A tree casts a shadow 38 m long.
At the same time, the shadow cast by a 37 cm tall
statue is 75 cm long.
Find the height of the tree. Use correct units.

As a set of inputs with one output for each, a function is defined as a relationship between them.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

When examining a graph, one method is to perform a "vertical line test" to see if a relationship is indeed a function. Anywhere on the graph where a vertical line can be created to cross the relation twice indicates that the relationship is not a function.

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A point-to-point graph, also called a line graph

To establish if a graph reflects a function, use the vertical line test. If a vertical line is dragged across the graph and only touches the graph at one location at any time, the graph is a function. If the vertical line intersects the graph more than once, the graph is not a function.

A line graph, also known as a point-to-point graph, is a visual representation of data in which precise values of a function are represented as dots on a coordinate plane. Straight lines link adjacent pairs of dots.

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The ratio of people in its simplest form is 1 : 3

The ratio of benches in its simplest form is 1 : 4

A ratio is the number representing a comparison between two named things.

It also refers to the relative magnitudes of two quantities usually expressed as a quotient.

For instance, if there are 12 students in a class which includes 8 girls and 4 boys,

The ratio of girls to all students = 8 : 12

= 8/12

= 2/3

= 2 : 3

The ratio of boys to girls = 4 : 8

= 4/8

= 1/2

= 1 : 2

The ratio of all students to boys = 12 : 4

= 12/4

= 3/1

= 3 : 1

Hence,

People = 6 : 18

= 6 / 18

= 3 / 9

= 1/3

= 1 : 3

Benches = 3 : 12

= 3 / 12

= 1 / 4

= 1 : 4

Therefore, the ratio of people and benches in its simplest form is 1 : 3 and 1 : 4 respectively.

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Suzanne pays $21.03 in sales tax for the computer upgrades.

Tax in math is a type of mathematical problem that involves the distribution of a certain amount of money among several parties. The problem is solved by calculating the amount of money each party needs to pay in order to make the distribution fair and equitable. This type of math problem is often used to determine the amount of taxes that need to be paid by individuals or businesses. Tax problems can also be used to analyze the effects of different tax policies on the economy.

This amount is rounded to the nearest cent and is calculated by multiplying the pre-tax cost of the upgrades ($311.60) by the sales tax rate (6.75%). Thus, the equation would be: $311.60 x 6.75% = $21.03.

Suzanne must pay an additional $21.03 for the sales tax on her purchase, making the total cost of the upgrades $331.60.

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The evaluation of the arithmetic series  gives 4545

An arithmetic progression ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.

From the given information, we can get the first term (a) and  last term (l) of the sequence by substituting n = 1  and n = 45 respectively into the given expression, (4n + 9). That is:

a = 4(1) + 9 = 13

l = 4(45) + 9 = 189

Sum of all terms in a finite AP with the first term (a) and last term (l) is given by:

S = n/2(a + l)

S = 45/2 (13+189) = 4545

Thus, the arithmetic series evaluates to

[tex]\sum_{n}^{45}(4n + 9) = 4545[/tex]

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Answer: The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.

To calculate the monthly payment on the bank loan, we can use the formula:

monthly payment = P * (r / (1 - (1 + r)^(-n)))

where P is the total loan amount, r is the annual interest rate as a decimal, and n is the number of months of the loan.

For a loan of $16,000 at 8% interest for 3 years (36 months)

r = 0.08/12 = 0.0067

n = 36

P = 16000

So, the monthly payment = 16000 * (0.0067 / (1 - (1 + 0.0067)^(-36))) = 480

To calculate the monthly credit card payment, we can use the formula:

M = P * r * (1 + r)^n / [(1 + r)^n - 1]

where P is the total loan amount, r is the monthly interest rate, and n is the number of months of the loan.

For a credit card with an annual rate of 15% for 7 years (84 months)

r = 0.15/12 = 0.0125

n = 84

P = 16000

So, the monthly payment = 16000 * 0.0125 * (1 + 0.0125)^84 / [(1 + 0.0125)^84 - 1] = 511.11

As we can see the monthly payment on the bank loan is lower than the monthly credit card payment. So, the correct answer is "The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment."

