Answer:
Option B is correct that is 8.
Step-by-step explanation:
Given Expression : [tex](16^{\frac{3}{2}})^{\frac{1}{2}}[/tex]
We use a law of exponent here to simplify it,
[tex](x^a)^b=x^{ab}[/tex]
Consider,
[tex](16^{\frac{3}{2}})^{\frac{1}{2}}[/tex]
[tex]=16^{\frac{3}{2}\times\frac{1}{2}}[/tex]
[tex]=16^{\frac{3}{4}}[/tex]
[tex]=(2^4)^{\frac{3}{4}}[/tex]
[tex]=2^{4\times\frac{3}{4}}[/tex]
[tex]=2^3[/tex]
[tex]=8[/tex]
Therefore, Option B is correct that is 8.
A pasture is twice as long as it is wide. its area is 88,200 ft2. how wide is the pasture?
The width of the pasture is 210 feet.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We are given that pasture is twice as long as it is wide. its area is 88,200 ft2.
If the width is w and the length is l, then the length is 2w=l.
In addition,
The area of the rectangle = length × Width
l x w=88200
Using the area formula, Plugging 2w in for l, we get ;
2w x w = 88200
88200= 2w².
Now Dividing both sides by 2, we get;
w²=44100
w= √(44100)
w =210.
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An earthquake registered 7.4 on the Richter scale. If the reference intensity of this quake was 2.0 × 1011, what was its intensity?
Answer:
The intensity was [tex]5.02377\times 10^{18}[/tex]
Step-by-step explanation:
We are given
An earthquake registered 7.4 on the Richter scale
so, RC=7.4
the reference intensity of this quake was 2.0 × 10^11
so,
[tex]I_r=2.0\times 10^{11}[/tex]
now, we can use formula
[tex]RS=log(\frac{I}{I_r} )[/tex]
now, we can plug values
[tex]7.4=log(\frac{I}{2.0\times 10^{11}} )[/tex]
now, we can solve for I
[tex]10^{7.4}=\frac{I}{2.0\times 10^{11}}[/tex]
[tex]I=10^{7.4}\times 2.0\times 10^{11}[/tex]
[tex]I=5.02377\times 10^{18}[/tex]
To find the intensity of an earthquake registered on the Richter scale, use the formula based on the magnitude difference and energy ratio.
The intensity of the earthquake can be calculated using the Richter scale formula, which relates the magnitude difference to the energy ratio.
Given that one step on the Richter scale corresponds to a factor of 100 in energy, a difference of 7.4 - 2.0 = 5.4 on the Richter scale results in a ratio of 100^5.4.Therefore, the intensity of the earthquake can be calculated as (100^5.4) * (2.0 x 10^11), which simplifies to approximately 2.52 x 10^17.One side of a triangle is three times the shortest side. the third side is three feet more then the shortest side. the perimiter is 13 feet.
If a line is perpendicular to another, and one slope is -2, what is the slope of the other line
Solve w = t(r1 + r2) for t.
Answer:
The solution for t is [tex]\frac{w}{(r_1+r_2)}[/tex]
Step-by-step explanation:
The given expression is [tex]w = t(r_1+r_2)[/tex]
We need to solve for the 't' ,
To solve for t, divide [tex]w = t(r_1+r_2)[/tex] by [tex](r_1+r_2)[/tex]
[tex]\frac{w}{(r_1+r_2)} = t[/tex]
Hence, The solution for t is [tex]\frac{w}{(r_1+r_2)}[/tex]
Consider a graph of the equation y = −3x + 4. What is the y-intercept?
4
−4
3
−3
Answer:
it will be 4
Step-by-step explanation:
The sum of the first 100 positive numbers?
50 students of a certain class took a test. how many of them got a score less than 82? (1) the average score is 82. (2) the median score is 82.
different lengths of crayons?
what is, x is at most 30 inequality
in each case are the 2 events dependent or independent toss a dime and then toss a quarter pick a card from a deck of cards keep the card and pick another one
Final answer:
Tossing a dime and then tossing a quarter are independent events because one toss does not affect the other. Picking a card from a deck, keeping it, and picking another is a dependent event because the first pick changes the composition of the deck for the second pick.
Explanation:
To determine whether the two events mentioned are dependent or independent, we can use the definition of statistical independence. If the outcome of the first event does not affect the outcome of the second event, then the events are independent. If the outcome of the first event influences the outcome of the second event, then the events are dependent.
