Alexa needs a total of 231.5 square inches of construction paper for her project.
To find the area of a rectangle, we multiply its length by its width. Let's calculate the area of each rectangle and then sum them up.
Rectangle 1:
Length: 9 inches
Width: 14 1/3 inches
To work with fractions more easily, let's convert the mixed fraction 14 1/3 into an improper fraction. The numerator of the fraction will be (3 * 14) + 1 = 43, and the denominator remains 3.
Area of Rectangle 1 = Length * Width
= 9 inches * (43/3) inches
= (9 * 43) / 3 square inches
= 387 / 3 square inches
= 129 square inches
Rectangle 2:
Length: 10 1/4 inches
Width: 10 or 30 inches
Again, let's convert the mixed fraction 10 1/4 into an improper fraction. The numerator will be (4 * 10) + 1 = 41, and the denominator remains 4.
Area of Rectangle 2 = Length * Width
= (10 1/4 inches) * (10 inches)
= (41/4 inches) * (10 inches)
= (41 * 10) / 4 square inches
= 410 / 4 square inches
= 102.5 square inches
Now, let's add the areas of the two rectangles to find the total square inches of construction paper Alexa needs:
Total Area = Area of Rectangle 1 + Area of Rectangle 2
= 129 square inches + 102.5 square inches
= 231.5 square inches
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please help solve for n. 5/15 = n/21 a. n = 35 b. n = 7 c. n = 5 d. n = 90
Answer:
b. n = 7
Step-by-step explanation:
You want to solve the proportion ...
5/15 = n/21
This is most easily done by multiplying by the inverse of the coefficient of the variable:
(21/1)(5/15) = (21/1)(n/21)
7 = n . . . . . . . . . simplify
__
Additional comment
The math is a little easier if you simplify 5/15 to 1/3. Then, n = 21/3 = 7.
Find the nth term an of the geometric sequence described below, where r is the common ratio.
a4 = -8, r= -2
Answer:
[tex]a_n=(-2)^{n-1}[/tex]
Step-by-step explanation:
So a geometric sequence can be explicitly defined as: [tex]a_n = a_1(r)^{n-1}[/tex]. IN this case we're given r, but we don't know what a_1 is. We can find this by lugging in 4 as n, and -8 as a_n, since they're given values
Plug known values in:
[tex]-8 = a_1(-2)^{4-1}[/tex]
Subtract the values in the exponent
[tex]-8 = a_1(-2)^3[/tex]
Simplify the exponent
[tex]-8 = a_1 (-8)[/tex]
Divide both sides by -8
[tex]1=a_1[/tex]
So the nth term can be defined as: [tex]a_n = 1(-2)^{n-1}[/tex], and since the 1 is redundant, the equation can simply be defined as: [tex]a_n=(-2)^{n-1}[/tex]
Anna is reading a 300-page book. She can read a page in two minutes. If she has finished reading 75 percent of the pages, how many minutes of reading does she have left
Answer:
150 minutes
Step-by-step explanation:
If Anna read 75% of her 300-page book, then she has already read:
300 × 75%
= 300×0.75
= 225
225 pages.
If Anna has already read 225 pages, then she has:
300 - 225 = 75
75 pages left still to read.
If Anna reads 2 minutes per page, then she has
75 × 2 = 150 minutes.
She has 150 minutes of reading left to finish her book.
By the way, it's weird to say you have 150 minutes of something to do. In real life 150 minutes = 2 1/2 hours. jfyi. Have a great day!
A rectangular rug is 12.5 feet long and 10 feet wide. The rug needs to be reduced by a factor of One-fifth. What is the area of the reduced rug?
