. If the angle of elevation of the top of a tower from a point of observation
at a distance of 100 m from its base is 45°, then the height of the tower is

The set of ordered pairs depicts the volume of water in the can in gallons (y) as a function of time in minutes (x), beginning with the first minute after the can begins distributing water and ending with {(1, 6.7) , (2, 6.4) , (3, 6.1)}.

An ordered pair is a pair of objects in mathematics. The order of the objects in the pair is important: the ordered pair differs from the ordered pair unless a = b. Ordered pairs are also known as 2-tuples or 2-length sequences. An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions.

Here,

A watering can dispenses water at the rate of 0.3 gallon per minute.

The original volume of water in the can was 7 gallons.

If you plot a graph of volume of water in the can (gallons) against time (minutes),

The set of points on the graph will be:

After 1 minute: (1, 7 - 0.3) = (1, 6,7)

After 2 minutes: (2, 7 - 0.6) = (2, 6.4)

After 3 minutes: (3, 7 - 0.9) = (3, 6.1)

i.e the set {(1, 6.7) , (2, 6.4) , (3, 6.1)}

The set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water is {(1, 6.7) , (2, 6.4) , (3, 6.1)}.

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Answer: 150 miles

Step-by-step explanation: the car goes 30 miles every half hours, therefore, in five half hours it goes 150 miles.

The expression 5+4*2+6-2*2-1 has a value of 14 using order of operations

The order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved. A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation

Parenthesis            (  )

Exponent                a⁷

Multiplication          x

Division                   ÷

Addition                  +

Subtraction             -

Let's use PEMDAS:

Remember, multiplication comes before addition and subtraction, thus, we have:  

5+4×2+6-2×2-1 = 5 + (4×2) + 6 - (2×2) - 1

                        =  5 + 8 + 6 - 4 - 1

                        =  14

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This is a convenience sample as it is based on accessibility and availability of visitors.

What is average ?

The average, also known as the mean, is a measure of central tendency that is commonly used to summarize a set of numerical data. It is calculated by adding all of the values in a dataset and then dividing by the number of values in the dataset.

This is an example of a convenience sample ,

A convenience sample is a type of sample where the researcher selects participants based on accessibility and availability, rather than using a random selection method. In this case, the librarian is only collecting data on visitors who are checking out books at her specific check-out station in the children's section of the library, which is a subset of the total population of visitors to the library. The data may not be representative of the entire population of visitors to the library, as it only includes data from visitors who are checking out books in the children's section of the library.

This is a convenience sample as it is based on accessibility and availability of visitors.

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Answer: x is 90 and y is 41

Step-by-step explanation: Since angle C is equal to 49 degrees, and angle D is noticeably 90, we can do the following:

90 + 49 = 139

180 - 139 = 41

Therefore, our answer is x = 90 and y = 41

So on n solving the provided question, we can say that the value of the slope intercept is 2x - 3y -12 =0

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

Given, x - intercept of a line is 6

so,

The line will pass through the point (6, 0)

Also given. the y - intercept ofthe line is —4 c = —4

So, the line will pass through the point (0, —4)

Now,

Slope, m = y2 - y1/x2 - x1

m = -4-0/0-6 = 2/3

y = mx + c

y = 2x/3 - 4

3y = 2x - 12

2x - 3y -12 =0

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The only option that represents the two possible transformations that together could have been used to create the image is; D. a translation of 6 units down followed by a reflection across the y axis

In geometry, a transformation is defined as an operation that moves, flips, or changes a shape that is called the preimage in order to create a new shape that is called the image. Some of the types of transformations includes; Translation, Reflection, Dilation e.t.c

Let us analyze each of the options;

A. This is not correct because the transformation rule for a reflection over the x -axis is (x, y) → (x, −y)  while the transformation rule for the reflection of point (x, y) across the y-axis is (-x, y). This will not correspond with the final transformation given.

B) This is not correct because it will not produce the complete match as the rotation given will not allow for proper mapping.

C) This is NOT correct just like is seen in option A above.

D) This is correct because after translation by 6 units downwards, when we reflect across the y-axis, it produces the final transformed image.

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Factors of polynomial x²+5x+6 are -2,-3.

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

The expression is categorised as monomial based on how many terms are included in it:

An expression with just one term is referred to as a monomial. A monomial expression must have a single term that is not zero in order to qualify. A Monomial examples include 5x and 3.

