Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.


What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle?
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You mean Sigma notation not stigma ^^

Answer:

Look the attachment

ANSWER

$3.60

EXPLANATION

We have to first find the total sum of everything that you bought

We have:

Drink = $2.95

Cheeseburger = $6.25

Blizzard = $4.35

Large Tater Tots = $2.85

The total sum is:

2.95 + 6.25 + 4.35 + 2.85

= $16.40

To find the amount of change you get back, we have to find the difference between the amount of money you paid and the total cost of the things you bought.

That is:

20 - 16.40 = $3.60

You will get a change of $3.60

Answer:

you can make 12 cans of them

Answer:

q = 6

Step-by-step explanation:

9q - 8 + 134 = 180

9q - 8 = 46

9q = 54

q = 6

Answer:

q=6

Step-by-step explanation:

First, subtract:

180-134= 46

Then make an equation:

9q-8=46

Add 8 to both sides:

9q=54

Then divide by 9:

q=6

Hope this helps!

Answer:

-2

Step-by-step explanation:

1. Rewrite the equation:

2(3x - 3) = -18

2. Use the distributive property:

2(3x - 3) = -18 ---> 6x - 6 = -18

3. Add 6 to both sides:

6x - 6 = -18 ---> 6x = -12

4. Divide both sides by 6:

6x = -12 ---> x = -2

Now we know our answer is -2, let's make sure it's correct:

2(3x - 3) = -18

2(3(-2) - 3) = -18

2(-6 - 3) = -18

-12 - 6 = -18

-18 = -18

This tells us our answer is true!

Hope this helps :D

Answer:

0.23

Step-by-step explanation:

Total number enrolled in the study = 460

Number of subjects in treatment group = 230

Number who developed sunburn in treatment group = 30

Number of subjects in placebo = 230

Number who developed sunburn in placebo = 130

Proportion of treatment group who developed sunburn = 30 / 230 = 0.130

Proportion of placebo who developed sunburn = 130 / 230 = 0.565

The relative risk of sunburn in treatment group compared with control group :

Proportion of sunburn in treatment / proportion of sunburn in placebo

0.130 / 0.565 = 0.23

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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Answer:

For a given confidence level, t* is never smaller than z*.

Step-by-step explanation:

t* and z* are the critical value of a confidence interval.  For example, at 95% confidence, z* = 1.96.  This is because 95% of a normal curve is within ±1.96 standard deviations.

A student's t distribution has the same bell-curve shape as a normal distribution, but is shorter and wider, which is why t* is always larger than z*.  As the sample size increases to infinity, the distribution approaches normal.

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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Answer:

Next time show a picture

Step-by-step explanation:

But! A way you could solve this is to look at the opposite angle of 1 and see what the number is. The number opposite of 1 is always equal to 1. You could also see if there is a number next to 1. The number next to 1 +1= 180 degrees. Good luck!

Answer:

Step-by-step explanation:

The area of a rectangle is represented with the formula below

(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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Since EF and WV are congruent, and the intersection of EF and WV to the diameter forms two right angles, they are parallel. We can conclude therefore that PG is congruent with GO

We can say that

Now that we have solved for x, substitute it to the given of PG

Therefore, PG is equal to 10 units.

Answer:

Cost of a coffee = $1.5

Cost of a muffin = $1.25

Step-by-step explanation:

Given:

Cost of 3 coffee and 2 muffins = $7

Cost of 2 coffee and 4 muffins = $8

Find:

Cost of each

Computation:

Assume;

Cost of a coffee = a

Cost of a muffin = b

So,

3a + 2b = 7 .......... Eq1

2a + 4b = 8 .......... Eq2

Eq1 x 2

6a + 4b = 14 ......... Eq3

From Eq3 - Eq2

4a = 6

a = 1.5

Cost of a coffee = $1.5

3a + 2b = 7

3(1.5) + 2b = 7

4.5 + 2b = 7

b = 2.5/2

b = 1.25

Cost of a muffin = $1.25

The assumptions required for making inference about a population using sample data include ;

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given that m is parallel to n,

the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.

using the corresponding angle rule we know that:

2x + 16 = 96

2x = 80

so x = 40

Answer:

$4860

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year,

then, solving our equation

I = 4500 × 0.04 × 2 = 360

I = $ 360.00

The simple interest accumulated

on a principal of $ 4,500.00

at a rate of 4% per year

for 2 years is $ 360.00.

Answer:

2250

Step-by-step explanation:

you times 4500 with 2 and get 9000. Then, you take the 9000 and divide it by 4 and get 2250.

Check the picture below.

Both of the intervals given are meaningful intervals in mathematics, but they are different types of intervals.Therefore, the interval (1, -13] is meaningless because it does not contain any real numbers.

An interval is a number or range of values ​​between two endpoints. 

The endpoints can be included or excluded from the interval, and the interval can be open, closed, or half-open depending on whether the endpoints are included or excluded.

The interval (-12, 0] is a closed interval, which includes the endpoint 0, and all real numbers between -12 and 0.

The square bracket indicates that the endpoint 0 is included in the interval.

The interval (1, -13] is an empty interval, which includes no real numbers, since there is no number that is greater than 1 and less than or equal to -13. This interval is meaningless because it does not contain any numbers.

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Answer:

1/4

Step-by-step explanation:

First you add all of the marbles in the bag which is 16 marbles.  The fraction of red marbles to the total would be 4/16.  In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.

The smallest integer that Pearl wrote down is -12.Let's assume the smallest integer that Pearl wrote down is represented by the variable "x."

According to the given information, the sum of the seven consecutive integers is equal to $\frac{21}{4}$ times the largest integer.

The sum of consecutive integers can be expressed as the sum of an arithmetic series. The sum of an arithmetic series can be calculated using the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is x and the last term is x + 6 (since there are seven consecutive integers). Therefore, the sum of the integers can be written as:

Sum = (7/2)(x + (x + 6))

Simplifying the equation:

(7/2)(2x + 6) = (21/4)(x + 6)

Multiplying both sides by 4 to eliminate the fractions:

14x + 42 = 21x + 126

Subtracting 14x from both sides:

42 = 7x + 126

Subtracting 126 from both sides:

-84 = 7x

Dividing both sides by 7:

-12 = x.

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The sequence of transformations that proves that the shapes are similar is given as follows:

B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5

First, we have that the orientation of the figure, hence it was reflected.

The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.

The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:

3/2 = 1.5.

Hence option B is the correct option for this problem.

The missing parts of the problem are given by the image presented at the end of the answer.

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Therefore, the solutions to the quadratic equation x² + 7x - 8 = 0 are -8 and 1. The answers are D and E.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.

Here,

To check which values are solutions to the quadratic equation, we can substitute each value into the equation and see if it equals zero.

Substituting -1 into the equation:

(-1)² + 7(-1) - 8 = 1 - 7 - 8 = -14, which is not equal to zero.

Substituting 2 into the equation:

2² + 7(2) - 8 = 4 + 14 - 8 = 10, which is not equal to zero.

Substituting -4 into the equation:

(-4)² + 7(-4) - 8 = 16 - 28 - 8 = -20, which is not equal to zero.

Substituting -8 into the equation:

(-8)² + 7(-8) - 8 = 64 - 56 - 8 = 0, which is equal to zero. Therefore, -8 is a solution to the equation.

Substituting 1 into the equation:

1² + 7(1) - 8 = 1 + 7 - 8 = 0, which is equal to zero. Therefore, 1 is a solution to the equation.

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Answer:

\(\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}\)

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

First, we can calculate the area of the circular base:

\(A_{\text{circle}} = \pi r^2\)

\(A_{\text{base}} = \pi (0.75 \text{ in})^2\)

\(A_{\text{base}} = 0.5625\pi \text{ in}^2\)

Next, we can calculate the area of the rectangular side:

\(A_\text{rect} = l \cdot w\)

\(A_\text{side} = (4\text{ in}) \cdot C_\text{base}\)

Since the width of the side is the circumference of the base, we need to calculate that first.

\(C_\text{circle} = 2 \pi r\)

\(C_\text{base} = 2 \pi (0.75 \text{ in})\)

\(C_\text{base} = 1.5 \pi \text{ in}\)

Now, we can plug that back into the equation for the area of the side:

\(A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})\)

\(A_\text{side} = 6\pi \text{ in}^2\)

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

\(SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2\)

\(\boxed{SA = 7.125\pi \text{ in}^2}\)

\(\boxed{SA \approx 22.4 \text{ in}^2}\)

Answer:

prime factors of 900 are 2,2,3,3,5,5

which is the same as 2^2×3^2×5^2