The area of the reduced rug is 25 square feet
How to determine the area?The dimensions are given as:
Length = 12.5 feet
Width = 10 feet
The area is calculated as:
Area = Length * Width
So, we have:
Area = 12.5 * 10
Evaluate
Area = 125
When reduced by one-fifth, we have:
Area =1/5 * 125
Evaluate
Area = 25
Hence, the area of the reduced rug is 25 square feet
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Make w subject of formula
C=(4+w)/(w+3)
Answer:
Step by Step Solution
More Icon
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
c-((4+w)/(w+3))=0
STEP
1
:
4 + w
Simplify —————
w + 3
Equation at the end of step
1
:
(w + 4)
c - ——————— = 0
w + 3
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using (w+3) as the denominator :
c c • (w + 3)
c = — = ———————————
1 (w + 3)
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
c • (w+3) - ((w+4)) cw + 3c - w - 4
——————————————————— = ———————————————
1 • (w+3) 1 • (w + 3)
Equation at the end of step
2
:
cw + 3c - w - 4
——————————————— = 0
w + 3
STEP
3
:
When a fraction equals zero :
3.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
cw+3c-w-4
————————— • w+3 = 0 • w+3
(w+3)
Now, on the left hand side, the w+3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
cw+3c-w-4 = 0
Solving a Single Variable Equation:
3.2 Solve cw+3cw-4 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
Answer:
w = (4 - 3C)/(C - 1).
Step-by-step explanation:
C=(4+w)/(w+3)
Multiply both sides of the formula by w+3:-
C(w + 3) = 4 + w
Cw + 3C = 4 + w
Cw - w = 4 - 3C
w(C - 1) = 4 - 3C
w = (4 - 3C)/(C - 1).
i need help with this page
I don’t get this either please save me from this ahhhhhh
Answer:
y=
[tex] - \frac{x {}^{2} + 8x + 16 }{2} - 7[/tex]
Step-by-step explanation:
calculate the product, use (a+b)^2=a^2+2ab+b^2
I know only one answer whats the other one help me image-
Answer:
A. 4(4a + 18)
B. 8(2a + 9)
Step-by-step explanation:
We know that :
16a = 4×4×a
72 = 4×18
Then
16a + 72 = 4×(4a) + 4×(18)
= 4 × (4a + 18)
On the other hand,
16a = 8×2×a
72 = 8×9
Then
16a + 72 = 8×(2a) + 8×(9)
= 8 × (2a + 9)
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.
The relationship between the elapsed time ttt, in seconds, and the number of bacteria, B_{\text{second}}(t)B
second
(t)B, start subscript, start text, s, e, c, o, n, d, end text, end subscript, left parenthesis, t, right parenthesis, in the petri dish is modeled by the following function:
Bsecond(t)=6000⋅(1516)t
Complete the following sentence about the rate of change in the number of bacteria in minutes.
After a special medicine is introduced into a petri dish full of bacteria, Every second, the number of harmful bacteria remaining in the body decays by a factor of 0.97
What is bacteria?Generally, a kind of unicellular bacteria that has characteristics with many disease-causing organisms, such as having a cell wall but lacking organelles and an organized nucleus.
In conclusion, When a certain medication is put into a petri dish that is full of bacteria, the amount of pathogenic bacteria that are still present in the body decreases by a factor of 0.97 every single second.
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The supervisor of a fish hatchery measures the length of a particular species every week after hatching to track their growth. If their average length is too short or too long, they are not maturing properly and further tests must be done to determine the cause. She randomly selects 30 fish from among those that hatched five weeks ago and measures their individual lengths in inches to determine if they have grown to an average length of 9.7 inches. She observes an average length of 10.1 inches among the sample. What set of hypotheses is she interested in testing
The z-test score is used for this hypothesis test to decide whether to reject or not to reject the null hypothesis. The z-test score for the given sample is 1.22.
How to calculate z-score for the hypothesis test?The z-score for the hypothesis test is calculated by,
z-score = (X - μ)/(σ/√n)
Where X - sample mean, μ - population mean, σ - standard deviation, and n - sample size.
Calculation:It is given that,
Sample size n = 30
Population mean μ = 9.7
Sample mean X = 10.1
Standard deviation σ = 1.8
So, the z-score is
= (10.1 - 9.7)/(1.8/√30)
= 0.4/0.328
= 1.219 ≅ 1.22
Therefore, the p-value for this z-score is 0.22. This value decides whether to reject or not to reject the null hypothesis.
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x + 6 x + 5
im trying to find the area of the rectangle in a polynomial standard form
Area of the entire rectangle is x² + 11x + 30. This can be obtained by adding area of each square.
Calculate the polynomial for area of the entire rectangle:Method 1
Area of rectangle = length × width
Area (blue) = length × width = (x) × (x) = x²Area (green) = length × width = (5) × (x) = 5xArea (pink) = length × width = (6) × (x) = 6xArea (orange) = length × width = (6) × (5) = 30Area of entire rectangle = x² + 5x + 6x + 30 = x² + 11x + 30
Method 2
Area of entire rectangle = length × width
= (x+6)×(x+5)
= x² + (6+5)x + (6×5) [∵(x+a)(x+b) =x² + (a+b)x + ab]
= x² + 11x + 30
Hence area of the entire rectangle is x² + 11x + 30.
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Diane is filling a candle order for a wedding. She needs 6 large arrangements and 13 small arrangements .The large arrangements each contain 25 candles. The small arrangements each contain 12 candles. How many candles does diane need in all?
Answer:
406 candles in all.
Step-by-step explanation:
She needs 6 large arrangements with 25 candles in each arrangement.
Multiply 25 and 6 to find how much candles for all large arrangements combined.
25*6=150
She also needs 13 small arrangements with 12 candles in each arrangement.
Multiply 13 and 12 to find how much candles for all the small arrangements combined.
13*12=156
Add the answers together to find how many candles in all.
156+150=406.
She needs 406 candles in all.
Hope this helps!
Answer:
306
Step-by-step explanation:
First we find the number of candles needed for each size of arrangement.
Large Arrangements:
6 large arrangements with 25 candles each:
25 × 6 = 150
Small Arrangements:
13 small arrangements with 12 candles each:
13 × 12 = 156
Now we add the results above to find a grand total:
total = 150 + 156 = 306
You must write your answer in fully simplified form.
2t= -12
Answer:
t=-6
Step-by-step explanation:
laura goes for a cycle from her house to the post office 4km away work out laura's speed cycling to the post office CORBETTMATHS 2016
ItItItIt takes Laura 15 minutes (0.25 hours) to cycle to the post office.
Speed and timea. It takes Laura 15 minutes (0.25 hours) to cycle to the post office.
b. Speed:
Speed=Distance/Time
Speed=4/0.25
Speed=16 km/hr
c. It takes Laura 20 minutes to cycle to the post office.
d. Time
Time=20 minutes (1/3 hour)
Speed:
Speed=Distance/Time
Speed=4÷1/3
Speed=12 km/hr
Therefore It takes Laura 15 minutes (0.25 hours) to cycle to the post office.
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Suppose you start at the origin, move along the x-axis a distance of 6 units in the positive direction, and then move downward parallel to the z-axis a distance of 4 units. What are the coordinates of your position
The coordinates of your position are (6, 0, -4).
2. Using the figure, find and y.
Answer: [tex]x=8, y=2\sqrt 2[/tex]
Step-by-step explanation:
By the Pythagorean theorem, x=8.
So, by the geometric mean theorem,
[tex]y^2 = (6)(2)=8\\\\y=2\sqrt{2}[/tex]
If a car manufacturer purchases new labor saving technology for its assembly line we would not expect
If a car manufacturer purchases new labour saving technology for its assembly line then we would not expect the production to be declined,wastage of time and money.
Given that a car manufacturer purchases a new labour saving technology.
We have to write the expectation that the car manufacturer would not make after buying such a technology.
We know that improvement of technology means abolition old technology and adoption of new and improved technology.
The advantages of new technology is:
1) It provides a competitive advantage over the competitor,
2) It increases the production,
3) It saves cost of the company,
4) It saves time also.
If a car manufacturer purchases new labour saving technology for its assembly line then he would not expect the production to be declined, wastage of time and money.
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The function G(x) = 2-sin(x) is the result of the application of
transformations on the original function F(x) = cos(x). Which of the following options correctly describes the transformations applied to F(x)?
The transformations applied to F(x) is a vertical shift of 2 and a phase shift of π/2.
What are transformations?When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects."
Function transformations are highly useful for graphing functions without having to start from scratch because they allow you to move, extend, compress, or reflect the curve.
The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:Translation,Dilation and Reflection.
The given function F(x)=cos x is transformed to G(x)=2-sin x, by applying a vertical shift of 2 units upwards and a phase shift of π/2.
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How did the temperature change it increased by 50% and then it decreased by 33 1/3%
There is no change in the temperature.
What is temperature?A temperature is a physical number that describes how hot matter is, or it can be used to calculate the average translational kinetic energy per atom or molecule in a system. It is the measurable fraction of matter's molar thermal energy; a temperature difference allows heat transfer to take place, as energy transfers from a hotter body to a colder body.To find how much temperature is changed:
Let, 'F' be the temperature.
Temperature decreased by [tex]33\frac{1}{3}[/tex]%.
F × (1-.33333) = Temperature increases by 50%.
(F × (1-.33333)(1.50)) = F = No net change, right back to the original temperature F.
Therefore, there is no change in the temperature.
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You have 17 photos.
You want to display as many photos as you can in 3 equal rows.
How many photos won't be displayed?
2 photos will not be displayed
How to determine the number of photos?The given parameters are:
Photos = 17
Rows = 3
Divide 17 by 3 and take note of the remainder
Photos left = 17/3
This gives
Photos left = 5 remainder 2
Hence, 2 photos will not be displayed
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c) 4x-9y = 17 6x - 5y = 17
Answer:
(2, - 1 )
Step-by-step explanation:
4x - 9y = 17 → (1)
6x - 5y = 17 → (2)
multiplying (1) by 6 and (2) by - 4 and adding will eliminate x
24x - 54y = 102 → (3)
- 24x + 20y = - 68 → (4)
add (3) and (4) term by term to eliminate x
0 - 34y = 34
- 34y = 34 ( divide both sides by - 34 )
y = - 1
substitute y = - 1 into either of the 2 equations and solve for x
substituting into (1)
4x - 9(- 1) = 17
4x + 9 = 17 ( subtract 9 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
solution is (2, - 1 )
The ratio of dogs to cats in a shelter is 9:15.if the total number of cats and dogs is 96.how many dogs are there?
There are 36 dogs in the shelter.
How to find the total number of dogs in the shelter?The ratio of dogs to cats in the shelter is given as 9:15.
The total number of dogs and cats is given as 96.
Let the constant of proportionality be x.
The total number of dogs is 9x and the total number of cats is 15x.
This means that:
9x + 15x = 96
24x = 96
x = 4.
The total number of dogs in the shelter = 9 × 4
= 36
Therefore, we have found that there are 36 dogs in the shelter.
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The ratio between Earth’s distance from the Sun and its scaled distance can be used to find the scaled distance for the other planets. Earth’s distance of 149.6 million kilometers to the Sun is scaled to 5.0 sheets of toilet paper as shown in the table. Now let’s find the scaled distance between Mars and the Sun as an example. Using the calculations shown, Mars’s distance to the Sun of 227.9 million kilometers would be scaled to 7.6 sheets of toilet paper.
d × 149.6 = 227.9 × 5.0
d = 7.6 sheets
Use this same process to complete the table with the scaled distances for the other planets. Round each answer to the tenths place. If you need additional math help, visit the Proportions section of the Math Review.
Using a proportional relationship, the scaled distances, in sheets of toilet paper, are given as follows:
Mercury: 1.9.Venus: 3.6.Jupiter: 26.Saturn: 47.8.Uranus: 95.8.Neptune: 149.9.What is the missing information?The real distances are missing, and they are given in the table at the end of the answer.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:
y = kx
In the case of an inverse relationship, we have that:
y = k/x.
k is the constant of proportionality for both cases.
For this problem, the constant for the Scaled Distances as a function of the Real Distances is given as follows:
k = 5/149.6 = 7.6/227.9 = 0.03334795963.
Hence, the relationship for the Scaled Distances is given by:
S = 0.03334795963R
In which R is the real distance.
Then the scaled distances for the planets are given as follows:
Mercury: 0.03334795963 x 57.9 = 1.9 sheets of toilet paper.Venus: 0.03334795963 x 108.2 = 3.6 sheets of toilet paper.Jupiter: 0.03334795963 x 778.6 = 26 sheets of toilet paper.Saturn: 0.03334795963 x 1433.5 = 47.8 sheets of toilet paper.Uranus: 0.03334795963 x 2872.5 = 95.8 sheets of toilet paper.Neptune: 0.03334795963 x 4495.1 = 149.9 sheets of paper.More can be learned about proportional relationships at https://brainly.com/question/10424180
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Answer:
edmentum/plato hope this can help someone :)
Step-by-step explanation:
if m<0 and b>0,the graph of y=max+b does not pass through which quadrant
Answer:are u sure its not y=mx+b? And it doesn’t pass thru 1 im pretty sure
Step-by-step explanation:
Answer: Quadrant III
Explanation:
Let's pick example values for m and b
I'll go for m = -2 and b = 5. Anything works as long as m is negative and b is positive.
We go from y = mx+b to y = -2x+5
Plot this graph as shown below. The line passes through quadrants I, II, and IV. Only quadrant III is not touched at all.
An airplane rises at an angle of 12 degrees with the ground. About how high, in feet will the plane be above the ground when it has traveled 500 yards fromt he airport horizontally? Round your answer to the nearest foot.
Please I’m giving away Brainly ASAP
Answer:
g and f are inverse functions because g(f(x)) = f(g(x)) = x
Step-by-step explanation:
Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):
[tex]f(g(x))=f(\frac{x+6}{7})=7(\frac{x+6}{7} )-6=x+6-6=x[/tex]
Now, let's find g(f(x)):
[tex]g(f(x))=g(7x-6)=\frac{(7x-6)+6}{7} =\frac{7x}{7}=x[/tex]
There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:
[tex]f(x)=y=7x-6[/tex]
Swap x and y:
[tex]x=7y-6[/tex]
Solve for y:
[tex]x+6=7y\\y=\frac{x+6}{7}[/tex]
Notice that we got g, which means f and g are inverse.
What do these values indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?
Because the sample statistic centers around a different value than the population parameter, the sample mean absolute deviation is a biased estimator of the population mean absolute deviation.
Reason Behind a Biased Estimator
The expected value (average) of all the sample absolute deviations must match the population absolute deviation in order for the absolute deviation to function as an unbiased estimator. It does not, however, which makes the values of sample mean absolute deviation behave as a biased estimator.
Brief Description of Sample Mean Absolute Deviation
The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection. It is a statistical summary of statistical variability or dispersion.
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The positive integers $1,$ $2,$ $3,$ $\dots$ are listed in order. What is the $1000^{\rm th}$ positive integer with an odd number of digits
There are 9 positive integers with 1 digit (1 - 9).
There are 90 integers with 2 digits (10 - 99).
There are 900 integers with 3 digits (100 - 999).
There are 9000 integers with 4 digits (1000 - 9999).
And so on. It stands to reason that there are [tex]9\times10^{n-1}[/tex] integers with [tex]n[/tex] digits.
Now,
1000 = 9 + 900 + 91
so the 1000th positive integer with an odd number of digits is the 91th number with 3 digits, which is 190.
. sipho buys a car for r169 000. he pays a deposit of 15% and then makes monthly installments of 1% of the leftover amount for 9 years. i) what amount must sipho pay for the deposit? ii) what is the monthly payment that sipho makes? iii) how much does sipho pay in total for the car?
The amount for the deposit is $25350, monthly payment is $1436.5 and the total amount that Sipho pays is $178492.
Given price of car $169000, deposit of 15%, monthly installments being 1% of left over price and number of years be 9 years.
We have to find the amount of deposit, monthly installments and the total amount paid by Sipho.
We have been told that deposit is 15% of total amount. So the deposit will be 15%*169000=$25350.
Monthly installment is 1% of the left over amount.
left amount=169000-25350=$143650.
Monthly installment being =143650*1/100
=$1436.5
Total amount paid by Sipho=deposit +installment amount * numberof installments
Number of installments=12*9
=108
Total amount=25350+1436.5*108
=25350+155142
=$178492
Hence deposit is $25350, monthly payment being $1436.5, total amount be $178492.
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Solve for X if possible:
5x -4y = 24
x =
Answer:
x=6 because if you multiple 4x6 you get 24
not exactly sure but try
Answer:
it is not possible
Step-by-step explanation:
there are two different variables in one equation, so you cannot solve for one. You would need a system of equations to do that.
you can solve for x in terms of y, which is x = (24+4y)/5 but i dont think thats what the question is asking so the answer is probably just that its not possible