Mary has two bags of sweets, each of which contains the same number of sweets. She eats four sweets. She then finds that she has 30 sweets left. How many sweets were in each bag to start with?

Answer: Speed of local bus is 50 mph  and speed of express bus is 75 mph

Step-by-step explanation:

let say speed of local bus = x

so speed of express bus = x + 25

Distance = Speed × Time

Distance traveled by local bus  = x × 10.2 = 10.2x

Distance traveled by express bus = (x + 25) × 6.8

since Distance traveled by local bus is same as Distance traveled by express bus

⇒10.2x = (x + 25) × 6.8

⇒ 10.2x = 6.8x + 170

⇒ 10.2x - 6.8x = 170

⇒ x = 170/3.4 = 50

So Speed of local bus = x = 50 mph

and Speed of express bus =  x + 25 = 50 + 25 = 75 mph

Final answer:

The speed of the local bus is 50 mph and the speed of the express bus is 75 mph.

Explanation:

Let's define the speed of the local bus as 'x'.

The speed of the express bus is 25 mph faster than the speed of the local bus, so the speed of the express bus can be represented as 'x + 25'.

We know that the time taken by the express bus is 6.8 hours and the time taken by the local bus is 10.2 hours.

Using the formula Speed = Distance / Time, we can set up two equations:

Distance / 6.8 = x + 25  (equation 1)

Distance / 10.2 = x  (equation 2)

Since the distance is the same for both buses (Sacramento to San Diego), we can equate the distances in equation 1 and equation 2:

x + 25 = (10.2/6.8) * x

x + 25 = 1.5x

0.5x = 25

x = 50

Substituting the value of x in equation 1, we can find the speed of the express bus:

Distance / 6.8 = (50 + 25)

Distance = 6.8 * 75

Speed of the express bus = Distance / 6.8 = 75

So, the speed of the local bus is 50 mph and the speed of the express bus is 75 mph.

Answer: The theoretical probability of choosing a tile with letter P =0.18

Step-by-step explanation:

Given word = MISSISSIPPI

Total number of letters in given the word = 11

Number of letter P in given word = 2

Let A be a event of choosing a tile with a letter P then

P(A) =Number of tiles with letter P / Total letters in given word

= 2 /11 = 0.18

The probability of choosing a tile with the letter P from the word 'Mississippi' is 1/11.

The probability of choosing a tile with the letter P can be calculated by determining the ratio of the number of P tiles to the total number of tiles.

In the word 'Mississippi', there is only 1 letter P. The total number of letters in 'Mississippi' is 11. Therefore, the probability of choosing a tile with the letter P is 1/11.

So, the theoretical probability of choosing a tile with the letter P is 1/11.

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To find the unit price of each item you want to divide:

Fresh water:

$1.76 / 16 = $0.11

Spring water:

$2.40 / 20 = $0.12

So the statement that is true is B) Fresh water has a lower unit price of $0.11/ounce.

Hope this Helps!!

I'm ASSUMING that we're talking about Three Ordered Ordered Pair Solutions.

If so, the answer is (0,−1),(1,2),(2,5).

The solution of equation are,

(0, - 1) ( 1, 2) and (2, 5)

We have to given that,

To find the solution of equation y = 3x - 1

Here, The equation is,

y = 3x - 1

Now, We can put x = 0 in above equation,

y = 3 (0) - 1

y = - 1

Put x = 1;

y = 3 (1) - 1

y = 3 - 1

y = 2

Put x = 2;

y = 3 (2) - 1

y = 6 - 1

y = 5

Thus, The solution of equation are,

(0, - 1) ( 1, 2) and (2, 5)

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ANSWER

The factory feels 65 bottles in one hour.

EXPLANATION

Total ounces processed in one hour.

[tex]=1,560[/tex]

Total ounces each bottle can take in one hour.

[tex]=24[/tex]

Number of bottles that can be filled in one hour

[tex]=\frac{1,560}{24}[/tex]

[tex]=65[/tex]

Therefore the factory fills 65 bottles in one hour.

yes rachel is correct.

1 yd=3 ft. 115*3=345 ft

345>327 so rachel is correct.

Hope this helps!

Yes, Rachel is correct.

What is Measurement unit?

A measurement unit is a standard quality used to express a physical quantity.

Given that;

Rachel says that she ran 115 yards.

And, She went farther then Beth who only ran 327 feet.

Since, 1 yards = 3 feet

Then, 115 yards = 115 × 3 feet

                        =345 feet

Now, Rachel ran 345 feet.

And, Beth run 327 feet.

Since, 345 > 327

Hence, Rachel went farther then Beth.

So, Rachel is correct.

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5(3 - x) - 4(2 - 3x) > 2

15 - 5x - 8 + 12x > 2        distributed 5 and 4 on the left side

              7 + 7x > 2         added like terms (15 and -8) and (-5x and 12x)

            -7           -7

                  7x > -5

                  [tex]\frac{7x}{7} > \frac{-5}{7}[/tex]

                   [tex]x > \frac{-5}{7}[/tex]

-19 < -30. You're welcome!!

Answer:

167

Step-by-step explanation:

I did my math check and got 167 hope its right :)

Pls make me brainliest

Answer: 14

Step-by-step explanation:

The ______ is asking what 140 ÷ 10 is

140 ÷ 10 = 14

This is the result :7(x-6)(x-6)

The 59th term of the sequence 29, 37, 45 is 493. The sequence is arithmetic with a common difference of 8. Applying the formula for the nth term of an arithmetic sequence, we calculate the 59th term as 493.

Finding the 59th Term of an Arithmetic Sequence

To find the 59th term of the sequence (29, 37, 45), we first need to determine the common difference of the sequence. We do this by subtracting any term from the term that follows it. For example:

37 - 29 = 8
45 - 37 = 8

The common difference is 8.

This sequence is an arithmetic sequence where each term increases by 8 from the previous term. The formula to find the nth term of an arithmetic sequence is:

an = a1 + (n - 1) * d

where:

Plugging in the values for the 59th term:

a59 = 29 + (59 - 1) * 8
a59 = 29 + 58 * 8
a59 = 29 + 464
a59 = 493

Therefore, the 59th term of the sequence is 493.

Answer:

1.  x= 4, 1, -1/2, -3

2. x= 3, 2+i , 2-i

The curve is bell shaped, the distribution of data is equal on both sides , that is from mid point called mean.

50% of Data lies on both side of mean.

So,Equation 1.→ Mean - 2 × standard deviation=3.5

or,Equation 2. →Mean + 2 × standard deviation=4.5

x -2 a= 3.5

4 -2 a=3.5

4-3.5=2 a

2 a=0.5

[tex]a=\frac{0.5}{2}=0.25[/tex]

Using equation (2)

→ 4 +2 a=4.5

2 a=4.5-4

2 a=0.5

[tex]a=\frac{0.5}{2}=0.25[/tex]

So, Standard Deviation = 0.25

→Variance =(Standard deviation)²=a²=(0.25)²=0.0625

Option (A)→0.0625

To find the variance of data, calculate the average of the squared differences between each data point and the mean.

To find the variance of the data, we need to calculate the average of the squared differences between each data point and the mean. To do this, follow these steps:

Based on the given options, we don't have enough information to calculate the variance.

In case of inequalities we have following two rules.

Rule 1:

If we have just greater than > or less than < sign , then we would use open cirlce.

An open dot means the function has no definition at the specific point

Greater Than, >, and Less Than, <, mean the solution does NOT contain the number

Rule 2:

For inequalities. Greater Than or Equal TO, >, and Less Than or Equal TO, <, mean the solution does contain the number.

So in that case we will use closed circle.

Hope that helps.

Closed circle for the first one

Open circle for the second one

Answer:  The required missing number is 10.

Step-by-step explanation:  We are given to find the missing number in the following proportion :

[tex]?:14=15:21.[/tex]

Let the missing number be represented by x.

Then, according to the given information, we have

[tex]x:14=15:21\\\\\Rightarrow \dfrac{x}{14}=\dfrac{15}{21}\\\\\\\Rightarrow \dfrac{x}{14}=\dfrac{5}{7}\\\\\\\Rightarrow x=\dfrac{5}{7}\times14\\\\\Rightarrow x=10.[/tex]

Thus, the required missing number is 10.

We are given: The number of bands in the chicken soup county battles of the bands = 40.

The percentage of the all virus state finals will compete = 15% of the total number of bands given.

We have given 40 number of bands.

Therefore, the bands will compete in the finals = 15% of 40.

15% can be written as 0.15.

Therefore, 15% of 40 = 0.15 × 40 = 6.

Suppose f(x)=6x-2 and g(x)= 2x+4

a.

(f+g) (x)  = 6x - 2 + 2x + 4

(f+g) (x)  = 8x + 2

b.

(f-g) (x) = 6x - 2 -( 2x + 4)

(f-g) (x) = 6x - 2 - 2x - 4

(f-g) (x) = 4x - 6

Final answer:

The combined function (f+g)(x) is 8x + 2, and the function (f-g)(x) is 4x - 6.

Explanation:

To find the combined functions (f+g)(x) and (f-g)(x) for the given functions f(x)=6x-2 and g(x)=2x+4, we carry out the operations as follows:

Function (f+g)(x)

(f+g)(x) = f(x) + g(x) = (6x - 2) + (2x + 4).

Combine like terms:

(f+g)(x) = 6x + 2x - 2 + 4.

(f+g)(x) = 8x + 2.

Function (f-g)(x)

(f-g)(x) = f(x) - g(x) = (6x - 2) - (2x + 4).

Combine like terms and distribute the negative sign:

(f-g)(x) = 6x - 2x - 2 - 4.

(f-g)(x) = 4x - 6.

1.  The inequality 8d ≤ 3000 when Andrew is renting a camera that cost d dollars per day for 8 days. He can only spend $3,000.

2. There are 5760 frames in that scene.

3. Andrew's footage ratio is 6, meaning he shot 6 times more film than what was eventually used in his 1 hour and 30-minute movie.

1. Let's create an inequality to represent Andrew's budget for renting the camera. The cost of renting the camera per day is represented by "d" dollars. He wants to rent it for 8 days, and his budget is $3,000.

The total cost of renting the camera for 8 days is 8d dollars. Andrew's budget is $3,000.

So, the inequality would be:

8d ≤ 3000

This inequality ensures that the total cost of renting the camera (8d) does not exceed his budget of $3,000.

2. To find the number of frames in a scene, we need to multiply the frame rate (frames per second) by the duration of the scene (in seconds).

Given:

Frame rate = 24 frames per second

Duration of the scene = 4 minutes

First, convert the duration to seconds since the frame rate is given in frames per second:

4 minutes * 60 seconds per minute = 240 seconds

Now, multiply the frame rate by the duration:

Number of frames = 24 frames/second * 240 seconds = 5760 frames

So, there are 5760 frames in that scene.

3. To find the footage ratio, we need to compare the amount of film shot to the amount of film used.

Film shot = 9 hours

Film used = 1 hour and 30 minutes

First, convert the film used to hours:

1 hour and 30 minutes = 1.5 hours

Now, divide the film shot by the film used:

Footage ratio = Film shot / Film used

Footage ratio = 9 hours / 1.5 hours

Footage ratio = 6

So, Andrew's footage ratio is 6, meaning he shot 6 times more film than what was eventually used in his 1 hour and 30-minute movie.

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The greatest number of tables needed to serve dinner to 55 guests, with each table having a different number of guests, is 10 tables.

To find the greatest number of tables needed to serve dinner to 55 guests so that each table has a different number of guests, we need to distribute the guests among the tables in a way that maximizes the number of tables. We can start by placing one guest at each table, then add one more guest to each subsequent table until there are no more guests remaining. This will result in the maximum number of tables, with each table having a different number of guests.

Let's see how this works:

After distributing the guests this way, we have used 10 tables, with each table having a different number of guests. Therefore, the greatest number of tables we could use to serve dinner to 55 guests, with each table having a different number of guests, is 10 tables.

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Answer:

The measure of angle RAN is 39 degrees.

Step-by-step explanation:

Given:

To Find:

Measure of angle RAN

Calculations:

STEP 1 : We note that angle RAN = angle RAI + angle IAN (by the construction of the angles given in the problem).

So, we need to individually find the angles RAI and IAN in order to find the angle RAN

STEP 2 : Finding angle RAI

Given that AR if the bisector of angle KAI, therefore angle KAR = angle RAI

Also given that angle KAR = 13 degrees.

Therefore, angle RAI = 13 degrees.

STEP 3 : Finding angle IAN

Given that AI is the bisector of angle KAN, therefore angle KAI = angle IAN

Now,

angle KAI = angle KAR + angle RAI

= 13 + 13 degrees (using what we found out in STEP 1)

= 26 degrees

Therefore angle IAN = angle KAI = 26 degrees

STEP 4 : Finding angle RAN

As we noted in STEP 1,

angle RAN = angle RAI + angle IAN

= 13 + 26 degrees (using Steps 2 and 3)

= 39 degrees

Therefore, angle RAN = 39 degrees

NOTE - A hand-drawn diagram has been attached so that it is easier to picture the solution. I hope this helps!

I really don't know what you are asking for but 280/40 is 7.

Answer:

7

Step-by-step explanation:

c.

is the answer

The answer is C. 9*(5+6)=(9*5)+(9*6)

Answer:

c

Step-by-step explanation:

To find the total snow fall you would multiply the amount of snow per hour by the number of hours it snows:

Total = 3/4 inch per hour x hours: Total = 3/4h

h = 12 hours:

Total = 3/4(12) = 9 inches total.

We know: The sum of the angles of each quadrilateral is 360°.

Therefore we have equation:

x + 3x + 4x + 2x = 360

10x = 360     |:10

x = 36

For this case we have:

By properties of the radicals [tex]\sqrt {a} = a ^{\frac {1} {2}}[/tex]

So:

[tex](\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2[/tex].

Now, for power properties we have:

[tex](b ^ {\frac {c} {d}}) ^ e = b ^ {\frac {c * e} {d}}[/tex]

Thus, [tex](7 ^ {\frac {1} {2}}) ^ 2 = 7 ^ {\frac {2} {2}} = 7[/tex]

So:

[tex]7 ^ {\frac {1} {2}} = \sqrt {7}[/tex]in its radical form

Answer:

[tex](\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2= 7 ^ {\frac {2} {2}} = 7[/tex] in its simplest form.

[tex]7 ^ {\frac {1} {2}} = \sqrt {7}[/tex]in its radical form

Answer:

in its radical form

explanation: