Write each set of fractions with the lowest common denominator and then find which fraction is greater. 4/7 and 5/8 3/8 and 4/9 5/6 and 7/8 3/10 and 4/15

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].

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:

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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the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D) is 0.557

Step-by-step explanation:

Here  we have ,A bag contains 52 balls lettered from a to z and A to Z (i.e. uppercase or lowercase letters). One ball is withdrawn. We need to find What is the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D)? Let's find out:

There are 26 lowercase letters and 26 uppercase letters  ! According to question we need to choose a ball which is either a lowercase ( i.e. from 26 letters ) or earlier in the alphabet than d ( or D ) which is A or B or , C  .

Probability = (Favorable outcome)/(Total outcome)

Favorable outcome = 26+3=29

Total Outcome = 52

So ,

⇒ [tex]Probability = \frac{29}{52}[/tex]

⇒ [tex]Probability = 0.557[/tex]

Therefore ,  the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D) is 0.557

Final answer:

To calculate the probability of drawing a ball that is lower case or earlier in the alphabet than 'd', we count the number of qualifying balls (29) and divide by the total number (52), resulting in a probability of 29/52.

Explanation:

The student's question is about calculating the probability of drawing a ball from a bag that either contains a lower case letter or a letter that comes earlier in the alphabet than the letter 'd'. Given that the bag contains 52 balls, with each letter of the alphabet represented in both upper and lower case, we can calculate the probability by counting the number of balls that satisfy the condition and dividing by the total number of balls.

There are 3 letters in the alphabet before 'd' (‘a’, ‘b’, and ‘c’) and each comes in two forms (upper and lower case), so there are 3 * 2 = 6 balls that meet the 'earlier in the alphabet than d' criterion. Since there are 26 letters in the alphabet and each has a lower case form, there are 26 balls that are lower case.

To avoid double-counting the lower case balls ‘a’, ‘b’, and ‘c’, we subtract those 3 balls from the 26 lower case balls, resulting in 23. Adding these 23 to the 6 balls already counted, we have a total of 29 balls that satisfy either condition. The probability is therefore 29/52.

Answer:

A and D

Step-by-step explanation:

Answer:

The answer is A and D

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:

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:

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

Answer:

  434,470 gallons

Step-by-step explanation:

The exponential equation for the volume v remaining after t hours can be written as ...

  v(t) = (initial amount)×(decay factor)^(t/(decay time))

  v(t) = 500,000×(1 -10%)^(t/3)

Then after 4 hours, the remaining volume is ...

  v(4) = 500,000×(0.90^(4/3)) ≈ 434,470 . . . . gallons

_____

Comment on the form of the equation

The decay factor is related to the decay rate by ...

  decay factor = 1 - (decay rate)

and the decay time is the time applicable to that decay rate. Here, the rate is 10% every 3 hours, so the decay time is 3 hours for a decay rate of 10%.

Answer:

-5/4

Step-by-step explanation:

change in y/change in x

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

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

-----------

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:

  x^2 + y^2 -2x +y -71 = 0

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is ...

  ((-3, -8) +(5, 7))/2 = (-3+5, -8+7)/2 = (1, -1/2)

The square of the radius of the circle can be found from the Pythagorean theorem. The x- and y- differences between an end point and the center are the legs of a right triangle with r as the hypotenuse.

  r^2 = (5 -1)^2 +(7 -(-1/2))^2 = 4^2 +7.5^2 = 16 +56.25

  r^2 = 72.25

__

The standard form equation of the circle with center (h, k) and radius r is ...

  (x -h)^2 +(y -k)^2 = r^2

  (x -1)^2 +(y -(-1/2))^2 = 72.25

Eliminating parentheses, we have ...

  x^2 -2x +1 +y^2 +y +0.25 = 72.25

Subtracting the right-side constant and rearranging to descending powers, we find the general form of the equation to be ...

  x^2 + y^2 -2x +y -71 = 0

_____

Comment on the work

Of course, you know that ...

  (a -b)^2 = a^2 -2ab +b^2

This helps you simplify the squares of binomials.

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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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!! :)

Answer:x= -54.7

Step-by-step explanation:

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

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.

Answer:

the correct A

Step-by-step explanation:

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

Step-by-step explanation:

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: 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

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.

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:

-4

Step-by-step explanation:

- - - - - - - -

+ + + +

4 negatives cancel out and leave you with -4

The answers is -8 + 4 = -4

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:

0.123

Step-by-step explanation:

Use the random variable E - S, which will follow a normal distribution with a mean of 70 - 60 = 10 and SD = \sqrt{5^2+7^}

P(E - S < 0) = 0.123

The probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.

Normally distributed data is the distribution of probability which is symmetric about the mean.

The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean and standard deviation,

[tex]\mu_S= 60[/tex]

[tex]\sigma_S = 5[/tex]

The number of miles that the extended life tires last has a mean and standard deviation,

[tex]\mu_E = 70[/tex]

[tex]\sigma_E = 7[/tex]

Use the E-S random variable rule,

[tex]E=\mu_E-\mu_s\\E=70-60\\E=10[/tex]

Similarly, the value of S,

[tex]E=\sqrt{\sigma^2_E+\sigma^2_s}\\S=\sqrt{7^2+5^2}\\S=\sqrt{49+25}\\S=\sqrt{74}\\S=8.60[/tex]

For this E-S value, the value of probability from the table of normal distribution, we get as 0.123.

[tex]P(E - S < 0)=0.123[/tex]

Thus, the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.

Learn more about the normally distributed data here;

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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:

.

Step-by-step explanation:

(3x-4)(x+9)

you can continue doing it :)

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.