Answer:
(2^8x3^-5x6^0)^-2x(3^-2)/(2^3x2^28) = 3,359,232.
Find the original price of a salt lamp that is $60 after a 25% discount.
The original price of the salt lapm os $80.
How to find the original price of the salt lamp?Let's assume that the original price of the salt lamp is P, if we apply a discount of x (a percentage in decimal form) then the new price will be:
P' = P*(1 - x)
Here we know that the discount is of 25%, then x = 0.25
And the final price is $60, then we can write:
$60 = P*(1 - 0.25)
Now we can solve this for P.
$60 = P*0.75
$60/0.75 = P
$80 = P
That is the original price.
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The counting principle lets you add the number of options per category to find the total number of possible outcomes. True False
Answer:
The Answer Is False
Step-by-step explanation:
Hope It Helps U
5. It took 400 rails to create one mile of track. Each rail had ten (10) spikes. Each spike needed three (3) strikes from a hammer. A fast crew could lay four (4) rails in one minute. Crews averaged five (5) miles of track per day. If the distance from Rock Island, Illinois to Sacramento, California is approximately 1800 miles: How many rails were needed? How many spikes were needed? How many hammer strikes were heard each hour? How many days were needed to complete the track?
if you choose 2 of the 16,701 mathematics degrees at random, what is the probability that at least 1 of the 2 degrees was earned by a woman? show your work.
When chosen 2 of the 16,701 mathematics degrees at random, the probability that at least 1 of the 2 degrees was earned by a woman is P(at least 1 women out of 2)= 70.4064%
P(women)=0.4560
We know the rule: P(not A) = 1−P(A)
We can then determine the probability of individuals who earned a degree but are not women:
P(not women) =1−P(women)=1−0.4560=0.5440
when we multiply we get,
P(A and B) = P(A)×P(B)
now we can then determine the probability of obtaining 2 individuals who earned a degree but are not women:
P(2 not women) = P(not women) × P(not women)
= 0.5440 × 0.5440 = 0.295936
now we can use the complement rule, and with this now we can then determine the probability of at least 1 degree earned by women:
P(at least 1 women out of 2) = 1−P(2 not women) = 1−0.295936
=0.704064
=70.4064%
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x/6=67 whats the answer?
Answer:
x would be equal to 11.66 you get this when you divide 67 by 6.
Step-by-step explanation:
what is the length x of a side of the small inner square?
The length x of a side of the small inner square can be determined using the properties of similar triangles.
To find the length x, we can set up a proportion between the small inner square and the larger outer square.
Let's denote the side length of the small inner square as s and the side length of the larger outer square as S.
Since the small inner square is completely contained within the larger outer square, the ratio of their side lengths will be the same as the ratio of their corresponding sides.
Therefore, we can set up the following proportion:
s / S = x / (x + 10)
Here, the x + 10 represents the side length of the larger outer square, as it is 10 units longer than the side length of the small inner square.
To solve for x, we can cross-multiply the proportion:
s * (x + 10) = x * S
Expanding the equation:
sx + 10s = xS
Rearranging the equation to isolate x:
sx - xS = -10s
Factoring out the common term x:
x(s - S) = -10s
Dividing both sides by (s - S):
x = -10s / (s - S)
Now, we have an expression for x in terms of s and S.
It's important to note that the given information is insufficient to find the exact value of x without additional measurements or equations. The value of x will depend on the specific dimensions of the small inner square and the larger outer square.
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Would you help me solve this question with steps? It would really help, and thank you.
5x + 3y = 6
Answer's too short so here's some extra text.
i need help with this
Answer:
1. measure of angle E is 90 degrees
2. Measure of angle F + measure of angle G is 90 degrees
Step-by-step explanation:
Angle E is 90 degrees because it is marked as a right angle (the square)
A triangle has 180 degrees so if E is 90 degrees then the other 2 also have to equal 90 degrees
The distribution of cell phone bills for families in Smithtown North High School has mean $183 and standard deviation 11. At Smithtown South High School, the mean is$181 and the standard deviation is 21. Which distribution is more spread out?
