6.
Let's start by distributing the 3 on the right side of the equation:
25 + 2x = 12x + 9
Next, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side. To do this, we'll subtract 2x from both sides:
25 = 10x + 9
Then, we'll subtract 9 from both sides:
16 = 10x
Finally, we'll divide both sides by 10:
x = 1.6
So the solution to the equation is x = 1.6.
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What is the value of
O
O
O
O
81
16
16
81
16
81
81
16
(3)*₂
?
The solution of the expression, [tex](\frac{2}{3} )^{-4}[/tex] is 81 / 16.
How to solve an exponential expression?An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as multiplication, subtraction, addition etc.
Therefore, lets solve the expression as follows:
[tex](\frac{2}{3} )^{-4}[/tex]
Using exponential laws,
b⁻¹ = 1 / b
Let's apply the law to the expression as follows:
[tex](\frac{2}{3} )^{-4} = \frac{1}{(\frac{2}{3})^{4} }[/tex]
Therefore,
1 ÷ (2 / 3)⁴ = 1 × (3 / 2)⁴ = 3⁴ / 2⁴
Finally,
3⁴ / 2⁴ = 81 / 16
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The world famous gambler from Philadelphia, Señor Rick, proposes the following game of chance. You roll a fair die. If you roll a 1, then Señor Rick pays you $55. If you roll a 2, Señor Rick pays you $10. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must pay Señor Rick $35, and if you roll a 6, you must pay Señor Rick $25. What is the expected value for this game if you pay $1 to play?
The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.
To calculate the expected value for the game, we need to multiply each outcome by its respective probability and then sum them up.
Let's calculate the expected value for each outcome:
Outcome 1: Roll a 1 and receive $55.
The probability of rolling a 1 on a fair die is 1/6.
Expected value = (1/6) × $55 = $9.17
Outcome 2: Roll a 2 and receive $10.
The probability of rolling a 2 on a fair die is 1/6.
Expected value = (1/6) × $10 = $1.67
Outcome 3: Roll a 3 and win nothing.
The probability of rolling a 3 on a fair die is 1/6.
Expected value = (1/6) × $0 = $0
Outcome 4: Roll a 4 or 5 and pay Señor Rick $35.
The probability of rolling a 4 or 5 on a fair die is 2/6 or 1/3.
Expected value = (1/3) × (-$35) = -$11.67 (negative because you have to pay)
Outcome 5: Roll a 6 and pay Señor Rick $25.
The probability of rolling a 6 on a fair die is 1/6.
Expected value = (1/6) × (-$25) = -$4.17 (negative because you have to pay)
Now, let's sum up the expected values:
Expected value = $9.17 + $1.67 + $0 - $11.67 - $4.17
= -$4.00
The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.
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I’m struggling please help thank you always
Answer:
- 3 , 7 , - 13 , 5x + 2
Step-by-step explanation:
A
to evaluate f(0) substitute x = 0 into f(x)
f(0) = 5(0) - 3 = 0 - 3 = - 3
B
substitute x = 2 into f(x)
f(2) = 5(2) - 3 = 10 - 3 = 7
C
substitute x = - 2 into f(x)
f(- 2) = 5(- 2) - 3 = - 10 - 3 = - 13
D
substitute x = x + 1 into f(x)
f(x + 1)
= 5(x + 1) - 3 ← distribute each term in the parenthesis by 5
= 5x + 5 - 3 ← collect like terms
= 5x + 2
Answer:
A) -3
B) 7
C) -13
D) 5x+2
Step-by-step explanation:
For A, B, and C substitute the value stated in the parenthesis.
A) f(0) means to find the value when x=0, so we substitute 0 where x is in the function.
[tex]5(0)-3[/tex]
Then use PEMDAS and multiply first and then subtract 3 from the product.
[tex]5(0)=0\\0-3=-3[/tex]
B) Take the same steps as before with a different value. Substitute 2 for x.
[tex]5(2)-3\\5(2)=10\\10-3=7[/tex]
C) Also the same thing as the previous problems. Substitute -2 for the value of x.
[tex]5(-2)-3\\5(-2)=-10\\-10-3=-3[/tex]
D) Similar to above substitute x+1 where x is.
[tex]5(x+1)-3\\[/tex]
Then distribute 5(x+1) to get
[tex]5x+1(5)\\5x+5[/tex]
Then simplify the equation
[tex]5x+5-3=5x+2[/tex]
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 ft.
hl
What is the volume of the sphere?
