The area of the entire figure below is 111 square unit.
A rectangle that has been split into 24 parts, set in 4 rows of 6 parts each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-sixth. Along the left side of the rectangle, the rows are labeled one-fourth.
A rectangle that has been split into 24 parts, set in 4 rows of 6 parts each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-sixth. Along the left side of the rectangle, the rows are labeled one-fourth.
What is the area of the striped rectangle?
The striped rectangle has a total area of 69,375 cm².
How to calculate the area of the striped rectangle?To find the area of the striped rectangle we must carry out the following procedures.
Find the area of each segment of the rectangle, that is, what is the area of each of the 24 squares that make up the rectangle, for that we divide the 111cm² of the total area into 24.
111cm² ÷ 24 = 4.625cm²According to the above, we infer that each square has an area of 4.625cm².
On the other hand, to find the area of the striped rectangle we must take into account that it is 5 squares long by 3 squares high, that is, its area is 15 squares.
3 × 5 = 15Finally, each square has an area of 4.625cm², so to find the total area of the striped area we must multiply the area of each square by the number of squares.
15 × 4.625cm² = 69.375cm²
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T=235+980d
The torque, TTT, in newton-meters, on a diving board with a 100 kilogram weight placed "d" meters from the diving board's fulcrum is given by the equation above. How much torque in newton-meters is on the diving board when the weight is placed at the fulcrum?
Questions:
1. what does 980 in the equation represent?
2. Why is the answer 235?
The answer is 235 because the weight is placed at the fulcrum
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
1. What does 980 in the equation represent?The linear equation is given as:
T = 235 + 980d
A linear equation is represented as:
T = b + md
Where m represents the slope
So, we have
m = 980
This means that 980 represents the amount of Torque per meter
2. Why is the answer 235?When the weight is placed at the fulcrum, the value of d is 0
So, we have
T = 235 + 980d
Evaluate
T = 235 + 980 * 0
This gives
T = 235
Hence, the answer is 235 because the weight is placed at the fulcrum
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f(t) = 0.25t2 − 0.5t + 3.5
The resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively
Function and valuesFunctions are expressions in form of variables. Given the following quadratic equation expressed as:
f(t) = 0.25t^2 − 0.5t + 3.5
We can find the equivalent value of the function when the value of t a re 2 and 6.
If the value of t is 2. hence;
f(2) = 0.25(2)^2 − 0.5(2) + 3.5
f(2) = 1 - 1 + 3.5
f(2) = 3.5
If the value of t is 6, hence;
f(6) = 0.25(6)^2 − 0.5(6) + 3.5
f(6) = 9 - 3 + 3.5
f(6) = 6.5
Hence the resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively
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Simplify the following expression:
( 4 + 5i ) / 4i
Select one:
a.
( 5 + 4i ) / 4
b.
( 5 - 4i ) / 4
c.
( 5i + 4i ) / 4
d.
( 5i - 4 ) / 4
Answer: B
Step-by-step explanation:
[tex]\frac{4+5i}{4i}\\ \\ =\frac{1}{4} \left(\frac{4+5i}{i} \right)\\\\=\frac{1}{4}((-i)(4+5i))\\\\=\frac{1}{4}(-4i-5i^2)\\\\=\frac{5-4i}{4}[/tex]
Elliot borrows $3,000 from a bank that is charging three percent simple interest per year. If he pays the loan back in six months, how much interest will he pay? $30.00
$45.00
$90.00
$300.00
Answer:
The answer to that question depends
beacuse where ever you are it changes like uk you can pay 100€
or japan it can be around 1000¥
Cannington, Inc., designs, manufactures, and markets personal computers and related software. The following information was taken from a recent annual report of Cannington industries: Property, Plant, and Equipment (in millions): Current Year Preceding Year Land and buildings $707,150 $410,147 Machinery, equipment, and internal-use software 671,793 530,363 Office furniture and equipment 106,073 91,930 Other fixed assets related to leases 855,652 643,507 Accumulated depreciation and amortization (898,081) (749,579) a. Compute the book value of the fixed assets for the current year and the preceding year. Current year book value $fill in the blank 1 Preceding year book value $fill in the blank 2
The book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.