Binomial:-

An expression of a polynomial with exactly two terms is called a binomial.  Examples of binomials are:

– 5x+3, 6a^4 + 17x.

Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:

– 8a^4+2x+7, 4x^2 + 9x + 7.

Now Given polynomial is x^2+5x+6

To find factors put it equal to zero

x^2+3x+2x+6=0

x(x+3)+2(x+3)=0

x+3=0, x+2=0

x=-2,-3

Hence, The factors of the given polynomial are -2,-3.

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An Equation of the tangent line to the curve is 18y=x+81

Given equation

y²=x

This is an equation of a parabola. graph{y^² = x [-10, 10, -5, 5]}

For finding the tangent to the equation, we first differentiate it.

The goal here is to find the value of dy/dx which will give the slope of the tangent to the parabola.

So,

[tex]\frac{d}{dy}(y^2)=\frac{dx}{dy} \\\\2y=\frac{dx}{dy} \\\\\frac{1}{2y} =\frac{dx}{dy} \\\\[/tex]

Now, we want to evaluate the slope at the given point. So substituting y we get,

[tex]\frac{1}{18} =\frac{dx}{dy}[/tex]

This is the slope of the tangent.

It passes through (81,9) [as per in the question]

The general equation of a line is y=mx+c

m is the slope of the line.

For the line/tangent that we got

[tex]m=\frac{dy}{dx}[/tex]

[tex]y=\frac{x}{18} +C[/tex]

The point should satisfy the equation of the line/ tangent. So,

[tex]9=\frac{x}{18} +C[/tex]

So, c=9/2

Finally, substitute the value in our equation of the line/tangent:

[tex]y=\frac{x}{18} +\frac{9}{2}[/tex]

18y=x+81

Therefore, the equation of the tangent line to the curve at the given point, y =√ x, (81, 9) is 18y=x+81

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Answer:

b

Step-by-step explanation:

sr =

[tex] \sqrt[10]{3} [/tex]

Answer:

Dawn is correct maybe because -3 is less than 4

correct if I'm wrong

Melissa's monthly payment is $450 if the down payment is $3,900.

To calculate the monthly payment, we first need to calculate the total amount financed. This is done by adding the list price of the car ($20,540), the sales tax (8.25% of $20,540 = $1,690.35), the registration fee ($995), and the documentation fee ($57) for a total of $23,282.35.

We then need to calculate the total amount of interest that Melissa will pay over the 5-year loan period. This is done by multiplying the interest rate (8.6%) by the total amount financed ($23,282.35) and multiplying that by the number of years (5).

This gives us a total interest payment of $7,634.84. We then add the total amount financed ($23,282.35) and the total interest payment ($7,634.84) and subtract the down payment ($3,900), which gives us the total amount that Melissa will pay over the 5-year loan period: $27,016.99.

We then divide this total amount by the number of months in the loan period (60) to get the monthly payment: of $450

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B-The two distributions for number of cars in line are both skewed right.

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Mariela's purchase of a house located in the V Zone of an NFIP participating community means that the house is located in a high amount of risk flood zone and that she is required to purchase flood insurance if she has a mortgage. This insurance will help to protect her investment in the event of a flood.

Mariela must purchase flood insurance if she has a mortgage on her house, which is located in a high amount of risk flood zone in an NFIP participating community. This insurance will help to protect her investment in the event of a flood.

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The final distance from U to T is 112 miles.

Since U and T are the midpoints of SR and ST respectively, we know that SU and RT are congruent and have the same length.

We need to find the overall displacement of U&T.

Also, we know that the distance between S and R is 56 miles.

Therefore, the distance from U to T is equal to twice the distance from S to U which is 2 * (distance from S to R) = 2 * 56 = 112 miles.

Therefore, The final distance from U to T is 112 miles.

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Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.

What is compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is different from simple interest, which is calculated only on the initial principal.

To find out how much Caleb needs to invest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal or initial investment

r = the annual interest rate (expressed as a decimal)

n = the number of times per year that interest is compounded

t = the number of years the investment will be held

We know that Caleb wants the future value of the investment to be $1,900 in 5 years and interest is compounded daily with an annual rate of 6%. So we can set up the equation as:

A = P(1 + r/n)^(nt)

1900 = P(1 + 0.06/365)^(365*5)

To solve for P, we can use a calculator to get the result:

P = $1,764.69

Hence, Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.

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a)

b) The slope-intercept definition of the linear function is given as follows:

y = 3x + 3.50.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points on the linear function in this problem are given as follows:

(2, 9.50) and (5, 18.50).

