If the area of a rectangle is x2 – 13x + 40, what are the lengths of
the two sides?

Answers

Answer 1

Answer:

5 and 8

Step-by-step explanation:

quadratic formula.

-(b)+sqrt(b)^2-4(a)(c)

^ans

divide the whole thing by 2(a).

If the formula isn't clear, search quadratic formula up.


Related Questions

a manufacturer produces computer monitors, each of which may have some defective pixels. the average number of defective pixels per monitor is known to be 3.8. the upper control limit is three standard deviations above the mean. what is the upper control limit? a. 7.0 b. 8.9 c. 4.5 d. 7.8 e. 5.6 f. 6.6 g. 9.6

Answers

The answer is b. 8.9.

The upper control limit is three standard deviations above the mean, which can be calculated by multiplying the standard deviation by 3 and adding it to the mean. However, the standard deviation is not provided in the question.

Assuming a normal distribution, we can use the empirical rule which states that approximately 99.7% of the data falls within 3 standard deviations of the mean.

Therefore, the upper control limit can be estimated by adding 3 times the square root of the average number of defective pixels to the mean:

Upper control limit = 3.8 + 3 x sqrt(3.8) ≈ 8.86

Therefore, the answer is b. 8.9.

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You asked the question “How many amusement parks have you visited this summer?” Four people said 1, seven people said 2, three said 3, four said 4, and two said 5. Explain how to make a dot plot to display the data

Answers

Answer:

Look at the image. I'm sorry but I'm not the best at drawing.

Step-by-step explanation:

Four people said 1, so we put 4 dots on 1 amusement park.

Seven people said 2, so we put 7 dots on 2 amusement parks.

Three people said 3, so we put 3 dots on 3 amusement parks.

Four people said 4, so we put 4 dots on 4 amusement parks.

Two people said 5, so we put 2 dots on 5 amusement parks.

You asked the question How many amusement parks have you visited this summer? Four people said 1, seven

I could use some help to find out Tony’s mistake(s)

I could use some help to find out Tonys mistake(s)

Answers

To find the shaded area you subtract the area of the triangle from the area of the rectangle:

\(A_{shaded}=A_{rec\tan gle}-A_{triangle}\)\(\begin{gathered} A_{shaded}=w\cdot l-\frac{1}{2}b\cdot h \\ \\ A_{shaded}=(5cm)(11cm)-\frac{1}{2}(5cm)(3cm) \end{gathered}\)

Then, Tony's mistake was that he added the areas instead of subtract it.

The shaded are is:

\(\begin{gathered} A_{shaded}=55cm^2-\frac{15}{2}cm^2 \\ \\ A_{shaded}=55cm^2-7.5cm^2 \\ \\ A_{shaded}=47.5cm^2 \end{gathered}\)Then, the shaded area is 47.5 square centimeters

PLEASE HURRY‼️‼️ 10 points

PLEASE HURRY 10 points

Answers

Answer:

y=x+7

Step-by-step explanation:

all the y values are 7 more than the corresponding values of x

Class 7. Fractions & decimals
1/2 of 2 3/4

Answers

Answer:

11/8 or 1.375

Step-by-step explanation:

2 3/4 => 11/4

1/2 x 11/4 = 11/8

Math help please show work

Math help please show work

Answers

Answer:

7 in

Step-by-step explanation:

Math help please show work

Answer:

a = 7 in

Step-by-step explanation:

\(Area = \frac{a+b}{2} \times h\\\\26.25 = \frac{a + 10.5}{2} \times 3\\\\26.25 \times 2 = (a+ 10.5) \times 3\\\\52.5 = (A + 10.5) \times 3\\\\\frac{52.5}{3} = a + 10.5\\\\17.5 = a + 10.5\\\\a = 17.5 - 10.5 = 7\)

A triangle has side lengths 35cm, 46cm, and 68cm. What true of triangle is this

Answers

The triangle is scalene triangle as none of the sides of a triangle are equal to each other.

Triangles are classified into three types on the basis of its sides.

Equilateral triangle =  If all sides of a triangle are equal then it is known as equilateral triangle.

Isosceles triangle =  If any two sides of a triangle are equal then it is known as isosceles triangle.

Scalene triangle = If none of the sides of a triangle are equal then it is known as scalene triangle.

