Three less than four times a number

The area of the composite figure = area of rectangle 1 + area of rectangle 2 + area of triangle = 56 km²

Find the area of each shape that make up the figure, then add up to get the area of the composite figure.

The area of the composite figure = area of rectangle 1 + area of rectangle 2 + area of triangle

Area of rectangle 1 = (length)(width) = (6)(3) = 18 km²

Area of rectangle 2 = (length)(width) = (7 + 3)(2) = 20 km²

Area of triangle = 1/2(base)(height) = 1/2(10 - 4)(6) = 18 km²

The area of the composite figure = 18 + 20 + 18 = 56 km²

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Answer:

the time at which P =15 is \({t_o = 0.54161 \ years}\)

the time at which P =20 is \({t_1 = 0.59914 \ years}\)

the doubling time \({t = 0.138629 \ years}\)

Step-by-step explanation:

From the information we are being provided with:

The quantity P i.e \(P(t) = e ^{5t}\)

In order to determine the time at which P = 15, we have the following:

\(t= t_o\)    when P = 15

∴ \(e^{5t_o} = 15\)

\(5t_o= In (15)\)

\(t_o = \dfrac{1}{5}In 15\)

\(t_o = \dfrac{1}{5} \times 2.70805\)

\({t_o = 0.54161 \ years}\)

Hence, the time at which P =15 is \({t_o = 0.54161 \ years}\)

In order to determine the time at which P = 20, we have the following:

\(t= t_1\)    when P = 20

∴ \(e^{5t_1} = 20\)

\(5t_1= In (20)\)

\(t_1= \dfrac{1}{5}In (20)\)

\(t_1 = \dfrac{1}{5} \times 2.9957\)

\({t_1 = 0.59914 \ years}\)

Hence, the time at which P =20 is \({t_1 = 0.59914 \ years}\)

The doubling time at t = 0, mean P = 2

∴ \(e^{5t} = 2\)

\(5t= In (2)\)

\(t= \dfrac{1}{5}In(2)\)

\(t = \dfrac{1}{5} \times0.693147\)

\({t = 0.138629 \ years}\)

Hence, the doubling time \({t = 0.138629 \ years}\)

Answer:

no

Step-by-step explanation:

The provided quadrilateral is a parallelogram because diagonals are bisecting each other option Yes is correct.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

A quadrilateral is given in the picture.

As we know, in the parallelogram the diagonals of the parallelogram bisect each other.

In the figure, it is given that the diagonals are bisecting each other.

From the figure, the two opposite sides are parallel.

In the parallelogram the pair of opposite sides are parallel.

Thus, the provided quadrilateral is a parallelogram because diagonals are bisecting each other option Yes is correct.

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The probability that at least 1000 cars will cross the intersection in the next hour depends on the assumptions made about the distribution of car arrivals.

The probability that at least 1000 cars will cross the intersection in the next hour can be determined by first finding the rate per hour.
Convert the rate from cars per minute to cars per hour.

Since there are 60 minutes in an hour, multiply the given rate (16 cars per minute) by 60 minutes:
16 cars/minute x 60 minutes/hour = 960 cars/hour
Compare the desired number of cars (1000) with the calculated rate per hour (960 cars/hour). Since 1000 cars are more than the rate of 960 cars/hour, the probability of at least 1000 cars crossing the intersection in the next hour is less than 100%.
To determine the exact probability, we need to make some assumptions about the distribution of car arrivals.

If we assume the car arrivals follow a Poisson distribution, we can use the Poisson probability formula to find the probability of at least 1000 cars crossing the intersection:
P(X ≥ 1000) = 1 - P(X < 1000) = 1 - (P(X=0) + P(X=1) + ... + P(X=999))
Where P(X=k) = (e^(-λ) * (λ^k)) / k!,

λ is the average rate (960 cars/hour), and k is the number of cars.
Calculate the probabilities for P(X=0) to P(X=999) and sum them up.

Then subtract the sum from 1 to get the probability of at least 1000 cars crossing the intersection in the next hour.
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The fractions are made to have common denominator such that the numerator are then re-represented based on their initial denominator , to represent the proportion of the  new denominator they had in the previous denominator.

A fraction is a representation of a part of a whole .

The fraction consists of a numerator and a denominator. The denominator indicates the divisor of the fraction.

Allowing the fraction to have the same denominator allows the numerator to be subtracted from each other, such that the values in the numerator are the same  multiples of a unit when the denominators are the same.

The fractions in the question are presented as follows;

\(\dfrac{2}{3} + \dfrac{1}{5}\)

The 2 in the numerator on the left indicates that when a length of 1  is divided into 3, the location is in the second division, while the 1 on the right indicates that when a length of 1 is divided into  5, it is in the first position

Therefore, to be able to add the numerator, the number 1 has to be divided into a common multiple of 3 and 5, which is 15, from which we get;

The 2 will now be located at 15/3 × 2 = 10, and the 1, will be located at the (15/5) × 1 = 3 position, the sum of the fraction is therefore;

(10 + 3)/15 = 13/15

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The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

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

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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Answer:

we have 8 quarts of 40% antifreeze,

according to the britain equivalent, 1 quart = 1.13L

so, we have 8 * 1.13L  = 9.04 L

out of the 9.04 L, 40% is antifreeze

amount of antifreeze = 0.4 * 9.04 = 3.616 L

moles of antifreeze present = 3.616/22.4 = 0.16 moles

moles of antifreeze in 60% solution = 0.6 * v/22.4 = 0.027 * v          

(where v is the volume of final solution)

molarity of initial solution = 0.16/9.04 = 0.018 M

molarity of final solution = 0.027*v/v = 0.027 M

m1*v1  = m2*v2

0.018 * 9.04 = 0.027 * v

v = 0.018 * 9.04/0.027

v = 6.026 L

amount if antifreeze in the final solution = 6.026 * 0.027 =  

0.163 Moles of antifreeze

amount in L = 0.163 * 22.4 = 3.65 L

amount in quarts  = 3.65/1.13 = 3.23 quarts

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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Every half hour Sid paints 6 yards, so by 4:30 PM he will have painted 62 yards.

To show the relationship between T and P, where P is the number of yards of painted fence, the following calculation must be performed:

Therefore, every half hour Sid paints 6 yards, so by 4:30 PM he will have painted 62 yards.

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Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165

This is further explained below.

Generally, The term "cumulative balance" refers to the total amount of money left over at the end of a fiscal year after all surplus amounts have been subtracted from deficit amounts. If there is a negative amount in the Cumulative Balance at the conclusion of a fiscal year, then that balance will be carried forward and used as the opening balance for the next fiscal year.

The term "cumulative account" refers to the total amount of an employee's account under a defined contribution plan (for an unaggregated plan) or the total amount of an employee's account under all defined contribution plans included in an Aggregation Group (for aggregated plans), both of which are determined as of the most recent plan valuation date within the most recent 12-month period that ends on the...

In conclusion, for the following data  July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165

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Answer:

33%

Step-by-step explanation:

6/9 = .66 which is the amount that do have it

1 - .66 = .33 which is the amount that dont.

.33 x 100 = 33%

Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

\(1/2 * 2 * 1 = 1\) square unit.

Step-by-step explanation:

To find the maximum area of the triangle, we need to locate the vertex of the parabola. This occurs when x=1. The y-coordinate at x=1 is 1. We can then use this as the height of the triangle. The base of the triangle is the distance between x=0 and x=2, which is 2. Therefore, the maximum area of the triangle is 1/2 * 2 * 1 = 1 square unit.

Answer:

31.) x = 3

32.) y = 49

Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

;>

✿————✦————✿

Answer: A

\(62=\frac{12(1.04^{12}-1) }{1.04-1}\)

✿————✦————✿

Given: The equation x² = 5x + 4

We have to draw the the graph for the given equation.

Consider the given equation,

x^2 - 5x - 4 = 0  

The vertex of the parabola of the form f(x) = ax^2 + bx + c   is given by x = -b/2a

Here,

a= 1

b= -5

c= -4

vertex = x = 5/2= 2.5

Also, the y coordinate at x = 2.5 is,

y = (2.5)^2 -5(2.5)-4

y = -10.25

Thus the vertex of parabola is (2.5 , -10.25)

y - intercept is the point where x = 0

put x = 0 in given equation

f(x) = 0 - 0 -4

f(x) = -4

hence y intercept is at (0, -4).

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

x^2 - 5x - 4 = 0

by using quadratic formula,

x = -b ±√b² - 4ac/2a

x=5 ±√-5² - 4 (1)(-4)/2

x= 5±√41/2.

Hence with the obtained values the graph of the equation is obtained.

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The increase in price would  increase the annual pass revenue of the museum.

In order to determine the effect the increase in price would have on revenue, we have to examine the elasticity of demand of the museum pass.

The point elasticity is 0.62. This means that demand is inelastic. This means that when price increases, there would be little or no change in the quantity demanded. As a result, revenue would increase.

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Answer:

hi

Step-by-step explanation:

Answer:

Let l be length and w be the width

l = 2w+12

Area = (2w+12)*w = 224

2w^2 + 12w - 224 = 0

w^2 + 6w - 112 = 0

using quadratic formula

w=[ -6 +- {36- 4*1*(-112)}^0.5]/2*1

w = [-6 +- {484}^0.5]/2

w = [-6 +- {22}]/2

w = 16/2 or -28/2

w = either 8 or -14

Width can not be a negative number

wI’d think= 8 ft

length = 2*8+12 = 28 ft

Step-by-step explanation:

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

The width of the rectangle is 2√23 feet.

The length of the rectangle is (4√23 + 8) feet

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area of the rectangle = 192 square feet

Width = W

Length

L = 2W + 8

Now,

The area of the rectangle.

= Length x Width

= (2W + 8)W

= 2W² + 8W

Now,

192 = 2W² + 8

192 - 8 = 2W²

184 = 2W²

W² = 92

W = √92

W = √4 X 23

W = 2√23

L = 2W + 8 = 2 x 2√23 + 8 = (4√23 + 8) feet

The width of the rectangle is 2√23 feet.

The length of the rectangle is (4√23 + 8) feet

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Answer:

The function g(x) is odd.

Step-by-step explanation:

Even and odd functions:

If for every value of x, f(x) = f(-x), the function is even.

If for every value of x, f(x) = -f(x), the function is odd.

If those statements are false, the function is neither even nor odd.

In this question:

\(g(x) = x^{3}\)

\(g(-x) = (-x)^{3} = -x^{3} = -g(x)\)

Since g(x) = -g(-x), the function g(x) is odd.

The point of intersection of the system of equations is (3, 4) and this is plotted in the graph shown below.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In conclusion, the coordinate (3, 4) is the point of intersection of the given system of equations.

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Answer:23

Step-by-step explanation:

Answer:

y+5 = 9/5(x+3)

y - 4 = 9/5(x-2)

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

    = ( 4- -5)/(2 - -3)

    = ( 4+5)/(2+3)

    = 9/5

Then using the point slope form

y -y1 = m(x-x1)  where x1 and y1 are a point on the line

y -  -5 = 9/5(x- -3)

y+5 = 9/5(x+3)

or using the other point

y - 4 = 9/5(x-2)

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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Answer:

Gievn that l=3m,b=5m,h=4m

L.S.A=2(l+b)h

=2×(3.5)×4

=2×8×4

=64sq.m

Step-by-step explanation:

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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