A rental car company charges $71.87 per day to rent a car and $0.09 for every mile driven. Aaliyah wants to rent a car, knowing that: She plans to drive 475 miles. She has at most $320 to spend. Which inequality can be used to determine dd, the maximum number of days Aaliyah can afford to rent for while staying within her budget?

From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC

The two column proof to show that ∠BAC ≅ ∠DAC is as follows:

Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD

Reason 1: Given

Statement 2: AB ≅ AD

Reason 2:  Definition of isosceles Triangles

Statement 3: ∠1 and ∠2 are right angles

Reason 3: Definition of perpendicular

Statement 4: AC ≅ AC

Reason 4: Reflexive Property

Statement 5: ΔABC and ΔADC are right triangles

Reason 5: Definition of right triangle

Statement 6: ΔABC ≅ ΔADC

Reason 6: HL Congruency

Statement 7: ∠BAC ≅ ∠DAC

Reason 7: CPCTC

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Answer:

The solution is x = -15.

Step-by-step explanation:

4x - 5 = 0

Add 5 to both sides:

4x = 5

Divide both sides by 4:

x = 5/4

Therefore, the solution is x = 5/4.

3x - 1/2 = 0

Add 1/2 to both sides:

3x = 1/2

Divide both sides by 3:

x = 1/6

Therefore, the solution is x = 1/6.

1/3x + 5 = 0

Subtract 5 from both sides:

1/3x = -5

Multiply both sides by 3:

x = -15

Therefore, the solution is x = -15.

Step-by-step explanation:

4x-5=0

collect like terms,

4x=5

divide both sides by the coefficient of x, 4

4x/4 = 5\4

4 cancels out on the LHS,

we have x=5\4 as the answer

3x-1\2=0

collect like terms..

3x=1\2

since the RHS is a fraction ,we multiply both sides by 2

6x=1

divide both sides by 6

x=1\6

1\3x+5=0

collect lkke terms...

1\3x=-5

cross multiply, we have

-5(3x)=1

-15x=1

x=1/-15

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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For us to be able to determine the possible combinations of 4 number from the list of 5 numbers (12, 13, 14, 15, 16), we will be using the following formula:

Where,

n = total numbers of sample in the list = 5

k = selected numbers in the list = 4

We get,

Therefore, the answer is letter B.

209 history textbooks and 124 chemistry textbooks were sold.

Two or more expressions with an Equal sign is called as Equation.

Let h be number of history textbooks sold

Let c be the number of chemistry textbooks sold

The total number of textbooks sold is 333:

h + c = 333

The number of chemistry textbooks sold was 85 less than the number of history textbooks sold:

c = h - 85

h + (h - 85) = 333

Simplifying the equation, we get:

2h - 85 = 333

Adding 85 to both sides, we get:

2h = 418

Dividing both sides by 2, we get:

h = 209

Now c = 209 - 85 = 124

Therefore, 209 history textbooks and 124 chemistry textbooks were sold.

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The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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A third variable associated with two variables under study that results in a correlation between the two variables, falsely implying a causal relationship between the pair, is a) a lurking variable.

A lurking variable is an uncontrolled and unknown variable but significant effect on both independent and dependent variables.

A lurking variable creates a correlation between the independent and dependent variables without being intended by the researcher.

We can differentiate a lurking variable from a confounding variable.

A confounding variable is taken into account in research and can also influence the variables of interest but it is not credited with any relationship between the independent and dependent (response) variables.

Thus, the existence of a third variable resulting in a correlation between the independent and dependent variables is called a lurking variable.

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Answer:

free points ty

Number of People who knows the Code are 6401

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of People who kows the Code be x

Number of Peoplee who do not know the Code be y

According to the Question:

x + y = 7338 ----------(i)

2x + 5y = 17487 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 14676 ---------(iii)

Substracting Equation (iii) from Equation (ii)

3y = 2811

y = 937

This means x = 6401

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Megan sent  792 text messages in the month of October .

In the question ,

it is given that

Cost for first 600 messages = $15

additional text message charge = $0.05

Amount owed by Megan for the month of October = $24.60

Let the number of Additional messages be x.

So, according to the question

15 + 0.05x = 24.60

0.05x = 24.60-15

0.05x = 9.6

x = 9.6/0.05

x = 192

number of extra messages = 192

total messages = first 600 messages + extra messages

= 600+192

= 792

Therefore , Megan sent 792 text messages in the month of October .

The given question is incomplete , the complete question is

Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month ?

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Answer:

Step-by-step explanation:

To conduct ANOVA, we first need to calculate the sum of squares (SS) for each factor and for error.

SS(total) = SS(Treatment) + SS(Error)

We can calculate the means and sum of squares for each treatment group:

Treatment One: Mean = 4.5, SS = 3.15

Treatment Two: Mean = 3.43, SS = 5.727

Next, we can calculate the grand mean:

Grand Mean = (4.5 + 3.43) / 2 = 3.965

Using the grand mean, we can calculate the total sum of squares:

SS(total) = ∑(X-Grand Mean)^2 = 17.7175

Using the sum of squares for each treatment group and the total sum of squares, we can calculate the sum of squares for error:

SS(Error) = SS(total) - SS(Treatment) = 9.335

Next, we can calculate the degrees of freedom:

df(Treatment) = k - 1 = 2 - 1 = 1

df(Error) = N - k = 8 - 2 = 6

df(total) = N - 1 = 8 - 1 = 7

Now we can calculate the mean squares:

MS(Treatment) = SS(Treatment) / df(Treatment) = 3.15 / 1 = 3.15

MS(Error) = SS(Error) / df(Error) = 9.335 / 6 = 1.556

Using the mean squares, we can calculate the F-ratio:

F-ratio = MS(Treatment) / MS(Error) = 3.15 / 1.556 = 2.022

To find the p-value, we need to compare the F-ratio to the F-distribution with (1, 6) degrees of freedom. Using a significance level of 0.05, we find that the critical F-value is 5.143. Since our F-ratio is less than the critical F-value, we fail to reject the null hypothesis.

Therefore, the results of the ANOVA suggest that there is not enough evidence to conclude that the means of the two treatment groups are significantly different.

Now we can conduct a t-test to compare the means of the two groups:

t = (mean1 - mean2) / (s / sqrt(n))

where mean1 and mean2 are the sample means, s is the pooled standard deviation, and n is the sample size.

Using the given data, we can calculate the sample means and standard deviations for each group:

Treatment One: Mean = 4.5, s = 0.72

Treatment Two: Mean = 3.43, s = 1.45

Using the pooled standard deviation formula, we can calculate the pooled standard deviation:

s = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2)) = sqrt(((7 * 0.72^2) + (7 * 1.45^2)) / (14 - 2)) = 1.074

Using the means, pooled standard deviation, and sample sizes, we can calculate the t-statistic:

t = (4.5 - 3.43) / (1.074 / sqrt(7)) = 2.046

To find the p-value, we need to compare the t-statistic to the t-distribution with (6) degrees of freedom. Using a significance level of 0.05 and a two-tailed test, we find that the critical t-value is approximately

Answer:

The answer would be -1

Step-by-step explanation:

Slope = ∆y/∆x

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

y2=3

y1= 7

x2=2

x1= -2

= (3-7)/(2--2)

= -4/(2+2)

= -4/4

= -1

Answer:

nn

Step-by-step explanation:

D. I and IV are the quadrants the cosine function is positive

To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.

The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.

Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.

Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.

Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.

It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.

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The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer:

it looks like the answer is the second one and makes more sense

Using the "fives fact" (5 x 6 = 30) as a starting point, we added one more group of 6 to reach the final result of 36.

To use the "fives fact" to solve 7 x 6, we can break it down into simpler calculations using the fact that 5 x 6 = 30.

Here's the step-by-step calculation:

1. Start with the "fives fact": 5 x 6 = 30.

2. Since we need to find 7 x 6, we can add another 6 to the result of 5 x 6:

  30 + 6 = 36

Therefore, 7 x 6 equals 36.

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Answer:

-2x + 9

Step-by-step explanation:

-2(x - 7) + (-5)

-2x + 14 -5

-2x + 9

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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Answer:

new area = 7m (length) x 4m (width) = 28; an increase of 12 sq meters

Step-by-step explanation:

Original area must have been 16 because both the length and width were 6 meters.

175% of 16 is 12, meaning the length must be increased from 4 to 7 to get 28 when multiplied by a width of 4m

The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)

= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

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Answer:

a. Weekly gross pay = $300

b. Federal taxes, F = $30

c. Fica taxes, K = 22.95

d. State taxes, S = $9

e. Weekly net pay =  238.05

Step-by-step explanation:

Gross pay, G = 15 $/h * 20 h = 300 / week

Fed taxes, F = 10%*G = $30

FICA, K = 7.65%*G = $22.95

State taxes, S = 3%*G = $9

a. Weekly gross pay = $300

b. Federal taxes, F = $30

c. Fica taxes, K = 22.95

d. State taxes, S = $9

e. Weekly net pay = 300 - (30+22.95+9) = 300 - 55.95 = 238.05

Answer:

X = 32

Step-by-step explanation:

Angle BEC = 43 degrees

You find X by setting up the equation 137 = 3x+41

Solve for x

You find angle BEC by subtracting 137 from 180, finding the acute angle that brings the obtuse angle up to 180 degrees (a flat line)

Answer:

x = 32 degree and angle BEC = 43 degree

Step-by-step explanation:

3x + 41 = 137 degree (being vertically opposite angles)

3x = 137 - 41

x = 96/3

x = 32

angle BEC be y

137 + y =180 degree (being linear pair)

y = 180 - 137

y = 43 degree

therefore angle BEC = 43 degree

Answer:

1/6

Step-by-step explanation:

1/2 1/3

lcd(least common denomitator)=6

there fore it is 1/6

Answer:

Graph is below.

Step-by-step explanation:

The solutions of the equations are : x = [8 ± √ 40] / 4

Given,

Y=2x² - 8x+3

Now,

To get the solution of equation equate it to 0 .

2x² - 8x+3  = 0

By quadratic formula,

x = -b ± √ b² - 4ac/2a

Substitute the values in the formula,

x = [8 ± √ 64 - 4(2)(3)] / 2* 2

x = [8 ± √ 40] / 4

Now plot the points in the graph. The graph is attached below.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the formula :

Pn = 25.8(1.0219)^h to predict the population of Ghana ;

The equation given is in the form of an exponential function:

The general form of an exponential distribution :

y = ab^x

a = Initial value ; b = constant multiplier or growth or Decay factor

Comparing :

The number in parenthesis = 1.0219 = b

b = Decay or growth factor :

Since b > 1 ; then We have a growth factor;

b = 1 + rate

1.0219 = 1 + rate

Rate = 1.0219 - 1

Rate = 0.0219

Hence, the population is growing at a rate of about (0.0219)*100% = 2.19%

Answer:

b option im not sure but

Step-by-step explanation:

The number of watts will be 4700 watts to the nearest 100 watt.

It should be noted that 1 watt equals to 3.41 Btu per hour.

In this case, the air conditioner is rated at 16000 BTU per hour.

Therefore, the number of watt will be:

= 16000/3.41.

= 4692

= 4700 watts to the nearest 100 watt.

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Answer:

The optimal production quantity is 9,322 cards.

Step-by-step explanation:

The information provided is:

Cost of the paper = $0.05 per card

Cost of printing = $0.15 per card

Selling price = $2.15 per card

Number of region (n) = 4

Mean demand = 2000

Standard deviation = 500

Compute the total cost per card as follows:

Total cost per card = Cost of the paper + Cost of printing

                                = $0.05 + $0.15

                                = $0.20

Compute the total demand as follows:

Total demand = Mean × n

                       = 2000 × 4

                       = 8000

Compute the standard deviation of total demand as follows:

\(SD_{\text{total demand}}=\sqrt{500^{2}\times 4}=1000\)

Compute the profit earned per card as follows:

Profit = Selling Price - Total Cost Price

         = $2.15 - $0.20

         = $1.95

The loss incurred per card is:

Loss = Total Cost Price = $0.20

Compute the optimal probability as follows:

\(\text{Optimal probability}=\frac{\text{Profit}}{\text{Profit+Loss}}\)

                               \(=\frac{1.95}{1.95+0.20}\\\\=\frac{1.95}{2.15}\\\\=0.9069767\\\\\approx 0.907\)

Use Excel's NORMSINV{0.907} function to find the Z-score.

z = 1.322

Compute the optimal production quantity for the card as follows:

\(\text{Optimal Production Quantity}=\text{Total Demand}+(z\times SD_{\text{total demand}}) \\\)

                                               \(=8000+(1.322\times 1000)\\=8000+1322\\=9322\)

Thus, the optimal production quantity is 9,322 cards.