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius.
Given that the sphere and the cylinder have the same radius and height, we can assume that the radius of both shapes is the same.
Let's denote the radius as 'r'. The volume of the cylinder is given as 50 ft³.
The volume of the cylinder is calculated using the formula V = πr²h, where h is the height.
Since the height of the cylinder is not given, we cannot determine the exact value of 'r' or calculate the volume of the sphere.
However, if we assume that the height of the cylinder is equal to its diameter (which is twice the radius), we can proceed with the calculation.
If the height of the cylinder is equal to 2r, the volume of the cylinder becomes:
50 = πr²(2r)
50 = 2πr³
Dividing both sides of the equation by 2π gives:
25 = πr³
Now, we can substitute this value of πr³ into the volume formula of the sphere:
V = (4/3)πr³
V = (4/3)(25)
V = 100/3
Therefore, if the height of the cylinder is equal to its diameter, the volume of the sphere would be 100/3 ft³. However, please note that this assumption might not necessarily be valid without further information about the relationship between the height and radius of the cylinder.
Answer: The Volume of the sphere is 100/3 cubic feet.
Step-by-step explanation:
It is clearly seen in the given figures, the height is two times the radius. Therefore, h is equal 2r.
We know that,
The volume of the sphere is π x r^2 x h. (r is radius and h is height)
So putting the values of height, h in the above formula, we get:
πxr^2x2r
= 2 * π * r^3.
= 2 * π * r^3 = 50
= π * r^3 = 25
We get, r^3 = 7.957747155
Therefore, r = 1.996472712
Now that we have the measure of the radius, we can find the volume of the sphere!
(4 / 3) * π * r^3
(4/3) * π * (1.996472712)^3
= (4/3) * π * 7.957747155
= (4/3) * π * (25 / π)
= (4/3) * 25
= 100/3 cubic feet.
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A submarine is 42 feet belpw rhe surface of water .a shark directly above the submarine is 19 feet below the surface of the water.how many feer above the submarine is to the shark
The number of feet above the submarine is the shark is 23 feet.
Given that, a submarine is 42 feet below the surface of the water and shark is 19 feet below the surface of the water.
Here, location of shark = 42-19
= 23 feet
Therefore, the number of feet above the submarine is the shark is 23 feet.
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"Your question is incomplete, probably the complete question/missing part is:"
A submarine is 42 feet below the surface of the water a shark directly above the submarine is 19 feet below the surface of the water how many feet above the submarine is the shark.
Sam invest $6500 into account earning 5% interest compounded quarterly how long will it take to double his money?
Answer:
20 quartesrs
Step-by-step explanation:
20 quarters
Timothy and Sean are masseur. Timothy charges $45 for each massage and Sean charges $55 for each massage. This week
Timothy made $102 in tips and Sean made $96 in tips. Given that T and S represent the number of massages given by Timothy
(T) and Sean (S), which expression can be used to represent their combined earnings for the week?
Answer: 45T + 55S +102 + 96= Combined income
Step-by-step explanation:
2079 [Optional] Set A Q.No. 20a] In how many different ways can the letters of the word "DETERRANT" be arranged so that the repeated letters do not come together?
There are 70,560 different ways to arrange the letters of the word "DETERRANT" so that the repeated letters do not come together.
How many ways the word "DETERRANT" be arranged so that the repeated letters do not come togetherThe word "DETERRANT" has 9 letters, out of which there are 2 E's, 2 R's, and 1 T.
To determine the total number of possible arrangements, we begin with 9! (9 factorial), which counts all possible arrangements if all letters are distinct.
We must, however, account for the repeated letters. For the two E's, we divide by 2, which is the number of different ways they can be arranged without changing the overall arrangement. Likewise, we divide by 2! for the two R's.
As a result, the total number of arrangements with repeated letters that do not come together is:
9! / (2! x 2!) - 8! / (2! x 2!) = 90720 - 20160 = 70560
Therefore, there are 70,560 different ways to arrange the letters of the word "DETERRANT" so that the repeated letters do not come together.
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The radius of a circle is 1.8cm. Find it’s circumference to the nearest tenth.
Answer:
[tex]C = 11.3 \text{ cm}[/tex]
Step-by-step explanation:
We can find the circumference of the circle by using the formula:
[tex]C = 2\pi r[/tex]
↓ plugging in the given radius
[tex]C = 2\pi (1.8 \text{ cm})[/tex]
[tex]C = 3.6\pi \text{ cm}[/tex]
↓ rounding to the nearest tenth
[tex]\boxed{C = 11.3 \text{ cm}}[/tex]
Find the missing side length.
a
26
24
Answer:
a = 10
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
a² + 24² = 26²
a² + 576 = 676 ( subtract 576 from both sides )
a² = 100 ( take square root of both sides )
a = [tex]\sqrt{100}[/tex] = 10
Here are two triangles show that the triangles are similar what is the scale factor from triangle abc to abc
The two triangles are similar because angle C = C' and angle A = A'. The scale factor is 4/3
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent.
Also, the ratio of corresponding sides of similar triangles are equal.
Therefore to show that that the two triangles are equal;
Tan A = 4/3
Tan A = 1.333
A = 53.1°
Tan A' = 5.3/4
Tan A' = 1.33
A' = 53.1°
Therefore the two triangles are similar.
The scale factor = 4/3
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Find the area of the regular polygon below and round your answer to the nearest tenth.
Explain your reasoning. Show all your work.
1) What is the perimeter of the regular polygon?
2) What is the apothem length? Show all your work and explain how you found the apothem.
3) What is the area of the regular polygon? Show your work.
7 sides each side is 10 in long
The area of the regular polygon is 311.5 in2.
We are given that;
A polygon
Now,
To find the perimeter of the regular polygon, we need to multiply the number of sides by the length of each side. The polygon has 7 sides and each side is 10 in long, so the perimeter is 7 * 10 = 70 in.
To find the apothem length, we need to use some trigonometry.
The central angle is 360/7 degrees, since there are 7 equal angles in a regular polygon. Half of the side length is 5 in, since each side is 10 in long. The apothem is the adjacent side of the right triangle. We can use the tangent function to find the apothem: tan(360/14) = 5/a, where a is the apothem. Solving for a, we get a = 5/tan(360/14) ≈ 8.9 in.
To find the area of the regular polygon, we need to plug in the values of P and a into the formula A = (1/2)P*a.
A = (1/2)708.9 ≈ 311.5 in2.
Therefore, by the area the answer will be 311.5 in2.
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Use the internet to identify a major league ballpark in which the distance from home plate to the center field fence and the height of the center field fence require that a ball hit 2 feet above the ground will necessitate an angle of elevation less than .86 degrees to just clear the center field fence. what is the name and location of the major league ballpark that you identified? what is the distance from home plate to the center field fence and what is the height of the center field fence in the ballpark? What is the angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground? Round to the nearest hundredth of a degree.
We can actually deduce here that the major league ballpark that I identified is T-Mobile Park in Seattle, Washington.
How to find the angle of elevation?The distance from home plate to the center field fence is 409 feet and the height of the center field fence is 8 feet.
Thus, to solve for the angle of elevation, we can use the following equation:
tan θ = (y - h) / d
Where:
θ is the angle of elevation
y is the height of the fence
h is the height of the ball
d is the distance to the fence.
tan θ = (8 - 2) / 409
tan θ = 0.602
θ = [tex]tan^{-1}[/tex] (0.602)
θ = 0.85°
The angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground is 0.85°.
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Identify the center, radius, domain and range of the circle eith equation. Make sure to scroll down through all thr answer choices
(x+2)^2+(y-5)^2 = 9
Answer: Centre: (-2,5)
Radius = 3
so
Diameter = 6
Domain: (-5,1)
Range: (2,8)
Answer:
center (-2,5)
radius =3
domain = -5< x <1
range 2 <y<8
Step-by-step explanation:
siiuu
what are the coefficients in the polynomial
Answer: 7 and -4
Step-by-step explanation:
Coefficients are numbers in front of variables
6 doesn't have a variable so it's a constant
7 and -4 are the coefficients
in how many ways can first , second , and third prizes be awarded in a cont with 925 contestants? assume there is no ties
Answer:
Step-by-step explanation:
[tex]\frac{925!}{(925-3)!}= 923*924*925=788,888,100[/tex]
To determine the number of ways the first, second, and third prizes can be awarded in a contest with 925 contestants, we can use the concept of permutations.
For the first prize, there are 925 contestants eligible to win. After the first prize is awarded, there are 924 remaining contestants for the second prize. Finally, for the third prize, there are 923 remaining contestants.
The number of ways to award the prizes can be calculated as the product of the number of choices for each prize:
Number of ways = 925 * 924 * 923
Calculating this expression, we find:
Number of ways = 779,449,100
Therefore, there are 779,449,100 ways to award the first, second, and third prizes in the contest with 925 contestants.
Enter your answer in the box.
Answer:
I think it may be 160?
Step-by-step explanation:
400/5 is 80 there's 2 yellow so 2x80= 160 times
7) The masses of 4 samples of
salt are measured to perform an
experiment in science class.
What is the total number of
grams of salt in the 3 samples
with the most mass? (Just put
the number but write it as a
decimal.)
The required total number of grams is 13.5 gram.
From figure we have,
The masses of 4 samples are the masses are 1.5 gram, 3.5 gram , 5 gram and 5 gram respectively.
To calculate the total number of grams of salt in the 3 samples with the most mass,
Add the masses of the three largest samples.
In this case,
The three largest samples are 3.5 grams, 5 grams, and 5 grams.
We have: 3.5 grams + 5 grams + 5 grams = 13.5 grams
Therefore, the total number of grams of salt in the 3 samples with the most mass is 13.5 grams.
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Please someone help me 28th this, eleven people are entered in a race if there are no ties in how many ways can first and second place come?
How to get the square root of a number?
Answer:
Step-by-step explanation:
What is the Formula for Calculating the Square Root of a Number? The square root of any number can be expressed using the formula: √y = y½. In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.
In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number.
The square root of a number "a" is denoted by the symbol "√a" or "a^(1/2)." For example, the square root of 9 is 3 because 3 * 3 = 9.
Drag each inequality to the column which is labeled with its solution.
( look at photo for reference )
Drag the solution of each inequality as shown below:
3(x - 5) + x < 13 : x<7
2(x + 8) > 4x + 2 : x<7
3x + 2(x - 8) > x : x > 4
2(x + 6) < 3x + 8 : x > 4
How to solve the inequalities?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
3(x - 5) + x < 13
3x -15 + x < 13
4x -15 < 13
4x < 13 + 15
4x < 28
x < 28/4
x < 7
2(x + 8) > 4x + 2
2x + 16 > 4x + 2
2x - 4x > 2 - 16
-2x > -14
x < -14/(-2) (Note: Sign will change if you divide with negative numbers)
x < 7
3x + 2(x - 8) > x
3x + 2x -16 > x
5x - 16 > x
5x - x > 16
4x > 16
x > 16/4
x > 4
2(x + 6) < 3x + 8
2x + 12 < 3x + 8
2x - 3x < 8 - 12
-1x < -4
x > -4/(-1)
x > 4
Therefore, drag the solution of each inequality accordingly.
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Sean says the value of a to the -3rd power is always less than 1 if a is positive.
Christine says the value of a to the -3rd power is always less than 1 when a is negative
Which one is correct, and for the one that is incorrect enter the number that proves in to be incorrect (if none say none).
Sean's statement is correct. Christine's statement is incorrect when a is negative.
The value of a to the -3rd power is always less than 1 if a is positive.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. Therefore, Sean's statement is correct.
The value of a to the -3rd power is always less than 1 if a is positive, but it is always greater than 1 if a is negative.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. But if a = -2, then a to the -3rd power is -1/8, which is greater than 1.
Therefore, Christine's statement is incorrect when a is negative.
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The distance between Marisa's house and the post office is 720 m. If she walks from her house to the post office at an average speed of 80 m/min, how long will she take?
Okay, let's break this down step-by-step:
* The distance between Marisa's house and the post office is 720 m
* Marisa walks at an average speed of 80 m/min
* To calculate the time:
** Distance / Speed = Time
** 720 m / 80 m/min = 9 minutes
Therefore, if the distance is 720 m and Marisa's average walking speed is 80 m/min, it will take her 9 minutes to walk from her house to the post office.
You apply for a debt consolidation loan for $43,000 for 4 years. If your credit score is 760 or greater, then the annual percentage rate is 6%. If your score is less than 760, then the rate is 7%. How much, in dollars, can you save per month by having a credit score of 760 or greater? Round your answer to the nearest cent