Answer:

Step-by-step explanation:

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The system of equations that can be used to find the price in dollars of each pencil, x, and each folder, y that Sally and Henry bought is D.

6x + 3y = 3.90

2x + 5y = 3.30.

A system of equations is also known as a simultaneous equation.

Simultaneous equations are equations solved concurrently.

                            Sally     Henry

Units of pencils     6            3

Units of folders     3            2

Total costs         $3.90    $3.30

Let pencils = x and folders = y

Sally's total cost = 6x + 3y = $3.90

Henry's total cost = 3 x + 2y = $3.30

In this situation, to find the price of each pencil and each folder, the system of equations that can be used is from Option D.

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Yes, for every 6 duck decoys big lake bob carves he must give up 20 fishing lures.

Production possibility schedule:-

Fish lures:

Fish lures in one week = 100

lures in a day = 20

So, 100-20 = 80

80 - 20 = 60

60 - 20 = 40

40 - 20 = 20

20 - 20 = 0

Duck decoys:

Duck in one day = 0

So, 0 + 6 = 6

6 + 6 = 12

12 + 6 = 18

18 + 6 = 24

24 + 6 = 30

number of duck decoy in a week = 30

Hence, For every 6 duck decoys Bob carves 20 lures.

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The amount in sale tax, Suzanne paid for the computer upgrades is 21.03 dollars.

Suzanne buys upgrades for her computer . The upgrades cost $311.60 before taxes. The sales tax rate is 6.75%.

Therefore, the amount of sales tax Suzanne paid for the computer upgrades can be calculated as follows;

A sales tax is a tax paid to a governing body for the sales of certain goods and services.

amount of the sale tax = 6.75% of 311.60

amount of the sale tax = 6.75 / 100 × 311.60

amount of the sale tax = 2103.3 / 100

Therefore,

amount of the sale tax = 21.033

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The completed statement would be

12ft/sec = 7.2 yd/min.

What is the unit conversion?

Unit conversion is the process of changing a measurement from one unit to another, while maintaining the same numerical value. It is used to convert measurements from one system of units to another, such as from metric units to imperial units, or from feet to meters.

To convert feet per second to yards per minute, we need to multiply the value in feet per second by the conversion factor of 1 yard/3 feet and then divide the result by the conversion factor of 1 minute/60 seconds.

12 ft/sec = (12 ft/sec) * (1 yard/3 feet) * (1 min/60 sec) = (12*1/3) * (1/60) = 4/5 = 0.8.

So, 12 ft/sec is equal to 0.8 yards per minute. Rounded to the nearest hundredth, this is 7.2 yards per minute

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The final value of the iterated integral is 945[tex]\sqrt{10}[/tex].

To calculate the iterated integral, we need to evaluate the inner integral with respect to y first and then the outer integral with respect to x.

The inner integral is to be integrated with respect to y is:

∫(6xy[tex]\sqrt{(x^2 + y^2)}[/tex])dy from 0 to 1 = [3y([tex]x^2 + y^2[/tex][tex])^{(3/2)}[/tex])] from 0 to 1

= [3y*[tex](x^2 + y^2[/tex][tex])^{(3/2)}[/tex]] from 0 to 1

= 3(1)*([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex]

= 3([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex]

Now, we can use this result as the inside function to evaluate the outer integral with respect to x.

The outer integral is to be integrated with respect to x is:

∫(3([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex])dx from 0 to 3

= [x([tex]x^2[/tex] + 1[tex])^{(5/2)}[/tex]] from 0 to 3

= [3[tex](3^2 + 1[/tex] [tex])^{(5/2)}[/tex] - 0(0^2 + 1[tex])^{(5/2)}[/tex]]

= [3(10 - 0]

= [945[tex]\sqrt{10}[/tex])]

So the final value of the iterated integral is 945[tex]\sqrt{10}[/tex].

