Answer:
( x + y + z )( x^2 + y^2 + z^2 - xy - yz - zx )
Step-by-step explanation:
Use Identity to factor this long expression.
Hope this helps.
The equation for photon energy, E , is
E=hcλ
where h = 6.626×10^−34 J⋅s (Planck's constant) and c = 2.99×10^8 m/s (the speed of light).
What is the wavelength, λ , of a photon that has an energy of E = 4.26×10^−19 J ?
The wavelength λ , of a photon that has an energy of E = 4.26×10^−19 J is 21504.29 meter.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now, the given equation for photon energy, E , is
E = hcλ
Here, h = 6.626×10^−34 J⋅s (Planck's constant) and
c = 2.99×10^8 m/s (the speed of light)
Therefore, we have
E = hcλ
⇒ λ = E/hc
Put the values of E, h and c we get,
λ = 4.26×10^−19 / (6.626×10^−34*2.99×10^8)
Solving we get,
λ = 4.26×10^−19 / 19.81×10^(−34+8)
⇒ λ = 4.26×10^−19 / 19.81×10^-26
⇒ λ = (4.26/19.81)*10^(-19+26)
⇒ λ = 0.215042×10^5 meter
⇒ λ = 21504.29 meter
Thus, the wavelength λ , of a photon that has an energy of E = 4.26×10^−19 J is 21504.29 meter.
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or
Steven measured a county park and made a scale drawing. The scale he used was 5 inches = 1 yard. What scale factor does the drawing use?
The scale factor used to draw is 7.2
What is scale factor?The size by which the shape is enlarged or reduced is called as its scale factor.
Given:
5 inches = 1 yard
Now, we know that
1 yd = 3 ft
now, to Convert yards to inches
1 yd = 3 x 12
i yards = 36 inches
and, the scale factor is
=36 ÷ 5
= 7 1/5
= 7.2
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Given the graph of the function f(x) below, estimate the slope of the tangent line to the curve at x=0. Select the answer that is closest.
Since f(x) appears to admit a local minimum at the point of abscissa zero, then the tangent drawn at that point must admit a slope equal to zero.
Option 3Elimination Method
Use the elimination method to solve the system of equations below.
0.12
x
−
0.09
y
=
0.45
−
0.3
x
+
1.6
y
=
8.5
Choose one • 4 points
x
=
−
15
y
=
7
x
=
5
y
=
7
x
=
9
y
=
5
x
=
9
The correct option D. x = 9, y = 7; obtained by the elimination method.
What is defined as the elimination method?The elimination method entails the procedure of eliminating a single variables in a system of linear equations by using addition or subtraction methods in combination with variable coefficient multiplication or division.Now, as per the given question;
The equations are-
0.12x − 0.09y = 0.45 (multiply both side with 100)
12x - 9y = 45 ......equation 1
and,
-0.3x + 1.6y = 8.5 (multiply both side with 40)
-12x + 64y = 340 .......equation 2
Add equation 1 and 2;
55y = 385
y = 5
Put y = 5 in equation 1
12x = 45 + 45
x = 9
Thus, the values of the variables are obtained as (x = 9) and ( y = 7).
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The correct question is-
Use the elimination method to solve the system of equations below.
0.12x − 0.09y = 0.45
-0.3x + 1.6y = 8.5
Choose one • 4 points
A. x = −15, y = 7
B. x = 5, y = 7
C. x = 9, y = 5
D. x = 9, y = 7
ln(3) - ln(2) + ln(1/x) =
A. 3 / (2x)
B. 3x/2
C. 1 + 1/x
D. 3/2 - 1/x
The required simplified solution for the given logarithm expression is y = 3 / 2x.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To simplify the given expression,
ln(3) - ln(2) + ln(1/x) = ln (y)
ln(3) + ln(1/x) = ln(2) + ln(y)
By the property of logarithm,
3/x = 2y
y = 3 / 2x
Thus, the required simplified solution for the given logarithm expression is y = 3 / 2x
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For the function f, construct and simpli
1) f(x)=9x+2
Pre-Calc
Answer:
For the function f(x) = 9x f(x + h) - f(x) construct and simplify the difference quotient h 3 1 The difference quotient for f(x) = is 9x
Step-by-step explanation:
PLEASE HELP
OFFERING 20 POINTS
Answer:
x = -4
Step-by-step explanation:
A perpendicular bisector is a line that divides the existing line or shape evenly and at 90° angles. First, we want to find the center point of our existing line. In this case, the center sits right at x = -4. Since the existing line is y = 3 and it is perfectly horizontal, we don’t need to do anything further. Our perpendicular bisector is x = -4.
*** When the existing line is y = [singular number], the perpendicular bisector will always be x = [midpoint of existing line], and vice versa.
Hope this helps!
During each shift, there are nurses needed at each ward. If
there are three shifts in a day, each nurse only can be on duty
for one shift each day. How many more nurses does the
hospital need to employ?
The hospital needs to employ 21 nurses, 7 for each shift.
What are permutations and combinations?Permutations and combinations are the various ways in which objects from a set can be selected, generally without replacement, to form subsets. When the order of selection is a factor, this selection of subsets is called a permutation; when order is not a factor, it is called a combination.So, there are 3 shifts in a day and 7 nurses are needed for each shift.
Then,
7 × 3 = 21Therefore, 21 nurses are needed, 7 for each shift.
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The complete question is given below:
During each shift, there are 7 nurses needed at each ward. If there are three shifts in a day, each nurse only can be on duty for one shift each day. How many more nurses does the hospital need to employ?
A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected:
Age Number of Customers
<20 78
20-30 58
30-40 53
40-50 77
50-60 52
>60 91
One customer is chosen at random for a prize giveaway.
What is the probability that the customer is at least 30 but no older than 60?
What is the probability that the customer is either older than 60 or younger than 40?
What is the probability that the customer is at least 60?
The probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.
We have the data:
Age Number of Customers
< 20 78
20 - 30 58
30 - 40 53
40 - 50 77
50 - 60 52
> 60 91
The probability that the customer is at least 30 but no older than 60 will be:
P = 182 / 409
P = 0.45
The probability that the customer is either older than 60 or younger than 40 will be:
P = 280 / 409
P = 0.68
The probability that the customer is at least 60 will be:
P = 91 / 409
P = 0.22
Therefore we get the probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.
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A sample of ore is found to be 0.0022% gold and 0.059% diamond. What is the percentage of matter in the ore that is neither gold nor diamond? Round your answer to the nearest ten thousandth.
The percentage of matter in the ore that is neither gold nor diamond is 99.9388%.
In the question, we are given that a sample of ore is found to be 0.0022% gold and 0.059% diamond.
We are asked for the percentage of matter in the ore that is neither gold nor diamond.
We know that in any quantity, the total is shown as 100%.
If we assume the percentage of matter in the ore that is neither gold nor diamond to be x%, then using the above theory, we can say that;
x% + 0.0022% + 0.059% = 100%.
This can also be shown as:
x + 0.0022 + 0.059 = 100, which can be simplified as:
x + 0.0612 = 100, which can be solved by subtracting 0.0612 from both sides to get:
x = 100 - 0.0612 = 99.9388.
Thus, the percentage of matter in the ore that is neither gold nor diamond is 99.9388%.
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Find slope of the line
The slope of the line having the points ( -1 , 8 ) and ( 8 , 9 ) is 1 / 9.
We are given the two points:
( -1 , 8 ) and ( 8 , 9 )
We need to find the slope of the line that contains these two points.
We know that the formula for calculating the slope of the line is given by:
m = y₂ - y₁ / x₂ - x₁
Here, we have:
x₁ = - 1 y₁ = 8
x₂ = 8 y₂ = 9
Substituting the values in the formula, we get that:
m = 9 - 8 / 8 + 1
m = 1 / 9
Therefore, the slope of the line having the points ( -1 , 8 ) and ( 8 , 9 ) is 1 / 9.
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A rental truck costs $53.45 for a day plus 69€ per mile.
(a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the truck for a day.
C=
Total cost is $ 11,369.45
Rental truck costs $53.45 for a day $69 per mile.
a) If x is the number of miles driven
So, c(x)=53.45+69(x)
c=53.45+69x
b) If x=164 miles
c=53.45+164
c=53.45+11,316
c=$11369.45
∴Total cost is $11,369.45
What does number of miles mean?
the aggregate number of miles traveled over in a given time. length, extent, or distance in miles. the number of miles or the average distance that a vehicle can travel on a specified quantity of fuel: the car gets good mileage.
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please help
please hury
the one you highlighted is right!
Answer:
The highlighted one is correct!
