Susan made 32 cookies. If 3/8 of the cookies
burnt in the oven, how many cookies were not
burnt?

Step-by-step explanation:

since im typing it out its neater to seperately do left side expression and right side expression

(a+b)(a+2ab) = a(a+2ab) + b(a+2ab) (expansion of terms)

=a^2 +2a^2b + ab + 2ab^2 (remember order of algebraic terms doesnt matter so for instance ab=ba)

other side

(2a-b)(a-b) = 2a(a-b) -b(a-b)

=2a^2 -2ab -ab +b^2 (remember -b x -b = b^2, negatives cancel out when they multiply by each other)

if you want to present this on paper, you would have done the both expansions in one line, to reach this line

.

.

.

= a^2 + 2a^2b + ab + 2ab^2 + 2a^2 -2ab -ab +b^2

=3a^2 + b^2 -2ab + 2a^2b + 2ab^2

Answer:

722.24 cm

Step-by-step explanation:

The volume formula is L X W X H = V  so using that information we can do 18.5 times 32 times 12.2 which gives us 722.24 cm.

The cutoff salary for teachers in the top 10% is approximately $43,120.

Since the salaries are normally distributed, we can use z-scores to find the cutoff point. The z-score represents the number of standard deviations a data point is from the mean. We can use the z-score formula:

z = (x - μ) / σ

Where:

z is the z-score

x is the cutoff salary we want to find

μ is the mean salary

σ is the standard deviation

We want to find the z-score that corresponds to the top 10% of salaries, which means we need to find the z-score that corresponds to the cumulative probability of 0.90 (1 - 0.10) from the standard normal distribution.

Using a standard normal distribution table or calculator, we can find that the z-score for a cumulative probability of 0.90 is approximately 1.28.

Now, we can rearrange the z-score formula to solve for x:

z = (x - μ) / σ

Rearranging:

x = μ + z * σ

Plugging in the values:

x = $38,000 + 1.28 * $4,000

Calculating:

x ≈ $38,000 + $5,120

x ≈ $43,120

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COMPLETE QUESTION :

Assume that the salaries of elementary school teachers in a particular country are normally distributed with a mean of $38,000 and a standard deviation of $4,000. What is the cutoff salary for teachers in the top 10%?

Answer:

  b.) intersection

Step-by-step explanation:

The given inequality can be rearranged so that you can see the solution space is one continuous interval.

__

It is described by the intersection of two inequalities.

  |y -3| -4 ≤ -3 . . . . . . given

  |y -3| ≤ 1 . . . . . . . . add 4

  -1 ≤ y -3 ≤ 1 . . . . . "unfolded", the intersection of two inequalities

  2 ≤ y ≤ 4 . . . . . . . add 3

This means 2 ≤ y and y ≤ 4, the intersection of the two inequalities.

_____

Additional comment

If the inequality were of the form ...

  |y -3| ≥ 1

then it would "unfold" to ...

  -1 ≥ y -3   or   y -3 ≥ 1

and the solution intervals would be disjoint. The solution would be the union of the solution intervals of the individual inequalities.

Answer:

intersection is right

Step-by-step explanation:

You should expect to spend $26 to win $100 playing this casino game.

This is a classic example of a geometric distribution, where each trial has two possible outcomes (win or lose) and the probability of winning remains constant at 1/13 (4 kings in a deck of 52 cards) across all trials.

The expected number of trials to win is 13, so the expected cost to win is 13 times the cost per trial, which is $2, giving an expected cost of $26. Note that this is the expected cost, not the guaranteed cost, and it is possible to spend more or less than $26 before winning.

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There are 56 possible ways to man the two sides of the boat with two crew members rowing on the stroke side and three crew members rowing on the bow side.

The number of ways to man the two sides of the boat can be calculated using the combination formula, C(n,r). In this case, n = 8 (the total number of crew members) and r = 5 (the number of crew members needed to man the two sides of the boat). The equation to calculate the number of ways to man the two sides of the boat can be written as C(8,5).

C(8,5) = 8!/(5!*3!) = 56.

This means that there are 56 possible ways to man the two sides of the boat with two crew members rowing on the stroke side and three crew members rowing on the bow side.