For the first scenario, tossing a dime and then tossing a quarter are independent events. This is because the result of tossing the dime has no effect on the result of tossing the quarter, much like having a nickel and a dime in your pocket and pulling one out, replacing it, and pulling one out again with probabilities being independent.
For the second scenario, when you pick a card from a deck of cards, keep the card, and then pick another one, the events are dependent. This is because the first card you draw and keep affects the composition of the deck from which the second card is drawn. It's like not replacing the first coin before pulling out the second one; your chances change based on the first outcome.
Using the concept of compound events and the law of the probability of compound events, we can see that independent events allow us to calculate the probability of any outcome when combining two independent events. Conversely, with dependent events, the probability of the subsequent event is influenced by the outcome of the preceding one.
30 packages a minute are unloaded from a truck that has 2700 packages. How long would it take to unload the truck?
It would take 90 minutes to unload a truck containing 2700 packages at a rate of 30 packages per minute.
Explanation:This problem involves performing a simple division operation. Given that 30 packages are unloaded from a truck each minute and there are a total of 2700 packages on the truck, we find the time it would take to unload the truck by dividing the total number of packages by the number of packages that can be unloaded each minute.
Solution:
We solve the problem as follows:
First, state the number of packages in the truck, which is 2700 packages. Next, note the rate at which packages are being unloaded per minute, which is 30 packages a minute. Then, we simply divide the total number of packages by the number of packages that can be unloaded per minute. This gives us the total time required to unload the entire truck, which is 2700⁄30 = 90 minutes.Therefore, it would take 90 minutes to unload the entire truck.
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Please help!! Will mark brainliest!!
Match each function to its domain.
Answer:
f(x) = sqrt(x-5) Domain: all real numbers greater or equal to 5 f(x) = 7/(x-8) Domain: all real numbers except 8 f(x) = sqrt(x) Domain: all positive real numbers and 0 f(x) = 8x Domain: all real numbers The domain of a function is the set of all numbers for which that function is valid.
Step-by-step explanation:
What is the vertex of the graph of y= x ^2+4x
Did i get this right?
A scientist is measuring the temperature change and a chemical compound the temperature dropped 11 Fahrenheit per hour from the original temperature after four hours the temperature was 90°F find the compounds original temperature
Answer: 134°F
Step-by-step explanation:
Given : A scientist is measuring the temperature change and a chemical compound the temperature dropped 11° Fahrenheit per hour from the original temperature .
Let x be the original temperature.
Then , the compound temperature after t hours is given by :_
[tex]y=x-11t[/tex]
At t= 4 hours and x= 90°F, we have
[tex]90=x-11(4)\\\\\Rightarrow\ x-44=90\\\\\Rightarrow\ x=90+44=134[/tex]
Hence , the compounds original temperature = 134°F
(2x-5)(4x+7) answer to this is?
If u(x)=-2x^2+3 and v(x)=1/x,what is the range of (uov)(x) ?
The range of the composition is:
R (-∞, 3)
How to find the range?
We have the functions:
u(x) = -2x² + 3
v(x) = 1/x
The composition gives:
(u o v)(x) = -2*v(x)² + 3
(u o v)(x) = -2(1/x)² + 3
Now, as x tends to infinity, the first term tends to zero (because the denominator is to large) then the function has an upper bound at 3.
Then as x decreases, the function decreases, when x tends to zero, the function tends to negative infinity.
So the range is:
R (-∞, 3)
What is the vertex of y=6x^2-24x+30
The vertex of the quadratic equation y = 6x^2 - 24 + 30 is (2, -6).
Explanation:The given equation is y = 6x^2 - 24x + 30.
To find the vertex of this quadratic equation, we can use the formula x = -b/2a.
In this equation, a = 6 and b = -24. Plugging these values into the formula, we get x = -(-24)/(2*6) = 24/12 = 2.
Now, substitute this value of x into the equation to find the corresponding y-coordinate of the vertex.
Substituting x = 2, we get y = 6(2)^2 - 24(2) + 30 = 12 - 48 + 30 = -6.
Therefore, the vertex of the given quadratic equation is (2, -6).
What are the zeros of the polynomial function f(x) = x3 − x2 − 20x?
The other two zeros, which are x = 5 and x = -4.
To find the zeros of the polynomial f(x) = x³ − x² − 20x, we need to set the polynomial equal to zero and solve for x. This can be done by factoring out the common term x from each term of the polynomial:
f(x) = x(x² - x - 20) = 0
The zeros of the polynomial will be the values of x for which the product is zero. Since we already have x as one factor, one zero is x = 0. We then need to factor the quadratic, which is:
x² - x - 20
We can factor this quadratic to
(x - 5)(x + 4)
Thus, the other two zeros of the polynomial are x = 5 and x = -4.
Can someone please help me. Preferably ASAP
q=
7(1-q)=-3(5+3q)
Line segment YV of rectangle YVWX measures 24 units. What is the length of line segment YX? 8 units units 12 units units
The length of the line segment YX in rectangle YVWX is [tex]\rm 8\sqrt{3} \; units[/tex] and it can be determine by using the trignometric properties and properties of rectangle.
Given :
YV = XW = 24 units[tex]\rm \angle VXW = 30^\circ[/tex][tex]\rm \angle XWV = 90^\circ[/tex][tex]\rm \angle XVW = 60^\circ[/tex]The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.
[tex]\rm tan \theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]\rm tan 60 = \dfrac{24}{VW}[/tex]
[tex]\rm \sqrt{3} = \dfrac{24}{VW}[/tex]
[tex]\rm VW =8\sqrt{3}\;units[/tex]
In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8\sqrt{3}\;units[/tex].
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[tex]\rm VW=YX = 8\sqrt(3)\;units.[/tex]
The length of the line segment YX in rectangle YVWX is \rm 8√(3) \; units and it can be determine by using the trignometric properties and properties of rectangle.
Given :
YV = XW = 24 units
[tex]\rm \angle VXW = 30^\circ\\\rm \angle XWV = 90^\circ\\\rm \angle XVW = 60^\circ[/tex]
The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.
[tex]\rm tan \theta = (Perpendicular)/(Base)\rm tan 60 = (24)/(VW)\rm √(3) = (24)/(VW)\rm VW =8√(3)\;units[/tex]
In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8√(3)\;units[/tex].
A point on the terminal side of an angle is given. find the exact value of the indicated trigonometric function of
At the restaurant, the cost of the meal before tax was $40. The tax is 8.5%, and Sheri wants to leave at least an 18% tip. Explain how to approximate the total cost of the meal.
18% + 8.5% = 26.5% which is close to 25%
25% of 40 is 10, 40 +10 = 50
so the total bill would be just over $50
real cost:
40*0.085 = 3.40 = 40 + 3.40 = 43.40
43.40 *0.18 = 7.81, 43.40 + 7.81 = 51.21
Answer:
The gratuity is about 20% of $40, which is $8. The tax is about 10% of $40, which is $4. So, the total cost is about $40 + $8 + $4 = $52.
What is the value of x in the equation 3x – 1/9y = 18, when y = 27?
A. 5
B. 7
C. 45
D. 63
The answer is x=7, because if you use PEMDAS you will come up with x=7.
Simplify by combining like terms: -18+3(5x-2)+8=46
-18 +3(5x-2)+8=46
-18 + 15x-6 +8 = 46
-18 + 15x +2 =46
-16 +15x =46
15x = 62
x = 62/15 = 4.1333
A carpenter has 16 1/2 m of wood. He cuts the wood into pieces that are each 2 3/4 m long. How many pieces of wood does the carpenter cut? please help ill mark brainliest
Answer:
the answer is 1/2
i think
Step-by-step explanation:
Given: f(x) =x^3 and g(x)= 4x+3
Find: g(f(3))
Jose heard a song on the radio as he was flipping between stations. He immediately remembered that his brother, Juan, played that piece on his guitar. Jose's response was _____ .emotional physical intellectual none of the above
Answer:
Option C, Intellectual Response
Step-by-step explanation:
Intellectual response comes after intellectual thinking which includes deep , intensive and focused thinking in a certain direction. In this case, Jose after hearing a song on radio remembers that his brother used to play the same song on guitar. This is an intellectual response as after listening the song Jose's brain must have evaluated the past interactions associated with this song and hence after the evaluation he comes to know that he had heard the same song in past when his brother played it on his guitar.
Thus, option C is correct.
A woman is 43 years old, and her daughter is 15 years old. How many years will it be before the woman’s age is just twice her daughter’s?
43 +x = 2(15+x)=
43 + x = 30 +2x
43 = 30 +x
13 =x
13 years
43+13 = 56
15 +13 = 28 ( 28*2 = 56)