A man went into a bank to cash a check. In handing over the money the cashier, by mistake,
gave him dollars for cents and cents for dollars. He pocketed the money without examining it,
and spent a nickel on his way home. He then found that he possessed exactly twice the amount
of the check. He had no money in his pocket before going to the bank. What was the exact
amount of that check?

Answer:

The sale price of a T-shirt is $24.

Step-by-step explanation:

1/4 off=25%=0.25

0.25*32=8

32-8=24

Answer:

Part 40) [tex]y=-2x+9[/tex]

Part 41) [tex]y=5x+6[/tex]

Part 42) [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Step-by-step explanation:

Remember that

If two lines are parallel, then their slopes are the same

Part 40) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (4,1)

Given line y=-2x+7

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=-2[/tex]

step 2

Find the y-intercept b

we have

[tex]m=-2[/tex]

[tex](4,1)[/tex]

substitute in the linear equation

[tex]1=(-2)4+b[/tex]

solve for b

[tex]b=1+8[/tex]

[tex]b=9[/tex]

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=-2[/tex]

[tex]b=9[/tex]

substitute

The equation of the line is

[tex]y=-2x+9[/tex]

Part 41) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (0,6)

Given line y=5x-3

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=5[/tex]

step 2

Find the y-intercept b

[tex]b=6[/tex] ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=5[/tex]

[tex]b=6[/tex]

substitute in the linear equation

[tex]y=5x+6[/tex]

Part 42) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (-5,-2)

Given line y=(2/3)x+1

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=\frac{2}{3}[/tex]

step 2

Find the y-intercept b

we have

[tex]m=\frac{2}{3}[/tex]

[tex](-5,-2)[/tex]

substitute in the linear equation

[tex]-2=(\frac{2}{3})(-5)+b[/tex]

solve for b

[tex]-2=-\frac{10}{3}+b[/tex]

[tex]b=-2+\frac{10}{3}[/tex]

[tex]b=\frac{4}{3}[/tex]

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=\frac{2}{3}[/tex]

[tex]b=\frac{4}{3}[/tex]

substitute

The equation of the line is

[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Final answer:

To find the equation of a line that is parallel to a given line and passes through a specific point, use the fact that parallel lines have the same slope. Find the slope of the given line, substitute the slope and the point into the slope-intercept form of a line to find the y-intercept, and write the equation with the new slope and y-intercept.

Explanation:

To find the equation of a line that is parallel to a given line and passes through a specific point, we need to use the fact that parallel lines have the same slope. The given line, y = -2x + 7, has a slope of -2. So, the parallel line we need to find will also have a slope of -2.

Now, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope is -2 and the point (4,1) lies on the line, we can substitute these values into the equation to find the y-intercept:

y = -2x + b

1 = -2(4) + b

1 = -8 + b

b = 9

Therefore, the equation of the line that passes through (4,1) and is parallel to y = -2x + 7 is y = -2x + 9.

Answer:

8/9hrs

Step-by-step explanation:

if 1/8 takes 1/9hrs

since there are 8 fractions , the entire package will take 1/9*8hrs

Answer:

x=-1, y=-5. (-1, -5).

Step-by-step explanation:

y=-x-6

y=x-4

----------

-x-6=x-4

-x-x-6=-4

-2x-6=-4

-2x=-4+6

-2x=2

x=2/-2

x=-1

y=-1-4

y=-5

Answer:

Step-by-step explanation:

Hajdiabndodisba djdk

Answer:

F, I’m not sure but i would go with F since you want the original cost or rather “c”, you want to divide that to get the $5.50 which it states that that’s the half price.

Answer:

Step-by-step explanation:

sale price = $5.50

(1/2) or 50% off the price.

let c = original price

c/2 = 5.50

c = $11

so the answer is F.

The only prime number that is a factor of 16 is 2, since 16 is a power of 2 (2⁴).

The student has asked to identify the only prime number that is a factor of 16. To find the factors of 16, we can break it down into its prime factors. The prime factorization of 16 is 2×4×4, which reduces further to 2×2×2×2 or 24. Since the prime factors of 16 are all 2s, the only prime number that is a factor of 16 is 2. It's important to note that a prime number is defined as a number that has exactly two distinct positive divisors: 1 and the number itself. In the case of 16, 2 is the only prime number that fits this definition and is a factor.

Answer:

-6

Step-by-step explanation: 2(n+5)=-2

Remove the bracket(expanding):

2×n+2×5=-2

2n+10=-2

collect like terms:

2n=-2+(-10)

2n=-12

Dividing both side by the coefficient of n i.e 2

2n/2=-12/2

n=-6

Answer:

30/10=10/3

Step-by-step explanation:

because 10/3 if you multiply 3 times 10 and keep 10 and switch it around you'll get 30/10

The mean score on this test is 8.8, and the median score is 9.4.

In order to find the mean of the scores, we use the formula:

[tex]\[ \text{Mean} = \frac{\sum (X \cdot f)}{N} \][/tex]

where X is the score, f is the frequency, and N is the total number of scores. Applying this formula to the given data:

[tex]\[ \text{Mean} = \frac{(4 \cdot 1) + (5 \cdot 1) + (6 \cdot 1) + (7 \cdot 2) + (8 \cdot 1) + (9 \cdot 5) + (10 \cdot 5)}{1 + 1 + 1 + 2 + 1 + 5 + 5} \][/tex]

[tex]\[ \text{Mean} = \frac{4 + 5 + 6 + 14 + 8 + 45 + 50}{15} \][/tex]

Mean = [tex]\frac{132}{15}[/tex]

Mean = 8.8

So, the mean score is 8.8.

To find the median using the formula:

[tex]\[ \text{Median} = L + \frac{\frac{N}{2} - F}{f} \times w \][/tex]

where:

- L is the lower class boundary of the median group,

- N is the total number of observations,

- F is the cumulative frequency of the group before the median group,

- f is the frequency of the median group,

- w is the width of the median group.

First, arrange the data and calculate cumulative frequencies:

Test Score  Frequency     Cumulative Frequency

3                    0                      0

4                      1                      1

5                      1                     2

6                       1                     3

7                       2                     5

8                       1                      6

9                       5                     11

10                     5                     16

The median position is [tex]\( \frac{N}{2} = \frac{16}{2} = 8 \)[/tex]  with a score of 9. The cumulative frequency before the median group is 6, and the frequency of the median group is 5.

Now, using the formula:

Median= 9 + [tex]\frac{8 - 6}{5} \times 1[/tex]

Median= 9 + [tex]\frac{2}{5}[/tex]

Median = 9 + 0.4

Median = 9.4

Therefore, the median score is 9.4.

Answer:

Step-by-step explanation:

1/6 and 1/13

Answer:

Your tip was $7.25 so you payed a total of $36.25 on your $29 bill.

Answer:

$36.25

Step-by-step explanation:

Multiply 29.00 by 0.25 to get 25% of 29.00. You would get 7.25. Then add the 25% tip to the dinner amount (29.00+7.25) and you would get 36.25.

Answer: She is earning $15 a week.

Step-by-step explanation:

Since she started with 50 dollars you need to subtract. So 140-50=90. Since she has been saving for 6 weeks, you need to divde, so 90÷6=15.

Answer:

B.

Step-by-step explanation:

This is only true if it is an isosceles trapezium so B is false.

Final answer:

The false statement is that the perpendicular bisector of the base of any trapezoid is always a line of symmetry. This is incorrect as only isosceles trapezoids, which have two non-parallel sides of equal length, are symmetrical in this way.

Explanation:

The statement that is FALSE is: B) The perpendicular bisector of the base of any trapezoid is always a line of symmetry. This statement is incorrect because a trapezoid, by definition, has only one pair of parallel sides, and not all trapezoids are symmetrical unless specified as an isosceles trapezoid. For instance, in irregular trapezoids where the non-parallel sides are of different lengths, the perpendicular bisector of the base does not act as a line of symmetry.

Moreover, statement C, which is true, specifies the conditions under which the perpendicular bisector of the base can be a line of symmetry - that is, in the case of an isosceles trapezoid. An isosceles trapezoid is specifically designed to be symmetrical along the perpendicular bisector of its bases, given its two non-parallel sides are equal in length, unlike general trapezoids.

Answer:

J

Step-by-step explanation:

All of the other ones have a value of -5 except for J which has a value of 5.

Answer:

  232 square feet

Step-by-step explanation:

The outside dimensions of the yard are 26 ft by 36 ft, so its total area is ...

  yard including walk = (26 ft)(36 ft) = 936 ft²

The dimensions of the yard inside the walkway are 22 ft by 32 ft, so that area is ...

  yard not including walk = (22 ft)(32 ft) = 704 ft²

The difference in these areas is the area of the walkway:

  walkway area = (yard including walk) - (yard not including walk)

  = (936 -704) ft² = 232 ft² . . . . area of the walk

_____

Another way to figure this is to consider the length of the centerline of the walkway. That is the perimeter of a rectangle that is 24 ft by 34 ft. The perimeter (centerline length) is 116 ft, and the width of the walk is 2 ft, so its area is ...

  (116 ft)(2 ft) = 232 ft²

Answer:

4 + x = 16

Step-by-step explanation:

In general, if we have an equation that has just one variable, such as x, then "solving the equation" means finding the set of all values that can be substituted for the one variable to produce a valid equation.

Isolate "x" on one side of the algebraic equation by adding the negative number that appears on the same side of the equation as the "x." For example, in the equation "x - 5 = 12", rewrite the equation as "x = 12 + 5" and solve for "x."

Answer:

aaaaaaaa

Step-by-step explanation:

Answer:

ionosphere

Step-by-step explanation:

In radio communication, skywave or skip refers to the propagation of radio waves reflected or refracted back toward Earth from the ionosphere, an electrically charged layer of the upper atmosphere

There are total 3500 students in the freshman class.

Radio waves are the electromagnetic radiations whose wave frequency lies in range of 10⁴ and 10¹¹ or 10¹² Hz. These waves are generally used in long distance communication.

Given is to find out which layer of the atmosphere reflects radio waves back to Earth.

None of the layers mentioned reflects radio waves back to Earth. Only the ionosphere reflects the radio waves back to Earth. It is a electrically conducting region extending between 80 km to 300 Km in altitude.

Therefore, there are total 3500 students in the freshman class.

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Answer:by $91

Step-by-step explanation:

In total she withdrew $91 for her piano lessons

22.75x4=91

Answer:

91$

Step-by-step explanation:

Answer:

120 ounces

Step-by-step explanation:

Answer:

y-2=2(x-6)

Step-by-step explanation:

y-y1=m(x-x1)

m=2

y-2=2(x-6)

Answer: (19,520-1,478) x 8

Answer:

[tex]59.19 ft^2[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=7.2\ ft[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]A=(3.14)(7.2)^{2}[/tex]

[tex]A=162.78\ ft^2[/tex]

step 2

we know that

The area of a circle subtends a central angle of 2π radians

so

using proportion

Find out the area of a sector with a central angle of 8 π/11 radians

[tex]\frac{162.78}{2\pi }\frac{ft^2}{rad} =\frac{x}{(8\pi/11)}\frac{ft^2}{rad} \\\\x=162.78(8/11)/2\\\\x=59.19\ ft^2[/tex]

Final answer:

The area of a sector with a central angle of 8π/11 radians and a radius of 7.2 ft, using 3.14 for π, is approximately 78.60 ft² when rounded to the nearest hundredth.

Explanation:

To calculate the area of a sector of a circle, we use the formula ½ θr², where θ is the central angle in radians, and r is the radius of the circle. For a sector with a central angle of ₈π/₁₁ radians and a radius of 7.2 ft, substituting 3.14 for π, we can find the area as follows:

Use the formula: Area = (½)(θ)(r²).

Substitute the given values to get: Area = (½)(₈π/₁₁)(7.2 ft)².

Calculating using 3.14 for π we get: Area = (0.5)*(8*3.14/11)*(7.2 ft)².

Simplify and calculate the result which gives us: Area = 78.5952 ft².

Round the final answer to the nearest hundredth: Area = 78.60 ft².

Answer:

106 slices left

Step-by-step explanation:

To solve this we need to multiply 19 and 6:

19 * 6 = 114

there was 114 slices of pizza

next subtract 114 and 8

114 - 8 = 106

there was 106 slices of pizza left after Miguel ate 8 slices of pizza

Final answer:

After calculating the total slices from 19 pizzas and subtracting the 8 slices consumed by Miguel, there are 106 pizza slices left for the rest of the French Club.

Explanation:

The student asked about the number of pizza slices left after Miguel ate some. To calculate this, we first need to find the total number of slices in 19 pizzas, each cut into 6 slices, and then subtract the 8 slices that Miguel ate.

Calculate the total number of slices: 19 pizzas × 6 slices/pizza = 114 slices.

Subtract the slices Miguel ate: 114 slices - 8 slices = 106 slices.

So, there are 106 pizza slices left for the rest of the French Club.

Answer:

y=8.99+3

Step-by-step explanation:

we will make

x=how many large pizzas are sold

and a flat fee of $3 because they did delivery and do not pick it up them selves

so it would look like this

y=8.99x+3 to find the total cost

and it's not

y=8.99x-3 because they are not getting $3 dollars off their purchase!

Answer:

0.54

Step-by-step explanation:

In Probability "OR" means "ADDITION" and "AND" means "MULTIPLICATION"

Here, we want probability of Jack "OR" Red, so we find individual probabilities and then "ADD" them.

There are 26 cards that are RED, half of the deck. So probability of RED CARD is:

P(red) = 26/52 = 1/2

Now, there are 4 Jacks in the whole deck, 2 red Jack and 2 black Jack. We already accounted for the 2 red jacks, so we have 2 black Jacks at hand. So

P(Jack) = 2/52 = 1/26

Now, we add the 2 probabilities:

P(jack or red) = 1/2 + 1/26 = 13/26 + 1/26 = 14/26 = 0.54 (rounded to 2 decimal places)

Answer:

a)  About 46.3 hours

b) About $1036.80

Step-by-step explanation:

a)

Break even means to make enough to cover her costs.

Given her cost is 1000, we need to find how many hours she will need to cover this up.

In 1 minute, she can type 90 words, that would pay her:

0.004 per word for 90 words = 0.004 * 90 = $0.36 per minute

Susan makes $0.36 per minute, so the amount of time (in minutes) it will take her to make $1000, is:

1000/0.36 = 2777.78 minutes

Converting that to hours, we divide by 60,

2777.78/60 = 46.3 hours

b)

4 hours per day for 3 days = 4 * 3 = 12 hours (per week)

Let there be 4 weeks in a month, so

12 hours per week * 4 = 48 hours per month

She will work 48 hours per month.

Given 90 words per minute, in 1 hour, she can type:

60 minutes * 90 = 5400 words per hour

In 48 hours, she can type:

5400 words per hour * 48 hours = 259,200 words

That would pay her:

0.004 per word for 259,200 words = 0.004 * 259,200 = $1036.80

92.004 = 92 + .004 = 92 + 4 = 92 + 1 = 92 1

                                            --            --      -----

                                         1,000       250   250

Answer:

[tex]\large\boxed{92.004=92\dfrac{4}{1000}=92\dfrac{1}{250}}[/tex]

Step-by-step explanation:

[tex]92.004=92+0.\underbrace{004}_{3}=92+\dfrac{4}{1\underbrace{000}_3}=92\dfrac{4}{1000}=92\dfrac{4:4}{1000:4}=92\dfrac{1}{250}[/tex]

The two numbers are -20 and -82. By creating two equations x + y = -102 and x = y - 62, substitute for x in the first equation and solve for y, then substitute y back into the second equation to solve for x.

To solve the problem, you can create two equations using the given information.

You can now substitute the equation from step 2 into equation 1:

(y - 62) + y = -102.

Combine like terms:

2y - 62 = -102.

Then add 62 to both sides of the equation:

2y = -40.

Finally, divide both sides by 2:

y = -20.

Substitute y = -20 back into x = y - 62:

x = -20 - 62 = -82.

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The graph that best represents the described temperature change is Graph A.

The description provided suggests a graph of temperature change over time.

In the morning, the temperature starts around 50°F, so the initial point on the graph would be at (0, 50). As the day progresses, the temperature rises first slowly and then more quickly, indicating a steeper slope.

After reaching a peak, the temperature stays constant for an hour, suggesting a flat line parallel to the x-axis.

Finally, the temperature drops slowly, indicating a decreasing slope.

Based on this description, Graph A represents the temperature change over the day.