The slope is given by the division of the change in y by the change in x, hence:

m = (18.50 - 9.5)/(5 - 2)

m = 9/3

m = 3.

Representing the hourly charge.

Hence:

y = 3x + b.

When x = 2, y = 9.50, hence the intercept b, representing the rental fee, is given as follows:

9.5 = 3(2) + b

b = 3.50.

Meaning that the function is defined as follows:

y = 3x + 3.5.

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The equations ( x1+4x2 ) = 11 and ( 2x1+7x2 ) = 18 give the solution as x1 = -5 and x2 = 4.

In order to solve the equation using elementary row operation it is required to multiply the first equation with -2, so that the term with x1 is eliminated from both equations and the value of x2 can be found.

Now

-2. ( x1+4x2 ) = -2 . 11

(-2x1 - 8x2 ) = -22

Now, this equation is added to the second equation (the left-hand sides of both equations are added together and the right-hand side of the equations are added together).

(-2x1 - 8x2 ) + ( 2x1+7x2 ) = ( -22 + 18 )

-2x1 + 2x1  - 8x2  + 7x2  = -4

-x2 =  -4

(x2 = 4)

The value of x2 = 4 is now put in equation 1 to get the value of x1,

( x1 + 4x2 ) = 11

x1+ 4 (4) =  11

x1 + 16 = 11

x1 = (11 - 16)

(x1 = - 5)

So solution is x1 =  -5 and x2 = 4.

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On solving the provided question we can say that by unitary method number of extra copies made by machine 2 = 192 – 180 = 12

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen.

In 8 minutes, Machine 1 produces 240 copies. In 5 minutes, machine 2 produces 240 copies. The rates of operation for each machine are constant.

machine 1 makes 240 = 8 mins

[tex]1 min = 240/8 = 30\\6 min = 3 X 6 = 180[/tex]

In 5 minutes, machine 2 produces 240 copies.

[tex]1 min = 240/5 = 48\\4 min = 192[/tex]

number of extra copies made by machine 2

[tex]= 192 – 180\\ = 12[/tex]

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N and f(n) is totally different by their own circumstances.

N is independent variables

And f(n) is dependent variable

These are the main difference about n and f(n),You can typically depend on f(n) to represent the value of the function f at n. fn might mean f(n), especially when the domain is natural numbers, but it usually denotes the nth function in a sequence of functions.

F(a,b) would mean that the function takes two values, a and b. Your function takes one argument, n.

For example, f(n) might be the number of eggs in n packages, where each package has a dozen eggs. That would be f(n) = 12n, so f(3) = 12 * 3 = 36.

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Sale price of the mattress is $700.

What is a sales price in math?

The price after the original price has been reduced by a discount.

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

Mattress that is of $1000 is sold at  discount 30%.

Original price of mattress = $1000

Percentage of discount on mattresses = 30%

So,

Amount of discount on mattresses

= [ 30 / 100 ] × 1000

= $300                        

sale price of the mattresses = $1000 - $300 = $700

Therefore, the sale price of the mattresses is $700.

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The measure of angle ∠CXA is 134°

What is the Isosceles triangle?

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Triangle ABC is an isosceles triangle where AB = BC

∵ AB = BC

- The base angles in the isosceles triangle are congruent

∴ m∠BAC = m∠BCA

∵ m∠ BCA = 46° ⇒ given

∴ m∠ BAC = 46°

- The sum of the measures of the interior angles in any triangle is 180°

∵ m∠BAC + m∠BCA + m∠ABC = 180°

- Substitute the values of angle BAC and BCA in the equation above

∴ 46 + 46 + m∠ABC = 180

∴ 92 + m∠ABC = 180

- Subtract 92 from both sides

∴ m∠ABC = 88°

- BF, AD, and CE are bisectors segments of angles B, A, and C and they are intersected at point X

∵ CE bisects ∠BCA

∵ X ∈ CE

∴ m∠XCA = 1/2 m∠BCA

∴ m∠XCA = 1/2 (46) = 23°

∵ AD bisects ∠BAC

∵ X ∈ AD

∴ m∠XAC = 1/2 m∠BAC

∴ m∠XAC = 1/2 (46) = 23°

- In Δ AXC

∵ m∠XAC = 23° ⇒ proved

∵ m∠XCA = 23° ⇒ proved

∵ m∠CXA + m∠XAC + m∠XCA = 180° ⇒ interior angles of Δ

Substitute the values of angles XAC and XCA

∴ m∠AXC + 23 + 23 = 180

∴ m∠CXA + 46 = 180

- Subtract 46 from both sides

∴ m∠CXA = 134°

Hence, The measure of angle ∠CXA is 134°.

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The complete question is:

Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X. triangle ABC with diagonals BF, AD, and EC that intersect at point X If segment BA is congruent to segment BC and m∠BCA = 46°, what is m∠CXA?

Step-by-step explanation:

your teacher gave you even the formula. so, what is still not clear ?

in regular words, the slope of a line is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

so, we have here (-2, 1) and (3, 2).

x changes by +5 (from -2 to 3).

y changes by +1 (from 1 to 2).

so, the slope is +1/+5 = 1/5

There are different tables used in mathematics i.e. logarithmic tables, semi-logarithmic tables, exponential tables, trigonometric function tables, etc.

The tables are provided with data that is needed for the calculations. For example: if the value of Sin 45° needs to be found then we have to move to the table of Sin Θ and then follow the rows of angles where the value of Sin 45° can be obtained. Similarly, the values of other functions can be found in this way. However, the trigonometric table also provides the relation between two functions like Tan Θ= [tex]\frac{SinΘ}{CosΘ}[/tex].

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The midpoint [tex]s_{2}[/tex] is = (0,4).

Midpoint refers to a point that is in the middle of the line connecting two points. The two mentioned points are the endpoints of a line and the midpoint is lying in between the two points. The midpoint divides the line connecting these two points into two equal halves

According to the question,

The endpoints [tex]s_{2}[/tex] are 2 units to the right and 3 units up from the endpoints [tex]s_{1}[/tex].

[tex]s_{1}[/tex] has endpoints at  (4, 1)  and  (-8, 15).

[tex]s_{2}[/tex] has endpoints at  (4+2, 1+3)  and  (-8+2, 1 +3)

[tex]s_{2}[/tex]  has endpoints at  (6, 4)  and  (-6, 4).

The midpoint of [tex]s_{2}[/tex] = [tex](\frac{6-6}{2} , \frac{4 + 4}{2} )[/tex] = ( 0, 4)

So, the midpoint [tex]s_{2}[/tex] is = (0,4).

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In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass. thus it is the correct option.

Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

The response variable (or the dependent variable) always belongs on the y-axis (represented as the second column of the table).

Since the explanatory variable (or the independent variable) always belongs on the x-axis (represented as the first column of the table).

According to the table of values showing the mass of a radioactive isotope over time.

Based on explanation above the correct choice is C which could be In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass.

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840  ways can we form a subcommittee with 3 republicans and 2 democrats

Given that

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical. (It is not important how each set's members are arranged.) If there are n elements in the set, then C kn is the number of k-combinations.

a senate committee has 8 republicans and 6 democrats.

now, we need to find how many ways can we form a subcommittee with 3 republicans and 2 democrats

= 8[tex]C_{3}[/tex] × 6[tex]C_{2}[/tex]

=[tex]\frac{8!}{5!3!}[/tex] × [tex]\frac{6!}{4!2!}[/tex]

=56 × 15

=840

840  ways can we form a subcommittee with 3 republicans and 2 democrats

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Answer:

  $12300

Step-by-step explanation:

You want to know the amount loaned at 7% if $19000 loaned at 7% and 17% earns $2000 in one year.

The interest on an investment P at rate r for t years is ...

  I = Prt

The sum of the amounts of interest on a 7% investment of x and a 17% investment of (19000 -x) is given as 2000:

  0.07x +0.17(19000 -x) = 2000

  -0.10x +3230 = 2000 . . . simplify

  1230 = 0.10x . . . . . . . . . . add 0.10x -2000

  12300 = x . . . . . . . . . . . . divide by 0.10

The amount loaned at 7% was $12,300.

Answer: The function rule C = 9n + 45 represents the cost of the shirts that the Math Club is selling. The variable C represents the total cost of the order and the variable n represents the number of shirts.

The number 9 in the function represents the price per shirt, this is because as the number of shirts increases by 1, the total cost increases by 9. This tells us that the cost of each shirt is $9.

The number 45 in the function represents the initial set-up fee charged to design the shirts. This is because even if no shirts are ordered, there is still a cost of $45. This represents a fixed cost that the Math Club must pay to have the shirts designed.

Step-by-step explanation: