The Math Club raised $400.
To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.
Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.
According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.
To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:
Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%
Now we can set up a proportion to determine the amount raised by the Math Club:
(x / $2000) = 20% / 100%
Cross-multiplying:
x = ($2000 * 20%) / 100%
Simplifying:
x = $400
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PLEASE HELP. The value of "y" varies directly with "x".
If y 6, then x = 2.
Find "y" if x = 5.
k = 3
y = [?]
Answer:
y=15
Step-by-step explanation:
y varies directly as x so:
y=k(x)
y = kx
if y is 6 and x is 2;
input the values
y=kx
6=k(2)
[tex] \frac{6}{2} = \frac{2k}{2} [/tex]
k = 3
then find y if x=5
use the previous formula
y=kx so:
y=3(5)
therefore y=15
Jabez was solving the math problem 54 x 0.06. Before solving, he estimates that his answer will be less than 54 but greater than 5.4. His classmate, Christina, disagrees and thinks the answer will be less than 5.4. Who is correct, Jabez or Christina? Explain how you know who is correct without calculating the product of 54 x 0.06.
Jabez is correct without calculating the product of 54 x 0.06 correctly because his estimation aligns with the mathematical principle that multiplying a number by a decimal less than 1 will result in a smaller product.
To determine who is correct without calculating the product of 54 x 0.06, we can use estimation.
Jabez estimated that the answer will be less than 54 but greater than 5.4. Let's analyze his estimation. When multiplying a number by a decimal less than 1, the product will always be smaller than the original number. In this case, 54 is the original number. Since 0.06 is less than 1, the product of 54 x 0.06 will definitely be smaller than 54.
On the other hand, Christina thinks the answer will be less than 5.4. Let's analyze her estimation. The original number, 54, is already greater than 5.4. When multiplying it by a decimal less than 1, the product will be even smaller. Therefore, Jabez's estimation is incorrect.
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I only need help with the f(0)= the equation is above all the rest is filled in thank you
f(0) = -3
I believe, since the graph has a closed circle/point at (0,-3), f(0) should equal -3. Also, the graph 3x-3 has a domain of x>=0.
However, in terms of limits, the limit approaching x-->0 does not exist since the left and right limits do not equal one another.
Hope this helps.
Type the correct answer in each box. Round your answers to the nearest thousandth.
A company has 200 machines. Each machine has 12% probability of not working.
If you were to pick 40 machines randomly, the probability that 5 would not be working is
and the probability that at least one machine would be working is
the probability that all would be working is
1) The probability that 5 will be working is: 0.187
2) The probability that at least one machine would be working is: 0.006
3) The probability that all would be working is : 1
How to find the probability of working?We are given the parameters as:
Total number of machines = 200
Probability that a Machine is working = 12% = 0.12
1) Now, you want to pick 40 machines and want to find the probability that 5 will be working.
This probability is given by the expression:
P(5 working) = C(40,5) * 0.12⁵·0.88³⁵ ≈ 0.187
where C(n, k) = n!/(k!(n-k)!)
2) The probability that at least one machine would be working is:
0.88⁴⁰ ≈ 0.006
3) The probability that all would be working is the complement of the probability that all have failed. Thus:
P(all working) = 1 - 0.12⁴⁰ ≈ 1
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Solve for each variable.
a = ___
b = ___
c = ___
d = ___
Answer:
a=55°
b=123°
c=55°
d=123°
Is the relation shown in the table below a function? (type in yes or no)
Answer:
Yes
Step-by-step explanation:
To know if a table is a function or not, we have to see if 1 input only has 1 output.
Looking at the table each input only has 1 output, so it is a function.
Ram borrowed Rs. 250000 from sit a at the rate of 21%: per annum. At the end of monts, how much should he pay compounde à half yearly ?
The end of 6 months, Ram should pay Rs. 276250 compounded half-yearly.
Ram borrowed Rs. 250000 from Sit at an interest rate of 21% per annum. To calculate the compound interest, we need to know the compounding period. In this case, the interest is compounded half-yearly, which means it is calculated twice a year.
To find out how much Ram should pay at the end of 6 months, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount to be paid at the end of the time period
P = the principal amount (the initial amount borrowed) = Rs. 250000
r = the interest rate per period (in decimal form) = 21% = 0.21
n = the number of compounding periods per year = 2 (since it's compounded half-yearly)
t = the number of years = 6 months = 6/12 = 0.5 years
Plugging in these values into the formula, we get:
A = 250000(1 + 0.21/2)^(2*0.5)
Simplifying the equation:
A = 250000(1 + 0.105)^(1)
A = 250000(1.105)
A = Rs. 276250
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I need to solve this, but the process is confusing and I need someone to help me understand it, please and thank you :))
[tex]\frac {x^2+5x+6}{x - 1}\ \textgreater \ 0[/tex]
Answer:
(-3, -2) ∪ (1, ∞)
Step-by-step explanation:
Given inequality:
[tex]\dfrac{x^2+5x+6}{x-1} > 0[/tex]
Begin by factoring the denominator:
[tex]\begin{aligned}x^2+5x+6&=x^2+2x+3x+6\\&=x(x+2)+3(x+2)\\&=(x+3)(x+2)\end{aligned}[/tex]
Therefore, the factored inequality is:
[tex]\dfrac{(x+3)(x+2)}{x-1} > 0[/tex]
Determine the critical points - these are the points where the rational expression will be zero or undefined.
The rational expression will be zero when the numerator is zero:
[tex](x+3)(x+2)=0 \implies x=-3,\;x=-2[/tex]
Therefore, -3 and -2 are critical points.
The rational expression will be undefined when the denominator is zero:
[tex]x-1=0 \implies x=1[/tex]
Therefore, 1 is a critical point.
So the critical points are -3, -2 and 1.
Create a sign chart, using open dots at each critical point (the inequality is greater than, so the interval doesn't include the values).
Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.
Chosen test values: -4, -2.5, 0, 2
For each test value, determine if the function is positive or negative:
[tex]x=-4 \implies \dfrac{(-4+3)(-4+2)}{-4-1} = \dfrac{(-)(-)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]
[tex]x=-2.5 \implies \dfrac{(-2.5+3)(-2.5+2)}{-2.5-1} = \dfrac{(+)(-)}{(-)}=\dfrac{(-)}{(-)}=+[/tex]
[tex]x=0 \implies \dfrac{(0+3)(0+2)}{0-1} = \dfrac{(+)(+)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]
[tex]x=2 \implies \dfrac{(2+3)(2+2)}{2-1} = \dfrac{(+)(+)}{(+)}=\dfrac{(+)}{(+)}=+[/tex]
Record the results on the sign chart for each region (see attached).
As we need to find the values for which the rational expression is greater than zero, shade the positive regions on the sign chart (see attached). These regions are the solution set.
Remember that the intervals of the solution set should not include the critical points, as the critical points of the numerator make the expression zero, and the critical point of the denominator makes the expression undefined. The intervals of the solution set are those where the rational expression is greater than zero only.
Therefore, the solution set is:
-3 < x < -2 or x > 1
As interval notation:
(-3, -2) ∪ (1, ∞)
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3) ABCD is a rectangle.
The line that contains BA is y=-x+3. Write the
equations of the lines that contain BC, AD, and CD
The equations of the other line are:
BC: y = 2x
AD: y = 2x + 2
CD = -¹/₂x + 5.5
How to find the equation of the Line?The formula for the equation of a line between two coordinates is expressed as:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
Thus, for the lines we have:
BC has B(-2, 4) and C(-1, 6)
Thus:
BC: (y - 4)/(x - 2) = (6 - 4)/(-1 + 2)
BC: (y - 4)/(x - 2) =2
BC: y - 4 = 2x - 4
BC: y = 2x
AD has A(2,2) and D(3, 4)
Thus:
AD: (y - 2)/(x - 2) = (4 - 2)/(3 - 2)
AD: y - 2 = 2x - 4
AD: y = 2x + 2
CD has C(-1, 6) and D(3, 4)
CD: (y - 6)/(x + 1) = (4 - 6)/4
CD: y - 6 = -¹/₂(x + 1)
CD = -¹/₂x + 5.5
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The uniform thin rod in the figure below has mass M 5.00 kg and length L = 2.17 m and is free to rotate on a frictionless pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of the rod's angular acceleration, the tangential acceleration of the rod's center of mass, and the tangential acceleration of the rod's free end. (a) the rod's angular acceleration (in rad/s2) rad/s2 (b) the tangential acceleration of the rod's center of mass (in m/s2) m/s2 (c) the tangential acceleration of the rod's free end (in m/s2) m/s2
(a) The magnitude of the rod's angular acceleration is (3g/2L) rad/s^2.
(b) The tangential acceleration of the rod's center of mass is (3g/4) m/s^2.
(c) The tangential acceleration of the rod's free end is (3g/2) m/s^2.
(a) To find the magnitude of the rod's angular acceleration, we can use the formula for rotational motion. The torque acting on the rod is due to the gravitational force acting at its center of mass.
The torque is given by τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
For a thin rod rotating about one end, the moment of inertia is (1/3)ML^2, where M is the mass of the rod and L is its length.
The torque is equal to the product of the gravitational force and the perpendicular distance from the pivot to the center of mass, which is (1/2)L.
So we have τ = (1/2)MgL, where g is the acceleration due to gravity. Substituting these values into the torque equation, we get (1/2)MgL = (1/3)ML^2 α.
Simplifying the equation, we find α = (3g/2L).
Therefore, the magnitude of the rod's angular acceleration is (3g/2L) rad/s^2.
(b) The tangential acceleration of the rod's center of mass can be found using the formula a = αr, where a is the tangential acceleration, α is the angular acceleration, and r is the distance from the center of mass to the pivot point.
In this case, the distance r is (1/2)L, so substituting the values, we get a = (3g/2L)(1/2)L = (3g/4) m/s^2.
Therefore, the tangential acceleration of the rod's center of mass is (3g/4) m/s^2.
(c) The tangential acceleration of the rod's free end is equal to the sum of the tangential acceleration of the center of mass and the product of the angular acceleration and the distance from the center of mass to the free end.
Since the distance from the center of mass to the free end is (1/2)L, the tangential acceleration of the free end is
a + α(1/2)L = (3g/4) + (3g/2L)(1/2)L = (3g/4) + (3g/4) = (3g/2) m/s^2.
Therefore, the tangential acceleration of the rod's free end is (3g/2) m/s^2.
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Find a polynomial with real coefficients that has the given zeros. 5+2i, 5-2i, -1 One such polynomial P(x) can be defined as P(x) = x³ - 9x² + x + 29.
The polynomial with real coefficients from the zeros is P(x) = 2x³ - 18x² + 2x + 58
Find a polynomial with real coefficients from the zeros.From the question, we have the following parameters that can be used in our computation:
zeros = 5+2i, 5-2i, -1
One such polynomial P(x) can be defined as
P(x) = x³ - 9x² + x + 29.
When this polynomial is multiplied by a costant, the roots and zeros remain the same
Let the constant be 2
So, we have
New P(x) = 2(x³ - 9x² + x + 29)
Evaluate
New P(x) = 2x³ - 18x² + 2x + 58
Hence, the function is P(x) = 2x³ - 18x² + 2x + 58
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Type the expressions as radicals. y 5/2
Type the expressions as radicals y^5/2.
Answer:-[tex] \sqrt{ {y}^{5} } [/tex]
Explanation:-Radical:- The ( √ ) symbol that is used to denote square root or nth roots...
Radicals ( Square roots , cube roots , fourth roots and so on )It can be rewritten as rational exponents ( exponents which are fractions ) using the formula:-
[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]
Generally, using the power rule of exponents:
[tex] \sqrt[n]{ {x}^{m} } = {( {x}^{m)} }^{ \frac{1}{n} } = {x}^{ \frac{m}{n} } [/tex]
Let's take an example to understand better:
• convertion between radicals and rational exponents:
[tex] \sqrt[7]{ {8}^{4} } = {8}^{ \frac{4}{7} } [/tex]
Since the type of radical corresponds with the denominator of a rational exponent, we know the denominator of the exponent will be 7 ..
So ,[tex] {y}^{ \frac{5}{2} } = \sqrt{ {y}^{5} } [/tex]
As , √ denotes ½ ..
Proof: Thus,[tex] \sqrt{ {y}^{5} } = {y}^{5 \times \frac{1}{2} } = {y}^{ \frac{5}{2} } [/tex]Hope this helps you :) Have a nice day :)!The expression "y 5/2" can be written as the fifth root of y squared: √[[tex]y^{2}[/tex]]^(1/5).
The expression "y 5/2" can be written as the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).
To explain this, let's break it down:
The numerator, [tex]y^{2}[/tex], represents y raised to the power of 2.