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Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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Answer:

\(12s-120\)

Step-by-step explanation:

Given the following question:

\(12(s-10)\)

To rewrite the expression using the distributive property we have to remember the rule that applies to all expressions, we have to multiply all the terms inside the paratheses by the terms outside of the paratheses.

\(12(s-10)\)
\(12\timess=12s\)
\(12s-10\times12\)
\(10\times12=120\)
\(12s-120\)

Your answer is "12s - 120."

Hope this helps.

Answer:

Approx 61.554 feet

Step-by-step explanation:

Since we are dealing with the opposite and adjacent sides, we will use tangent as our ratio.

Since the angle of elevation is 72 degrees, the left side of our equation is \(tan(72)\).

The right side of the equation is opposite over adjacent.

\(x/20\)

Set these equal to each other.

\(tan(72) = x/20\)

Simplify.

\(20 tan(72)=x\)

\(20(3.078) = x\)

x is approximately 61.554.

SOLUTION

Consider the image given below.

From the image above,

To find the measures of each angle, we need to obtain the value of small x in the diagram.

Applying the rule: Sum of angle in a triangle is 180 degrees

Then substitute the given expression, we have

Collect like terms and add

Divide both sides by 6, we have

hence, x=30

Then substitute the value of x to obtain the measure of each angles.

Since the triangle is an issoceles triangle, then

Hence

Therefore

Answer : ∠V= 28°, ∠W=28°, ∠X=124°

Water cycle involves all processes in which water circulates

The water cycle labeled C is precipitation

From the figure, we can see that the step C represents water falling down from the sky to the earth surface.

This can represent rain, sleet, or snow.

Any of the above forms represent precipitation

Hence, the water cycle labeled C is precipitation

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The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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The length of the rectangle is 10, the width is 2.5 and the perimeter is 25

Let the width of the rectangle be x

The length of rectangle = 2x + 5

The overall length of the outline determines a rectangle's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter.

Perimeter = 10 times of width

= 10*x

= 10x

The formula for the perimeter of a rectangle is given:

Perimeter = 2(Length+Breadth)

10x = 2(x + 2x+5)

10x = 2(3x+5)

10x = 6x + 10

4x = 10

x=2.5

Length = 10

Width = 2.5

Perimeter = 25

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Answer:

The rectangular prism building.

Step-by-step explanation:

The rectangular prism building will require more gallons of paint to completely cover because, compared to the rectangular pyramid, the rectangular prism has a larger surface area, thus it would need more paint to completely cover it.

1 is not a prime number. Also 1 is not a composite number.

What is a prime number?

A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components.

1 is divisible by 1.

The factors of 1 is 1 and itself that is 1.

The number of factor of 1 is 1.

But a prime number has 2 factors.

But the number of factor of 1 does not fulfil the criteria of prime number.

Thus 1 is not a prime number.

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Answer:

z = 150

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

6-4=2

200/100=2

i think

Answer:

y-intercept (b): 3

slope: 3/2

equation: y= 3/2x+3

(1) Standard hours allowed for actual output are 6000 Hours.

(2) Standard labor cost allowed is 102,000.

(3) Labor spending variance is $350 unfav.

(4) The labor rate variance is $4600 unfav.

(5) Variable rate is $1150 Fav and efficiency variance is $1000 Fav.

What is labor spending variance?

The labor rate variance, sometimes referred to as the spending variation for direct labor, is calculated by multiplying the number of hours worked by the difference between the actual and standard labor rates per hour.

Given: Erie Company manufactures a mobile fitness device called the Jogging Mate.

The company uses standards to control its costs.

During August, 5,750 hours of direct labor time were needed to make 20,000 units of the Jogging Mate.

The direct labor cost totaled $102,350 for the month.

(1) Standard hours allowed per unit:  18 min      

Actual output: 20000 units        

Standard hours allowed for actual output (20000(18/60)):  6000 Hours

(2) Standard labor hours allowed: 6000 hours      

Standard rate per hour: $ 17        

Standard labor cost allowed: (6000 hours  at 17): 102,000

(3) Labor Spending Variance: (Standard hours*Standard rate)  - (Actual                          hours*Actual rate)

6000 *17 - 102350 = $ 350 Unfav

(4)  Actual labor rate per hour (102350/5750):  $ 17.80 per hour  

Labor Rate variance: Actual hours (Standard rate-Actual rate)             5750 hours (17.00-17.80)=  $ 4600 Unfav

(5) Standard Variable rate per hour: $ 4 per hour      

      Actual rate per hour (21850/5750): $ 3.80 per hour    

Variable rate variance: Actual hours (Standard OH rate-Actual OH rate)  

5750 (4.00-3.80)= $ 1150 Fav  

Variable OH efficiency variance: Standard rate (Standard hours-Actual hours)  

4.00 (6000-5750)= $ 1000 Fav

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Hi!

You cannot.

This is because ALL triangles MUST have 180 degrees, so if it doesn't it's not even a triangle. Therefore you cannot use it because, well, it's not a triangle.

Answer:

The sum of interior angles is 180 degrees (Triangle Angle Sum Theorem). All interior angles of a triangle are more than 0° but less than 180°.

Step-by-step explanation:

The current rate of sea level rise stays constant, the sea level would increase by about 1.05 feet over the next 100 yea

To answer this question, we need to know the current rate of sea level rise. According to the National Oceanic and Atmospheric Administration (NOAA), the current rate of global sea level rise is about 3.2 millimeters per year.

Therefore, over the next 100 years, the sea level would rise by:

3.2 millimeters/year * 100 years = 320 millimeters

To convert millimeters to feet, we can use an online conversion calculator. 320 millimeters is equivalent to 1.05 feet (rounded to two decimal places). Therefore, if the current rate of sea level rise stays constant, the sea level would increase by about 1.05 feet over the next 100 years.

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The statement that best describes the composition of most foods is: "They contain mixtures of the three energy nutrients, although only one or two may predominate."

Most foods contain mixtures of the three energy nutrients, namely carbohydrates, proteins, and fats. However, the relative proportions of these nutrients can vary significantly from one food to another. In some foods, one or two of these nutrients may predominate, while others may contain relatively equal amounts of all three.

Carbohydrates are a primary source of energy for the body and can be found in various forms such as sugars, starches, and fibers. Foods like grains (e.g., rice, wheat, oats), fruits, vegetables, and legumes tend to be rich in carbohydrates. However, the specific types and amounts of carbohydrates can vary widely.

Proteins are crucial for building and repairing tissues, as well as for various metabolic functions. Foods like meat, poultry, fish, eggs, dairy products, legumes, nuts, and seeds are excellent sources of protein. Again, the protein content in different foods can vary.

Fats, also known as lipids, are an important energy source and provide essential fatty acids. Foods such as oils, butter, avocados, nuts, and fatty meats are high in fats. Like carbohydrates and proteins, the fat content in foods can differ significantly.

It's worth noting that some foods may predominantly consist of one specific nutrient. For example, pure sugar is almost entirely composed of carbohydrates, while pure oil is almost entirely composed of fats. However, most whole foods, such as fruits, vegetables, grains, meats, and dairy products, contain a mixture of these energy nutrients.

Furthermore, a balanced diet typically includes a combination of these nutrients in appropriate proportions. A varied diet that incorporates a range of foods from different food groups helps ensure an adequate intake of carbohydrates, proteins, and fats, along with other essential nutrients required for optimal health.

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Step-by-step explanation:

step 1. <2 + <3 = 180° (supplementary angles)

step 2. 130 + <3 = 180

step 3. <3 = 50°.

From the graph shown on the coordinate grid, the only correct option is shown in option 4.

When the input value is -4, then the function is shown at 2. Similarly when the input value is 0, the function is shown at 2.

The minimum score required for the job offer is 589.17

Given, GRE Verbal scores are normally distributed with a mean of 456 and a standard deviation of 123.

A university plans to offer tutoring jobs to students whose scores are in the top 14%.We need to find the minimum score required for the job offer.

So, we have to find out the z-score corresponding to the top 14% using the z-table or calculator.

We know that,

Z = (X - μ) / σ,

where X is the score, μ is the mean and σ is the standard deviation.

So, the z-score corresponding to the top 14% is given by:

Z = InvNorm(0.86) = 1.0803 [using calculator or Z-table].

Now, substituting the value of Z, we get:

1.0803 = (X - 456) / 123

Multiplying both sides by 123, we get:

X - 456 = 133.1699or X = 589.1699

Therefore, the minimum score required for the job offer is 589.17

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Answer:

Step-by-step explanation:

Check register

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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a. The sequence is 4, 5, 7, 11, 19, 35. Observe the differences between consecutive terms: 1, 2, 4, 8, 16. These differences form a geometric sequence with a common ratio of 2. Thus, the closed formula for an is an = a0 + (2^n - 1).

b. The sequence is 0, 3, 8, 15, 24, 35. Observe the differences between consecutive terms: 3, 5, 7, 9, 11. These differences form an arithmetic sequence with a common difference of 2. Thus, the closed formula for an is an = a0 + n(n+1).

c. The sequence is 6, 12, 20, 30, 42. Observe the differences between consecutive terms: 6, 8, 10, 12. These differences form an arithmetic sequence with a common difference of 2. Thus, the closed formula for an is an = a0 + n(n+4).

d. The sequence is 0, 2, 7, 15, 26, 40, 57. Observe the differences between consecutive terms: 2, 5, 8, 11, 14, 17. These differences form an arithmetic sequence with a common difference of 3. Thus, the closed formula for an is an = a0 + n(n+1)/2 + n(n-1)/2.

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The closed formula for aₙ in each sequence is the following,

a) \(a_n = 4+ 2^{n-1} \), a₀ = 4.

b) \(a_n = n² + 2n\),a₀ = 0

c)\(a_n = a_0+n² + 5n\), a₀ = 6

d)\(a_n = a_0 +n(n+1)+ \frac{n(n-1)}{2}\), a₀ = 0.

A sequence is a list of elements (usually numbers) that exhibits a particular order. Each element of sequence is called term. There are different types of sequences, we have to check these and determine the nᵗʰ term expression for all. Consider the first sequence,

a) 4, 5, 7, 11, 19, 35,....

First term of sequence, a₀ = 4

We can rewrite the expression,

= 4, 4+1, 4+3, 4+7,.....

= \(4, 4 + 2¹⁻¹ , 4 + 2²⁻¹,... \)

So, it is a sequence with \(a_n = 4+ 2^{n-1} \).

b) 0, 3, 8, 15, 24, 35,.

First term of sequence, a₀ = 0

We can rewrite the sequence expression,

= 0, 0+3, 3+5, 8+7, .....

= 0, 1² + 2, 2² + 4, 3² + 6, ......

so, the nth term of this sequence is written as \(a_n = n² + 2n\).

c) 6, 12, 20, 30, 42,..

First term of sequence, a₀ = 6

We can rewrite the sequence expression,

= 6, 6+6, 12+ 8, 20+10,....

= 6, 6+1² + 5×1, 6+ 2²+ 5×2, 6+3²+ 5×3,...

so, the nth term of this sequence is written as \(a_n = 6+n² + 5n\).

d) 0, 2, 7, 15, 26, 40, 57,..

First term of sequence, a₀ = 0

We can rewrite the sequence expression,

= 0, 0+2, 2+ 5, 7+8, 15+11,....

= 0, 0+ 1(1+1) + ((1-1)1)/2, 0+ 2(2+1)+2(2- 1)/2, ...

so, the nth term of this sequence is written as \(a_n = a_0 +n(n+1)+ \frac{n(n-1)}{2}\). Hence, required value is \(a_n = a_0 +n(n+1)+ \frac{n(n-1)}{2}\),

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The true statements are

i. probability is usually between 0 and 1, inclusive.

ii. an event that is likely has a probability that is close to 1.

(option i and ii).

Probability is an important concept in mathematics and statistics that allows us to quantify the likelihood or chance of an event occurring. It is often represented as a number between 0 and 1, inclusive. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain to occur.

Now, let's examine each of the statements to determine which ones are true.

The first statement, "probability is usually between 0 and 1, inclusive," is true. As mentioned earlier, probability is always represented as a number between 0 and 1, inclusive.

The second statement, "an event that is likely has a probability that is close to 1," is also true. If an event is likely to occur, it means that there is a high probability of it happening. Therefore, the probability assigned to that event would be close to 1.

Hence the correct option is (a) and (b)..

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