Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph slower than Cynthia's. At the end of one hour, they are 70 miles apart. Find Cynthia's average speed. (Round your answer to the nearest tenth.)

Part A

Sue

A = P*(1+r/n)^(n*t) is the compound interest formula

A = 2300*(1+0.024/1)^(1*3)

A = 2469.6061952

A = 2469.61

A - P = 2469.61-2300 = 169.61

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Bill

A = P*(1+r/n)^(n*t)

A = 1800*(1+0.034/1)^(1*3)

A = 1989.9131472

A = 1989.91

A-P = 1989.91-1800 = 189.91

Bill has earned more in interest.

=====================================================

Part B

By year 2, Bill has 1924.48 pounds in his account based on the work shown below

A = P*(1+r/n)^(n*t)

A = 1800*(1+0.034/1)^(1*2)

A = 1924.4808

A = 1924.48

This amount is the new deposit, so to speak, when we change the interest rate. Now r = 0.034 changes to r = 0.04. We only go for one year so t = 1

A = P*(1+r/n)^(n*t)

A = 1924.48*(1+0.04/1)^(1*1)

A = 2001.4592

A = 2001.46

Bill has 2001.46 pounds in his account after 3 years if the interest rate for the 1234 account changes to 4% in the third year.

Now subtract off the original amount Bill deposited to get

2001.46-1800 = 201.46

For this scenario, Bill earns 201.46 pounds in interest.

Therefore, Bill has earned the most interest for both cases of the interest rate staying at 3.4% or changing to 4% for that third year.

Answer:

A) 3.9 dollars

B) 126.38 dollars

Step-by-step explanation:

Given that Denise Robb's account statement shows a $210.94 unpaid balance. With a periodic rate of 1.85%

The finance charge = 1.85/100 × 210.94 = 3.9 dollars

If She had new purchases of $341.22. The new balance will be

341.22 - ( 210.94 + 3.9 )

126.38 dollars

Answer:

Periodic Rate: $3.902 or $3.9

New Balance: $556.06

Step-by-step explanation:

To get the periodic rate, do 1.85/100 to get 0.0185 and then multiply that by the unpaid balance ($210.94). This gets you $3.902 or $3.9.

to ge the new balance, add everything together to get $556.06

I can guarantee this is all correct

Answer:

-4

Step-by-step explanation:

- - - - - - - -

+ + + +

4 negatives cancel out and leave you with -4

The answers is -8 + 4 = -4

Answer:

7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg

8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg

Step-by-step explanation:

Law of Cosines

[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.

Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.

7.

We use the law of cosines to find C.

[tex] 18^2 = 12^2 + 16^2 - 2(12)(16) \cos C [/tex]

[tex] 324 = 144 + 256 - 384 \cos C [/tex]

[tex]-384 \cos C = -76[/tex]

[tex]\cos C = 0.2[/tex]

[tex] C = \cos^{-1} 0.2 [/tex]

[tex] C = 78.6^\circ [/tex]

Now we use the law of sines to find angle A.

Law of Sines

[tex] \dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C} [/tex]

We know c and C. We can solve for a.

[tex] \dfrac{a}{\sin A} = \dfrac{c}{\sin C} [/tex]

[tex] \dfrac{12}{\sin A} = \dfrac{18}{\sin 78.6^\circ} [/tex]

Cross multiply.

[tex] 18 \sin A = 12 \sin 78.6^\circ [/tex]

[tex] \sin A = \dfrac{12 \sin 78.6^\circ}{18} [/tex]

[tex] \sin A = 0.6535 [/tex]

[tex] A = \sin^{-1} 0.6535 [/tex]

[tex] A = 40.8^\circ [/tex]

To find B, we use

m<A + m<B + m<C = 180

40.8 + m<B + 78.6 = 180

m<B = 60.6 deg

8.

I'll use the law of cosines 3 times here to solve for all the angles.

Law of Cosines

[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]

[tex] b^2 = a^2 + c^2 - 2ac \cos B [/tex]

[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]

Find angle A:

[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]

[tex] 8^2 = 18^2 + 12^2 - 2(18)(12) \cos A [/tex]

[tex] 64 = 468 - 432 \cos A [/tex]

[tex] \cos A = 0.9352 [/tex]

[tex] A = 20.7^\circ [/tex]

Find angle B:

[tex] b^2 = a^2 + c^2 - 2ac \cos B [/tex]

[tex] 18^2 = 8^2 + 12^2 - 2(8)(12) \cos B [/tex]

[tex] 324 = 208 - 192 \cos A [/tex]

[tex] \cos B = -0.6042 [/tex]

[tex] B = 127.2^\circ [/tex]

Find angle C:

[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]

[tex] 12^2 = 8^2 + 18^2 - 2(8)(18) \cos B [/tex]

[tex] 144 = 388 - 288 \cos A [/tex]

[tex] \cos C = 0.8472 [/tex]

[tex] C = 32.1^\circ [/tex]

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Switch sides

[tex]28+7x =14[/tex]

Subtract 28 from both sides

[tex]28+7-28=14-28[/tex]

Simplify

[tex]7x=-14[/tex]

Divide both sides by 7

[tex]\frac{7x}{7} = \frac{-14}{7}[/tex]

Simplify

[tex]x=-2[/tex]

Answer:

BC = 12 inches

Step-by-step explanation:

As the triangle is isosceles, we have that AE = CF and EB = FB

If we call AE by x, we have that EB = 2x, FB = 2x and CF = x

As E and D are points tangent to the circle, we have that AE = AD = x

As D and F are points tangent to the circle, we have that CD = CF = x

So if the perimeter is 32, we have that:

AE + EB + BF + FC + CD + DA = 32

x + 2x + 2x + x + x + x = 32

8x = 32

x = 4

The length of BC is equal BF + FC = 2x + x = 3x = 12 inches

Answer:x= -54.7

Step-by-step explanation:

-66.5-66.5= -133+ 78.3= -54.7

Answer:

A and D

Step-by-step explanation:

Answer:

The answer is A and D

Answer:

El tren tardo 0.82 minutos .

To calculate the travel time of the train, we subtract the departure time (07:34) from the arrival time (08:16), which equals 42 minutes. Thus, the duration of the train's journey is 42 minutes.

Calculating Travel Time:

The given problem is a straightforward task of subtracting the time the train left from the time it arrived at its destination. The train leaves at 07:34 and arrives at 08:16. To find out how long the journey took, we simply calculate the difference in time.

To perform the calculation, convert the times into a 24-hour format if they are not already. Since both times are in the morning, we just need to calculate the minutes. From 34 minutes past the hour to 60 minutes past the hour is 26 minutes. Then, there are an additional 16 minutes from 08:00 to 08:16. Add these two segments together to find the total duration of the trip.

The total duration is 26 minutes + 16 minutes = 42 minutes.

Therefore, it took the train 42 minutes to reach its destination.

Answer:

There is a 1/2 chance of getting tails on the coin and there is 3/8 chance of the spinner landing on red. hope this helps

Final answer:

To find the probability of "tails" on the coin, and the spinner landing on red, you should multiply the probability of getting tails (0.5) by the probability of landing on red (0.375), resulting in 0.1875 or 18.75%

Explanation:

The probability of a particular outcome in a compound event (two or more independent events happening together) is the product of the probabilities of the individual events. Tossing a coin has two possible outcomes: heads or tails, each with a probability of 0.5. Spinning a spinner with 8 equal regions, where 3 are red, gives a probability of landing on red as 3 out of 8, which simplifies to 0.375.

Therefore, the probability of getting "tails" on the coin and the spinner landing on red can be calculated by multiplying the probability of getting tails on the coin (0.5) by the probability of the spinner landing on red (0.375):

Probability(Tails and Red) = Probability(Tails) × Probability(Red)

Probability(Tails and Red) = 0.5 × 0.375

Probability(Tails and Red) = 0.1875 or 18.75%

Answer:

D. Kailey is not correct:  [tex]89.12 \times 10^5[/tex] is not written in scientific notation.

Step-by-step explanation:

We have been given that Kailey wrote 8,912,000 in scientific notation as [tex]89.12 \times 10^5[/tex]. We are asked to choose the statement that best describes Kailey's work.    

We know that to convert a number into scientific notation, we write the given number as product of two numbers. One factor is a number between 1 and 10, while the 2nd factor is power of 10.  

Upon looking at [tex]89.12 \times 10^5[/tex] , we can see that 1st factor is 89.10, which is greater than 10. This means that Kailey did not write 8,912,000 in scientific notation.

Therefore, option D is correct choice.

Answer:

d

Step-by-step explanation:

Answer:

314

Step-by-step explanation:

Answer:

314

Step-by-step explanation:

I got it right.

Answer

Given expression,

[tex](81x^2-25)\times \dfrac{6}{18x+10}[/tex]

We have to find the value of x for which the expression is undefined.

Simplifying the given expression

[tex]((9x)^2-5^2)\times \dfrac{3}{9x+5}[/tex]

[tex](9x-5)(9x+5)\times \dfrac{3}{9x+5}[/tex]

[tex]3(9x-5)[/tex]

On solving we can see that the expression is defined for all value of x.

After applying a 10% coupon and 12.75% sales tax, the total cost for one night at the Great Wolf Lodge is approximately $252.67.

To find the total cost for one night at the Great Wolf Lodge including a 10% discount and 12.75% sales tax, we first need to calculate the amount of the discount. Since the discount is 10% off, you would multiply the original cost of $249 by 0.10 to get $24.9. Then subtract this from the original cost to find the discounted cost: $249 - $24.9 = $224.1. Next, apply the 12.75% sales tax to the discounted cost. Multiply $224.1 by 0.1275 to get $28.5725. Add this to the discounted cost: $224.1 + $28.5725 = $252.6725. So, including the discount and sales tax, the total cost for one night would be approximately $252.67.

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To find the total cost for one night, calculate the discount, subtract it from the original price, calculate the sales tax, and add it to the discounted price.

To find the total cost for one night at the Great Wolf Lodge, you need to calculate the discount from the coupon and add the sales tax to the discounted room rate.

The total cost for one night at the Great Wolf Lodge, after applying the 10% discount and including the 12.75% sales tax, is $252.68.

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Answer:

.

Step-by-step explanation:

(3x-4)(x+9)

you can continue doing it :)

Answer:

A. [tex]7-3.25+4[/tex]

Step-by-step explanation:

Because [tex]5^2=5\times5=25[/tex], the expression [tex]7-3\times5^2+4[/tex] can be rewritten as [tex]7-3\times25+4[/tex].

The 7 in the tenth place is equal to 7 times the value on the right

Answer:

The volume is 58.64.

I hope this helps you out :)

Answer: 700.56

Step-by-step explanation:

A heptagon has 7 sides, therfore a regular heptagon will have 7 equal sides

n = 7 (number of sides)

s = 13.9 (length of each sides of the heptagon)

r = 14.4 (The apothem)

The area of the regular heptagon can be calculated by:

Area = ½ n × s × r

Area = ½ × 7 × 13.9 × 14.4

Area = 700.56 square units

Answer:

60.75

Step-by-step explanation:

Since he earns a 4.5% commission

you need to find 4.5% of $1,350

1350 x 0.045 = 60.75

The graph of y - 2g(x) - 1 is obtained by applying vertical stretching, reflection, and vertical translation to the original function g(x). The transformed points are (0, -1), (-2, -9), and (4, -5).

To draw the graph of y - 2g(x) - 1, we first need to understand the transformations applied to the original function g(x). The given coordinates (0, 0), (-2, -4), and (4, -2) correspond to points on the graph of g(x).

Now, consider the expression y - 2g(x) - 1. This involves subtracting twice the values of g(x) from y and then subtracting 1. This process suggests vertical stretching, reflection, and vertical translation.

Starting with the points on g(x), let's apply these transformations:

Vertical Stretching: The factor of 2 before g(x) indicates vertical stretching by a factor of 2.

Reflection: The subtraction of 2g(x) reflects the graph over the x-axis.

Vertical Translation: Finally, subtracting 1 shifts the graph downward by 1 unit.

Applying these transformations to the given points, we get the transformed coordinates: (0, -1), (-2, -9), and (4, -5).

Now, plot these transformed points on the graph. Connect the points smoothly to represent the new function y - 2g(x) - 1.

The length of minor arc AC is calculated by finding the proportion of the total circumference that the arc's angle represents. In this case, the length of minor arc AC is 3π units.

In circle geometry, the length of an arc (minor arc AC in this case) is proportional to the measure of its central angle. By knowing the central angle and the circumference of the circle, we can calculate the length of the arc. The formula for the circumference of a circle is 2πr, where r is the radius. In this case, AB is the radius, which equals to 15 units. So the circumference of the circle would be 2π * 15 = 30π units.

Now, the measure of the entire circle in terms of degrees is 360º. The measure of AC is given as 36º. Hence, minor arc AC is 36º out of the total 360º, which is (36/360) = 1/10. Therefore, the length of minor arc AC would be 1/10 of the total circumference.

Calculating the length of minor arc AC would be = 1/10 * 30π =  3π units.

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Answer:

Step-by-step explanation:

to find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.

Answer:

the correct A

Step-by-step explanation:

Answer: A) ABCD can be carried onto WXYZ using only dilation.

Step-by-step explanation:

4 2/3 cups of popcorn, 1 1/4 cups of peanuts, 1 1/3 cups of raisins, 3/4 cups of sunflower seeds

4 2/3 + 1 1/3 = 6

1 1/4 + 3/4 = 2

6 + 2 = 8 cups of trail mix total

8 / 5 = how much each friend gets

1 3/5

Each of Luis's friends get 1 3/5 cups of trail mix.

Hope this helps!! :)

Final answer:

The equation of the line that contains the point (-2,1) and has a slope of 4 is y = 4x + 9.

Explanation:

To find the equation of a line that contains a given point and has a given slope, you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). In this case, the given point is (-2,1) and the given slope is 4. Plugging these values into the point-slope form, we get y - 1 = 4(x - (-2)).

Simplifying the equation, we have y - 1 = 4(x + 2). To get the equation in slope-intercept form, solve for y by distributing 4 to both terms inside the parentheses: y - 1 = 4x + 8. Finally, move the constant term (-1) to the other side of the equation: y = 4x + 8 + 1. The equation of the line is y = 4x + 9.

Answer:

0.0499

Step-by-step explanation:

This is a binomial probability  function expressed as:

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\[/tex]

Given that n =8, and p(male)=1-0.6=0.4, the probability of at least 6 being male is calculated as:

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 6)=P(X=6)+P(X=7)+P(X=8)\\\\={8\choose 6}0.4^6(0.6)^{2}+{8\choose 7}0.4^7(0.6)^{1}+{8\choose 8}0.4^8(0.6)^{0}\\\\=0.0413+0.0079+0.0007\\\\=0.0499[/tex]

Hence, the probability of at least 6 males is 0.0499

To find the probability of having at least 6 male students in a sample of 8 from a population where 40% are male, you need to calculate the sum of binomial probabilities for 6, 7, and 8 males.

In this problem, we are dealing with the subject of binomial probabilities. Given that 40% of the population are male students (100% - 60% = 40%), we need to find the probability that at least 6 out of 8 randomly selected students are male.

This involves calculating the binomial probability for 6, 7, and 8 males, and then adding them together.

The formula for binomial probability is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

Thus, the probability of getting at least 6 males would be calculated as the sum of the probabilities of getting exactly 6, 7, and 8 males. Before doing the calculations, keep in mind that we would use 0.4 for p (probability of picking a male student) and n=8 (the total number of sampled students).

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Answer:

1/2

Step-by-step explanation:

The first thing you want to do is get y by itself. Subtract 7 from both sides:

2x-4y=-7

and then subtract 2x ( the goal is to make your equation look like this: y=mx+b):

-4y= -2x-7

Now, y is mostly isolated, all you have to do now is divide both sides by -4 in order for y to be completely by itself:

y=-2/-4x -7/-4

Simplify completely:

y=1/2x+7/4

Now you have your equation you can easily read it as y=mx+b.

** m is slope & b is the y-intercept**

So your slope would be: 1/2

Answer:

-5/4

Step-by-step explanation:

change in y/change in x