during the last 3 years consolidated oil company expanded its gasoline stations into convenience food stores (cfss) in an attempt to increase total sales revenue. the daily sales (in hundreds of dollars) from a random sample of 10 weekdays from one of its stores are:

A line segment is a piece of a line that can connect two places. Hence  ar (ABC) = ar (ABD)

Given

[tex]$\triangle \mathrm{ABC}$[/tex] and [tex]$\triangle \mathrm{ABD}$[/tex] are two triangles on the same base [tex]$\mathrm{AB}$[/tex].

To show :

ar(ABC)=ar(ABD)

Proof :

Since the line segment [tex]$\mathrm{CD}$[/tex] is bisected by [tex]$\mathrm{AB}$[/tex] at [tex]$\mathrm{O}[/tex] . [tex]\mathrm{OC}=\mathrm{OD}$[/tex].

In [tex]$\triangle \mathrm{ACD}$[/tex], We have [tex]$\mathrm{OC}=\mathrm{OD}$[/tex].

So, [tex]$\mathrm{AO}$[/tex] is the median of[tex]$\triangle \mathrm{ACD}$[/tex]

Also we know that median divides a triangle into two triangles of equal areas.

∴ar(ΔAOC)=ar(ΔAOD) _______ (1)

Similarly , In[tex]$\triangle \mathrm{BCD}$[/tex],

[tex]$\mathrm{BO}$[/tex]is the median. ([tex]$\mathrm{CD}$[/tex] bisected by [tex]$\mathrm{AB}$[/tex] at [tex]$\mathrm{O}$[/tex])

∴ar(ΔBOC)=ar(ΔBOD) _______ (2)

On adding equation (1) and (2) we get,

ar(ΔAOC)+ar(ΔBOC)=ar(ΔAOD)+ar(ΔBOD)

∴ar(ΔABC)=ar(ΔABD)

The complete question is,

In figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar (ABC) = ar (ABD).

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Scalar quantities of these do not include direction distance, Force, Acceleration, or Velocity.

scalar, a physical quantity whose sole description is its magnitude. Scalars include, but are not limited to, time, energy, mass, volume, density, and speed.

A scalar quantity is one that doesn't depend on movement in any direction. Vector quantities can have a magnitude and a direction. Scalar quantities have just a magnitude.

All of the option values are scalar, with the exception of impulse. A force can be an impulse. Similar to force, it has both magnitude and direction.

Additional examples of scalar quantities are mass, velocity, distance traveled, time passed, energy, density, volume, temperature, work, etc.

Since speed has a simple magnitude and no discernible direction, it is a scalar number.

A scalar quantity is something like distance. Any quantity that has both a direction and a magnitude is a vector.

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The area of the region inside the circle (x−1)^2+y^2=1 and outside the circle x^2+y^2=1  is 4.

The area of the region inside the circle (x−1)^2+y^2=1 and outside the circle x^2+y^2=1 can be calculated using polar coordinates.

The equation of the inner circle in polar coordinates is r_1^2=1+2cosθ and the equation of the outer circle in polar coordinates is r_2^2=1.

The intersection points of the two circles can be found at θ=±π/3.

The area of the region can be calculated using the integral:

Area=∫_π/3^-π/3 (1+2cosθ)dθ=(2+4sinθ)|_π/3^-π/3=(2+4sin(-π/3))-(2+4sin(π/3))=4.

Therefore, the area of the region is 4.

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The inequality equation which represents Ten less than twice a number is equal to at least 52 is 10 - 2x ≥ 52 and x ≤ -21

Let

The unknown number = x

Ten less than twice a number is equal to at least 52;

10 - 2x ≥ 52

Subtract 10 from both sides

- 2x ≥ 52 - 10

- 2x ≥ 42

divide both sides by - 2

x ≤ 42/-2

x ≤ -21

Hence, x ≤ -21 is the solution to the inequality 10 - 2x ≥ 52 if x comes first.

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Answer:

B, C

Step-by-step explanation:

A) No, factors of 15 = 1, 3, 5, 15... so 45 is not a factor of 15

B) yes, 45 is the third multiple of 15 ( 15×3=45)

C) yes, factor of 45 is the number that divides 45 without leaving any remainders (45÷15=3), therefore 15 is a factor of 45

D) No, multiples must be bigger in value than the actual number because( a multiple of 45) means, the number we get when we multiply 45 by an integer... Here we can't multiply an integer by 45 and get the answer 3

When two or more variables vary jointly, their product is always constant. In this case, if 'a' varies jointly with 'b' and 'c' it means that their product is always constant, so abc = k, where k is a constant value.