Book valueCurrent year book value
Land and buildings $707,150
Machinery, equipment, and internal-use software $671,793
Office furniture and equipment $106,073
Other fixed assets related to leases $855,652
Less Accumulated depreciation and amortization ($898,081)
Book value $1,442,587
Preceding year book value
Land and buildings $410,147
Machinery, equipment, and internal-use software $530,363
Office furniture and equipment $91,930
Other fixed assets related to leases $643,507
Less Accumulated depreciation and amortization ($749,579)
Book value $926,368
Therefore the book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.
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find the square roots by division method of 151,321
Answer: 389 is the square root.
Answer:
389 is the square root
Step-by-step explanation:
BRAINIEST PLS
Select the correct answer.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
OA.
y=3x+4
OB. y=3x-14
OC. y=3x-4
OD. y=3x + 12
Answer: [tex]\Large\boxed{A.~y=3x+4}[/tex]
Step-by-step explanation:
Given information
Slope = 3
Point = (-3, -5)
Given the format of the equation
Slope-intercept form: y = mx + b
m = Slopeb = y-interceptSubstitute values into the equation
y = (3)x + b
y = 3x + b
Substitute the given point into the equation to get the value of [ b ]
(-5) = 3(-3) + b
-5 = -9 + b
b = -5 + 9
b = 4
Therefore, the equation of the line is [tex]\Large\boxed{y=3x+4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What is the ordered pair of X' after point X (3, 4) is rotated 180°?
OX' (3,-4)
OX' (-3,-4)
OX' (-4, 3)
OX' (-4,-3)
The volume of a packing box is 5 - x cubic feet. The width of the box is x feet and the length is x - 2 feet
Answer:
Step-by-step explanation:
A strain of bacterial cells doubles inpopulation every 2 days. A single cell is placed in a dish with sufficient nutrients to sustain a colony. Which equation will
calculate d, the number of days after which there will be 256 bacterial cells in
the dish?
The equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256
How to determine the equation of the number of days?The given parameters are:
Rate, r = doubles every two days
Initial number of strain, a = 1
This means that the function is an exponential function.
An exponential function is represented as:
A(d) = a * r^d
Since the strain doubles every two days, we have:
A(d) = a * r^(d/2)
Substitute the known values in the above equation
A(d) = 1 * 2^(d/2)
Evaluate the product
A(d) = 2^(d/2)
When there are 256 bacterial cells, the equation becomes
2^(d/2) = 256
Hence, the equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256
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Instructions: Match the following data with the correct stem and leaf.
Helped need please
Based on the stem and leaf plots given, the correct stem and leaf plot for the first table on per capita income is the third stem and leaf diagram.
For the table on the basketball tornament, the correct stem and leaf plot would be the last one.
How are stem and leaf plots used?First look at the key to the bottom right of the plot to see how to interpret the data.
The key on the third stem and lead plot says 1 I 2 = 12,000. This means that every steam and lead pairing is in thousands.
Based on the income per capita being in thousands, this is the most likely stem and lead plot for the first table on income per capita.
The second table about basketball tornament appearances is on single and double digits. Only a small stem and leaf key will do.
Look at the number of appearances. The minimum is 1. On a stem and leaf, this is shown as 0 I 1. Options A and B don't have this so we go to Options C and D.
As established, Option C is for data in their thousands so it is out. The correct stem and leaf plot is therefore Option D.
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The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 20 trials and got the following results.
Using the probability concept, we have that:
a) The experimental probability is of 0.75 = 75%.
b) The theoretical probability is of 0.5 = 50%.
c) As the number of trials increases, the probabilities are expected to get closer, though they might not be equal.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials. A theoretical probability is calculated before any trial, and as the number of trials increase, the experimental and theoretical probabilities get closer.
From the table, there were 20 trials, and 2 + 3 + 4 + 4 + 2 = 15 resulted in even numbers, hence the experimental probability is:
p = 15/20 = 0.75 = 75%.
For a fair machine, even and odd numbers should be equally as likely, hence the theoretical probability is of 0.5 = 50%.
For item c, we have that as the number of trials increases, the probabilities are expected to get closer, though they might not be equal.