The question states that a triangle has side lengths 35cm, 46cm, and 68cm

so, none of the side are equal so the given triangle is scalene triangle

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the domain of the exponential function f(x)=ax, a>0, a≠1, is the set of all real numbers. true or false

Answers

The given statement  the domain of the exponential function f(x)=a^x, a>0, a≠1, is the set of all real numbers is true.

The domain of the exponential function f(x) = a^x.

where a is a positive real number .

And a is not equal to 1 is the set of all real numbers.

This means that the function is defined for every real number x.

The exponential function grows or decays rapidly as x moves away from 0, and its graph never touches the x-axis.

Therefore, the exponential function f(x) =a^x for a>0, a≠1 having domain set of all real numbers is true.

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The above question is incomplete, the complete question is:

The domain of the exponential function f(x)=a^x, a>0, a≠1, is the set of all real numbers. true or false

write the sequence of natural numbers which leaves the remainder 3 on didvidng by 10

Answers

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing the tile numbered 2 from the first bag and the tile numbered 3 from the second bag? Wh

Answers

Complete question:

Jason has two bags with 6 tiles each. The tiles in each bag are shown below:

1 2 3 4 5 6

Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing the tile numbered 2 from the first bag and the tile numbered three from the second bag?

Answer: 1/36

Step-by-step explanation:

Number of tiles in each bag = 6

Probability of drawing tile numbered 2 from the first bag and the tile numbered 3 from the second

Probability of drawing number 2 from first bag :

P(numbered 2) = (required outcome / possible outcome)

P(numbered 2) = 1/6

Probability of drawing number 2 from first bag :

P(numbered 3) = 1/6

Since they are independent events :

P(drawing 2 from bag one and 3 from bag 2) :

1/6 × 1/6 = 1/36

4. Find the center and radius of the circle given by this equation: x2 – 8x + y2 + 4y - 16 = 0

Answers

Answer:

Center ( 4 , -2) and r = 6

Step-by-step explanation:

x² - 8x + y² + 4y - 16 = 0

x² - 8x  + y² + 4 y = 16

x²- 2*4x + y² + 2 *2y = 16

(x² - 2*4x + 16 ) - 16 + (y² + 2*2y + 4) -4 = 16

(x - 4)² + (y + 2)² = 16 + 16 + 4

(x - 4)² + (y -[-2])² = 36

(x- 4)² + ( y - [-2] )² = 6²

Compare with (x - h)²+ (y - k)² = r²

Center ( 4 , -2) and r = 6

if the area of a right isosceles triangle is 128 sq . m, what will be length of the identical side of the triangle​

Answers

Let's see. What is a right isosceles triangle?

A right isosceles triangle is a triangle with one right angle with at least two equal sides. In this case, it would have to be ONLY two because it has a right triangle.

What is the formula for the area of an isosceles triangle?

When y = the identical side lengths of the triangle,

and A = area,

(y × y) ÷ 2 = A

Note: Remember to compute from left to right! :)

We divide by two because when you multiple the two identical sides, you would get a square. However, we're trying to find the right isosceles triangle, and we divide by two.

Now, we can plug-in our values!

(y × y) ÷ 2 = 128

(y × y) = 64

Now, we square root both sides!

y = √64

y = 8

The length of the identical sides of the triangle is 8 meters.

\(\large\underline{\underline{\red{\sf \blue{\longmapsto} Step-by-step\: Explanation:-}}}\)

Given that area of an isosceles triangle is 128m² .

And the triangle is right Angled ∆ .

So , the measure of sides along 90° that is perpendicular and the base will be equal .

Let us say that each of the equal sides is x .

Then , we can find the area of the triangle as ,

\(\boxed{\bf{\red{ Area_{triangle}=\dfrac{1}{2}\times(base)\times(height)}}}\)

Now , here substitute the respective values ,

\(\implies \sf \dfrac{1}{2}\times(base)\times(height)=128m^2\)

\(\sf\implies \dfrac{1}{2}\times x \times x = 128m^2\)

\(\sf \implies \dfrac{x^2}{2}=128m^2\)

\(\sf\implies x^2=128\times2 m^2\)

\(\sf\implies x^2=256 m^2\)

\(\sf\implies x=\sqrt{256m^2}\)

\(\underline{\boxed{\red{\sf\longmapsto x=16m}}}\)

Hence the value of value of identical side of the triangle is 16m .

Write the liner equation (Picture attached)

Write the liner equation (Picture attached)

Answers

The linear equation from the equation given in the picture, would be  y = - 0. 2x + 2

How to write a linear equation ?

A linear equation is used to determine the direction and values of a line in a chart or graph. It takes the form shown below of :

y = mx + b

y is the dependent variable

m is the slope of the line

x is the independent variable

b is the y - intercept

When given the formula, x + 5y = 10, the linear equation can be found in the steps of :

x + 5y = 10

5y = 10 - x

Divide all sides by 5 to get rid of the 5 next to y:
5y / 5 = 10 / 5 - x / 5

y = 2 - 1 / 5 x

y = - 0. 2x + 2

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j^2+5.10
question: if j=2 the value of the following expression is 90.
TRUE OR FALSE?

Answers

It’s wrong it doesn’t add up to 90

show that every infinite turing-recognizable language has an infinite decidable subset

Answers

The set of all strings accepted by M is an infinite decidable subset of L.

Every infinite Turing-recognizable language has an infinite decidable subset.

Let's prove this theorem.

We must know the properties of the Turing recognizable language before the proof. A language is considered Turing recognizable if a Turing machine M accepts all strings in the language, and either rejects or loops forever on all strings not in the language. We can define that any language is infinite if it contains infinite strings.

Similarly, the set of all strings in the language is infinite if the language is infinite.

Let us suppose that L is an infinite Turing-recognizable language over the alphabet Σ. It implies that there exists a Turing machine M that accepts all the strings in L. We need to consider the following facts to prove that every infinite Turing-recognizable language has an infinite decidable subset:

If a Turing machine accepts an infinite number of strings in a language L, then it accepts at least one infinite subset of the language.

Suppose that a Turing machine accepts a language L, then the set of all strings accepted by the Turing machine is decidable.

Now, let's construct a new Turing machine M′ that works in the following manner:

In the first step, M' simulates M on the input w.

In this step, M' generates the strings of Σ* in some order.

In this step, for each string generated in step 2, M' runs M on that string. If M accepts that string, then M' outputs the string.

Suppose that there are only finite strings of L that are accepted by M. It implies that M has an infinite loop on all other strings not in L.

since M′ generates the strings of Σ* in some order, M′ will eventually simulate M on the string w for which M has an infinite loop.

Therefore, M′ will be in an infinite loop and will never halt.

So, the set of all strings accepted by M is infinite. We can say that the set of all strings accepted by M is an infinite decidable subset of L.

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quizletmeasures of central tendency include all except: a. standard deviation b. median c. mean d. mode

Answers

Answer:

a. standard deviation

Step-by-step explanation:

Standard deviation measures the variation (how spread out the data is from the mean) of a data set.  

Logarithms PLS HELP
Using the logarithm table find the logarithm of 238.2
A. 2.3766
B. 2.3772
C. 2.3770
D. 2.7677

Answers

your answer would be B

Suppose there are 20 people in a room and the mean amount of cash held by these 20 people is $14.50 per person. If two people enter the room carrying $4.00 and $5.00 respectively, what does the mean amount of cash in the room become? Give your answer in dollars and cents; that is, precise to two decimal places.

Answers

Answer:

13.59

Step-by-step explanation:

The calculation of amount of cash in the room is shown below:-

\(\$14.50 = \frac{\Sigma xi}{20}\)

= 20 × $14.50

= $290

Now, the new sum is

= ∑xi + $4.00 + $5.00

= $290 + $4.00 + $5.00

= $299

Total person in the room is

= 20 + 2

= 22

So,

Mean amount of cash in the room = New sum ÷ Total person in the room

= $299 ÷ 22

= 13.59

for each pair of hypotheses that follows, decide whether h₀ and h₁ are set up correctly as the null and alternative hypotheses for a hypothesis test. if so, select "valid" from the drop down menu. if not, select "invalid".

Answers

To determine whether the null (h₀) and alternative (h₁) hypotheses are set up correctly for a hypothesis test, we need to consider the specific pair of hypotheses provided.

Based on the information given, we cannot determine the exact hypotheses being referred to, as the question only mentions a drop-down menu. Therefore, we are unable to assess whether the hypotheses are valid or invalid. The question states that we need to decide whether the null (h₀) and alternative (h₁) hypotheses are correctly set up for a hypothesis test. However, the question does not provide any specific hypotheses or context to analyze.

Without knowing the specific pair of hypotheses, it is not possible to determine whether they are valid or invalid. It is important to have a clear understanding of the hypotheses being tested, the research question, and the desired outcome in order to assess the validity of the hypotheses.

In hypothesis testing, the null hypothesis typically represents the default or existing belief, while the alternative hypothesis represents the claim or new theory being tested. Without further information, it is not possible to determine the correctness of the hypotheses in question.

Without specific hypotheses provided, it is not possible to determine whether the null (h₀) and alternative (h₁) hypotheses are valid or invalid. It is crucial to have clear and specific hypotheses in order to conduct a hypothesis test and assess their validity.

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Help ya girl out please

Help ya girl out please

Answers

Answer: 2,592











Calculator

what is the degree of curvature, by the arc definition, for a circular curve of radius 500 ft ?

Answers

The degree of curvature, by the arc definition, for a circular curve of radius 500 ft is approximately 0.11.

When it comes to a circular curve, the degree of curvature is defined as the central angle subtended by a 100-foot arc length.

In other words, the degree of curvature is the amount of angle subtended by a 100-foot arc.

This definition is also applicable to circular curves that are larger or smaller than 100 feet in length, with no changes required.

The formula for calculating the degree of curvature (D) is:D = 57.3/r

where r is the radius of the curve in feet. Here, the radius of the curve is 500 ft.

Using this formula, we can determine the degree of curvature as:D = 57.3/500D = 0.1146 ≈ 0.11

Therefore, the degree of curvature, by the arc definition, for a circular curve of radius 500 ft is approximately 0.11.

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gem has x toys. max has 5 more toys than gem. jamie’s has three times as many toys as max. how many toys does gem have?

Answers

Jamie's has 3(x+5) toys.

From the question, we have

gem = x toys

max = (x+5) toys

jamie’s = 3(x+5) toys.

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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3 7th grade math questions please answer asap will give brainlist thingy

3 7th grade math questions please answer asap will give brainlist thingy
3 7th grade math questions please answer asap will give brainlist thingy
3 7th grade math questions please answer asap will give brainlist thingy

Answers

Answer:

1. Equation: x/-9=-16

solution: x=144

2. Equation:15*x=-75

solution: x=-5

3.Equation:0.75n=36

solution: n=48

Step-by-step explanation:

Please answer in an hour! You will get a thumbs up.
Question 1 (a)

Assume you purchase a new tractor on Jan 1, 2022 for a cost of $200,000. You estimate you will be able to use the tractor for 10 years, and it will have a salvage value of 10% of the original by the end of its useful life. Determine the book value at the end of the first year (December 31, 2022) using straight-line depreciation.

options:

$18,000

$180,000

$185,000

$182,000

Question 1 (b)
A balance sheet (using current and noncurrent assets and liabilities- no intermediate) shows that a farmer has current assets of $80,000 and owner equity of $100,000. Her current ratio is 2 and her debt/equity ratio is 1.0. Determine the farmer's noncurrent liabilities.

Question 1 (b) options:

$40,000

$60,000

$100,000

unable to determine

Answers

Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

Deon runs each lap in 4 minutes. He will run at most 32 minutes today. What are the possible numbers of laps he will run today? Use n for the number of laps he will run today.
Write your answer as an inequality solved for n.

Answers

Answer:

4n ≤ 32

/4      /4

n ≤ 8, he could run less than 8 or just 8 laps,

so possible laps:

1, 2, 3, 4, 5, 6, 7, or 8 laps he could've ran.

The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are _____.

Answers

The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are the true values that would be obtained if the entire population were measured.

The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are the true values that would be obtained if the entire population were measured. The y-intercept is the value of y when x equals 0, and it represents the starting point of the line. The slope represents the change in y for every one unit change in x, and it determines the steepness of the line. To estimate these population parameters, we use sample statistics such as the sample mean and sample standard deviation. The sample y-intercept and slope are calculated using regression analysis, which involves fitting a line to the data points in order to determine the relationship between x and y. It is important to note that the sample statistics may not be equal to the population parameters, as there is always some degree of error and variability in data. However, by using statistical inference techniques such as confidence intervals and hypothesis testing, we can make inferences about the population parameters based on the sample data. In summary, the population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are the true values that would be obtained if the entire population were measured. These parameters can be estimated using sample statistics and statistical inference techniques.