When a variable 'a' varies inversely as the square of another variable 'd', it means that a*1/d^2 = k, where k is a constant value.

So, if 'b' is tripled, 'c' is doubled and 'd' is doubled, we can see the effect on 'a' by substituting the new values into the equations.

abc = k => a3b2c = k

a1/d^2 = k => a1/(2d)^2 = k

So the effect on 'a' if 'b' is tripled, 'c' is doubled, and 'd' is doubled is that it will be divided by 4.

a3b2c = a1/(2d)^2 => a = k / (3b2c*(2d)^2) = (k/(12bcd^2))

So a = k/(12bcd^2) = a/4.

Therefore, the value of 'a' is decreased by a factor of 4.

Answer:

The rectangle (option 2)

Step-by-step explanation:

A quadrilateral is any enclosed polygon with four sides. Only the rectangle (option 2) is a quadrilateral.

The other options are not quadrilaterals because they don't have four sides (options 1 and 3) or are not enclosed (option 4). Hope this helps!

The solution for the given equation; 7x+5(x-1)=-5+12x as required to be determined is; Infinitely many solutions.

It follows from the task content that the solution for the given equation; 7x+5(x-1)=-5+12x is to be determined.

Since the given equation is; 7x + 5 (x-1) = -5 + 12x

Hence, by the distributive property; we have that;

7x + 5x - 5 = -5 + 12x

12x - 5 = 12x - 5

On this note, since both sides of the equation are same, it follows that the equation has infinitely many solutions.

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The solution for h according to the given equation a = bh as required is; h = a / b.

It follows from the task content that the solution for the given equation for variable, h be determined.

On this note, since the given equation is;

a = bh

To solve for variable, h; divide both sides of the equation by b so that we have;

h = a / b.

Ultimately, the required solution for variable, h is; h = a / b.

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Answer:

the distance between (4,-2) and (0,4) is √(52) or approximately 7.2 units.

Step-by-step explanation:

To find the distance between two points in a Cartesian coordinate plane, we can use the distance formula:

distance = √((x2-x1)² + (y2-y1)²)

In this case, the two points are (4,-2) and (0,4). So,

x1 = 4, y1 = -2 and x2 = 0, y2 = 4

By substituting these values in the distance formula, we get:

distance = √((0-4)² + (4-(-2))²)

distance = √((-4)² + 6²)

distance = √(16 + 36)

distance = √(52)

So the distance between (4,-2) and (0,4) is √(52) or approximately 7.2 units.

Answer: D. 0.70

Step-by-step explanation:

42/60= 0.7

At 95% confidence level, the proportion will be between .0.19912815 and 0.200086, when you have a mean of 0.2 and a standard error of 0.00053.

How do you calculate population proportion?

P′ is equal to x / n, where x is the total number of successes and n is the sample size. As a point estimate for the genuine population proportion, the variable p′ represents the sample proportion.

FPC = (N-n)/(N-1), where Z/2 is the critical value of the Normal distribution at /2, p is the sample proportion, n is the sample size, and N is the size of the population (for example, at a confidence level of 95%, is 0.05 and the critical value is 1.96).

A portion of a population that possesses a certain characteristic, given as a percentage, fraction, or decimal of the entire population. The population percentage for a finite population is equal to the population's size divided by the proportion of its members who possess a given attribute.

Given data :

p = 60 / 300 = 0.2

q = 1 - p = 0.8

mean proportion = p = .2

standard error = sqrt(p * (1-p / 300) = sqrt(0.2 * 0.8/ 300) =0.00053333333

critical z-score at 95% confidence level is plus or minus 1.645.

use the z-score formula to find the critical raw score.

for the low side, z = (x - m) / s becomes:

-1.645 = (x - 0.2) / 0.00053

solve for x to get:

x = -1.645 * 0.00053 + 0.2 = 0.19912815

for the high side, z = (x - m) / s becomes:

1.645 = (x - 0.2) / 0.00053

solve for x to get:

x = 1.645 * 0.00053 + 0.2 = 0.200086125

At 95% confidence level, your proportion will be between .0.19912815 and 0.200086, when you have a mean of 0.2 and a standard error of 0.00053.

Here's what it looks like on a z-score normal distribution calculator output.

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Based on this information, the conclusion about weight and calories burned per minute that is true is: D. For each additional pound of weight, calories burned per minute increases by 0.05 calories.

In Mathematics, the slope-intercept form of a line can be represented or modeled by using this linear equation:

y = mx + c

Where:

Based on the information provided about the data for weight (in pounds) and calories burned per minute, a regression equation that models the situation is given by:

ŷ = 2.2 + 0.05x

Where:

In conclusion, we can logically deduce that the amount of calories burned per minute increases by 0.05 calories for each additional pounds of weight.

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Complete Question:

a.) For each additional pounds of weight, calories burned per minute increases by 2.2 calories.

b.) For each additional pounds of weight, calories burned per minute stays relatively the same.

c.) For each additional pounds of weight, calories burned per minute decreases by 0.05 calories.

d.) For each additional pounds of weight, calories burned per minute  increases by 0.05 calories.

The above equation's midpoint is represented by the expression Midpoint = (3.5,2,2) (1.5,-4.8). ( 2.5,-1.3 )

Midpoint =( 2.5,-1.3 )

The formula for determining the midpoint is

[tex]$\left(x_m, y_m\right)=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$[/tex]

[tex]$\left(x_m, y_m\right)=$[/tex]the midpoint's coordinates

[tex]$\left(x_1, y_1\right)=$[/tex] the first point's coordinates

[tex]$\left(x_2, y_2\right)=$[/tex] the second point's coordinates

Divide the distance between the two endpoints by 2, then multiply it by 3. The middle of that line is at these distances from each end. As an alternative, multiply the sum of the two endpoints' x coordinates by 2. For the y coordinates, repeat the process. the location on a line when the distances to both ends are equal. a period of time midway between the start and finish of an event.

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For the first graph, the function is increasing when the graph is sloping upwards, which is the case between the points (-1,1) and (1,3). For the second graph, the function is increasing when the graph is sloping upwards, which is the case between the points (0,2) and (2,4).

For the first graph, the function is increasing from interval (-1,1) and decreasing from interval (1,3).

For the second graph, the function is increasing from interval (0,2) and decreasing from interval (2,4).

For the first graph, the function is increasing when the graph is sloping upwards, which is the case between the points (-1,1) and (1,3). This indicates that the function is increasing on the interval (-1,1). Similarly, the function is decreasing when the graph is sloping downwards, which is the case between the points (1,3) and (3,1). This indicates that the function is decreasing on the interval (1,3).

For the second graph, the function is increasing when the graph is sloping upwards, which is the case between the points (0,2) and (2,4). This indicates that the function is increasing on the interval (0,2). Similarly, the function is decreasing when the graph is sloping downwards, which is the case between the points (2,4) and (4,2). This indicates that the function is decreasing on the interval (2,4).

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Taking w as the unknown number, the equation for the given statement is 2(w-8) = 5.

To solve this problem, we need to convert the given statement in mathematical form.

We assume that "w" is the unknown number in the equation.

First, we have to take a closer look at the given statement. It was stated that "twice the different of...  is equal to 5".  It shows that the result of equation 5 is the double value of another equation. We assume the unknown equation as y. Then:

2y = 5

Next, the rest of the statement stated that "a number and 8". From this part of statement, we know that the unknown equation "y" we assume above should be replace with "w-8". Hence:

2(w - 8) = 5

If we want to solve this question, we can solve it by dividing both sides with 2:

2(w - 8) = 5

------------------- : 2

w - 8 = 5/2

w = 5/2+ 8

w = 10.5

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Answer:

The company's largest rug dimensions are either 18 ft by 27 ft Or 12 ft by 18 ft.

Step-by-step explanation:

Given:

Dimension of the smaller rug are 2 ft by 3 ft.

Also One side of the largest rug is 18 ft.

We need to find the possible dimension of largest rug.

Also Given:

Both the smaller rug and larger rugs are similar.

Now By Similar rectangles property which states that;

"When 2 rectangles are similar then their lengths are in proportion."

In this case there are 2 possibilities.

either the largest rug's 18 ft side is similar to the 2 ft side or the 3 ft side

Now let us consider the other side be 'x'.

Now when he largest rug's 18 ft side is similar to the 2 ft side we get;

Now when he largest rug's 18 ft side is similar to the 3 ft side we get;

Hence the company's largest rug dimensions are either 18 ft by 27 ft OR 12 ft by 18 ft.

Since Zach isolated x^2 in the first equation and then substituted it into the second equation, the resulting equation is equal to: C. 25 - y^2/16 - y^2/9 = 1.

In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more quantities are equal.

From the information provided above, we have the following system of equations;

x^2 + y^2 = 25 ....... equation 1.

x^2/16 - y^2/9 = 1   ....... equation 2.

By making x^2 the subject of formula in equation 1, we have the following:

x^2 = 25 - y^2     ....... equation 3.

By substituting equation 3 into equation 2, we have the following:

25 - y^2/16 - y^2/9 = 1

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The sampling distribution is approximately normal.

What is the standard deviation?

Standard Deviation is calculated by first squaring the differences between the observations and the mean and then taking the square root of the sum of the squares of the differences divided by the number of observations - 1.

The Central Limit Theorem tells us that the sampling distribution for the population proportion is approximately normal.

The mean of the sampling distribution is equal to the true population proportion and the standard deviation of the sampling distribution is equal to the true population proportion times (1 - true population proportion) divided by the sample size.

So, the sampling distribution is approximately normal, with the true population proportion as its mean and the true population proportion times (1 - true population proportion) divided by the sample size as its standard deviation.

Hence, the sampling distribution is approximately normal.

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In part a, since the population mean  is small, selections are independent and can be assumed to be so. In part b, the population size is too large for selections to be independent, so independence can not be assumed.

a. If mathematics departments had only four recent graduates total, the chance that the sample will consist of two graduates who intend to teach high school is

0.5 * 0.5

= 0.25.

b. If mathematics departments had 10 million recent graduates, the chance that the sample will consist of two graduates who intend to teach high school is

0.5 * 0.5

= 0.25.

c. The selections are technically independent in part a, since the population size is small enough that the selection of one person will not affect the probability of selecting the other person. The selections are not technically independent in part b, since the population size is so large that selecting one person affects the probability of selecting the other person. In part a, you can assume independence since the population size is small enough that it is reasonable to assume that the selections are independent. In part b, you cannot assume independence since the population size is too large to make this assumption.

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The result of the convolution integral is the same as the solution obtained in part (a).

a. Solving the ODE with y(0) = 0 using integrating factors,

multiplying both sides of the equation by e^4t, we get

e^4t y' + 4e^4t y = 4e^-te^4t

Integrating both sides,

∫ (e^4t y' + 4e^4t y) dt = ∫ 4e^-te^4t dt

Therefore,

e^4t y = ∫ 4e^-te^4t dt + C

Since y(0) = 0, C = 0,

y = 1/4 ∫ 4e^-te^4t dt

Using integration by parts,

y = 1/4 [te^-t + 4/3 e^-t]

Therefore,

y(t) = 1/4 [te^-t + 4/3 e^-t]

b. The transfer function of the system is given by

H(s) = Y(s)/F(s) = 1/4s/(s+4)

c. The impulse response of the system is given by

h(t) = L^-1[H(s)] = 1/4e^-t

d. The convolution integral (h*f)(t) can be evaluated as follows,

(h*f)(t) = ∫ h(t-w)f(w)dw

= ∫ 1/4e^-(t-w) 4e^-w dw

= 1/4 ∫ 4e^-(t+w) dw

= 1/4 [te^-t + 4/3 e^-t]

The result of the convolution integral is the same as the solution obtained in part (a).

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The bookstore has 30 copies of books left after they sold (4/7)th today.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A bookstore had 84 copies of a magazine.

Yesterday it sold 1/6 of them which is, (84 - (1/6)×84).

= 84 - 14 books remaining.

= 70 books remaining.

Today it sold 4/7 of what remaining which is,

= (70 - (4/7)×70).

= 70 - 40.

= 30 books.

So, Now the bookstore has 30 books left.

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Answer:

6 days

Step-by-step explanation:

12 workers will clean up in 4 days

how many days would it take 8 workers?

let the number of days be x

x=(12×4)/8

x= 6 days

Answer:The t-intercept of a function is the point at which the function crosses the t-axis. To find the t-intercept of the function A(t) = 14,820 - 247t, we need to find the value of t when A(t) = 0. Setting A(t) = 0 and solving for t, we get:

14,820 - 247t = 0

t = (14820/247)

The t-intercept of the function is 60 months, which means that after 60 months (or 5 years) the amount owed on the car will be $0.

The y-interval of a function is the point at which the function crosses the y-axis. To find the y-intercept of the function A(t) = 14,820 - 247t, we need to find the value of A(t) when t = 0.

At t = 0, A(t) = 14,820 - 247(0) = 14,820.

The y-intercept of the function is $14,820 which means that before making the first payment, the cost of the car including tax and interest is $14,820.

Step-by-step explanation:

Numbers written from 30 to 65 including 30 and 65 = 36 numbers

A number is a basic component of mathematics. Numbers are used for counting, measuring, keeping things in order, indexing, etc. We have different types of numbers based on their properties such as natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc.

Given,

Numbers 30 to 65

30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65

Total count of numbers 30 to 65 = 36

Hence, 36 numbers are written from 30 to 65 including 30 and 65.

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The value of the expression 59 + (1/6)r at r = - 1/2 will be 707/12.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 59 + (1/6)r

The value of the expression at r = - 1/2 will be given as,

⇒ 59 + (1/6)(-1/2)

⇒ 59 - 1 / 12

⇒ (708 - 1) / 12

⇒ 707 / 12

The value of the expression 59 + (1/6)r at r = - 1/2 will be 707/12.

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The decimal representation of 1/70000000 is 0.0000000142857142857....

In math, what is a fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To find the digit that occurs in the 2023rd place after the decimal point, we can use long division to divide 1 by 70000000 and track the remainders.

Since the decimal representation of 1/70000000 is repeating every 6 digits, we can find the digit at the 2023rd place by taking the remainder when 2023 is divided by 6.

2023 % 6 = 1

So the digit in the 2023 place is the first digit after the repeating decimal, which is 4.

Therefore the digit in the 2023rd place after the decimal point is 4.

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It will take approximately 270.28 minutes, or 4 hours and 30.28 minutes, to fill the reservoir at a rate of 250 gallons per minute.

we can use the formula:

time = volume ÷ flow rate

where volume is the capacity of the reservoir in cubic feet and flow rate is the rate at which the reservoir is filled in cubic feet per minute.

Since the capacity of the reservoir is given in cubic feet and the flow rate is given in gallons per minute, we need to convert the flow rate to cubic feet per minute. One gallon is equal to 0.133681 cubic feet, so:

250 gallons/minute x 0.133681 cubic feet/gallon = 33.342 cubic feet/minute

So the flow rate in cubic feet per minute is 33.342. Now we can calculate the time it takes to fill the reservoir:

time = 9000 cubic feet ÷ 33.342 cubic feet/minute = 270.28 minutes

So it will take approximately 270.28 minutes, or 4 hours and 30.28 minutes, to fill the reservoir at a rate of 250 gallons per minute.

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the height from B to c is 54.95 feet and B to D is 35.01 feet and the height of the steeple is 19.94 feet.

at a point 50 feet from the base of a church, the angle of elevation to the bottom of the steeple and top of steeple are 35 and 47 40' respectively.

We need to find out the height of steeple.

observe the right-angle triangle corresponding to the given problem,

let find the height from the point B to the point D.

the angle of elevation =35

we know about the trigonometric representation of the function tan is.

[tex]tan\theta=\frac{opposite}{adjacent}[/tex]

observing the right-angle triangle ABD as we know

angle =35, adjacent =50 and the opposite leg is x,

[tex]tan35=\frac{35}{50} \\\\x=50tan35\\\\x=35.01 feet[/tex]

now let's find the height from B to C.

angle 2=47°40'

[tex]\theta2=47+\frac{40}{60} \\\\\theta=47.7\\\\now, tan47.7=\frac{y}{50} \\\\y=54.95 feet\\[/tex]

therefore the height of steeple is 54.95-35.01=19.94 feet.

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Mean Absolute Deviation (MAD) is a measure of accuracy for a forecasting model.

It measures the average distance between the actual value and the predicted value, and can be calculated using the following formula: MAD = 1/n * Σ |Ai-F i |, where n is the number of data points, Ai is the actual value, and Fi is the forecasted value. MAD is often used to compare the accuracy of different forecasting models. A lower MAD value indicates that the model has a better accuracy in predicting future values. Additionally, MAD can also be used to measure the accuracy of a single forecasting model over time. If MAD increases, then the accuracy of the forecasting model is decreasing.

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