Considering that it has a higher coefficient of variation, the distribution of cell phone bills at Smithtown South High School is more spread out.
What is the coefficient of variation of a distribution?The coefficient of variation for a distribution is given by the standard deviation of the distribution divided by the mean of the distribution. The higher the coefficient, the more spread out the distribution is.
For the distributions in this problem, the coefficients are given as follows:
Smithtown North High School: 11/183 = 0.0602. Smithtown South High School: 21/181 = 0.1160.Due to the higher coefficient of variation, the distribution of cell phone bills at Smithtown South High School is more spread out.
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(a) Find the sum of the first 200 natural numbers. (b) A golfball is dropped from a height of 30ft to the pavement. It always rebounds three fourths of the distance that it drops. How far (up and down) will the ball have traveled when it hits the pavement for the 6th time? (5)
a. the sum of the first 200 natural numbers is 20,100. b. when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).
(a) To find the sum of the first 200 natural numbers, we can use the formula for the sum of an arithmetic series.
The sum of the first n natural numbers is given by the formula: Sn = (n/2)(a + l), where Sn represents the sum, n is the number of terms, a is the first term, and l is the last term.
In this case, we want to find the sum of the first 200 natural numbers, so n = 200, a = 1 (the first natural number), and l = 200 (the last natural number).
Substituting these values into the formula, we have:
Sn = (200/2)(1 + 200)
= 100(201)
= 20,100
Therefore, the sum of the first 200 natural numbers is 20,100.
(b) The ball rebounds three-fourths of the distance it drops, so each time it hits the pavement, it travels a total distance of 1 + (3/4) = 1.75 times the distance it dropped.
For the 6th rebound, we need to find the distance the ball traveled when it hits the pavement.
Let's represent the initial drop distance as h (30 ft).
The total distance traveled after the 6th rebound is given by the sum of a geometric series:
Distance = h + h(3/4) + h(3/4)^2 + h(3/4)^3 + ... + h(3/4)^5 + h(3/4)^6
Using the formula for the sum of a geometric series, we can simplify this expression:
Distance = h * (1 - (3/4)^7) / (1 - 3/4)
Simplifying further:
Distance = h * (1 - (3/4)^7) / (1/4)
= 4h * (1 - (3/4)^7)
= 4 * 30 * (1 - (3/4)^7)
Calculating the value:
Distance ≈ 4 * 30 * (1 - 0.1335)
≈ 4 * 30 * 0.8665
≈ 104 ft
Therefore, when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).
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six positive integers are written on the faces of a cube. each vertex is labeled with the product of the three numbers on the faces adjacent to the vertex. if the sum of the numbers on the vertices is equal to $1001$, then what is the sum of the numbers written on the faces?
Answer:
31
Step-by-step explanation:
7+11+13=31
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Jodie wanted to match  Mandys obstacle course record of 68.2 seconds. She had already spent 40 1/4 seconds on rock climbing and 12.84 seconds on the ropes how much time did she have left to match the record
The time Jodie have left to match the record of Mandy is 15.11 seconds
TimeMandy's obstacle course = 68.2 secondsJodie:
Time spent climbing rock = 40 1/4 seconds= 40.25 seconds
Time spent on the rope = 12.84 seconds
Total time spent = 40.25 seconds + 12.84 seconds
= 53.09 seconds
Total time she have left to match the record = Mandy's obstacle course - Total time spent
= 68.2 seconds - 53.09 seconds
= 15.11 seconds
Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds
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If x= -2 find (1+x) + (1-x) and x-(x-1
Answer:
i have made it in above pic hope it helps
Answer:
\(2 \: and \: 1\)
Step-by-step explanation:
\((1 + x) + (1 - x) \\ = (1 + ( - 2)) + (1 - ( - 2)) \\ = ( - 1) + (3) \\ = 2 \\ \\ x - (x - 1) \\ = ( - 2) - (( - 2) - 1) \\ = - 2 + 2 + 1 \\ = 1\)
\(plzz \: mark \: as \: brainliest... \\ hope \: it \: helpss\)
Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers? a. mean b. median c. 2nd quartile d. 50th percentile
The least appropriate measure of central tendency for a data set that contains outliers is the mean. This is because the mean is calculated by taking the sum of all the values in the data set and dividing it by the number of values. This means that the mean is heavily influenced by outliers, as they are included in the calculation.
The median, 2nd quartile, and 50th percentile are all more appropriate measures of central tendency for a data set that contains outliers, as they are not affected by the presence of outliers. The median is calculated by taking the middle value of the data set, the 2nd quartile is calculated by taking the median of the upper half of the data set, and the 50th percentile is calculated by taking the value at the 50th percentile of the data set.
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I need some help better understanding Area Volume/Differential Equations, as ive been stuck on this single string of questions in my workbook for some time now, any and all help would be appreciated.
"Let R be the region in quadrant 1 bounded by y=3sin(2x) and y=e^x "
1) Find the area of R
2) Let S be the solid generated by rotating R around the x-axis. Find the volume of S.
3) Let Q be the solid generated by rotating R around the horizontal line y=5. Find the volume of Q
4) Let P be the solid whose base is R and whose cross sections perpendicular to the x-axis are semicircles. Find the volume of P.
Answer: Sure, I'd be happy to help you with these questions! Here are the solutions:
To find the area of R, we need to find the points of intersection between the two curves.
Setting y = 3sin(2x) and y = e^x equal to each other, we get:
3sin(2x) = e^x
Taking the natural logarithm of both sides, we get:
ln(3sin(2x)) = x
Now, we can find the x-coordinates of the intersection points by graphing the two curves or using a numerical method, such as a graphing calculator or Newton's method. The intersection points are approximately x = 0.306 and x = 2.313.
To find the area of R, we can integrate the difference between the two curves with respect to x:
A = ∫(e^x - 3sin(2x)) dx from x = 0.306 to x = 2.313
This integral can be evaluated using integration by substitution or a numerical method, such as a calculator or computer software. The area of R is approximately 2.828 square units.
To find the volume of S, we can use the formula for the volume of a solid of revolution:
V = ∫πy^2 dx from x = 0.306 to x = 2.313
Here, y = e^x - 3sin(2x) is the radius of the cross sections of the solid generated by rotating R around the x-axis.
This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of S is approximately 41.201 cubic units.
To find the volume of Q, we can use the formula for the volume of a solid of revolution around a horizontal line:
V = ∫π(y - 5)^2 dx from x = 0.306 to x = 2.313
Here, y = e^x - 3sin(2x) is the distance from the horizontal line y = 5 to the cross sections of the solid generated by rotating R around the line y = 5.
This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of Q is approximately 14.503 cubic units.
To find the volume of P, we can use the formula for the volume of a solid with known cross-sectional area:
V = ∫A(x) dx from x = 0.306 to x = 2.313
Here, the cross sections of P are semicircles perpendicular to the x-axis. The radius of each semicircle is given by:
r = (1/2)(e^x - 3sin(2x))
So the area of each semicircle is:
A = (1/2)πr^2 = (1/8)π(e^x - 3sin(2x))^2
Therefore, the volume of P is:
V = ∫(1/8)π(e^x - 3sin(2x))^2 dx from x = 0.306 to x = 2.313
This integral can be evaluated using numerical methods, such as a calculator or computer software. The volume of P is approximately 5.654 cubic units.
I hope this helps! Let me know if you have any further questions.
Step-by-step explanation:
What is the exponential of 1?
Exponential of 1 is equal to the number itself which means 1.
Exponent is usually described as the method of demonstrating large numbers in terms of powers. It means, exponent refers to the count, that how many times a number is multiplied to itself to calculate that exponent.
In accordance with the exponent rule, any number raised to power of 1 would always be equal to 1 that is because it doesn't matter how many times we multiply 1 to itself. It is going to yield 1. For example, multiplying 1 hundred times i.e. 1^100 also results in 1.
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70 = -7 k solve the equations
Answer:
-10
Step-by-step explanation:
70= -7k
70 -7k
-- --
-7 -7
-10=k
Have a great day
Answer:
k= -10
Step-by-step explanation:
70= -7k
Divide both sides by -7
-7k/-7 = 70/7
Simplify
k=-10
Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written
using function notation?
flv -v+
f(x) = - 3x + 4
f(x) = - *x+
f(V) = - 3y + 4
Answer:
b) y = f(x) = -3x+4
Step-by-step explanation:
Explanation
Given that the equation 9x+3y =12
Let 'x' be an independent variable and 'y' be the dependent variable then the function is of the form
y = f(x)
3 y = 12 - 9x
\(y = \frac{-9x+12}{3}\)
y = -3x+4
The function represented by y = -3x+4
c and d are positive integers quantity A c/d quantity B c+3/d+3
quantity A is greater
quantity B is greater
the two quantities are equal
the relationship cannot be determine from the information given
The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. The relationship between the quantities A and B cannot be determined from the information given.
The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. However, no specific values or constraints are given for c and d. Without knowing the specific values or any relationship between c and d, it is impossible to determine the relationship between A and B.
The relative magnitudes of A and B will depend on the values of c and d. If the value of c is greater than d, then A would be greater than B. Conversely, if the value of d is greater than c, then B would be greater than A. However, without any information about the values of c and d or any relationship between them, we cannot determine the relationship between A and B.
Therefore, based on the given information, the relationship between quantities A and B cannot be determined.
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please help with this question, I am quite confused
Answer:
Step-by-step explanation:
A-domain (-∞,∞)
B- Range(0,∞) the range is the set of values tat correspond with the domain
C- the y intercept (0,1) , y intercept is when x =0 (2/3)^0=1
D-the horizontal asymptote is x-axis y=0
E- the graph is always decreasing
F-it depend on the base
Using the letters $A$ and $B$, the following two-letter code words can be formed: $AA$, $AB$, $BB$, $BA$. Using the letters $A$, $B$, and $C$, how many different three-letter code words can be formed
Given that using the letters A and B, the numbers two-letter code words can be formed: AA, AB, BB, BA. We are asked to use the letters A, B, and C to determine the number of different three-letter code words that can be formed.
A code word is a string of characters used to represent a message, where each character is usually represented by a unique symbol.A code word is a set of $3$ distinct elements of since it is three letters long. There are a total of $3$ choices for the first letter, $3$ choices for the second letter, and $3$ choices for the third letter.
We then have $3\times3\times3$ or $27$ possible code words that can be formed using these letters. Thus, the number of different three-letter code words that can be formed using the letters A, B, and C is $27$.
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Find an equation of the tangent plane to the given parametric surface at the specified point. Graph the surface and the tangent plane.r(u,v)=u2i+2usinvj+ucosvk; u=1, v=0.
The equation of the tangent plane to the given parametric surface at the specific point is -2x + 4z = 0 .
In the question ,
it is given that ,
the function is r(u,v) = u²i + 2usin(v)j + ucos(v)k ; u = 1, v = 0 .
Now,
According to the give function,
r(u,v) = (u² , 2usin(v) , ucos(v))
Then, solving it , We get ,
r(u,v) = (u² , 2usin(v) , ucos(v))
\(r_{u}\) = (u , 2sin(v) , cos(v))
\(r_{u}\) (1,0) = (2 , 0 , 1)
\(r_{v}\) = (0 , 2ucos(u) , -sin(v))
\(r_{v}\) (1,0) = (0 , 2 , 0)
So , the matrix become
\(\left[\begin{array}{ccc}i&j&k\\2&0&1\\0&2&0\end{array}\right]\)
On simplifying , we get
i(−2) −j(0) \(+\) k(4) = (−2 , 0 , 4)
r(2,0) = (2 , 0 , 1)
The plane is
r = −2x \(+\) 4z
r(2,0,1) = −2(2) \(+\) 4(1) = d
−4 \(+\) 4 \(=\) d
d = 0
Therefore , the equation of tangent is -2x + 4z = 0 .
The given question is incomplete , the complete question is
Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v) = u²i + 2usin(v)j + ucos(v)k ; u = 1, v = 0 .
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Which problem is best represented by the equation 19 + 3x = 40?
Select one:
Ricardo spent $19 then bought 3 boxes of golf balls. If Ricardo had $40, how much
does he have left after shopping?
Yen earned $3 an hour cleaning houses. If Yen worked 19 hours, how many more
hours would she have to work to earn $40?
Gail paid $19 for a pair of jeans, $3 for a pair of socks and then bought a sweater. If
Gail spent $40, how much did she spend on the sweater?
Juan earned $19 baby-sitting and then earned $3 an hour for raking leaves. If Juan
earned $40, how long did it take Juan to rake leaves?
Answer:
a
Step-by-step explanation:
Find the area of the
shaded region
A 576 square feet?
Answer:
it's c
Can i be the brainlest?
Write 20.65 in expanded notation
Answer:
2 * 10 + 6 * .1 + 5 * .01
Step-by-step explanation:
for the graph of a certain quadratic $y = ax^2 + bx + c$, the vertex of the parabola is $(3,7)$ and one of the $x$-intercepts is $(-2,0)$. what is the $x$-coordinate of the other $x$-intercept?
The \($x$\)-coordinate of the other \($x$\)-intercept is \($\boxed{3-2\sqrt{39}}$\).
Since the vertex of the parabola is\($(3,7)$\), we know that the axis of symmetry is\($x=3$\). Since \($(-2,0)$\) is one of the\($x$\)-intercepts, we can write the quadratic equation in factored form as:
\($$y=a(x+2)\left(x-x_1\right)$$\)
where \($\$ x_{-} 1 \$$\) is the \($\$ \times \$$\)-coordinate of the other \($\$ \times \$$\)-intercept.
We know that the vertex is on the axis of symmetry, so we can use this information to find the value of \($\$ x_{-} 1 \$$\). Since the axis of symmetry is \($\$ \mathrm{x}=3 \$$\), the distance between the vertex at \($\$(3,7) \$$\) and the\($\$ \times \$$\)-intercept at \($\$(-2,0) \$$\) must be the same as the distance between the vertex and the other \($\$ \times \$$\)-intercept, which we don't know yet.
The distance between \($\$(3,7) \$$\) and \($\$(-2,0) \$$\) is:
\($$\sqrt{(3-(-2))^2+(7-0)^2}=\sqrt{25+49}=2 \sqrt{39}$$\)
So the distance between the vertex and the other \($\$ \times \$$\)-intercept is also \($\$ 2$\) |sqrt\($\{39\} \$$\). This means that the\($\$ \times \$$\)-coordinate of the other \($\$ \times \$$\)-intercept must be \($\$ 3+2 \mid$\) sqrt \($\{39\} \$$\) or \($\$ 3$\) 21 sqrt \($\{39\} \$$\).
So the distance between the vertex and the other \($x$\)-intercept is also
\($2\sqrt{39}$\). This means that the \($x$\)-coordinate of the other \($x$\)-intercept must be \($3+2\sqrt{39}$\) or \($3-2\sqrt{39}$\).
Therefore, the \($x$\)-coordinate of the other \($x$\)-intercept is \($\boxed{3-2\sqrt{39}}$\).
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Dave was on a high-rise platform when he jumped off and into the pool below. His height as a function
of time can be modeled by the function, f(t) = -16² +16t+15. Graph the function and answer
the questions that follow.
Dave reached his maximum height at ____ seconds
The highest distance from the water that Dave reached was__ feet
How tall was the platform?
Dave hit the water at approximately ____ seconds
tenth.).
the platform was 192 feet tall.
Dave was on a high-rise platform when he jumped off and into the pool below. His height as a function of time is given by h(t) = -16t^2 + 64t + 192, where h(t) is his height (in feet) above the water at time t seconds. Find the highest distance from the water that Dave reached, and determine how tall the platform was.To determine the highest distance from the water that Dave reached, we need to find the vertex of the parabolic function h(t) = -16t^2 + 64t + 192. Recall that the vertex of a parabola in the form y = ax^2 + bx + c is given by the point (x = -b/2a, y = c - b^2/4a).In this case, we have a = -16, b = 64, and c = 192.
Therefore, the vertex of the parabola is located att = -b/2a = -64/(2*(-16)) = 2h(t) = -16(2)^2 + 64(2) + 192 = 256 ftHence, the highest distance from the water that Dave reached was 256 feet.To determine the height of the platform, we need to find the initial height from which Dave jumped. Recall that the initial height is given by the constant term in the function h(t).In this case, we have h(0) = -16(0)^2 + 64(0) + 192 = 192 ft
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A pair of weak earthquakes are modeled by nonlinear inequalities. One earthquake occurred roughly 15 km south and 18 km west of the center of Salt Lake City, Utah. The quake could be felt 16 km away. A couple of days later another earthquake occurred 9 km north and 4 km east of the center of Salt Lake City and could be felt 21 km away. If Salt Lake City is located at (0, 0) on a coordinate grid, the system below represents this scenario.
StartLayout Enlarged Left-brace first row (x + 18) squared + (y + 15) squared less-than-or-equal-to 256 Second row (x minus 4) squared + (y minus 9) squared less-than-or-equal-to 441 EndLayout
Which location in relation to Salt Lake City felt both earthquakes?
12 km east and 2 km north
12 km east and 2 km south
12 km west and 2 km north
12 km west and 2 km south
2 km east and 10 km north
Step-by-step explanation:
I did the activity and got the right answer.
Answer: 12km west and 2km south
Step-by-step explanation:
Just did it
What value of n makes the equation 4(0.5n − 3) = n − 0.25(12 − 8n) true?
3
-9
0
-1
Answer:
n = -9
Step-by-step explanation:
4(0.5n − 3) = n − 0.25(12 − 8n)
2n - 12 = n - 3 + 2n
2n - 12 = 3n - 3
2n - 3n = - 3 +12
-1n = 9
n = -9
Sketch a 30∘−60∘−90∘ triangle with your hypotenuse length, and then find the exact length (not a decimal approximation) of each leg. hypolenuse length =20 2. Sketch a 45∘−45∘−90∘ triangle with your hypotenuse length, and then find the length (not a decimal approximation) of each leg. hypotenuse =20
In a 30∘−60∘−90∘ triangle with a hypotenuse length of 20, the exact lengths of the legs are 10 and 10√3.
In a 45∘−45∘−90∘ triangle with a hypotenuse length of 20, the exact lengths of the legs are both 10.
In a 30∘−60∘−90∘ triangle, the ratio of the lengths of the sides is 1:√3:2. Given that the hypotenuse has a length of 20, the shorter leg can be found by dividing the hypotenuse by 2, resulting in a length of 10. The longer leg is then found by multiplying the shorter leg by √3, giving a length of 10√3.
In a 45∘−45∘−90∘ triangle, the ratio of the lengths of the sides is 1:1:√2. Since the hypotenuse has a length of 20, both legs must have the same length. Therefore, each leg has a length of 20 / √2, which simplifies to 10√2.
Hence, in the 30∘−60∘−90∘ triangle, the exact lengths of the legs are 10 and 10√3, while in the 45∘−45∘−90∘ triangle, both legs have an exact length of 10.
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