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Similarly, converting between units can be very important, and it can be done by canceling units. For example, suppose that I want to convert 66 feet/second into miles per hour. If I know that there are 5280 feet in a mile, 60 seconds in a minute, and 60 minutes in an hour, then I can convert the quantity by multiplying it by those conversion factors in such a way that they cancel: ( 1 s
66ft )( 1 min60 s )( 1hr 60 min )( 5280ft1 mile )=45mile/hr I can do this because each conversion factor is equal to one, and multiplying by one does not change anything. Notice that if you cancel all the units that you can, you are left with the desired units. The numbers are evaluated with normal arithmetic. Cglints = 1 filn 4 ZCOS=1 strord Now you try, except I'm going to make up some fictional units for you to work with: There are 12 grees in a zool. There are 2 grees in 10 twibbs. There are 5 grees in a blob. There are 6 glints in a filn. There are 4 zools in a strord. 12 grees =1 ZOO 2 grees =10 twibs 5 grees =1 bic (a) Convert the quantity 7 glint/twibb (i.e., 7 glints-per-twibb) into filn/strord (i.e., filns-per-strord). As always, show your work. (b) Often we use prefixes for scientific units. For example, there are one-hundred centimeters in a meter. Similarly, the prefix kilo- means a factor of 10
3. For example, a kilometer is 10 3 meters or 1000 meters. If you need to review these prefixes, there is a handy chart on Wikipedia: ht tpa://en.wikipedia.org/wiki/Metric_prefix. Convert your answer from part (a) into megafiln/strord (i.e., megafilns-per-strord). (Hint: Check your answer for plausibility. Should the number of megafilns-per-strord be bigger or smaller than the number of filns-per-strord? If someone is going 1 foot-per-hour, are they going a larger number of feet-per-hour or a larger number of miles-per-hour?)

Answers

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.

(a) The given units can be converted as follows: 6 glints = 1 filn...

(1)12 grees = 1 zool...

(2)2 grees = 10 twibbs...

(3)5 grees = 1 bic...

(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:

7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord

(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.

1 mega = 106

Thus 1 megafiln = 106 filn

16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.

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what kind of polynomial is 8(x+2) - 9 ?

Answers

Answer:

first degree

Step-by-step explanation:

Answer:

I believe that this would a first degree polynomial :)

Hope this helps :)

Leah is going to invest $30,000 and leave it in an account for 7 years. Assuming the interest is compounded daily, what interest rate, to the nearest tenth of a percent, would be required in order for Leah to end up with $40,000?

Answers

The interest rate which is required in order for Leah to end up with $40,000 in his account which is compounded daily, is 4.11%.

What is compound interest?

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

\(A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\\)

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

Leah is going to invest P=$30,000 and leave it in an account for t=7 years.

The interest is compounded daily.The final amount of A is $40,000?

Put the values in the above formula to find rate of interest.

\(A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\40000=30000\times\left(1+\dfrac{r}{12\times30\times100}\right)^{12\times30\times(7)}\\r=4.11 \5\)

Thus, the interest rate which is required in order for Leah to end up with $40,000 in his account which is compounded daily, is 4.11%.

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h e l p p l e a s e

h e l p p l e a s e

Answers

Answer:

17.) 12

18.) 1/15

Step-by-step explanation:

2 ÷ \(\frac{1}{6}\)

This problem is asking how many \(\frac{1}{6}\) 's can go into 2 blocks.  If you divide one box into 6 parts, each tiny box will be \(\frac{1}{6}\) of the whole. Divide the other box into 6 parts as well, and you will get 12 of these \(\frac{1}{6}\) parts.  Check your answer by multiplying 12 by \(\frac{1}{6}\).  The answer is \(\frac{12}{6}\) which is also equal to 2.

\(\frac{1}{3}\) ÷ 5

For this one, think of it as we have one big box divided into thirds. We want to divide each  \(\frac{1}{3}\) portion by 5. So you should have 5 tiny boxes in each \(\frac{1}{3}\) which gives you a total of 15 boxes.  But if we look at it as one big box divided into 15 parts, we know that each of those is \(\frac{1}{15}\).  Check your answer by multiplying \(\frac{1}{15}\) by 5 and you get \(\frac{5}{15}\) which is equal to \(\frac{1}{3}\).  

Let me know if you have any questions, and good luck!

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