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What is the next number in the following sequence 0 0 1 2 2 4 3 6 4 8 5
Answer:
10
Step-by-step explanation:
the sequence follows the rule of adding the number and then the number -1 depending on the number before it. for example, you can see in order to get from 2 to 2, it adds 0 or subtracts by 0. After that to get from 2 to 4, you add 2. After that, you subtract 1 from 2 and you subtract that number which is 1 from 4 to get 3 and so on. Following that rule, you get 10 as the next number in the sequence
what base could be written in the blank to make the exponential function model 15% decay ? y= (___) ^t\12
The base of the exponential function model in order to get 15% decay should be 0.85
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.
The first step would be figuring out the function's base.
The function's form should be, [tex]y=a*b^{t}[/tex]
Here,
'a' denotes the starting value.
'b' denotes the decrease rate.
't' denotes time.
According to the question, the exponential function model is,
[tex]y=b^{\frac{t}{12} }[/tex]
In order to get a 15% decay,
The base of the function should be (100-15)/100 = 0.85
Thus, Base of function(b) = 0.85
The exponential function model is written as:
[tex]y=0.85^{t/12}[/tex]
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a studio has 1600 square feet of floor space. the studio then buys the neighboring building and expands by 75%
Answer:
the total new area is 2800 ft²
Step-by-step explanation:
original area: 1600 ft²
new expanded area: 1600 ft² + 75% of 1600 ft²
new expanded area = 1600 ft² + 0.75 × 1600 ft²
new expanded area = 1600 ft² + 1200 ft²
total new area = 2800 ft²
A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days.
With the use of formula, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams
Word Problem Leading to Exponential FunctionFirst analyze the problem and represent them in exponential function. The decay rate is different from increase rate with minus and plus sign.
Given that a tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Let
I = initial amount injected = 0.9 gramsR = decay rate = 1.15%t = number of days = 60 daysA = the remaining amount of Iodine - 125An exponential model representing the amount of Iodine-125 remaining in the tumor after t days will be
A = I( 1 - R%)^t
Let us use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days by substituting all the given parameters into the formula
A = 0.9 ( 1 - 1.15/100)^60
A = 0.9 ( 1 - 0.0115)^60
A = 0.9 ( 0.9885)^60
A = 0.9 x 0.4995
A = 0.45 grams
Therefore, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams
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On a map, 3 inches represents 50 miles. Which proportion can be used to find the actual distance represented by 5 inches on the map?
StartFraction 3 over 50 EndFraction = StartFraction x over 5 EndFraction
StartFraction 3 over 50 EndFraction = StartFraction 5 over x EndFraction
StartFraction 3 over x EndFraction = StartFraction 50 over 5 EndFraction
StartFraction x over 3 EndFraction = StartFraction 50 over 5 EndFraction
The correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Given that 3 inches on a map represents 50 miles.
We are told to find the proportion which can be used to represent 5 inches.
Multiplication is basically finding the product of two numbers but it can be used to convert the units also.
If 3 inches represents 50 miles then,
1 mile=50/3
Multiply both sides by 5.
5 miles=5*50/3
If we see the options then we will get that the most appropriate and correct option which represents 5 inches is that start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Hence the correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
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Answer:
B
Step-by-step explanation:
3/50 = 5/x
Scenario 2
You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.
The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.
What is the equivalent of the 20% tip as indicated in the task content?The percentage represented as; 20% can be expressed as a fraction.
This follows from the fact that the percentage, % symbol translates to divided by 100.
Consequently, we must note that the 20% translates to; 20/100 = 1/5.
Hence, the 20% tip is one-fifth of the total amount.
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What is the resulting polynomial when -7w² +13 is subtracted from -2w²+6w - 19?
Answer:
5w^2 + 6w - 32
Step-by-step explanation:
Subtract as needed and combine like terms
(-2w^2 + 6w - 19) - (-7w^2 +13) dont forget to distribute the negative
so you get this:
-2w^2 + 7w^2 = 5w^2
6w
-19 - 13 = - 32
your answer is 5w^2 + 6w - 32
hope this helps :)
Hi :)
Let's solve by combining like terms
——————————Combining like terms means you add or subtract
terms with the same variable (if any)terms with the same exponentSolve by combining like terms
[tex]\implies\darkblue\sf{-2w^2+6w-19-(-7w^2+13)}\\\implies\darkblue\sf{-2w^2+6w-19+7w^2-13}\\\implies\darkblue\sf{-2w^2+7w^2+6w-19-13}\\\implies\darkblue\sf{\underline{5w^2+6w-32}}[/tex]
[tex]\tt{Learn\:More;Work\:Harder}[/tex]
:)
(SAT prep) If the lengths of two sides of a triangle are 3 and 5 then the lenght of the third side cannot be:
Answer:
A)
Step-by-step explanation:
3+3=6 6>5
3+5=8 3<8
A)
ASAP Please help me with this questions ASAP
46) True
47) False
These are true by definition.
what is the area of a polygon with verticies of (-2,2), (3,2), (7,-5) and (-2,-5)
Check the picture below.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=5\\ b=9\\ h=7 \end{cases}\implies \begin{array}{llll} A=\cfrac{7(5+9)}{2}\implies A=\cfrac{7(14)}{2} \\\\\\ A=49 \end{array}[/tex]
I really need help I work a 12 hr shift in less then 3 hrs and if I don't answer this correct I don't graduate and have to redo over 100 questions so please if you answer please make it the right answer please someone show mercy and help me
Answer:
72 Degrees
Step-by-step explanation:
10 / 50 = 0.2
A circle has 360 degrees.
0.2 X 360 = 72
Please help!!!!! Two copies of the same Rational Function are shown below.
On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath.
The equation for the horizontal asymptote will be y = -2.
How to illustrate the information?Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:
y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)
= y = -2/1
= y = -2
The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0
= x + 3 = 0
= x = -3
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a number line shows the whole numbers from 0 to 10 describe where you would plot square root 30
graphs of exponential functions
An example of an exponential graph function has been attached and its' properties are as below.
How to draw the graph of an exponential function?The general formula for exponential functions is: f(x) = aˣ, a > 0, a ≠ 1.
The reasons for the restrictions are because;
If a ≤ 0, then when you raise it to a rational power, you may not get a real number.
The graph of an exponential function y = 2ˣ is shown in the attached file. Here are some properties of the exponential function when the base is greater than 1.
The graph passes through the point (0,1)The domain is all real numbersThe range is y>0.The graph is increasingThe graph is asymptotic to the x-axis as x approaches negative infinityThe graph increases without bound as x approaches positive infinityThe graph is continuousThe graph is smoothRead more about Exponential Function Graphs at; https://brainly.com/question/2456547
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classify the numbers in the image to be either a whole number integer rational number irrational number real number
what is the equation of the parabola passing through the points
(0,6). (3, 15.6), and (10,-4)?
Answer:
y = -0.6x^2 + 5x + 6
Step-by-step explanation:
First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.
y = mx + b
15.6 = 3m + 6
9.6 = 3m
m = 3.2
y = 3.2x + 6
y = a(x - 0)(x - 3) + 3.2x + 6
y = a(x)(x - 3) + 3.2x + 6
Finally, substitute 10 for x and -4 for y in the equation above to find a.
-4 = a(10)(10 - 3) + 3.2*10 + 6
-4 = a(10)(7) + 32 + 6
-4 = 70a + 38
-42 = 70a
a = -0.6
Simplify to write in standard form.
y = -0.6(x)(x - 3) + 3.2x + 6
y = -0.6x^2 + 5x + 6
Adisa borrows $5,000 at 14% interest, compounded twice a year. How much does she owe at the end of 8 years?
The borrower owes $14,760.82 at the end of 8 years
What is compounding interest?
Compounding interest means that earlier interest would earn more interest in the future alongside the loan principal.
Note that in this case the loan continues to accumulate interest because there no repayments, in other words, the loan balance after 8 years, which comprises of the principal and interest for 8 years can be computed using the future value formula of a single cash flow(the single cash flow is the principal) as shown thus:
FV=PV*(1+r/n)^(n*t)
FV=loan balance after 8 years=unknown
PV=loan amount=$5,000
r=annual interest=14%
n=number of times in a year that interest is compounded=2(twice a year)
t=loan period=8 years
FV=$5000*(1+14%/2)^(2*8)
FV=$5000*(1.07)^16
FV=$5000*2.95216374856541
FV=loan balance after 8 years=$14,760.82
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