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The complete question is -

Calculate the iterated integral. Integral from 0 to 3 integral from 0 to 1 of 6xy[tex]\sqrt{(x^2 + y^2)}[/tex] dy dx

The equation of the perpendicular line is y = -5

We have to recall that the general form of the equation of a line can be given by the expression that is written as y = mx + c. m is the slope of the graph while c is the intercept of the graph.

We would then have;

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

We can see that m = 0 from the first line that has been given the we have;

y - (-5) = 0(x - 4)

y + 5 = 0

y = -5

This is the equation that has been required in the problem above.

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The final solution is -sin(1).

To evaluate the iterated integral, we need to integrate with respect to the outer variable first, then integrate with respect to the inner variable.

The given iterated integral is:

[tex]∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds[/tex]

To evaluate this, we need to integrate with respect to t first, and then integrate with respect to s.

[tex]∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds = ∫(1 to 0) [∫(s^4 to 0) cos(s^5) dt] ds= ∫(1 to 0) (-1/s^5 * sin(s^5)) \\ds= [-1/s^5 * sin(s^5)] \\evaluated at s = 1,0= (-1/1^5 * sin(1^5)) - (-1/0^5 * sin(0^5))= (-1/1 * sin(1)) - (0)= -sin(1)[/tex]

So the final solution is -sin(1)

Note that the integral is not defined for s=0, [tex]s^5=0[/tex] , as the function is not defined there.

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While calculating the measurements given.The correct answer is 384 ft.

Given,

Inches when drawing =1/4

Actual feet according to the drawing =12 ft

To calculate the The mesurement of 8 inch

8 ÷ 1/4 = 8/1 x 4/1 = 32

32 x 12 = 384

Sometimes we find the value in feet and inches rather than converting the amount to decimals. For instance, 71 inches is equivalent to 5 feet, 11 inches. It's because we get 5 as the quotient and 11 as the remainder when we divide 71 by 12. The residual value will be expressed as the number of inches it is. This is known as converting inches to feet and feet to inches. Let's examine a few of the instances below.

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An Experimental study is used. As subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. after months, the numbers of respiratory tract infections each group had were compared.

Experimental investigations or study involve introducing an intervention and observing its results. Typically, volunteers in experimental research are grouped randomly, or by chance.

During a randomized controlled trial (RCT), participants are divided into two or more groups at random. While the control group is given nothing or a placebo, the intervention group is given the new drug, for example. The outcome of each group is then investigated by the researchers. The intervention can thus be blamed for any variations in the results.

Whereas, Observational study is the Studies in which researchers look at how a risk factor, diagnostic test, treatment, or other intervention affects a population without attempting to alter who is or is not exposed to it.

Hence, it is experimental study.

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Answer:

2x² + 7x + 2

Step-by-step explanation:

f(x) = 3x² + 5

g(x) = 4x - 2

h(x) = x² - 3x + 1

f(x) + g(x) — h(x) =

(3x² + 5) + (4x - 2) - (x² - 3x + 1) = ==> plugin the values of f(x), g(x), and h(x)

3x² + 5 + 4x - 2 - (x² - 3x + 1) =

3x² + 5 + 4x - 2 - x² + 3x - 1 =  ==> distribute the negative sign to x², -3x, 1

                                                     x² ==> -x², -3x ==> 3x, 1 ==> -1

3x² - x² + 4x + 3x + 5 - 2 - 1 =  ==> combine like terms

2x² + 7x + 2 = ==> simplify

The value of sum of squared deviations is 12.

The given population is 1,1,1,5

First find the mean:

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Mean = (Sum of all the observations/Total number of observations)

Mean=[tex]\frac{1+1+15}{4}=\frac{8}{4}=2[/tex]

The Mean is 2.

The symbol of mean is usually given by the symbol [tex]\bar x[/tex]. The bar above the letter x, represents the mean of x number of values.

[tex]\bar X[/tex] = (Sum of values ÷ Number of values)

Subtract the mean from each observation and square the resulting difference. Then add the differences to get SS:

SS=[tex](1-2)^{2}+ (1-2)^{2}+ (1-2)^{2}+ (5-2)^{2}[/tex]

[tex]=1+1+1+(3)^{2} \\=3+9\\=12[/tex]

Therefore, the value of SS is 12.

