The length of each factory worker on average is 25.57 lengths
How to determine the length of each on average?From the question, we have the following parameters that can be used in our computation:
Total length of the pool = 179 lengths
Number of workers = 7
The length of each on average is calculated as
Average length = Total length of the pool/Number of workers
Substitute the known values in the above equation
So, we have the following equation
Average length = 179/7
Evaluate the quotient
Average length = 25.57
Hence, the average length is 25.57 lengths
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what is 5\sqrt(3ft *3\sqrt(12))
The solution of 5√3 × 3√12 = 30√3.
What is square root?Square root of a number is defined as the number in which the multiplication by itself gives the original number. That is the square root of 9 would be = 3 in which when multiplied by itself gives the original number being 9.
Other examples include √ 4 = 2, √ 25 = 5, √100 = 10.
To simplify the give expression;
5√3 × 3√12= 5√3 × 3√4×3
= 5√3 × 3×2√3
= 5√3 × 6 √3
= 30√3.
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3.201 x 10^9 and 4.85 x 10^3
(3.201 x 10^9) * (4.85 x 10^3) =
15524850000000
in scientifc notation
1.552485 x 10^13
What is the y-intercept of this line?
Answer:
The Y intercept of this line is -3.
Step-by-step explanation:
The X intercept of the crossing line is about -1.4.
On finding the Y intercept:
Step 1: look at the vertical black line (Y Axis)
Step 2: Locate where the blue line crosses on this line.
Step 3: graph Y function of the point as your answer.
Hope this helped a bunch!
Have a great day!
- Kit-Kat~
Find the exact solutions of the given equation in the interval .
sin 4x= –2sin 2x
The exact solutions of the given equation in the interval are;
A: x = 0, π/2, π, ³/₂π
How to find the exact solutions of trigonometric equations?
We are given the equation as;
sin 4x = –2sin 2x
Writing the equation in standard form gives;
sin 4x + 2sin 2x = 0
Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;
2sin 2x cos 2x + 2sin 2x = 0
Factorize to get;
2sin 2x(cos 2x + 1) = 0
A. sin 2x = 0
The unit circle will give us 3 solutions for 2x as follows;
2x = 0
Thus; x = 0
2x = π
Thus; x = π/2
2x = 2π
Thus; x = π
B. cos 2x = - 1
The unit circle gives 2 solutions for 2x as;
2x = π
Thus; x = π/2
2x = 3π
Thus; x = ³/₂π
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Complete question is;
How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?
Determine whether the percent of change is a percent of increase or a
percent of decrease. Then find the percent of change.
%
original: 20
new: 18
by
Answer:
the change is in %age of decrease of 10%
Step-by-step explanation:
original value = 20
new value = 18
decrease = 2
%age decrease = decrease/original value * 100
= 2/20 * 100
= 10%
F(x)=3x^4-4x^3+x^2+6x-2
The rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).
We will use the synthetic division method to determine the rational zeros and linear factors of given polynomials.
Polynomials are divided via synthetic division.
The procedure entails of synthetic division:
Step 1: Create a synthetic divide.
Step 2: Bring the leading coefficient down to the bottom row.
Step 3: Divide this by the value stated in the bottom row.
Step 4: Finally, add the column you defined in step 3.
This can proceed as:
Given: f(x) = 3x⁴- 4x³ + x² + 6x - 2
3x⁴ - 4x³ + x² + 6x - 2 = 0
We will put x = -1 in f(x). In this case, replace x with -1. This will be:
f(-1) = 3 * 1⁴ - 4 * 1³ + 1² + 6 * 1 - 2 = 0
Since f(-1) = 0, so (x + 1) is a factor of f(x).
Using synthetic division:
-1)....3....-4....1....6....-2
.........3.....-7...8....-2..|..0
Remainder = 0
Quotient = 3x³ - 7x² + 8x - 2
For 3x³ - 7x² + 8x - 2, f(1/3) = 0, so (x - 1/3) is a factor.
1/3)....3....-7....8....-2
..........3.....-6...6...|..0
Remainder = 0
Quotient = 3x² - 6x + 6 = 3(x² - 2x + 2)
Because x² - 2x + 2 has no more rational zeros or linear components. The rational zeros are hence x = -1 and x = 1/3.
Thus, the rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).
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Completely factor the expression -4/5yn6 - 5/6y4n8
Answer:
See below
Step-by-step explanation:
You can pull one y and 6 n's out to start
then 4/5 = 24/30 and 5 / 6 = 25/30
and you can factor out a -1
- y n^6 /30 ( 24 + 25 y^3n^2 )
How can I find the scale factor of the two similar triangles and how can I use similarity and scale factor to find the length?
Answer:
i think, x equal 12 and y equal 20
Which expression has the same value as 3 ÷ 5/9? A. 3 × 5/9 B. 1/3 ÷ 5/9 C. 3 ÷ 9/5 D. 3 × 9/5
Answer:
D: 3x9/5
Step-by-step explanation:
the formula for dividing fractions is skip flip multiply where we keep the first term the same and then flip the second to multiply
Hopes this helps please mark brainliest
On Saturday, 120 hotel guests used the valet service, and 280 hotel guests did
not use the valet services. What percentage of the guests at this hotel used the
valet service on Saturday?
Answer: 42.86%
Step-by-step explanation: 120/280*100 = 42.86%
Randy is 8 years old. His brother is twice as old as randy. Randys sister is three years younger than randy. Write a expression to represent the age of randys brother
The expression that represents the age of randy's brother is
2x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Randy age = 8 years old
Randy's brother age = 2 x 8 = 16
Randy's sister age = 8 - 3 = 5
The expression that represents the age of randy's brother.
Let the age of Randy = x.
= 2x
= 2x
= 2 x 8
= 16 years old.
Thus,
The expression that represents the age of randy's brother is
2x.
Where x is the age of Randy.
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The ages of people visiting a senior center one afternoon are recorded in the line plot
Does the data contain an outlier? If so, explain its meaning in this situation.
A: No, there is no outlier. This means that the data was not collected correctly, as there would be lots of age ranges at the center.
B: No, there is no outlier. This means that the people at the center were all seniors around the same age.
C: Yes, there is an outlier of 85. This means that one person was age 85, which is 15 years older than the next closest age.
D: Yes, there is an outlier of 105. This means that someone at the center is 105 years old.
Answer:
b
Step-by-step explanation:
The correct option is (b) The data does not contain an outlier. This means that the people at the center were all seniors around the same age.
What is an Outlier in a Dataset?Outlier in a data set is simply the extremely low data point or an extremely high data point compared to other points in the dataset.
It will stand out from the other values in the dataset.
The line plot shows the ages of people visiting a senior center one afternoon.
The data points are,
70, 70, 70, 75, 75, 80, 80, 85, 90, 90, 95, 95, 95, 100.
If there is an outlier in the set, it would be extremely low or high compared to other points.
But there are no such points.
So there are no outliers.
This means that people visited at the center were all seniors around the same age.
Hence the correct option is (b).
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Represent the following expressions as a power of the number a where a ≠ 0: (a^3)^-2. PLEASE ANSWER I WILL GIVE BRAINLYEST
Answer:
a^-6 or 1/a^6
Step-by-step explanation:
(a³)-²
=a^-6
=1/a^6
0°F; drops 15° what’s the new temperature
The new temperature is given as -15°F.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The present temperature is 0°F.
And, the drop in the temperature is 15°.
The new temperature after the drop can be found by subtracting the amount of drop from the initial temperature as follows,
0 - 15°F
= -15°F
Hence, the new temperature after the drop is -15°F.
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PLEASE HELP ME
Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
3x - 2 (2.3x + 2.5) = -1.6x -5
5 - 3 (-1.6x - 2.1) = 4.8x - 1.3
3x - 2 (2.3x + 2.5) = -1.6x-5 are equivalent expressions while 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3 are not equivalent expressions
How to determine if the linear expressions are equivalent?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)
Given: 3x - 2 (2.3x + 2.5) = -1.6x -5 and 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3
For 3x - 2 (2.3x + 2.5):
First, clear the parenthesis by using -2 to multiply what's in the parenthesis. Then add/subtract like terms:
3x - 2 (2.3x + 2.5) = 3x-4.6x- 5 = -1.6x-5
For 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3:
First, clear the parenthesis by using -3 to multiply what's in the parenthesis. Then add/subtract like terms:
5 - 3 (-1.6x - 2.1) = 5 + 4.8x + 6.3 = 4.8x + 11.3
Since 3x - 2 (2.3x + 2.5) is equal to -1.6x-5 and 5 - 3 (-1.6x - 2.1) is not equal to 4.8x - 1.3.
Therefore, 3x - 2 (2.3x + 2.5) = -1.6x-5 are equivalent expressions and 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3 are not equivalent expressions
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A 2-column table with 9 rows. The first column is labeled year with entries 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013. The second column is labeled precipitation with entries 5.98, 6.05, 7.59, 5.27, 3.11, 7.18, 2.95, 7.22, 2.61. The table shows the precipitation in December, in inches, for Washington state from 2005 to 2013. What was the mean amount of precipitation during this time? Round to the nearest hundredth. 1.97 inches 2.61 inches 5.33 inches 5.98 inches
Answer:
5.33 inches
Step-by-step explanation:
Mean is another term for average. Therefore, we add up all precipitation items from Column B and divide by the total number of items (9):
[tex]5.98+6.05+7.59+5.27+3.11+7.18+2.95+7.22+2.61=47.96[/tex]
[tex]47.96\div{9}\approx{5.33}[/tex]
When Nathaniel moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 38 inches tall and Tree B was 20 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.
The equations of both trees are Tree A = 38 + 6t and Tree B = 20 + 9t and the growth interval of tree A is t < 6
The equations of the growth of both treesFrom the question, we have the following parameters that can be used in our computation:
Tree A
Initial height = 38 inchesRate = 6 inches each yearTree B
Initial height = 20 inchesRate = 9 inches each yearThe height after t years is
Tree = Initial height + rate * t
So, we have
Tree A = 38 + 6t
Tree B = 20 + 9t
The interval of timeRecall that
Tree A = 38 + 6t
Tree B = 20 + 9t
When Tree A is taller than Tree B, we have
38 + 6t > 20 + 9t
Evaluate the like terms
-3t > -18
Divide
t < 6
Hence, the interval is t < 6
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Find two vectors that are orthogonal to u = -2i +5j -3k and w = 3i +2j + k
Show work, please
After solving the equation of vector, the value obtained is equal to one, which shows that vectors are orthogonal.
What are vector?A vector is a quantity with both magnitude and bin physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector has magnitude and the direction, but no position. As soon as a vector's length remains unchanged, it is consequently untouched by movement perpendicular to itself.
In contrast to vectors, scalars are normal variables having a magnitude but no direction. Displacement, velocity, and acceleration are all vector quantities, unlike speed, time, or weight, which are scalar variables.
uw = -6 + 10- 3
uw = 1.
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What are the zeros of the parabola in #1? (that is, at what points does the graph cross the x-axis?)
Picture is number one
The zeroes of the parabola is -1, -5.
What is parabola and zeroes of parabola?
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The equation of parabola can be expressed in two different ways, such as the standard form and the vertex form. The standard form of parabola equation is expressed as follows:
f(x) = y= ax2 + bx + c
To find zeroes of parabola
x = -b ±[tex]\sqrt{b^{2}-4ac } /2[/tex]
Given equation is
f(x) = [tex]x^{2} +6x+5[/tex]
a = 1, b = 6, c = 5
x = -6 ±[tex]\sqrt{36-4(5)}[/tex]/2
x = -6 ±[tex]\sqrt{16} /2[/tex]
x = -6 ± 4 /2
hence,
x = -6-4/2 and x = -6 +4/2
x = -5 or x = -1
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Gayle Miller works 43 hours every week. Her weekly salary is $397.75. How much overtime does Gayle make each week?
Answer:
$9.25
Step-by-step explanation:
$397.75÷43=$9.25
Weekly salary divided by hours of work = hourly pay
You want to open an account with $1,700. You can earn 2.7% interest each year, and you plan to leave this account for 9 years. How much more would the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest?
$2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.
Given that, principal = $1700, rate of interest = 2.7% and time period = 9 years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Here, simple interest = (1700×2.7×9)/100
= 41310/100
= $413.10
Amount = Principal + Simple interest
= 1700+413.10
= $2113.1
Compound interest:
[tex]Amount=P(1+\frac{R}{100} )^{nt}[/tex]
[tex]=1700(1+\frac{2.7}{100} )^{4\times9}[/tex]
[tex]=1700(1.027)^{36}[/tex]
= 1700×2.609
= $4435.3
Now, 4435.3-2113.1=$2322.2
Therefore, $2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.
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Help! I’m so confused
The measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.
First, let us understand the types of angles formed by parallel and transversal lines:
Corresponding Angles — Corresponding angles are angles on the same side of a transversal that are either above or below the lines.
Alternate Interior Angles - Alternate interior angles are the pairs of interior angles on opposing sides of the transversal.
Alternate Exterior Angles - Alternate exterior angles are the pairs of exterior angles on opposing sides of the transversal.
Consecutive interior angles - Internal angles on the same side of a transversal are also known as consecutive interior angles, related angles, or co-interior angles.
We are given:
∠2 is 48 degrees and ∠3 is 62 degrees.
We need to find the ∠5.
From the given figure we can see that;
∠3 and ∠5 are alternate interior angles.
So, ∠3 = ∠5 = 62 degrees.
So, the measure of ∠5 is 62 degrees.
Thus, the measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.
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the sum of two numbers is 33. the sum of 3 times the larger and 4 times the smaller is 107
The value of the larger number and the smaller number are 25 and 8 respectively.
What is Simultaneous Equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.
They are called simultaneous equations because the equations are solved at the same time.
If the bigger value is represented by x and the smaller value is represented by then
x+y= 33 equation 1
3x+ 4y= 107 equation 2
using Elimination method,
we multiply the coefficients of x by opposite equation
3x+3y=99 equation 3
3x+4y= 107 equation4
subtracting equation 3 from 4
y=107- 99
y= 8
substituting 8 for y in equation 1
x+8= 33
x= 33-8=25
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Given loga(m) = 10 and loga(n) = 20, find loga(mn2). (Enter an exact number.)
Answer:
log(mn^2) = 50
Step-by-step explanation:
assuming base a for the logs
log(mn^2) = log m + 2log n
Find the rate if a principal of $1,100 earned $1,089 interest in 12 years.
Answer:
8.25
Step-by-step explanation:
How many times greater is 5.96 × 10^4 then 2.98 × 10^3?
Answer: 2.5>9.5
Step-by-step explanation: maybe we should both pay attention to math
Aim: How can you earn money with a Savings Account?
Exit Ticket #5 Simple Interest
Find the simple interest on a $2,350 principal
deposited for 6 years at a rate of 2.77%
I =
P =
t =
I = prt
I=( )( )( )
Answer:
I = (2350)(0.0277)(6)
Step-by-step explanation:
We're told the principal, rate, and time so we just plug in.
We must convert the 2.77% to a decimal by moving the period two places to the left to get the rate 0.0277
there are 32 steps in one floor of a tower max lives .he climbs 6 floors of his building. if he clims 6 floor every day , how many steps does he climb every week
Answer:
1,344
Step-by-step explanation:
First, find how many steps he climbs every day
32*6=192
Now, multiply that by 7 to see how many he climbs in a week
192*7=1,344
Write an equation in standard form of the line that passes through (-4,1) and has the slope m=3
An equation in standard form is ____ = -13
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y -1= 3 (x +4) \\\\\\ y-1=3x+12\implies y=3x+13\implies -3x+y=13\implies \boxed{3x-y=-13}[/tex]
1) Use the scale factor to
determine the new area of each
scale drawing.
Scale factor = 3
2 meters
4.5 meters
