8. How many factors are there for 36?
Write them. What do
you notice about the number of factors of 36 and the number of arrays Courtney can make with the photos ?

Using the formula of compound interest, the number of years is 7.6 years

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula of compound interest is given as;

\(A = P(1 + \frac{r}{n} )^n^t\)

But in this case, the interest was compounded continuously

\(A = Pe^r^t\)

Substituting the values into the formula;

\(7450 = 5500e^(^0^.^0^5^2^5 ^* ^t^)\)

Solving for t;

t = 7.6 years

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The value of z for the given set of parallel lines is 100 and value of y is 32.

In geometry, a line is an infinitely long and straight one-dimensional figure that extends in both directions. A line is defined by two points and can be represented by a straight line with arrows at both ends to indicate its infinite length. Lines have many properties, such as slope, y-intercept, and equation forms like slope-intercept form and point-slope form. They are fundamental concepts in geometry and are used in various fields, including mathematics, physics, engineering, and architecture.

Here,

80°+z=180°

z=100°

6y-92°=z

6y-92°=100°

6y=192°

y=32

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Answer:

Step-by-step explanation:

The questions are:

a. Compute the markup percentage using the total cost concept.

b. Compute the selling price of Product B.

a. The mark up percentage will be calculated as:

= Desired Profit / Total Cost

= ($785000 × 12%) / [($15 × 100,000) + $70,000]

= ($785,000 × 0.12) / [($15 × 100,000) + $70,000]

= $94,200 / $1,570,000

= 0.06

= 6%

b. Selling price of Product B will be calculated as:

= Cost amount per unit + Markup

= $15.70 + ($15.70 × 6%)

= $15.70 + $0.94

= $16.64

Hence the conversion of given numbers according to given demand is

a) N=217 in binary = 11011001

b) N=99 in hexadecimal = 63

c) N= 344 in hexadecimal = 158

d) N= 136 in base 7 = 253.

e) N= 542 in base 5 = 4132.

f) N= 727 in base 8= 1327

g) N= 171 in hexa =1011

h) N=91 in base 3=10101.

i) N= 840 in base 9 =  1133

a) A good method to convert a decimal number to binary is dividing it by 2 and using the remainder of the division as the converted number, starting by the most significant bit (the right one). We can't divide anymore. So we have:

217÷2 = 108 + 1

108÷2 = 54 + 0

54÷2 = 27 + 0

27÷2 = 13 + 1

13÷2 = 6 + 1

6÷2 = 3 + 0

3÷2 = 2 +1

2÷2 = 1

The binary equivalent to 217 is 11011001

b) To convert a number from decimal to hex we can divide the number by 16, taking out the decimal part and multiplying it by 16 using that as our most significant number while using the result of the original division to continue our conversion. So we have:

99÷16 = 6.1875

The decimal part is 0.1875, we multiply it by 16 and obtain 3 as our most significant number. Since we can't divide 6 by 16 we have that as our least significant number then the hexadecimal equivalent is 63.

c) We follow the same steps as in item b:

344÷16 = 21.5

The most significant number is 0.5*16 = 8

21÷16 = 1.3125

The next number is 0.3125*16 = 5

Since we can't divide it anymore we have our result which is 158 in hex.

d) To convert from decimal to base 7 we'll use the same method as to hex, but this time dividing and multiplying by 7.

136÷7 = 19.428571

The most significant number is 0.428571 * 7 = 3

19÷7 = 2.71428571

The next number is 0.71428571*7 = 5

Since we can't divide it anymore we have our result which is 253.

e) To convert from decimal to a base 5 we'll use the same method as before but dividing and multiplying by 5.

542÷5 = 108.4

The most significant number is 0.4*5 = 2

108÷5 = 21.6

The next number is 0.6*5 = 3

21÷5 = 4.2

The next number is 0.2*5 = 1

Since we can't divide it anymore we have our result which is 4132.

f) To convert from decimal to a base 8 we'll use the same method as before but dividing and multiplying by 8.

727÷8 = 90.875

The most significant number is 0.875*8 = 7

90÷8 = 11.25

The next number is 0.25*8 = 2

11÷8 = 1.375

The next number is 0.375*8 = 3

Since we can't divide anymore we have our result which is 1327

g) Following the same steps as before:

171÷16 = 10.6875

The most significant number is 0.6875*16 = 11

Since we can't divide anymore we have our result which is 1011

h) Following the same steps as before:

91÷3 = 30.333333333

The most significant number is 0.333333*3 = 1

30÷3 = 10

The next number is 0

10÷3 = 3.3333333333

The next number is 0.333333*3 = 1

3÷3 = 1

Since we have the final value remainder as 0 the least significant number is 1

Since we can't divide anymore we have our result which is 10101.

i) Following the same steps as before:

840÷9 = 93.333333

The most significant number is 0.33333*9 = 3

93÷9 =  10.3333333

The next number is 0.333333*9 = 3

10÷9 = 1.11111111

The next number is 0.11111111*9 = 1

Since we can't divide anymore we have our result which is 1133

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Answer:

Predicting requires the reader to do two things: 1) use clues the author provides in the text, and 2) use what he/she knows from personal experience or knowledge.

Step-by-step explanation:

Two factors that make a prediction reasonable are the support of the evidence or context or the presence of knowledge in that stream.

Prediction is the act of speculating about future events or possible character behavior based on information from a text. a crucial aspect of the understanding.

A statistical method is known as correlation is used to quantify and explain a link between two variables. The two variables are often just observed, not changed.

Correlations serve as the foundation for linear regression. Then one may utilize linear regression to forecast dependent variable results for people not included in the data set you have. Its predictive power decreases as its correlation factor increases in absolute value.

The significance level of one dependent variable can also be predicted using the metrics of multiple independent variables at the same time, which is another common use.

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Answer:  The slope is 0.

Step-by-step explanation: If the line is horizontal, the slope is 0

The rise is 0.  0 divided by any number is 0.

If the line is vertical, the slope is undefined.

No number can be divided by 0, so mathematicians call this situation "undefined."

Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.

Mary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.

Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.

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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.

Step-by-step explanation:

12- 2*6

26- 2*13

gcf =2

the least greatest common factor is 2

Answer:

Step-by-step explanation:

We will develop a test to compare the mean of two population

Population 1.

population mean μ₀₁  = 25  ; Sample variance 27 ; and sample size n = 45

Population 2.

population mean μ₀₂  = 23 ; Sample variance 7,56; and sample size n = 36

As our major interest is to investigate if the new machine uses less time for the same production, the test will be a one tail test ( left test)

Test Hypothesis        

Null Hypothesis                   H₀     ⇒         μ₀₂ -  μ₀₁  = 0    

Alternative Hypothesis       Hₐ     ⇒         μ₀₂ -  μ₀₁ < 0

We will use  confidence of 90 %, therefore α = 10 %   α = 0,1

α  = 0,1    

We get    z score of z = 1,28   or   z = - 1,28   ( left tail)

And  compute z(s)  = ( μ₀₂ -  μ₀₁ ) /√ (s₁)²/n₁   + (s₂)²/n₂

z(s) = -  2 / √(729/45) + (57,15/36)

z(s) = - 2 / √16,2  + 1,59

z(s) =  - 2 / 4,2178

z(s) =  - 0,4742

As |z(s)|  < |z(c)|

We are in the acceptance region. If we lok at 90 % as Confidencial Interval α = 0,1 and  α/2 =  0,05 in this case

₀,₉CI (  μ₀₂ -  μ₀₁)  =  [  -2  ± z(0,05)√  (s₁)²/n₁   + (s₂)²/n₂ )

From z Table  z ( 0,05 )   ⇒ z score   z = 1,64

And √  (s₁)²/n₁   + (s₂)²/n₂ ) =  √(729/45) + (57,15/36)  =  4,2178

₀,₉CI (  μ₀₂ -  μ₀₁)  = [ -2  ± 1,64 *4,2178]

₀,₉CI (  μ₀₂ -  μ₀₁)  = (  - 8,917 ;  4,917 )

We can see that 0 is a possible value in the ₀,₉CI (  μ₀₂ -  μ₀₁) so again we cannot reject H₀. Then as we are not quite sure about the strengths of the new machine over the old one  we should not recomend to purchase the new machine

Answer:

I think only 1 but not 100% sure

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

Combine like terms and simplify.

20z - 5 - 12z = 10z + 8

⇒ z(20 - 12) - 5 = 10z + 8

⇒ z(8) - 5 = 10z + 8

⇒ 8z - 5 = 10z + 8

Subtract 8z both sides.

⇒ 8z - 8z - 5 = 10z + 8 - 8z

⇒ -5 = 2z + 8

Subtract 8 both sides.

⇒ -5 - 8 = 2z + 8 - 8

⇒ -13 = 2z

⇒ -13/2 = 2z/2

⇒ -6.5 = z

Thus, there is 1 solution.

On solving the provided question we can say that equation of new line is y + 2 = -1/3(4x + 2)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

lines,

y - 1 = -3(x-2)

3y = x- 9

here slope, m is -3

equation of new line is

y + 2 = -1/3(4x + 2)

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The expression that shows the result of that transformation are:

3f(x) = 3.4ˣ

f(3x)=4³ˣ

f(x+3)=4ˣ⁺³

f(x)+3=4ˣ+3.

The given function is f(x) =4ˣ.

We have to find the transformations applied to the function f(x).

Graph transformation involves modifying an existing graph or graphed equation to create a different version of the original graph.

f(x) =4ˣ

We have to find 3f(x), f(3x), f(x+3) and f(x)+3.

3f(x) = 3.4ˣ

f(3x)=4³ˣ

f(x+3)=4ˣ⁺³

f(x)+3=4ˣ+3.

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F(-7) = -3

F(0) = 4

.

.

SO A

Answer:

Equation: (14.71-4.48) [divided by] 3 =x

"Answer x": 3.41

Explanation:

14.71-4.48=10.23

10.23/3 = 3.41

3.41

Answer:

Your answer is

1/2 <x<8

as per triangular rules

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The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

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Explanation is in the file

tinyurl.com/wpazsebu

Answer:

X = 8

Step-by-step explanation:

A triangle's degrees always add up to 180, this is a right triangle meaning that one of the degrees is 90, and we see the other one is 54, so we add these together and subtract them from 180 and set that equall to 3x+12.  

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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The Interest (simple interest) will be less on Loan A.

What exactly is simple interest?

Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.

The simple interest formula is as follows:

SI=P*R*T/100

SI stands for simple interest.

P stands for principal.

R is the interest rate (in percentage)

T denotes the length of time (in years)

The following formula is used to compute the total amount:

Amount (A) = Principal (P) x Simple Interest (SI)

Now,

For A Principal=$10000, Time = 3 years, Rate=5%

then interest paid=10000*3*5/100

=300*5=$1500

For B  Principal=$10000, Time = 5 years, Rate=8%

Interest=10000*5*8/100

=500*8

=$4000

That means SI(B)>SI(A)

Hence,  

          The Interest will be less on Loan A.

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Answer:

pic?

Step-by-step explanation:

send me the picture please

Answer:

1) y=1/5x +0.8

2) y= -2x +10

Step-by-step explanation:

It's been a while, but I think this is right:

1)

For 2 lines to be parallel they must have the same slope

Recall that the equation of a line is

y-y1 = m (x- x1)

m being slope

So looking at equation 1, we can tell that the slope is 1/5 because it has already been distributed to the x.

So we know our equation will look something like this

y-y1 = 1/5 (x- x1)

We also know that the line passes through the point (8,1)

So, you plug in those points to your equation

y- 1 = 1/5(x - 8)

Simplifying and distributing the equation, we end up with

y= 1/5x + 0.8

(if you would like me to explain the simplification plz ask in a comment.)

2)

First you have to move -x from the left side of the equation to the right, making the equation

2y= x+10

then divide by 2 on both sides (im writing x/2 as 1/2x, because they are the same)

y= 1/2x + 5

For 2 lines to be perpendicular they must have the opposite reciprocal slope

Meaning if you had a slope of 2, the opposite would be -2 and the reciprocal would be 1/2, so your slope would be -1/2

Knowing this and keeping in mind our equation of a line from the first question, our slope of a perpendicular line (or m in our equation) of y= 1/2x + 5

would be -2

So far we have an equation that looks like

y-y1 = -2 (x- x1)

So now we plug in our points (6, -2)

(y- -2)

y + 2 = -2 (x - 6)

Simplifying and distributing the equation, we end up with

y= -2x +10

(if you would like me to explain the simplification or have a question don't hesitate to ask in a comment.)

Answer:  1.)  y = 1/5 x - 3/5

2.) y = -2x + 10

Step-by-step explanation:

1.)  Keep the same slope. Substitute the y and x-values from the given coordinate into the slope-intercept form and solve for the new b

1 = 1/5(8) + b    1 = 8/5 +b .subtract  8/5 form both sides:

-3/5 = b

y = 1/5 x - 3/5

2.) Rewrite the given equation in slope-intercept form

-x + 2y = 10  becomes y= 1/2 x +10

Take the reciprocal of the slope and reverse the sign:  1/2 becomes -2

Substitute the y and x-values from the given coordinate into the slope-intercept equation and solve for b.

-2 = -2(6) + b

-2 = -12 + b   Add +12 to both sides

10 = b

y = -2x + 10   Standard form: 2x + y = 10

Attachment shows the graphs and coordinates.

From the situation described in this problem, it is found that:

A. The composite function is: f(s(w)) = 36w + 30.

B. The unit of measurement of the composite function is: flowers.

C. After 36 weeks, Daisy can expect to bloom 1326 flowers.

For a composite function, the output of the inner function serves as the input of the outer function.

In the context of this problem, the functions are given as follows:

Hence the composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks is:

f(s(w)) = f(12w) = 3(12w) + 30 = 36w + 30.

The unit of measurement of the composite function is the unit of the outer function, which is flowers.

After 36 weeks, the number of flowers that Daisy can expect to bloom is given as follows:

f(s(36)) = 36(36) + 30 = 1326 flowers.

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Answer:5% = 0.05 . Then multiply the original amount by the interest rate. $1,000 * 0.05 = $50 . That's it.

Step-by-step explanation:

please give me brainliest

we have following:

When Jonah studies 6 hours, Sierra studies 3 hours

When Jonah studies 6 hours, Williams studies 2 hours

Therefore, Sierra stuty one hour longer than Wiliam

its upsidedown what are you doing

Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"