Taking the square root of [tex]y^{2}[/tex] simplifies it to √([tex]y^{2}[/tex]).
Finally, raising the result to the power of 1/5 gives us the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).
In other words, the expression "y 5/2" represents the operation of first squaring y, then taking the fifth root of the resulting value. This is equivalent to finding the value that, when raised to the power of 5, yields [tex]y^{2}[/tex].
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4 is the product of 8 and b simplify all fractions
The value of b in the Problem given is 0.5
Simplifying Word problemsThe given problem can be represented mathematically as below :
4 = 8 * bWe can find be in the expression thus :
4 = 8b
divide both sides by 8 in other to isolate b
4/8 = 8b/8
0.5 = b
Therefore, value of b in the expression is 1/2.
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(4x³+6x²+20x+9)/2x+1
divide using long polynomial division
The result of dividing (4x³ + 6x² + 20x + 9) by (2x + 1) using long polynomial division is 2x² + 2x + 9 with a remainder of 0.
To divide the polynomial (4x³ + 6x² + 20x + 9) by (2x + 1) using long polynomial division.
Arrange the terms of the dividend and the divisor in descending order of the degree of x:
2x + 1 | 4x³ + 6x² + 20x + 9
Divide the first term of the dividend by the first term of the divisor and write the result on the top line:
2x + 1 | 4x³ + 6x² + 20x + 9
| 2x²
Multiply the divisor (2x + 1) by the quotient obtained in the previous step (2x²) and write the result below the dividend:
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
Subtract the result obtained in the previous step from the dividend and bring down the next term.
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
- (4x² + 2x)
---------------
18x + 9
Repeat the process by dividing the term brought down (18x) by the first term of the divisor (2x):
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
- (4x² + 2x)
---------------
18x + 9
- (18x + 9)
---------------
0
The division is complete when the degree of the term brought down becomes less than the degree of the divisor.
In this case, the degree of the term brought down is 0 (a constant term). Since we can no longer divide further, the remainder is 0.
Therefore, the result of the division is:
Quotient: 2x² + 2x + 9
Remainder: 0
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35 is what percent of 105
Answer:
33.33%
Step-by-step explanation:
We Take
(35 ÷ 105) x 100 ≈ 33.33%
So, 35 is 33.33% of 105
Please answer all correctly!
Answer:
Step-by-step explanation:
For the left graph g:
The absolute max is 4 because the highest it goes is to 4 but there is no min because the arrows at bottom means it keeps going
For right graph h:
The absolute max is 3 because that's the highest point
The absolute min is -5 because that's the lowest but there are no arrows so the curve ends on both ends.
Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
9x2 − y2 + 3z2 = 0
(Write an equation for the cross section at
z = 0
using x and y.)
(Write an equation for the cross section at
y = −9
using x and z.)
(Write an equation for the cross section at
y = 9
using x and z.)
(Write an equation for the cross section at
x = 0
using y and z.)
Answer:
Step-by-step explanation:
To sketch the surface represented by the equation 9x² - y² + 3z² = 0 and find the equations for the cross sections, we can start by isolating each variable and considering different values for the fixed variables.
(1) - Cross section at z = 0:
Substituting z = 0 into the equation, we get 9x² - y² = 0 . Rearranging this equation, we have:
9x² = y²
Taking the square root of both sides, we get:
y = ±3x
So the equation for the cross section at z = 0 is y = ±3x and our trace is a line in the xy-plane.
(2) - Cross section at y = -9:
Substituting y = -9 into the equation, we get 9x² - (-9)² + 3z² = 0. Simplifying this equation, we have:
9x² - 81 + 3z² = 0
Rearranging, we obtain:
9x² + 3z² = 81
Dividing by 3, we get:
3x² + z² = 27
So the equation for the cross section at y = -9 is 3x² + z² = 27 and our trace is an ellipse in the xz-plane.
(3) - Cross section at y = 9:
Substituting y = 9 into the equation, we get 9x² - (9)² + 3z² = 0. Simplifying this equation, we have:
9x² - 81 + 3z² = 0
Rearranging, we obtain:
9x² + 3z² = 81
Dividing by 3, we get:
3x² + z² = 27
So the equation for the cross section at y = -9 is 3x² + z² = 27 and our trace is an ellipse in the xz-plane.
(4) - Cross section at x = 0:
Substituting x = 0 into the equation, we get - y² + 3z² = 0. Rearranging this equation, we have:
y² = 3z²
Taking the square root of both sides, we get:
y = ±√3z
So the equation for the cross section at x = 0 is y = ±√3z and our trace is a parabola in the yz-plane.
Given the following rectangles, identify all combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping. You can't cut any of the rectangles but you may use some of them multiple times. More than one answer may be correct; mark all that apply.
Rectangles you are given:
answer options:
two C rectangles, two D rectangles, and two B rectangles
one each of rectangles A, B, C, and D
one A rectangle and four B rectangles
three E rectangles and two B rectangles
one E rectangle, one C, one D, and three B rectangles
The combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping are:
One each of rectangles A, B, C, and D.One A rectangle and four B rectangles.What is a rectangle?A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides.
Required
Which group forms a rectangle of
[tex]\text{Length}=15[/tex]
[tex]\text{Width}=11[/tex]
First, calculate the area of the big rectangle
[tex]\text{Area}=\text{Length}\times\text{Width}[/tex]
[tex]\text{A}_{\text{Big}}=15\times11[/tex]
[tex]\text{A}_{\text{Big}}=165[/tex]
Next, calculate the area of each rectangle A to E.
[tex]\text{A}_{\text{A}}=11\times7[/tex]
[tex]\text{A}_{\text{A}}=77[/tex]
[tex]\text{A}_{\text{B}}=2\times11[/tex]
[tex]\text{A}_{\text{B}}=22[/tex]
[tex]\text{A}_{\text{C}}=6\times6[/tex]
[tex]\text{A}_{\text{C}}=36[/tex]
[tex]\text{A}_{\text{D}}=6\times5[/tex]
[tex]\text{A}_{\text{D}}=30[/tex]
[tex]\text{A}_{\text{E}}=13\times4[/tex]
[tex]\text{A}_{\text{E}}=52[/tex]
Then consider each option.
(a) 2C + 2D + 2B
[tex]2\text{C}+2\text{D}+2\text{B}=(2\times36)+(2\times30)+(2\times22)[/tex]
[tex]2\text{C}+2\text{D}+2\text{B}=72+60+44[/tex]
[tex]2\text{C}+2\text{D}+2\text{B}=176[/tex]
(b) A + B + C + D
[tex]\text{A}+\text{B}+\text{C}+\text{D}=77+22+36+30[/tex]
[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]
(c) A + 4B
[tex]\text{A} + 4\text{B}=77+(4\times22)[/tex]
[tex]\text{A} + 4\text{B}=77+88[/tex]
[tex]\text{A} + 4\text{B}=165[/tex]
(d) 3E + 2B
[tex]3\text{E}+2\text{B}=(3\times52)+(2\times22)[/tex]
[tex]3\text{E}+2\text{B}=156+44[/tex]
[tex]3\text{E}+2\text{B}=200[/tex]
(e) E + C + D + 3B
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+(3\times22)[/tex]
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+66[/tex]
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=184[/tex]
Recall that:
[tex]\text{A}_{\text{Big}}=165[/tex]
Only options (b) and (c) match this value.
[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]
[tex]\text{A} + 4\text{B}=165[/tex]
Hence, options (b) and (c) are correct.
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Predict the population in 2016, as a decreases at a constant rate
Answer:
We need more information to accurately predict the population in 2016. The following information is needed:
The initial population (population in a given baseline year)
The known population decrease rate as a percentage or absolute number per year
For example, if:
The initial population (in 2010) was 10,000
The population is decreasing at a constant rate of 100 people per year
Then we can calculate the population in 2016 as follows:
2010 population: 10,000
2011 population: 10,000 - 100 = 9,900
2012 population: 9,900 - 100 = 9,800
2013 population: 9,800 - 100 = 9,700
2014 population: 9,700 - 100 = 9,600
2015 population: 9,600 - 100 = 9,500
2016 population: 9,500 - 100 = 9,400
Therefore, based on this information, the predicted population in 2016 would be 9,400.
In summary, to accurately predict population changes over time, we need to know the initial population and population decrease rate. With that information, we can calculate the population for each subsequent year by subtracting the decrease amount from the population in the previous year.
Hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
help please ill give brainliest!! please show work
find x
Answer:
x = 10
Step-by-step explanation:
the figure inscribed in the circle is a cyclic quadrilateral , all 4 vertices lie on the circumference.
the opposite angles in a cyclic quadrilateral sum to 180° , that is
6x + 1 + 10x + 19 = 180
16x + 20 = 180 ( subtract 20 from both sides )
16x = 160 ( divide both sides by 16 )
x = 10
2(x+5)-5 x 12 example pls
When x = 3, the expression 2x - 50 evaluates to -44.
To demonstrate an example using the expression 2(x + 5) - 5 × 12, let's simplify it step by step:
Start with the given expression.
2(x + 5) - 5 × 12
Apply the distributive property.
2x + 2(5) - 5 × 12
Simplify within parentheses and perform multiplication.
2x + 10 - 60
Combine like terms.
2x - 50
The simplified form of the expression 2(x + 5) - 5 × 12 is 2x - 50.
Let's consider an example for substituting a value for the variable x:
Suppose we want to evaluate the expression when x = 3. We substitute x = 3 into the simplified expression:
2(3) - 50
Now, perform the calculations:
6 - 50
The result is -44.
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Question
evaluate the expression 2(x+5)-5 x 12.
Nicole, Miguel, and Samuel served a total of 115 orders Monday at the school cafeteria. Miguel served 3 times as many orders as Samuel. Nicole served 10 more orders than Samuel. How many orders did they each serve?
Answer:
Samuel = 21 orders
Nicole = 31 orders
Miguel = 63 orders
Step-by-step explanation:
Let N represent Nicole's orders, M represents Miguel's orders, and S represent Samuel's orders.
We know that the sum of their tree orders equals 115 as
N + M + S = 115
Since Miguel served 3 times as many orders as Samuel, we know that
M = 3S.
Since Nicole served 10 more orders than Samuel, we know that
N = S + 10
Samuel's Orders:
Now we can plug in 3S for M and S + 10 for N to find S, the number of Samuel's orders:
S + 10 + 3S + S = 115
5S + 10 = 115
5S = 105
S = 21
Thus, Samuel served 21 orders.
Nicole's Orders:
Now we can plug in 21 for S in N = S + 10 to determine how many orders Nicole served:
N = 21 + 10
N = 31
Thus, Nicole served 31 orders.
Miguel's Orders:
Now we plug in 19 for S in M = 3S to determine how many orders Miguel served:
M = 3(21)
M = 63
Thus, Miguel served 63 orders.
Kemani Walker
Law of Sines
Jun 15, 9:29:00 PM
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In ATUV, t = 820 inches, m/U=132° and m2V=25°. Find the length of u, to the
nearest inch.
Answer: u =
Submit Answer
The length of u, to the nearest inch, is 1818 inches.
To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
In this case, we'll use the following formula:
a/sin(A) = b/sin(B) = c/sin(C)
Let's label the sides and angles of the triangle:
Side a = u (length of u)
Side b = t (820 inches)
Side c = v (length of v)
Angle A = m/U (132°)
Angle B = m2V (25°)
Angle C = 180° - A - B (as the sum of angles in a triangle is 180°)
Now, we can use the Law of Sines to set up the equation:
u/sin(A) = t/sin(B)
Plugging in the given values:
u/sin(132°) = 820/sin(25°)
To find the length of u, we'll solve this equation for u.
u = (820 [tex]\times[/tex] sin(132°)) / sin(25°)
Using a calculator, we can evaluate the right side of the equation to get the approximate value of u:
u ≈ (820 [tex]\times[/tex] 0.9397) / 0.4226
u ≈ 1817.54 inches
Rounding to the nearest inch, we have:
u ≈ 1818 inches
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how do u solve it step by step?
Answer:
(8,5)(0,-3)
Step-by-step explanation:
-y=-x+3
y=x-3
Substitute for y:
(x-3)^2-2x=9
x^2-6x+9-2x=9
x^2-8x=0
x(x-8)=0
x=0,8
if x=0,
0-y=3
y=-3
if x=8
8-y=3
-y=-5
y=5
Answer :
x - y = 3
x = 3 + y
y^2 - 2x = 9
y^2 - 2(3+y) = 9
y^2 - 2y -6 -9 = 0
y^2 - 2y -15 = 0
Factorize
y = -3 y = 5
when y = -3
x -(-3) = 3
x = 0
when y = 5
x - 5 = 3
x = 8
Is this relation a function yes or no?
Answer:
Yes
Step-by-step explanation:
Yes, it is a function. If you perform the vertical-line test, the line only touches a point once.
40,328*77 =
Remainder:
Answer: Step-by-step work:
40,328
77
3,105 (Carry the 3)
27,468
302,976
1,609,432
Add the numbers horizontally:
2,943,941
So, 40,328 * 77 = 2,943,941
The remainder when divided by 10 is:
2,943,941 % 10 = 1
Therefore, the remainder is 1.
More concisely:
40,328 * 77 = 2,943,941
2,943,941 % 10 = 1
So the remainder when 2,943,941 is divided by 10 is 1.
Hope this helps! Let me know if you have any other questions
Step-by-step explanation:
Bookwork code: G15
There are two bags of marbles. The first contains
one blue, one yellow and two red marbles. The
second contains one red, one blue and two yellow
marbles. A random marble from each bag is
removed. What is the probability of removing a
blue and a yellow? Give your answer as a fraction
in its simplest form.
Bag 1
Bag 2
R
BYY
BB, RB, BB,Y B,Y
Y Y,RY,BY,YY,Y
RR,RR, BR,Y R,Y
RR,RR, BR,Y R,Y
Answer: 5/ 16
explanation: total= 4x4=16
red and yellow : (r,y) or (y,r)
n= 5
p= 5 1/1 16
p = 5 over 16
if (2i/2+i) - 3i(3+i) = a + bi then a= ____ and b=_____
A = 1/10, -10, 1/50, -1/10
B = i/10, -10i, -1/10, -1/50
The value of a and b in the given complex expression is 1/10 and -1/10 respectively.
This is a problem related to the complex numbers. The complex numbers has a general form of (a+bi) where 'i' is the imaginary number or √-1. The part without an 'i' is called Real Part and the part with an 'i' is called Imaginary Part.
(2i/2+i) - 3i/(3+i) = a + bi
{ 2i(3+i) - 3i(2+i) }/ (2 + i)(3 + i) = a+bi
6i + 2i² - 6i - 3i² / (2 + i)(3 + i) = a+bi
(-2 + 3) / (6 + 5i - 1) = s+bi
1 / (5 + 5i) = a+bi
Now we multiply top and bottom by 5 - 5i :
5 - 5i / (5 + 5i)(5 - 5i) = a+bi
5 - 5i / 25 -25i² = a+bi
5 - 5i / 50 = a+bi
1/10 - 1/10i = a+bi
On comparing the real and imaginary part on the both sides:
a= 1/10 , b= -1/10.
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Please show the graph with correct points in x and y. Please specify if it’s a hollow dot or solid dot for each point. I’ll give good rating! Thank you!
The graph of the solution to the inequality is attached as image to this answer.
Understanding Piece-Wise FunctionThe piece-wise defined function h(x) represents different values of y (the output) depending on the value of x (the input). Each interval of x has a different value assigned to it.
In this particular case, the inequality statements define the intervals for x and their corresponding output values.
Let's break it down:
- For values of x that are greater than -3 and less than or equal to -2, h(x) is assigned the value of -1.
- For values of x that are greater than -2 and less than or equal to -1, h(x) is assigned the value of 0.
- For values of x that are greater than -1 and less than or equal to 0, h(x) is assigned the value of 1.
- For values of x that are greater than 0 and less than or equal to 1, h(x) is assigned the value of 2.
Any values of x outside of these intervals are not defined in this piece-wise function and are typically represented as "not a number" (NaN).
For example, if you were to evaluate h(-2.5), it falls within the first interval (-3 < x ≤ -2), so h(-2.5) would be equal to -1. Similarly, if you were to evaluate h(0.5), it falls within the fourth interval (0 < x ≤ 1), so h(0.5) would be equal to 2.
The graph of the piece-wise function h(x) consists of horizontal line segments connecting the specified values of y for each interval, resulting in a step-like pattern.
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find g[h(-2)] from f(x)=x^(2),g(x)=5x , h(x)=x+4
Explanation:
Plug x = -2 into h(x)
h(x) = x+4
h(-2) = -2+4
h(-2) = 2
This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.
g(x) = 5x
g(2) = 5*2
g(2) = 10
Therefore, g[ h(-2) ] = 10