The sum of the measures of two complementary angles is 90°. If one angle measures
15° more than twice the measure of the other, find the measure of the smaller angle.
The smaller angle measures: ?
Answer: 75°
Step-by-step explanation:
Solution;
Here:. let, one angle be x
From the question ,
x+15=90(Being sum of complementary angle)
x=90-15
x=75
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation
(-9,-7) y= -3x+5
Answer:
y = -3x -34
Step-by-step explanation:
m= -3
plug the point in to find b
slope intercept form: y=mx+b
-7 = -3(-9) +b
-7 = 27 = b
-7 -27 = b
b= -34
plug in the m and b you found into the final equation:
y = -3x -34
Answer:
y = -3x -34
Step-by-step explanation:
Find the standard deviation and variance for the following data. These are the heights (cm) of 5
students from a class of 30.
162, 166, 179, 170, 175.
The standard deviation is 6.09
The variance is 37.04.
What is the standard deviation and variance?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation: (162 + 166 + 179 + 170 + 175) / 5 = 170.40Determine the difference between each value and the mean and then square the result:(162 - 170.40)² + (166- 170.40)² + (179 - 170.40)² + (170 - 170.40)² + (175 - 170.40)²
70.56 + 19.36 + 73.96 + 0.16 + 21.16 = 185.20
Determine the mean of the sum of the squared differences and then find the square root of the mean:√185.20 / 5 = 6.09
Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset.
6.09² = 37.04
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Need help I ready pls help me
Answer:
(9+b)+(10+s)
Step-by-step explanation:
Which of the following are factors of 96? Select ALL that apply.
018
6
04
012
014
Answer:04,6and 12
Explation:factors are numbers which divide the original number without leaving a remainder.The factors are:1,2,3,4,6,8,12,16,32,48and 96
K(2, 7), L(6, 12), M(13, 13), N(9.8) (Slope Formula) is it a parallelogram?
angles and sides opposite one another on a parallelogram are congruent, we can say this is a parallelogram because there are congruent.
What in mathematics is a parallelogram?
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.Slope Formula: y2-y1/x2-x1
KL: 12-7/6-2 = 5/4
LM; 13-12/13-6 = 1/7
MN: 8-13/9-13 = 5/4
KN: 7-8/9-2 = 1/7
Since angles and sides opposite one another on a parallelogram are congruent, we can say this is a parallelogram because there are congruent.
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XZ is the angle bisector of angle WXY. Solve for m. Enter a NUMBER only.
The value of m would be 7 if XZ is the angle bisector of the angle ∠WXY which are the angles ∠WXM and ∠YXZ would be 42°.
What is an angle bisector?An angle bisector is defined as a line that divides an angle into two equal angles. Draw the given angle first, then cut it in half, and then draw the angle's bisector.
We have been given that XZ is the angle bisector of angle WXY.
⇒ ∠WXM = ∠YXZ
Solve for m
⇒ 10m -28 = 5m + 7
⇒ 10m - 5m = 28 + 7
⇒ 5m = 35
⇒ m = 35/5
⇒ m = 7
So ∠WXM = 10(7) -28 = 42
And ∠YXZ = 5(7) + 7 = 42
Therefore, the value of m would be 7.
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Pllzzzzzz help
What number should be placed in the box to help complete the division calculation?
Answer:
160
Step-by-step explanation:
1 is in 10s place 16x10=160
Points: 0 of T
Christine went shopping and bought each of her five nephews a gift, either a video costing $14.95 or a CD
costing $16.88. She spent $78.61 on the gifts. How many videos and how many CDs did she buy?
...
Save
The number of videos will be 3 and the number of CDs will be 2.
What is an expression?Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Christine went shopping and bought each of her five nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $78.61 on the gifts.
The number of the videos and CD will be calculated by forming an equation:-
14.95x + 16.88y = 78.61
From heat and trial, we put x = 3 and y = 2 then calculate.
14.95 x ( 3 ) + 16.88 x ( 2 ) = 78.61
44.85 + 33.76 = 78.61
78.61 = 78.61
Therefore, the number of videos will be 3 and the number of CDs will be 2.
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656 divded by 9 and 3.6 divded by 17
Answer: 72.8 and 0.21
Answer:
72.8888888889
and
0.5142857143
If x=2 and y =3 what is the value of 2x^3 +5-10
Answer: 11
2x^3 + 5 - 10 =
2(2)^3 + 5 - 10 =
2(8) - 5=
16-5=11
Step-by-step explanation:
The table below shows the assets and liabilities of the Tanner family.
