Simplify 3y – 5(y + 2)

Answer:

1) 7:10

2) $8 per hour

Step-by-step explanation:

Question 1

What we know:

- there are 10 seventh grade students

- there are 7 sixth grade students

Therefore, the ratio of sixth-grade students to seventh-grade students is 7:10.

Question 2

What we know:

- Janice babysat 3 hours each night

- Janice babysat for 8 nights

- she earned $192

First, we need to find the total number of hours that she babysat. Because she babysat for 3 hours each night for 8 nights, we can find this by multiplying 3 and 8:

3×8=24

Therefore, Janice babysat for 24 hours in total.

Because she earned a total of $192, divide 192 by 24 to find her hourly rate:

192÷24=8

Therefore, Janice has an hourly rate of $8 per hour.

I hope this helps!

Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

The perimeter of the figure is 58 m.

To find the perimeter of the given figure we can divide the figure in three rectangles.

Rectangle 1:

Perimeter= 2 (l + w)

= 2(5 + 2)

= 2 x 7

= 14 m

Rectangle 2:

Perimeter= 2 (l + w)

= 2(5 + 1)

= 2 x 6

= 12 m

Rectangle 3:

Perimeter= 2 (l + w)

= 2(14 + 2)

= 2 x 16

= 32 m

So, the perimeter of the figure is

= 14 + 12 + 32

= 58 m

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Answer:

20th percentile.

Step-by-step explanation:

Concept of a percentile:

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

Determine the percentile of the condo with a monthly rent of $1,150

There are 10 values.

8 are higher than $1,150.

2 are $1,150 or lower.

2/10 = 0.2 = 20%

So the condo with a monthly rent of $1,150 is in the 20th percentile.

Answer:

this is a tough one but i know that sometimes it may seem hard but, with the right amount of practice, the hardest equations become the easiest to overcome. (Hint: Use PEMDAS)

Step-by-step explanation:

hope this helps you!

Answer:

I cant answer it i just need to talk to you its mya......

Step-by-step explanation:

Answer:

2800

Step-by-step explanation:

2826 to the nearest hundred is 2800

Therefore, at least 49 street lights can be installed along one side of the street with equal distance between the lights.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

The distance between point A and B is AB, and the distance between point B and C is BC. Let's assume that the distance between each street light is "d".

Since there must be a street light at points A, B, and C, there will be a total of two gaps between these three street lights, which are AB and BC. Thus, the number of street lights required is equal to the sum of the lengths of AB and BC, divided by the distance "d" between the street lights, plus 1 for the street light at point B.

So, the total number of street lights required is

Number of street lights = (AB + BC) / d + 1

We know that AB = 1170 m and BC = 1625 m, and the distance between each street light should be equal. Therefore, we need to find the greatest common factor (GCF) of 1170 and 1625 to determine the distance between each street light.

1170 = 2 x 3 x 3 x 5 x 13

1625 = 5 x 5 x 13

The GCF of 1170 and 1625 is 65, which means the distance between each street light should be 65 meters.

Now we can calculate the total number of street lights required:

Number of street lights = (1170 + 1625) / 65 + 1

= 49

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Answer:

x = 5

Step-by-step explanation:

3x + 10x =65

13x = 65

/13     /13

------------------

x = 5

Answer:

x = 5

Step-by-step explanation:

add both x values --> 13x

divide both sides by 13 ---> 5

so, x = 5

Answer :

a) It is given that

Everyday a machine makes 500000 staples and puts them into the boxes.

The machine need 170 staples to fill a box

One box contans = 170 staples.

Total number of staples = 500000

Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.

\( \: :\implies \) 500000 /170

\( :\implies \: \) 2941 (approx)

Therefore, 2941 boxes are required to fill with 500000 staples.

b) It is given that,

Each staple is made of 0.21 g of metal .

Total weight of metal = 1 kg = 1000 g

1 staple = 0.21 g

Number of staples = weight of metal/ Weight of 1 staple.

\( \: :\implies \) 1000/0.21

\( \: :\implies \) 4761 (approximately)

Therefore, 4761 staples can be made from 1 kg of the metal.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

A

Step-by-step explanation:

F test is a statistical method used to determine which models best fits the population from which the sample is derived. It is a ratio of two variances. Variance measure the rate of dispersion

The formula for calculating f-test = explained variance / unexplained variance

There are two hypothesis in an f test :

1. the  null hypothesis  - all slope coefficient are equal to zero

the alternative hypothesis : at least one of the slope coefficient is not equal to zero

Answer:

40.5

I hope u get a good mark glll

Step-by-step explanation:

The solved for x round to the nearest tenth is x≈ 14.

What is meant by round ?

Remember Sine of an angle is = opposite side /hypotenuse

So let the hypotenuse be  x :

sin(54°) = opposite side / x

sin(54°) = 12 / x

To solve for x, divide sin(54°) by 12:

x = 12 / sin(54°)

x≈14

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The exact value of sin(pi/3) is √3. By definition, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(pi/3) = √3/1 = √3.

The exact value of sin(pi/3) can be determined using trigonometric properties and identities.

First, we know that pi/3 is equivalent to 60 degrees. In a unit circle, the point corresponding to 60 degrees forms an equilateral triangle with the origin and the x-axis. This triangle has side lengths of 1, 1, and √3.

To find the sine of pi/3, we consider the side opposite the angle (pi/3) in the triangle. In this case, the opposite side has a length of √3. The hypotenuse of the triangle is 1, as it is the radius of the unit circle.

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The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

Answer: A ≈ 74.35

Step-by-step explanation: Explanation below.

If A, B and C be events relative to the sample space S, then the Venn diagram of the representing event has been plotted

Let A, B and C be events relative to the sample space S.

The sample space is the set of all possible outcomes of the experiment.

The Venn diagram is the pictorial representation of the sample space of the experiment by using the circles and the overlapping of the circles.

Here we have to plot the each representing events using the Venn diagram representation

Part a

The event is (A ∩ B)'

Plot the Venn diagram

Part b

The event is (A ∪ B)'

Plot Venn diagram

Part c

The event is (A ∩ C) ∪ B

Plot the Venn diagram

Therefore, the Venn diagram of the each event has been plotted

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Answer: 3.84

Step-by-step explanation:

cause it is use calculator

Answer:

8.64 ÷ 2.25=3.84

Your answer: 3.84

Step-by-step explanation:

Answer:

60cm

Step-by-step explanation:

radius of 3 ×2=6

6 is your diamiter

6×10=60your answer

Answer: 2g - 32

Step-by-step explanation:

-2 (3g - 8g + 8) - 9g - 2 (3g - 8g + 8) - 9g

First step is to use the distributive property to distribute 2.

The expression is now:

-6g + 16g - 16 - 9g - 6g + 16g - 16 - 9g

Now you put the like terms together..

-6g + 16g - 9g - 6g + 16g - 9g -16 - 16

All that is left to do is combine them!

(-6g + 16g - 9g - 6g + 16g - 9g) + (-16 - 16)

2g + (-32)

2g - 32

Hope that helped!

The experimental probability of the next balloon sold being green is 4/15.

Probability is a crucial concept in the field of mathematics that is used to measure the likelihood of an event happening.

According to the information given, the number of green balloons sold is 20, and the total number of balloons sold is the sum of all the colors, which is:

20 + 17 + 12 + 19 + 7 = 75

Now we can use these numbers to calculate the experimental probability of a green balloon being sold:

Experimental probability of a green balloon being sold = Number of green balloons sold / Total number of balloons sold

Experimental probability of a green balloon being sold = 20 / 75

Experimental probability of a green balloon being sold = 4/15

This means that if we randomly select a balloon from the store, the likelihood of it being green is 4 out of 15 or approximately 0.27 or 27%.

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Answer:

4/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, we need to determine the total number of drops that need to be delivered in 1 hour (60 minutes). To do this, we can multiply the volume to be delivered by the number of drops per mL:

300 mL x 15 gtt/mL = 4500 gtt

So 4500 drops need to be delivered over 1 hour. To find the IV flow rate in drops per minute, we can divide the total number of drops by the number of minutes:

4500 gtt ÷ 60 min = 75 gtt/min

Therefore, the IV flow rate in drops per minute is 75 gtt/min.

The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

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Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

40 dollar

Step-by-step explanation:

half of 80 is 40

Answer:

40$

Step-by-step explanation:

sale price(S.P.)=discount% of M.P.(marked price)

S.P.=50% of 80$

S.P=50/100*80$

Hence,S.P.(selling price)=0.5*80$=40$

Answer:

1,280

Step-by-step explanation:

prob(spots) = 12/180 = 1/15

so of the 1200 frogs, (1/15)(1200) should have spots, so ..

how many should not have frogs ?

or

prob(not spots) = 14/15

number who don't have spots = (14/15)(1200) = 1,280

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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