Answer:
[tex] {4}^{ - 3} \times {4}^{2} \times {4}^{5} = {4}^{ - 3 +2 + 5} = {4}^{4} [/tex]
False. The missing exponent is 4.
What is the area of quadrilateral QRST if QS=18 and RT=24. Show work.
Answer:
[tex]\text{Area of quadrilateral QRST}=216[/tex]
Step-by-step explanation:
Please find the attached image for the quadrilateral QRST.
We have been given that [tex]QS=18 \text{ and } RT=24[/tex]. We are asked to find the area of quadrilateral QRST.
Upon looking at the image of quadrilateral QRST, we can see that quadrilateral QRST is a kite as it has one pair of diagonally opposite equal angles (98 degrees).
We know that area of kite is equal to half the product of its diagonal.
We can see from our image that QS and RT are diagonal of kite, so the area of quadrilateral QRST would be:
[tex]\text{Area of quadrilateral QRST}=\frac{QS\cdot RT}{2}[/tex]
[tex]\text{Area of quadrilateral QRST}=\frac{18\cdot 24}{2}[/tex]
[tex]\text{Area of quadrilateral QRST}=\frac{432}{2}[/tex]
[tex]\text{Area of quadrilateral QRST}=216[/tex]
Therefore, the area of quadrilateral QRST is 216 square units.
simplify (-8.5)(-5)( -2).
Answer:
-85
Step-by-step explanation:
Answer:
-85
Step-by-step explanation:
The scores on the Unit 1 Exam are listed below. What is the probability that a student picked at
random scored 75% or above?
61 74 60 70 83 90 90 80 100 102 28 75 98 21 49
car ofaenorting goods store was analyzing a frequency tahle identifving the number of
To calculate the probability of a student scoring 75% or above, count how many scores are 75 or higher, and then divide by the total number of scores. In this case, the probability is 6 out of 15, or 0.4.
The question asks about the probability that a student picked at random scored 75% or above based on a list of exam scores.
To find this probability, one must count the number of scores that are 75% or higher and divide by the total number of scores.
Out of the provided scores (61, 74, 60, 70, 83, 90, 90, 80, 100, 102, 28, 75, 98, 21, 49), we see that there are 6 scores that are 75 or above (83, 90, 90, 80, 100, 102, 98, 75).
Since there are 15 scores in total, the probability is calculated as -
= 6/15
= 0.4.
George is comparing three investment accounts offering different rates.
Account A: APR of 3.75% compounding monthly
Account B: APR of 3.85% compounding quarterly
Account C: APR of 3.95% compounding daily
Which account will give George at least a 4% annual yield? (4 points)
Account A
Account B
Account C
Account B and Account C
Answer:
Account C will give George at least a 4% annual yield.
Step-by-step explanation:
This problem can be solved by using simple maths formula given below
Year rate = (1+i)^n-1
where i = compounding rate and n = interval period
Now checking annual rate for each option using above formula
Account A)
Yr = 3.8% ( n= 12 and i= 3.75/12)
Account B)
Yr = 3.9 % ( n= 4 and i= 3.85/4)
Account C)
Yr = 4 % ( n= 365 and i= 3.95/365)
Find the slope of the line that passes through (1,6) and (4,4)
Rise =
Run =
Slope = -2/3
Equation (y = mx + b form):
Answer:
y=-2/3x+20/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-6)/(4-1)
m=-2/3
y-y1=m(x-x1)
y-6=-2/3(x-1)
y=-2/3x+2/3+6
y=-2/3x+2/3+18/3
y=-2/3x+20/3
write an equation of the line that passes through (-4, 4) and is perpendicular to the line y=1/2x + 1
Answer:
y-4=-2(x+4)
Step-by-step explanation:
Perpendicular means negative reciprocal of the slope.
y-y1=m(x-x1)
y-4=-2(x-(-4))
y-4=-2(x+4)
The equation of the line that passes through the point (-4, 4) and is perpendicular to the line [tex]y = \frac{1}{2}x + 1[/tex] is [tex]y = -2x - 4[/tex].
To find the equation of the line that passes through the point (-4, 4) and is perpendicular to the line [tex]y = \frac{1}{2}x + 1[/tex], we need to do the following steps:
Determine the slope of the given line:
The slope of the given line [tex]y = \frac{1}{2}x + 1[/tex] is [tex]\frac{1}{2}[/tex].
Find the slope of the perpendicular line:
The slopes of two perpendicular lines are negative reciprocals of each other. Therefore, if the slope of the given line is [tex]\frac{1}{2}[/tex], the slope of the perpendicular line will be [tex]-2[/tex] (since [tex]-1 \div \frac{1}{2} = -2[/tex]).
Use the point-slope form to find the equation:
The point-slope form of a line is [tex]y - y_1 = m(x - x_1)[/tex], where [tex](x_1, y_1)[/tex] is a point on the line, and [tex]m[/tex] is the slope.
Here, the point is [tex](-4, 4)[/tex] and the slope [tex]m = -2[/tex].
Substituting these values into the point-slope form, we get:
[tex]y - 4 = -2(x + 4)[/tex]
Simplify the equation:
Distribute the slope on the right side:
[tex]y - 4 = -2x - 8[/tex]
Add 4 to both sides to solve for [tex]y[/tex]:
[tex]y = -2x - 4[/tex]
A student used the following table of values and stated that the function described by the tables was a linear function
The question is missing the table. So, it is attached below.
Answer:
The function is not linear. The student didn't evaluate the rate of change for the given points on the function.
Step-by-step explanation:
Given:
From the table, the set of points of the function are:
(-1, -5), (0, 0), (2,5), (3, 10), and (4, 15)
A function is said to be linear if the rate of change of the function is always a constant.
Rate of change for any two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, the rate of change for the points (-1, -5) and (0, 0) is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-(-5)}{0-(-1)}\\\\m=\frac{5}{1}=5[/tex]
Now, the rate of change for the points (0, 0) and (2, 5) is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{5-0}{2-0}\\\\m=\frac{5}{2}=2.5[/tex]
Hence, we can observe that, the rate of change is different for the given points. Hence, it is not a linear function.
Therefore, the student didn't evaluate the rate of change for the given points on the function.
A function is linear if the difference between y-values is constant when the difference between the corresponding x-values is constant. This is known as a constant rate of change and can be identified in a table of values for an x-y relationship. However, without the actual table's values, it's impossible to confirm its linearity.
Explanation:In mathematics, a function is said to be linear if its graph forms a straight line. When analyzing a table of values, a function is linear if the difference between y-values is constant when the difference between the corresponding x-values is also constant. This is often called a constant rate of change.
For example, let's say we have an x-y table: for every 1 unit increase in x, if y increases by 2 units consistently, then the function represented by that table is linear. It directly satisfies the general definition of a linear function, y = mx + b, where 'm' is the slope (rate of change) and 'b' is the y-intercept.
However, without the actual values from the student's table, it's impossible to confirm whether the function is indeed linear. Always remember to check for a constant rate of change when reasoning about linearity.
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What are the values of a 1 and r of the geometric series? 1 + 3 + 9 + 27 + 81 a 1 = 1 and r = one-third a 1 = one-third and r = 1 a 1 = 1 and r = 3 a 1 = 3 and r = 1
Answer:
a₁ = 1 and r = 3Step-by-step explanation:
[tex]1+3+9+27+81\\\\a_1=1,\ a_2=3,\ a_3=9,\ a_4=27,\ a_5=81\\\\r=\dfrac{a_{n+1}}{a_n}\Rightarrow r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\dfrac{a_5}{a_4}\\\\r=\dfrac{3}{1}=\dfrac{9}{3}=\dfrac{27}{9}=\dfrac{81}{27}=3[/tex]
Good evening ,
Answer:
a₁ = 1 r = 3Step-by-step explanation:
Since it’s a geometric series then
a₁ = 1 ( because 1 is the first term of the series)
3/1 = 9/3 = 27/9 = 81/27 = 3 then r=3.
:)
Find the value of x by filling the blanks in the provided statement-reason solutions
WILL NAME BRAINLIEST NEED by 12:40 pm right now it’s 12:30 where I am
Answer:
1][tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]
2][tex]measure\ angle\ A+measure\ angle\ B+measure\ angle\ C=180\ degree[/tex]
3][tex]18\ degree+3x+3x=180\ degree[/tex]
4][tex]x=27[/tex]
Step-by-step explanation:
Given:-measure angle DCA = 18 degree
line AB II line DC
Solution:-
1] measure angle DCA and measure angle CAB are interior alternate angles and interior alternate angles are equal.
[tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]------------------ (Equation 1)
Therefore the equation for statement number 1 is [tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]
2]Sum of interior angles of triangle is equal to 180 degree.
In Triangle ABC,
measure angle A+measure angle B+measure angle C=180 degree
Therefore the equation for statement number 2 is measure angle A+measure angle B+measure angle C=180 degree
3] In Triangle ABC,
[tex]measure\ angle\ B=3x---------------(Given)[/tex]
[tex]measure\ angle\ C=3x---------------(Given)[/tex]
[tex]measure\ angle\ A=18\ degree---------------(from\ equation\ [tex]measure\ angle\ A+measure\ angle\ B+measure\ angle\ C=180\ degree[/tex]
Now substituting the value of angles we get,
[tex]18\ degree+3x+3x=180\ degree-------------(Equation\ 2)[/tex]
Therefore the equation for statement number [tex]3\ is\ 18\ degree+3x+3x=180\ degree[/tex]
4] After solving the equation 2 we get,
[tex]18+3x+3x=180[/tex]
[tex]6x=180-18[/tex]
[tex]6x=162[/tex]
[tex]x=27\ degree[/tex]
Therefore value of [tex]x=27\ degree[/tex]
(-3,-8)( -12,-20) find the slope
Answer:
4/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-20-(-8))/(-12-(-3))
m=(-20+8)/(-12+3)
m=-12/-9
m=12/9
simplify
m=4/3
Which expressions are equivalent to 5^2/5^8
The equivalent expressions to [tex]5^2/5^8[/tex] are [tex]5^(^-^6^)[/tex] and [tex]\frac{1}{5^6}[/tex]
How to find the equivalent expressions?The expression[tex]5^2/5^8[/tex]can be simplified using the properties of exponents. When you have the same base raised to different exponents and they are being divided, you can subtract the exponents.
So, [tex]5^2/5^8 = 5^(^2^-^8^)[/tex] = 5^(-6).
Therefore, the equivalent expressions are [tex]5^(^-^6^)[/tex] and [tex]\frac{1}{5^6}[/tex]
In mathematics, equivalent expressions are algebraic expressions that have the same value for all possible values of the variables involved
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The expression 5^2/5^8 simplifies to 5^-6 due to the laws of exponents that allow subtracting of exponents when dividing like bases.
Explanation:The expression 5^2/5^8 can be simplified by understanding the laws of exponents. When dividing like bases, you subtract the exponent in the denominator from the exponent in the numerator. By applying this law, the expression 5^2/5^8 simplifies to 5^(2-8) which equals 5^-6.
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Evaluate BD fo A = 5, B = -2, C = 4, and D = -6.
-12
-8
8
12
Answer:
12
Step-by-step explanation:
B is equal to -2, and D is equal to -6. A negative times a negative is a positive, and 2 x 6 = 12 (aka 6+6)
88+88+88+88+88+88+88+88 times 88=_________
If somebody creates a question like this for free for 100 points i'll do another one of these and award yo brainliest,
Answer:
It's your friend at school. 8360 is your answer.
Step-by-step explanation:
88 + 88
= 176 + 88
= 264 + 88
= 352 + 88
= 440 + 88
= 528 + 88
= 616 + 88 =
704 x 88
= 8360
Answer:
8,360
Step-by-step explanation:
88 + 88 + 88 + 88 + 88 + 88 + 88 + 88 × 88 is our problem.
Instead of adding all of these 88's together, we will just multiply 88 by 8 because there are 8 of these 88's.
That will leave us with: 704
But that is not our answer.
We still have one more step, and it is to multiply 704 by 8.
After we do that we will have: 8,360 as our answer.
I hope this helps! :>
Nichior compared the slope of the function graphed to the slope of the linear function that has an x-intercept of 2/3 and a y-intercept of -1. If (x) represents the function with the smaller slope, what is the slope of f(x)?
Answer:
The slope of f(x) is 1.5
Step-by-step explanation:
step 1
Find the slope of the linear function that has an x-intercept of 2/3 and a y-intercept of -1
so
we have the points
(2/3,0) and (0,-1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-1-0}{0-2/3}[/tex]
[tex]m=\frac{-1}{-2/3}[/tex]
[tex]m=\frac{3}{2}=1.5[/tex]
step 2
Find the slope of the function graphed
take the points
(0,-1) and (3,6) approximately
substitute in the formula
[tex]m=\frac{6+1}{3-0}[/tex]
[tex]m=\frac{7}{3}=2.33[/tex]
step 3
we know that
f(x) represents the function with the smaller slope
The smaller slope is 1.5
therefore
The slope of f(x) is 1.5
A truck can carry a maximum of 1350 ponds of weight .how many 250- pound of dirt can the truck hold
Answer:
5.4
Step-by-step explanation:
1350/250=5.4
Final answer:
A truck with a maximum capacity of 1350 pounds can carry 5 full 250-pound loads of dirt, as partial loads cannot be accommodated.
Explanation:
How many 250-pound loads of dirt can a truck carry?
To determine how many 250-pound loads of dirt a truck can carry if its maximum capacity is 1350 pounds, you need to divide the truck's maximum capacity by the weight of one load of dirt:
1350 pounds ÷ 250 pounds per load = 5.4 loads
Since the truck cannot carry a fraction of a load, it can carry a maximum of 5 full 250-pound loads of dirt before it reaches its weight limit.
the rayhills are buying new windows for their house the company installs the new windows for 3,325 total cost for buying the windows and having them installed is 7,699.25 if the rayhills pay 230.25 per window how many windows did they buy
Answer:
Step-by-step explanation:
buying the windows and having them installed costs $ 7699.25
installation alone costs 3325
therefore, the cost of the windows is : 7699.25 - 3325 = 4374.25
and if they are paying 230.25 per window, then there is
4374.25 / 230.25 = 18.997 windows
let me check something...
18 * 230.25 = 4144.50
19 * 230.25 = 4374.75
if ur numbers are written correctly, they can only buy 18 windows.....they would be short 50 cents from buying 19 windows
To determine the number of windows the Rayhills purchased, the total cost minus the installation cost was divided by the cost per window, leading to an estimate of approximately 19 windows.
To find out how many windows Rayhills bought, we need to subtract the installation cost from the total cost and then divide the result by the cost per window. The total cost of buying the windows and having them installed is $7,699.25, and the company charges $3,325 for the installation. If each window costs $230.25, we can calculate the number of windows as follows:
Subtract the installation cost from the total cost: $7,699.25 - $3,325 = $4,374.25.Divide the remaining amount by the cost per window: $4,374.25 / $230.25.Now let's perform the division:
$4,374.25 / $230.25 ≈ 19 windows (rounded to the nearest whole number since you can't buy a fraction of a window).
Therefore, the Rayhills bought approximately 19 windows.
Which expressions are equivalent to 4(-52 + 2) + (-6) ?
Choose all answers that apply:
203 - 2
2-102 + 1)
None of the above
PLEASE HELP ME ASAP, AND FIND THE LENGTH OF BC
Answer:
BC=16.992
Step-by-step explanation:
Answer:
16.992
Step-by-step explanation:
-2x-16+0
Solve for X
Answer:
x = -8
Step-by-step explanation:
-2x-16+0 = 0
Combine like terms.
-2x-16 = 0
Add 16 to both sides (to isolate the -2x from -16)
-2x = 16
Divide both sides by -2 to isolate the x from -2
x = -8
I NEED HELP ASAP!!
Find the value of x in each case:
PU ∩ RT = S, Q ∈ PR
You know that m<TSU=m<PSR because they make a vertical angle pair.
So...m<PSR=4x.
If, m<QSR=3x then m<PSQ=4x-3x=x because they are adjacent.
And, m<PQS=180-68=112 degrees (linear pair).
Now we know all the interior angles in triangle PQS so we can say that...
x+x+112=180 (sum of interior angles in triangle)
2x=68
x=34 degrees
The requried value of x is 34 in each case, as of the given conditions
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
As given in the question,
PU ∩ RT = S, Q ∈ PR
Since the sum of the remote interior angles is equal to the sum of the remote exterior angles.
∠SPQ + ∠PSQ = ∠SQR
∠PSQ = 68 - x
Now, When two lines intersect each other, their alternate angles are equal,
∠TSU = ∠PSR
4x = ∠PSQ + ∠QSR
4x = 68 - x + 3x
2x = 68
x = 34
Thus, the requried value of x is 34.
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Find the equation of a circle with a center of(5, 7) where a point on the circle is (10, 19)
Answer:
(x - 5)² + (y - 7)² = 169
Step-by-step explanation:
The standard form of the equation of a circle is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (5, 7), thus
(x - 5)² + (y - 7)² = r²
The distance from the centre to a point on the circle is the radius
Calculate the radius using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (5, 7) and (x₂, y₂ ) = (10, 19)
r = [tex]\sqrt{(10-5)^2+(19-7)^2}[/tex]
= [tex]\sqrt{5^2+12^2}[/tex]
= [tex]\sqrt{25+144}[/tex] = [tex]\sqrt{169}[/tex] = 13, hence
(x - 5)² + (y - 7)² = 169 ← equation of circle
Can someone please help me answer this question, I am stuck on this question
Step-by-step explanation:
The answer will be 380 inches as of what I have done
multiply the following complex numbers (6+3i)(3+i)
Answer:
15i+15
Step-by-step explanation:
(6+3i)(3+i)
18+9i+6i+3i^2
18+15i+3(-1)
18+15i-3
15i+15
After multiplyinh complex numbers (6+3i)(3+i), the final answer will be 15+15i.
Explanation:To multiply complex numbers, we can use the distributive property.
First, distribute 6 to both terms of (3+i), giving us 18+6i.
Then, distribute 3i to both terms of (3+i), resulting in 9i+3i².
We can simplify 3i² by using the fact that i²=-1, so 3i²=-3.
Putting it all together, we have (6+3i)(3+i)
= 18+6i+9i-3
= 15+15i.
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Perl made the following conjecture.
The sum of a multiple of 4 and a multiple of 8 must be a multiple of 8.
Red more in the image
Answer:
No, it's not a counterexample, because 48 is a multiple of 8
Step-by-step explanation:
I think like 4 x 3 + 8 x 2 = 28 is a counterexample, because 28 is not a multiple of 8.
Perl's conjecture that the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8 is incorrect. In fact, the sum would definitely be a multiple of 4 but not necessarily a multiple of 8, since the sum of integers multiplied by 4 does not guarantee that it's a multiple of 8.
Explanation:The subject of this question is Mathematics, specifically dealing with number theory and the properties of multiples and factorization. Perl's conjecture is that the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8. We can examine this by understanding how multiples work.
A multiple of 4 can also be considered as 4n, where n is an integer. Similarly, a multiple of 8 is 8m, where m is integer. If we add both, we get 4n+8m. Now, as per distributive property of multiplication over addition, the expression becomes 4n+4(2m), which can be further simplified as 4(n+2m).
We can now see that the sum is actually 4 times the sum of some integer, so it must indeed be a multiple of 4. However, since it's not necessarily the case that 'n+2m' itself is a multiple of 2, we cannot say that the overall sum is guaranteed to be multiple of 8.
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Percent change, "a price of a dirt bike dropped from $872 to $600"
Answer:
Percent change is −31.19%.
Step-by-step explanation:
It is given that "a price of a dirt bike dropped from $872 to $600".
Initial price = $872
New price = $600
We need to find the Percent change.
[tex]\text{Percent change}=\dfrac{\text{New price - Initial price}}{\text{Initial price}}\times 100[/tex]
[tex]\text{Percent change}=\dfrac{600-872}{872}\times 100[/tex]
[tex]\text{Percent change}=\dfrac{-272}{872}\times 100[/tex]
[tex]\text{Percent change}=-31.19266[/tex]
[tex]\text{Percent change}\approx -31.19[/tex]
Therefore, the percent change is −31.19%.
Final answer:
The chance change in the price of the dirt bike is-31.2, indicating a drop in price from$ 872 to$ 600.
Explanation:
To calculate the chance change in the price of a dirt bike that dropped from$ 872 to$ 600, we follow this formula given in the reference Chance change = (( change in value)/( original value)) × 100
First, we find the change in value, which is the new price abated from the original price $ 600-$ 872 = -$ 272 also, we divide this change by the original price -$ 272/$ 872 ≈-0.312
Eventually, to find the chance change, we multiply this bit by 100 -0.312 × 100 = -31.2 This means the price of the dirt bike dropped by31.2.
22. Sue can paint a chair in 3 hours. Jerry can paint the same size chair in 2 1/2
hours. Working together, how long would it take them to paint 10 chairs?
People leaving an ice cream store were asked to name their favorite flavor of ice cream. Fifty-one people said chocolate was their favorite flavor. If 68% of the people surveyed said chocolate, how many people were surveyed?
To find the total number of people surveyed, you divide the number of people who chose chocolate (51) by the percentage that represents (0.68), resulting in 75 people surveyed.
Explanation:The question posed involves determining the total number of people surveyed based on the percentage who favored chocolate ice cream. Since 68% of the people surveyed stated that chocolate was their favorite flavor, and it is known that 51 people chose chocolate, we can set up a proportion to find the total number of people surveyed. The proportion to find the total number of respondents (let's call it x) is as follows:
0.68 x = 51
To solve for x, you would divide both sides of the equation by 0.68, which gives you:
x = 51 / 0.68
x = 75 people
Therefore, the total number of people surveyed was 75.
If g(x)=1/x were shifted 4 units to the left and 4 units up what would the new equation be?
The new equation will be:
[tex]g(x) =\frac{1}{x+4}+4[/tex]
OR
[tex]g(x) = \frac{x+5}{x+4}[/tex]
Step-by-step explanation:
The function transformations are defined as:
Shifting function upwards b units
[tex]f(x) => g(x) = f(x)+b[/tex]
Shifting functions to the left b units
[tex]f(x) => g(x) = f(x+b)[/tex]
Given function is:
[tex]g(x) = \frac{1}{x}[/tex]
Shifting the function 4 units to the left will give us:
[tex]g(x) => g(x+b)\\= \frac{1}{x+4}[/tex]
Now shifting the function 4 units upwards
[tex]g(x) = \frac{1}{x+4} + 4[/tex]
Simplifying
[tex]g(x) = \frac{1+x+4}{x+4}\\= \frac{x+5}{x+4}[/tex]
The new equation will be:
[tex]g(x) =\frac{1}{x+4}+4[/tex]
OR
[tex]g(x) = \frac{x+5}{x+4}[/tex]
Keywords: function, transformations
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What percent of 20
is 16
well 4 is basically 1/5 of 20, so that would be about 20%
and since 4 x 4 is 16, my guess is that 16 is 80% of 20
Answer: 80%
Step-by-step explanation: To answer the question what percent of 20 is 16, we translate the question into an equation.
So we have "what percent" that's x, "of 20" means times 20, "is 16" = 16. So now we have the equation (x)(20) = 16.
Now to solve for x, since x is being multiplied by 20, we need to divide by 20 on both sides of the equation. On the left side of the equation the 20's cancel and we have x and on the right side of the equation we have 16 divided by 20 which is 0.8.
Now, remember that we want to write our answer as a percent so we need to convert 0.8 into a percent.
We can convert a decimal into a percent by moving the decimal point two places to the right so we can change 0.8 to a percent by simply moving the decimal point two places to the right and we have 80%.
This means that 80% of 20 is 16.
(SHOW WORK NEED IT BY TONIGHT! )Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Nick, a caterer, is investing some money in equipment and employees to help grow his business. Recently he spent $47 on equipment and hired a server who makes $15 per hour. Nick is hoping to make up these expense at the next job that is scheduled, which pays a base of $54 in addition to $14 per hour that the server works. In theory, this event could pay enough to cancel out Nick's expenditures. How much would the job pay? How long would the job have to be?
The expenditures and pay would both be $_ if the job lasted for _ hours.
Let X = the number of hours the server works.
The equation for the amount Nick spends is 15x + 47
The next job pays 14x + 54
Set the equations to equal and solve for x:
15x + 47 = 14x +54
Subtract 14x from both sides:
X + 47 = 54
Subtract 47 from both sides:
X = 7
Now replace x with 7 in the second equation:
14x + 54 = 14(7) + 54 = 98 +54 = 152
The job would pay $152 and be 7 hours long.