Assets and Liabilities Amount
Checking account $17,532
Car (paid off) $12,225
Retirement Savings $43,675
Credit Card Debt $7,876
Home Loan Balance $65,225
What is the net worth of the Tanner family?
If checking account has $17,532,car (paid off) is $12,225,retirement savings are $43,675,credit card debt is $7,876,home loan balance has $65,225, the the net worth of the Tanner family is $331.
Given that checking account has $17,532,car (paid off) is $12,225, retirement savings are $43,675,Credit Card Debt is $7,876,Home Loan Balance has $65,225.
We are required to find the net worth of the Tanner family.
Net worth is basically the value of the assets a person or corporation owns, minus the liabilities they owe.
Net worth=Checking account+Car +Retirement savings-credit card debt-Home loan balance
=17532+12225+43675-7876-65225
=$331
Hence if checking account has $17,532,Car (paid off) is $12,225 ,retirement Savings are $43,675,credit card debt is $7,876,home loan balance has $65,225, the the net worth of the Tanner family is $331.
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Suppose that approximately 273,000,000 people live in the United States. Of these people, 31,200,000 speak a language other than English at home. Of those who speak another language at home, over 50 percent speak Spanish.
• E = speak English at home
• E' = speak another language at home
• S = speak Spanish at home
Finish each probability statement by matching the correct answer.
P(E' )
Part (b)
P(E)
Part (c)
P(S)
Part (d)
P(S | E' )
The required probability is given by P(E') =4/35 .
Probability is the study of chance. It can also be defined as the ratio of the favorable outcomes to an event to the total number of outcomes of the event.
Given the total number of people in the USA = 273000000
Let E be the number of people who speak English at home.
Therefore the number of people who don't speak English at home is E'.
∴ E' = 31200000
S speak Spanish in their homes.
∴ S = 50% of 31200000 = 15600000
Now let us find the required probabilities.
We know that probability = favorable outcome ÷ total outcome
total outcome = 273000000
a) favorable outcome(E') = 31200000
P(E')=31200000/273000000
P(E') =4/35
b)favorable outcome(E) = 273000000 - 31200000 = 241800000
P(E) = 241800000/273000000
P(E)={31}/{35}
c)favorable outcome = 15600000
P(S)={15600000}/{273000000}
P(S)={2}/{35}
Therefore the required probability is given by P(E') =4/35 , [tex]P(E)=\frac{31}{35}[/tex] P(E)=31/35 and P(E)=2/35and .
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61% of 407
rounding pls <3
Answer:
Step-by-step explanation:
61.407
Answer:
248.3
Step-by-step explanation:
61% of 407
61% = 0.61
0.61 * 407 = 248.27
248.27 = 248.3
248.3
What is the difference when 54.89 is subtracted from 235.987?
29.0877
1,810.97
290.877
181.097
ill brainlist the right answer
[tex]{ \blue{ \tt{option(d)}}} \: { \boxed{ \red{ \sf{181.097}}}}[/tex]
Step-by-step explanation:
[tex] \: \: \: \: 235.987[/tex]
[tex] - \: \: \: 54.89[/tex]
_______________
[tex]{ \boxed{ \red{ \sf{= 181.097}}}}[/tex]
In the figure below, mz1 = (4x + 50)° and
mz3 = (2x + 66)°.
3
a. What is the value of x?
b. What is the measure of m<3?
c. What is the measure of m22?
the measure of m22 = 98° by linear pair .
What is linear pair?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Given , mz1 = (4x + 50)°
mz3 = (2x + 66)°.
a) mz1 = mz3
(4x + 50)° = (2x + 66)°
4x - 2x = 66 - 50
2x = 16°
x = 8°
b) mz3 = (2x + 66)°.
put value of x
2x + 66 = 2 * 8 + 66
= 16 + 66 ⇒ 82°
c) mz2 = ∠ 1 + ∠ 2 = 180° { linear pair }
4x + 50 + ∠2 = 180°
4 × 8 + 50 + ∠2 = 180°
82° + ∠2 = 180°
∠2 = 180° - 82°
∠2 = 98°
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Given f(x) = x^2 - 3x + 5, what is f(-2)?
A. f(-2) = 3
B. f(-2) = -5
C. (-2) = 15