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This is $20,330.08 more than the total cost of the bank loan.

Payment is the transfer of money from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment is an important part of any transaction, as it is the final step that completes the exchange of goods or services.

Therefore, the lowest monthly payment would be the credit card payment of $511.11. Paying with a credit card at 15% compounded monthly would be the least expensive option for Genesis. With this option,  would pay a total of $36,330.08 over the 7 years, including the interest. This is $20,330.08 more than the total cost of the bank loan.

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The equation of the line that passes through the point (5, 3) and has a slope of - 6/5 is y = -6/5x - 3.

What is Slope?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

What is Equation of line?

The equation for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

Given that ;

point passes through is (5,3)

and has slope of (-6/5)

We have equation of line;

y = mx+c

3 = -6/5(-5)+b

3 = 6 + b

Eliminate 6 by using the equality's subtraction property, then isolate b. (subtract 6 from 6 to cancel it out and to 3).

b = -3

So, the equation of the line that passes through the point (5, 3) and has a slope of - 6/5 is y = -6/5x - 3.

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The probability that all 4 computers with the critical file fail in this incident is given as follows:

0.0046 = 0.46%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of these parameters for this problem are given as follows:

N = 30, k = 4, n = 9.

The probability that all fail is P(X = 4), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,30,9,4) = \frac{C_{4,4}C_{26,5}}{C_{30,9}} = 0.0046[/tex]

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The number of meters that the truck could go given the energy provided by the students combined, would be 800, 000 meters

To find the distance the truck would go, first find the number of meters the truck would go with the energy your heart provides :

= 32 x 1, 000 meters per kilometer

= 32, 000 meters

There are 25 people in the math class so the distance the truck would go is:

= Number of students x Distance per person

= 25 x 32, 000

= 800, 000 meters

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Answer:

54

Step-by-step explanation:

[tex]f(x)=x^2+10x+29 \\ \\ f(x)=(x^2+10x+25)+29+25 \\ \\ f(x)=(x+5)^2+54 \\ \\ \therefore (x+5)^2 \geq 0 \implies (x+5)^2+54=f(x) \geq 54[/tex]

Answer: 0.25 30% 1/3  

Step-by-step explanation:

1/3 is the largest because when made in a decimal it would be 3.3 reapeting, 30 % is 0.3 and 0.25 . So the order will be 0.25 30% and 1/3.

The equation formed by the sentence is 9b - 7 = 8.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let the variable be b

By the given sentence we get the equation

9b - 7 = 8

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Therefore , the solution to the given problem of unitary method comes out to be Henry uses the scooter for 143 minutes after that.

In order to solve an issue, one can use the unit technique, which involves first multiplying the worth of one unit by the number of units needed. Simply said, the unit function is used to extract a single entity number from a given many. 40 needle would cost 400 rupees, or the price of one pen. There may be a standard method for checking this out. one country only. anything has a distinctive element. Mathematical analysis, algebra, matrix logic, and its interpellation and inverse are all equivalent.

Here,

Start the scooter for $7.00

$0.07 for each minute

$17.01 in total.

1. Subtract the cost of starting the scooter from the total bill:

The price for Henry's entire ride is $10.01.

2. Subtract the price for each minute to get the price per minute:

=> 10.01/0.07 * 100/100

=> 1001/7

=> 143

Henry uses the scooter for 143 minutes after that.

Therefore , the solution to the given problem of unitary method comes out to be Henry uses the scooter for 143 minutes after that.

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The histogram for the stickers from the small package is distributed as follows:

Normally.

To obtain the distribution of the histogram, we must correctly identify the mean and the median of the distribution.

Hence the distribution is defined as follows:

The ordered distribution is given as follows:

13, 15, 18, 19, 22, 24.

Hence the median is of:

(18 + 19)/2 = 18.5.

The mean is of:

(13 + 15 + 18 + 19 + 22 + 24)/6 = 18.5.

They are equal, hence the histogram is normal = symmetric;

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