(-4,-2) and (4,0) in linear equations

The area of trapezoid with sides 125ft and 81ft with height 75ft is: 7,725ft².

Area of a trapezoid,

A = 1/2 x (b1 x b2)h

Here given,

b1 = 125ft

b2 = 81ft

h = 75ft

By substituting the values ,

A = 1/2 ( 125 + 81 ) x 75

A = 1/2 x 206 x 75

A = 0.5 x 206 x 75

A =  7,725 ft²

The complete question is "To answer the question, use the formula for the area of a trapezoid A=h((b1+b2)/2), where A is the area, b1 and b2 are the lengths of the bases, and h is the height. What is the area of grass on a trapezoidal field with a height of 75 feet and bases of 125 feet and 81 feet? HINT: Use the values given for h, b1, and b2.".

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The area of trapezoid is 7725 ft²

What is a trapezoid?

In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. Unlike the specific situations below, a scalene trapezoid is a trapezoid that lacks equal-sized sides.

Given, the expression for the area a is given as

a = [(b₁ + b₂)/2]*h

where b₁ = 125ft, b₂ = 81ft, h = 75ft.

Substituting these values in the above area expression, we get,

a = [(125+81)/2]*75

a = 103*75

a = 7725 ft²

Thus, the area of trapezoid is 7725 ft²

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The exponential function that determines the value of the car after x years is y = 18000(0.65)ˣ. Here the rate of decrease is the same each year.

The exponential function is the function that gives the relationship between the input and the output with a rate of increase or decreases exponentially. It is given by the formula,

y = abˣ

Where 'a' is the initial value, 't' is the time, and 'b' is the rate. If b > 1, then the function is said to be the exponential growth function, and if b < 1, the function is said to be the exponential decay function.

Given that, a car is sold for $18,000.

So, the initial value a = 18000.

After one year (x = 1), the value of the car is $11,700 i.e., y = 11700. So we can write the exponential function as

11700 = 18000(b)¹

⇒ b = 11700/18000 = 0.65

Since b < 1, the function is exponentially decaying.

Then, the value of the car after 'x' years is given by the exponential decay function as

y = 18000(0.65)ˣ

(It is given that, the rate of decrease is the same each year).

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The Binomial expansion of given expression, (1+x)⁻¹ is 1 − x + x² - x³+ x⁴ + ...

Binomial theorem primarily helps to find the expanded value of the algebraic expression of the form (x + y)ⁿ

Using the Binomial theorem we can expand the series of ( x + y )ⁿ as

( x + y)ⁿ = ∑ ⁿCₖ xⁿ⁻ᵏ yᵏ

k= 0 to n

= xⁿ + (n(n-1)/2!)x⁽ⁿ⁻¹⁾y + (n(n-1)(n-2)/3!)x⁽ⁿ⁻²⁾y² + .......

where n ≥ 0 and (ⁿCₖ ) is known as a binomial coefficient and they should be positive integers.

We have given that (1+x)⁻¹ comparing it with ( x + y )ⁿ we get, y = 1 ; n = -1

Binomial expansion for this is followed the same way as expanding larger power expansion,

So (1+x)⁻¹ = 1 + (-1)x + (-1)(-1–1)/2! x² + (-1)(-1–1)(-1–2)/3! x³+…….

= 1 -x + x²- x³ +….

but this will result in an infinite series and will converge for values belonging to

|x|<1. So, the required binomial series is

1 -x + x² - x³ +….

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Percentage of 18-year-old women have a systolic blood pressure between 108 mm hg and 132 mm hg is 68.27 %

z - score :

mean = 120

standard deviation = 12

you want to find the area under the distribution curve between the scores of 108 and 132 .

z - score low :

low z-score = ( 108 - 120 ) / 12 = -12 / 12 = -1.

z - score high :

high z-score = (132 - 120) / 12 = +12 / 12 = +1.

the + sign is normally silent (not shown) but i show it here to emphasize that you are going from a low z-score of -1 to a high z-score of +1.

so here probability = 0.6827

= 0.6827 * 100 %

= 68.27 %

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Answer:

3.15

Step-by-step explanation:

In equations, you need to get the variable on one side and the answer on the other. In this instance, you divide both sides by 5.24 so you're left with w = 3.15.

Hope this helps, have an amazing day!

Answer:

d) 3.15

Step-by-step explanation:

Given equation,

→ 5.24w = 16.506

Now the value of w will be,

→ 5.24w = 16.506

→ w = 16.506 ÷ 5.24

→ [ w = 3.15 ]

Thus, the value of w is 3.15.

Therefore the maximum revenue company will generate is $8,910,000 and thus price should be increased by $2

In mathematics, an equation is a logical statement with two algebraic expressions on either side of the equals (=) sign. In relation to one another, the expressions on the left and right are equal. Every mathematical equation begins with the expression LHS = RHS (left hand side = right hand side). The value of a variable or quantity can be found by solving an equation. Unless the statement contains the "equal to" sign, it is not an equation.

Here,

The company charges a monthly fee of $31 to deliver a box of pet supplies each month

x be the number of subscribers and y be the price.

equation used is

Since , company currently has 290,000 subscribers. For each $1 increase in price ,the company loses 10,000 subscribers

Therefore to  to maximize monthly revenue

he has to increase the price by $2

Therefore he will loose 20,000 subscribers

and the maximum revenue he will generate is

=> 270,000 * 33

=>8,910000

Therefore the maximum revenue company will generate is $8,910,000 and thus price should be increased by $2

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You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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The expression evaluates because the variable truck weight's true value is present. The correct answer is (C).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given,

In the following expression, the variable truck weight has the value 70000 and the variable weight limit has the value 80000.truck weight < weight limit.

Expression,

Truck weight < Truck limit

The value of expression evaluate,

It is true.

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The number of words he still need to write in one of his writing sessions would be = 95 minutes.

A graduate is an individual that has completed studies in an institution for a number of years and is being issued a certificate afterwards.

The number of words committed for a day by Nick = 500 words.

He writes 120 words = 30 mins

The total number of words remaining = 500 - 120 = 380 words.

Therefore the time it will take to finish the remaining 380 words in the day = X mins.

If 30 mins= 120 words

X mins = 380 words.

Make X mins the subject of formula;

X mins = 380× 30/120

X mins = 11,400/120

X mins= 95 minutes.

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The amount of tax is  $4,622.40 owed on a taxable income of $38,520. which is the correct answer would be option (C).

As per the given question, the marginal tax rate chart as

Marginal Tax Rate           Chart Tax Bracket

$0 –$10,275                                  10%

$10,276 –$41,175                           12%

$41,176 –$89,075                          22%

$89,076 –$170,050                      24%

$170,051 –$215,950                      32%

$215,951 –$539,900                     35%

> $539,901                                     37%

So, the effective tax rate for income of $38,520 lies in the range of a marginal tax rate of 12%.

So, the effective tax ;

⇒ 12% of $38,520

⇒ (12/100)38,520

⇒ $4,622.40

Thus, the amount of tax is  $4,622.40 owed on a taxable income of $38,520.

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The equation is false (we can remove the dependence with the variable x) that is why the equation has no solutions.

Here we have the following linear equation:

5 - 4x - 7 - 10x = -8x - 4 - 6x - 10

We want to see why we don't have any solutions, to check that, we need to simplify both sides of the equation. Let's start by grouping like terms:

5 - 4x - 7 - 10x = -8x - 4 - 6x - 10

(5 - 7) + (-4x - 10x) = (-4 - 10) + (-8x - 6x)

-2 - 14x = -14 - 14x

Notice that now we can add 14x in both sides of the equation, then we will get:

-2 -14x + 14x = -14 - 14x + 14x

-2 = -14

So we have a false equation, this happens because the equation does not truly depend of the value of x.

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Answer:

20.8

Step-by-step explanation:

y = x^2

Given the value of y = 432, the equation would be:

432 = x^2

x is found by finding the square root of 432

sqrt 432 = sqrt (x^2)

x = 20.8

Check:

20.8^2 = 432.64

Your final answer would be 20.8.

(a) The rectangles represent a left sum, as the rectangles are drawn starting from the left endpoints of the intervals.

(b) The rectangles lead to a lower estimate of the integral, as the rectangles are drawn underneath the curve of the function.

(c) The value of n is 5, as there are 5 rectangles drawn.

(d) The value of Δx is 1, as the interval between the limits 0 to 6 is divided into 5 equal parts.

(e) The approximate value of the integral g(x)dx between the limits 0 to 6 is 22.5.

left-end points:

[tex]g(0)[/tex]Δ[tex]x[/tex] [tex]+ g(2)[/tex]Δ[tex]x + g(4)[/tex]Δ[tex]x[/tex]

Right-end points:

[tex]g(2)[/tex]Δ[tex]x + g(4)[/tex]Δ[tex]x + g(6)[/tex]Δ[tex]x[/tex]

[tex](g(2)+g(4)+g(6))^{2}[/tex]

Δ[tex]x=\frac{b-a}{n}[/tex]

   [tex]2=\frac{6-0}{n} \\\\2=\frac{6}{n}\\\\n=\frac{6}{2}=3 \\\\n=3[/tex]

Δ[tex]x=2-0=2[/tex] (each sub-interval length)

[tex]g(x)=x^{2} \\\\\int\limits^6_0{g(x)} \, dx = \int\limits^6_0 {x^{2} } \, dx[/tex]

              [tex]=[\frac{x^3}{3} ]^6_0\\\\=\frac{6^3}{3} -0\\\\=72[/tex]

The integral can be evaluated using the Fundamental Theorem of Calculus, which states that the integral of a function [tex]f(x)[/tex] with respect to [tex]x[/tex]from [tex]a[/tex] to [tex]b[/tex] is equal to the difference between the values of the antiderivative of [tex]f(x)[/tex] evaluated at [tex]b[/tex] and at [tex]a[/tex].

Therefore, the integral of [tex]f(x)[/tex] from [tex]a[/tex] to [tex]b[/tex] is given by:

[tex]\int\limits f{(x)} \, dx =f(b)-f(a)[/tex]

where[tex]F(x)[/tex] is the antiderivative of [tex]f(x)[/tex].

In this case, the antiderivative of f(x) is given by [tex]F(x) = \frac{x2}2 + c[/tex], where [tex]c[/tex] is the constant of integration. Therefore, the integral of f(x) from [tex]a[/tex] to [tex]b[/tex] is given by:

[tex]\int\limits f(x)dx = F(b) - F(a)\\\\= (\frac {b2}{2} + c) - (\frac{a2}{2} + c)\\\\= \frac{(b2 - a2)}{2}[/tex]

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The volume of both prisms is B. 105.34 cubic units

The volume of a prism is given by V = lwh where

Given the diagram If

The volume of the top prism is V = lwh where

Given that

So, V = abd

Also, the volume of the bottom prism is V' = lwh where

Given that

So, V' = a²c

So, the volume of the two prisms is V" = V + V'

= abd + a²c

= a(bd + ac)

Substituting the values of the variables into the equation, we have

V" = a(bd + ac)

= 2.3(4 × 8 + 2.3 × 6)

= 2.3(32 + 13.8)

= 2.3(45.8)

= 105.34 cubic units

So, the volume is B. 105.34 cubic units

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Answer:

i have done this mano time ago, but problaply the answer is x=3

Since the probability is 33% which is less than 47% as claimed by the basketball player, it can be concluded that there is convincing evidence that she is less than a 47% shooter.

It is given to us that -

A basketball player claims to make 47% of her shots from the field

The player takes sets of 10 shots

Assuming that her claim is true, a total of 25 repetitions of a simulation were performed

The number of makes in each set of 10 simulated shots was recorded on the dot plot

We have to suppose this player attempts 10 shots in a game and makes only 3 of them.

For the simulation of the player taking sets of 10 shots, we have to determine if we have enough convincing evidence that she is less than a 47% shooter.

From the given information, the approximate probability of finding out that a 47% shooter makes only 3 of the 10 attempted shots can be determined as -

P (x = 3) = 3/10 = 0.33 = 33%

Since the probability is 33% which is less than 47% as claimed by the basketball player, it can be concluded that there is convincing evidence that she is less than a 47% shooter.

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Inequality #1: x + y ≤ 28

Inequality #2: 0.05x + 0.1y ≥ 2

Mav could have 5 nickles and 20 dimes.

    It's given that Mav has less than or equal to 28 coins, so we can write the following inequality:

       x + y ≤ 28

    We know that a nickel is work 0.05 and a dime is worth 0.1. Using the given information, the following inequality is true since the coins must be greater than or equal to $2 combined:

       0.05x + 0.1y ≥ 2

       Now, we will graph them. Both graphed lines will use solid lines since both include equal to. We will shade below #1 and above #2. I used Desmos Graphing Calculator, you can find it online for free. Once we type in our equations, we get the needed graph.

       The overlapping portion contains our possible solutions. There are many, but one possible solution is (5, 20), with 5 nickels and 20 dimes.

The answer to this Question is YES. Inequalities do show the relation between Numbers.

What are Inequalities?

Inequalities are the operators the we want to compare the data when equality is not valid

Solution:

The Inequalities shows nice relation between numbers like when we say for example 2 and 4 we know that 2 is not equal to 4 but we know that

2 is less than 4 in this case inequalities help us to develop relations between numbers that are not equal

Inequalities are also used in inequations where they represents large set of data .

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Answer:

D

Step-by-step explanation:

|x+2|<2

|x+2|<2 --> split abs. value equations into two parts. Flip the sign for the negative value

x+2<2 and x+2>-2

x+2<2 --> x<0

x+2>-2. --> x>-4

solituon. -4<x<0

This indicates that the probability is 0.4402% without replacement.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

n = 5

x = 1

p = 5/20 = 0.25

15C4 = 15! / 4! * 11! = 1365

P = (5C1 * 15C4) / 20C5

Replacing:

P = 5 * 1365/15504

P = 0.4402

Hence, This indicates that the probability is 0.4402% without replacement.

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56% interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

Given that,

Amira will put $580 into an account and let it sit there for 17 years.

We have to find what interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

We know that,

We have a formula

A=P(1+r/n[tex])^{nt}[/tex]

Here,

A=$840

P=$580

n=12

t=17

We get

840=580(1+r/12[tex])^{12\times17}[/tex]

840=580(1+r/12)²⁰⁴

42/29=(1+r/12)²⁰⁴

r=0.56

Therefore, 56% interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

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Step-by-step explanation:

first thing that seems to be a given (and not mentioned in the description) : QM is a diameter (straight line) through the circle. otherwise this cannot be solved without further information.

remember, a half-circle has 180°.

so, arc angle MAP = 180 - 33 = 147°.

arc angle RMP = RM + MAP = 46 + 147 = 193°.

arc angle RSQ = 180 - 46 = 134°.

arc angle MRQ is the full half-circle = 180°.

arc angle MAP (as above) = 147°.

slope is 6-5/2-3 = - 1.....

Answer: -1

Step-by-step explanation:

The function f(x) = −16x² + 48x + 64 represents the height of an object above the ground in feet, x seconds after being launched.

To find f(-1), we plug -1 into the function:

f(-1) = −16(-1)² + 48(-1) + 64

= 16 - 48 + 64

= 32

This means that 1 second after the object was launched, it was 32 feet above the ground.

To find f(0.5), we plug 0.5 into the function:

f(0.5) = −16(0.5)² + 48(0.5) + 64

= −16(0.25) + 24 + 64

= −4 + 24 + 64

= 84

This means that 0.5 seconds after the object was launched, it was 84 feet above the ground.

Since the function represents the height of the object above the ground, the domain of the function would be the set of all real numbers x such that x represents the number of seconds after the object was launched.

This would include all positive and negative values of x, since the object could have been launched at any time in the past or future. However, if the problem specifies a specific range of time, then the domain would be limited to that range.

Therefore, the correct answer is as given above

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A process is said to be out of control if proportion of defective lies outside the control limits. Since 8% and 7% are outside our upper control limit (UCL) So, 2 batches are defective.

Given that,

100-piece batches of canned soup are produced by Company X. They estimate that there are 2% faulty soup cans in circulation.

We have to find how many of the 3%, 8%, 1%, 2%, and 7% defective can percentages in the five batches fell beyond the higher or lower control limits for the percentage of defective soup cans in the batch.

We know that,

LCL= p-3√(p(1-p)/n)

=0.02-3√(0.02(1-0.02)/100)

=-0.022

Since probability can not be negative.

LCL=0

UCL= p-3√(p(1-p)/n)

=0.02-3√(0.02(1-0.02)/100)

=0.062

Therefore. A process is said to be out of control if proportion of defective lies outside the control limits. Since 8% and 7% are outside our upper control limit (UCL) So, 2 batches are defective.

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Answer:

The last one on the right

Step-by-step explanation:

The others are 2 equations in x and y, while the last is one equation in x  only and another in y only

The solution is Option D.

The system of equations 3 = y + 1 and x = -6 are equations is one variable

What is Linear Equation in 2 variables?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the system of equations be

y = 3x - 1   be equation (1)

y = 3x + 1   be equation (2)

Now , the equations are linear equations in 2 variables

b)

Let the system of equations be

-2x + y = 2   be equation (1)

-4x + 2y = 4   be equation (2)

Now , the equations are linear equations in 2 variables

c)

Let the system of equations be

y - 1 = 2 ( x + 4 )   be equation (1)

y + 3 = -5 ( x + 1 )   be equation (2)

Now , the equations are linear equations in 2 variables

d)

Let the system of equations be

3 = y + 1   be equation (1)

y = 2

x = -6   be equation (2)

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution

So , the equation is linear equation is one variable

Hence , the equations y = 2 and x = -6 are equations in one variable

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The measurement of side DF is 4cm.

Here in the figure attached below,

Given two triangles ΔABC and ΔDEF

Also given that,

ΔABC and ΔDEF are congruent to each other.

Given AC = 4cm

Since both triangles are congruent ,

Side AC is congruent to DF

Therefore DF = 4cm (based on SSS theorem).

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The measure of DF is 4cm.

What is congruent triangle?

When two triangles are congruent, their three sides and their three angles match precisely.

If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.

Here in the figure attached below,

There are two triangles ΔABC and ΔDEF and it is given that ΔABC and ΔDEF are congruent to each other.

From the figure, side AC = 4cm

The side DF = AC = 4cm, because the triangles  ΔABC and ΔDEF are congruent to each other and based on Side-Side-Side Theroem, we can confirm that.

Hence, DF = 4cm.

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Answer:

-6y + 13.3 = 0

y = 13.3/6

Step-by-step explanation:

This equation don't need any step-by-step explanation :). Hope it helps!

Answer:

There are 1,680 possible committees if there have to be at least two housekeepers.

Step-by-step explanation: