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Related Questions
a lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. Describe what is being measured in this experiment and what variable is being manipulated?
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Two sandboxes with the same area are shown. The equation w(3w+1)=5^2 represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter.
A.) 2.72 meters
B.) 3.06 meters
C.) 9.16 meters
D.) 10.18 meters
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sandbox 1 area = 5*5 = 25 square m
sandbox 2
25=w*(3w+1)=
3w^2+w-25=0
w=2.7248 (round to 2.72 m)
2.72*3=8.16+1 = 9.16
Longest side = 9.16 meters
Answer:
C.) 9.16 meters
Step-by-step explanation:
We are given that the two sandboxes have same area and the equation is given by 25 = w*(3w+1).
Now, we simplify this equation in order to find the value of unknown variable 'w'.
i.e. 25 = 3[tex]w^{2}[/tex]+w
i.e. 3[tex]w^{2}[/tex]+w-25=0
The two factors of this quadratic equation are w=2.72 and w= -3.05.
But, as 'w' represents the length of the box, so it cannot be negative.
Therefore, w = 2.72
So, the longest side of the box is (3w+1) = 3*2.72+1 = 9.16 meter
Hence, the length of longest side to the nearest hundredth is 9.16 meter.
Can square root of 32 be simplified
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√32 = √8*4 = 4√2
Yes it can
First, we have to break 32 into its primes.
[tex]32=2^5[/tex]
[tex]=\sqrt{2^5}[/tex]
Since we don't want an odd number, we can split it into two.
[tex]=\sqrt{2^4\cdot \:2}[/tex]
[tex]=\sqrt{2}\sqrt{2^4}[/tex]
Since we want to remove one of the square roots, we have to do something like this: [tex]\sqrt{2^4}=2^{\frac{4}{2}}=2^2[/tex]
We would be left with,
[tex]=2^2\sqrt{2}[/tex]
Simplify the exponent.
[tex]=4\sqrt{2}[/tex]
This tells us that the square root of 32 can be simplified.
Thanks!
-TetraFish
Sec^-1(-square root 2)
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[tex]\bf cos^{-1}\left( -\frac{\sqrt{2}}{2} \right)=\measuredangle \theta \implies \measuredangle \theta = \begin{cases} \frac{3\pi }{4}\\ \frac{5\pi }{4} \end{cases}[/tex]
A roller coaster climbs 84 feet on the first hill then drop 60 feet down. on the second hill the roller coaster climb another 32 feet then drops 44 feet. what is te height at the end of the second hill ?
Answers
24 + 32 = 56
56 - 44 = 12
The answer is 12.
Answer:
12 feet.
Step-by-step explanation:
A roller coaster climbs the height on first hill = 84 feet.
Then drops down = 60 feet.
Height gained by the roller coaster = 84 - 60
= 24 feet
On other hill roller coaster climbs = 32 feet
Height gained by the roller coaster = 24 + 32 = 56 feet.
It drops again to the height = 44 feet
So the final height at the second hill = 56 - 44
= 12 feet
Therefore, height of roller coaster on the second hill is 12 feet.
The average grade mark received on 4 tests was 94. if he drops his lowest grade of 85, what will his new average be
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After dropping his lowest marks of 85 the new average test mark is 97.
Given, average test score of 4 tests is 94.
Average concept:
Average = sum of all the observations / total number of observations.
Average of 4 test marks = 94
94 = Sum of all the marks obtained in 4 tests / 4
Sum of all the marks obtained in 4 tests = 94 × 4
Sum of all the marks obtained in 4 tests = 376
Now the lowest marks of 85 are removed,
Remaining sum of 3 test marks = 376 - 85
Remaining sum of 3 test marks = 291
New average of 3 tests:
Average of 3 test marks = 291/3
Average of 3 test marks = 97
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In the diagram below, line segment bc is an altitude of triangle abd. What is the length of line age meant cd? If necessary, round your answer to two decimal places, PLEASE HELP ME IM REALLY STUCK
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running a perpendicular line like so from the right-angle, makes three similar triangles, the large, containing the smaller ones, and a medium and a small one. Now, using proportions, you can just use there, the medium and smalle to get "x".
At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]
Answers
Answer:
21
Step-by-step explanation:
A triangle has side lengths 9, 10, and 12. is it acute, obtuse, or right? explain.
Answers
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²
We have a=9, b=10 and c=12
a² + b² = 9² + 10² = 81 + 100 = 181
and
c² = 12² = 144
181 > 144 ⇒ аcute triangle.
Final answer:
By applying the Pythagorean theorem and comparing the square of the longest side to the sum of the squares of the other two sides, it is determined that a triangle with sides of 9, 10, and 12 is an acute triangle since 144 is less than 181.
Explanation:
To determine whether a triangle with side lengths of 9, 10, and 12 is acute, obtuse, or right, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides. If this condition is met, the triangle is right-angled. If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse. Conversely, if the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute.
For this triangle, the side lengths squared are:
9² = 8110² = 10012² = 144Adding the squares of the two shorter sides: 81 + 100 = 181.
Since 144 < 181, the square of the longest side (12²) is less than the sum of the squares of the other two sides, indicating that this triangle is acute.
In a large bag of marbles, 30% of them are red. a child chooses 4 marbles from this bag. if the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles? 0.0756 0.1764 0.2646 0.0810
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P[k] = nCk * p^k *q^(n-k)
P[3] = 4c3 * 0.3^3 * 0.7 = 0.0756
HELP Please THANKS:((((
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w + c <= 27
hope it helps
w>5.
Up to 27 acres will be filled with wheat and corn, so
w+c<=27
Final answer: A C
If the sum of 7 and 9 is more than 12 add 3; if less, subtract 2. the correct answer is
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The sum of 7 and 9 is:
7 + 9 = 16
The sum which is 16 is greater than 12. Therefore we add 3 to the sum:
16 + 3 = 19
Therefore the correct answer to this problem is 19.
Hot dogs come in packs of 10 and buns come in packs of 8. Whats the least amount of packs you can buy to have the same amount of hot dogs and buns.
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y=4x -1 and 12x=3y+7
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Use the first equation to substitute 4x - 1 for y in the second equation:
12x = 3(4x - 1)+7
12x = 12x - 3 + 7
12x = 12x +4
0 = 4
The last equation is FALSE, indicating the system of two equations has no solution.
For the function f(x) = –5x, which ordered pair will be a point on the graph of the function?
A.
(–5, 1)
B.
(2, 10)
C.
(15, –3)
D.
(0, 0)
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when x = 0, f(x) = –5(0) = 0
answer is D.
(0, 0)
Answer:
0,0 i think.. not sure so dont get mad at me
Step-by-step explanation:
You're 35 years old now, and you want to purchase life insurance which will cover your spouse for your lost income in the event of your death. You want this policy to last until what would be your normal retirement age of 65. Based on the given information, what is the best policy to buy?
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what is the value of x to the nearest tenth
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If the discriminant of an equation is negative, which of the following is true of the equation
A it has two complex solutions
B it has one real solution
C it had two real solutions
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Answer:
A. It has two complex roots.
Step-by-step explanation:
We are given that
Discriminant of an equation =negative
We have to find which is true about the equation .
Let quadratic equation
[tex]ax^2+bx+c=0[/tex]
Discriminant=[tex]D=b^2-4ac[/tex]
If D < 0 , then the equation has complex roots.
Therefore, if the discriminant of an equation is negative then the equation has two complex roots.
Answer:A. It has two complex roots.
A man paid $71.40 for a radio. The radio was marked 15% off the original selling price. What was the original selling price?
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Choose the missing exponent to create a polynomial: 3x^4+4x^2-9x^-?+2
A)2
B)3
C)-9
D)7
E)4
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we see we are given 9x^-?
so (-) times what=positive?
the answer is negative
so we must pick a negative exponent
so the answer is C -9
For a Polynominal 3x^4+4x^2-9x^-?+2 the missing part is mathematically given as
3x^4+4x^2-9x^-(-9)+2
-9, Option C is correct
What is a Polynomial?
Polynomials are summations of elements of the format of kxn, having k as any digit and n is +ve integer
Generally, the expression for the Polynominal is mathematically given as
3x^4+4x^2-9x^-?+2
In conclusion, the Polynominal must have all positive exponents, hence the value must be negative to give a positive exponent
Hence, -9 is correct
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Does anyone know the answer to this question?
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f(x) = x-3
g(x) = 2f(x)
g(2) = 2(2-3) = 2 * -1 = -2
Find a and b so that the polynomial, p(x)=x^2+ax-b passes through the points (6,-9) and (1, 16)
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The given equation is:
p(x) = x^2 + ax - b
We write this in terms of y:
y = x^2 + ax – b
To solve for the values of the constants a and b, we are given the following conditions:
When x = 6, y = -9
When x = 1, y = 16
From these conditions, we can formulate two equation by substituting the values of y:
-9 = 6^2 + a(6) – b
6a = b – 45 ---> 1
16 = 1^2 + a(1) – b
a = b + 15 ---> 2
Combining equations 1 and 2:
6 (b + 15) = b – 45
6b + 90 = b – 45
5b = -135
b = -27
calculating for a using equation 1:
a = b + 15
a = -27 + 15
a = -12
Answers:
a = -12
b = -27
The equation of a line is y = mx + 2. What is the value of m (the slope) if the line passes through point A(−5, −18)?
M=-4
M=4
M=1/4
M=7/8
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remember that (x,y)
so we are given (-5,-18)
so when x=-5, y=-18
so
-18=-5m+2
minus 2 both sides
-20=-5m
divide both sides by -5
4=m
m=4
answer is 2nd option
What is the work done by moving in the force field f~ (x, y) = h2x 3 + 1, 2y 4 i along the parabola y = x 2 from (−1, 1) to (1, 1)?
a.compute directly
b.use the theorem?
Answers
[tex]\mathbf f(x,y)=\langle2x^3+1,2y^4\rangle[/tex]
(though it's not entirely clear whether that's it...)
The parabolic path can be parameterized by
[tex]\mathbf r(t)=\langle t,t^2\rangle[/tex]
where [tex]-1\le t\le1[/tex]. Then the work done by the field along the path is
[tex]\displaystyle\int_C\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{t=-1}^{t=1}\langle2t^3+1,2t^8\rangle\cdot\langle1,2t\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_{-1}^1(2t^3+1+4t^9)\,\mathrm dt[/tex]
[tex]=2[/tex]
Not sure what theorem is being referred to in part (b). Perhaps you mean the gradient theorem? In which case you would need to show that there's a scalar function [tex]f(x,y)[/tex] such that [tex]\nabla f(x,y)=\mathbf f(x,y)[/tex]. We have
[tex]\nabla f(x,y)=\left\langle\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y}\right\rangle=\left\langle2x^3+1,2y^4\right\rangle[/tex]
from which we have
[tex]\dfrac{\partial f}{\partial x}=2x^3+1\implies f(x,y)=\displaystyle\int(2x^3+1)\,\mathrm dx[/tex]
[tex]\implies f(x,y)=\dfrac12x^4+x+g(y)[/tex]
[tex]\implies\dfrac{\partial f}{\partial y}=g'(y)=2y^4[/tex]
[tex]\implies g(y)=\dfrac25y^5+C[/tex]
[tex]\implies f(x,y)=\dfrac12x^4+x+\dfrac25y^5+C[/tex]
We have a candidate for a potential function, so we apply the gradient theorem, which asserts that the value of the line integral is path independent and can be determined by evaluating the potential function at the endpoints of the path. We then have
[tex]\displaystyle\int_C\mathbf f(x,y)\cdot\mathrm d\mathbf r=f(1,1)-f(-1,1)[/tex]
[tex]=\dfrac{19}{10}-\left(-\dfrac1{10}\right)[/tex]
[tex]=2[/tex]
as expected.
An angle measures 7pi/9 radians. What is the degree measure of the angle?
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1. You should know the percentage of the angle with respect to 2pi:
(7pi/9) / (2pi) = 7/18
2. Then, multiply the ratio to the 2pi angle in degrees, which is 360
360 * (7/18) = 140
140°
multiplying by 180/pi give you a degree measure
In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.
Find a quadratic model for the data in the table. Type your answer below. Show your work.
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Start with the first values of x=0 and y=5.1 to solve for c:
[tex]5.1=a(0) ^{2} +b(0)+c[/tex] so c = 5.1
Next use the second x and y values along with the value of c in the next equation:
[tex]3.03=a(1) ^{2} +b(1)+5.1[/tex] gives you
-2.07 = a + b. Solve this for a:
a = -2.07 - b
Finally use the third set of numbers with the c value AND the subbed value for a:
[tex]1.17=a(3) ^{2} +b(3)+5.1[/tex]
1.17 = 9(-2.07 - b)+ 3b + 5.1 which simplifies to:
1.17 = -18.63 - 9b + 3b + 5.1 which further simplifies to:
14.7 = -6b and b = -2.45
Now you have c and b, let's find a using one of the simplified equations:
-2.07 = a + b
-2.07 = a - 2.45
a = .38
So here's your equation:
[tex]y=.38 x^{2} -2.45x+5.1[/tex]
f(x) = Square root of x plus eight.; g(x) = 8x - 12 Find f(g(x))
Answers
Final answer:
To find f(g(x)), substitute g(x) into f(x) and simplify the expression to get the final answer. The final answer to the question would be as f(g(x)) = 8x⁴ - 32x³ + 32x² + 3
Explanation:
To find the value of f(g(x)) the following steps to be followed where the value of f(x) be substituted in g(x).
f(x) = 2x² + 3; g(x) = −2x² + 4x
Find f(g(x)) by substituting g(x) into f(x): f(g(x)) = 2(-2x² + 4x)² + 3
Simplify the expression: f(g(x)) = 2(4x⁴ - 16x³ + 16x²) + 3
Final answer after expansion: f(g(x)) = 8x⁴ - 32x³ + 32x² + 3
The original price of a couch is $650. It is on sale for $546. What is the percent change in the price off the couch?
Answers
%change=100(546-650)/650
%change= -16%
So 16% was taken off of the original price.
What value should go in the empty box to complete the calculation for finding the product of 62.834 × 0.45?
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So the product is: 28.2753. No tricks, better to use calculator, but you can do by hand too, not that hard.
The average of six numbers is 4. a seventh number is added and the new average is 5. what is the seventh number?
Answers
t/6 = 4.....t = 24 (the total of the 6 numbers)
(24 + x) / 7 = 5
24 + x = 35
x = 35 - 24
x = 11 <== ur 7th number
According to the question, the seventh number is 11.
Use the concept of average defined as:
Average, also known as the mean, is a statistical measure that represents the central value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total count of numbers.
To find the seventh number,
If the average of six numbers is 4, then the total sum of those six numbers would be 6 multiplied by 4, which is 24.
Assume the seventh number is 'x'.
If the new average (after adding the seventh number) is 5, then the total sum of all seven numbers would be 7 multiplied by 5, which is 35.
To find the seventh number 'x',
Subtract the sum of the initial six numbers (24) from the sum of all seven numbers (35).
This gives us 35 - 24 = 11.
Hence,
The seventh number is 11.
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