Samantha is in a book club. She has read 7 books this month. Her book club requires her to read 4 books in one month. How many
more books did she read than what she was required?

Answer:

Step-by-step explanation:

Square A:

Area = 225 square feet

side *side = 225

        Side =√225

                 \(=\sqrt{15*15}\)

   Side of square A = 15 ft

Square B:

Area = 400 square feet

Side =√400

       = \(\sqrt{20*20}\)

Side of square B = 20 ft

Use Pythagorean theorem for finding the side of Square C.

Side of square A is the altitude ;  side of square B is the base and side of square C will be the hypotenuse

hypotenuse² = base² + altitude²

                      = 15² + 20²

                       = 225 + 400

                       = 625

hypotenuse = \(\sqrt{625} =\sqrt{25*25}\) = 25 ft

Area of square C = 625 square ft

In short,

Area of square C = area of square B + area of square A

                             = 400 + 225

                             = 625 square ft

The percentage of people in each of the age groups that die in a given year is creasing The formula implies that even one will be dead by age 112.

What is the exponential function?

Although the exponential function was derived from the concept of exponentiation (repeated multiplication), contemporary formulations (there are numerous comparable characterizations) allow it to be rigorously extended to all real arguments, including irrational values.

Here, we have

Given: The percentage of people of any particular age group that will die in a given year may be approximated by the formula

P(t) =  0.00236 \(e^{0.0953t}\)....(1)

(a) We have to find the value of P(25).

When t = 25

Now we put the value of t in equation (1) and we get

P(25) =  0.00236 \(e^{0.0953(25)}\)

= 0.02556

P(25) = 0.026

We have to find the value of P(50).

When t = 50

Now we put the value of t in equation (1) and we get

P(50) =  0.00236 \(e^{0.0953(50)}\)

P(50) = 0.277

We have to find the value of P(75).

When t = 75

Now we put the value of t in equation (1) and we get

P(75) =  0.00236 \(e^{0.0953(75)}\)

P(75) =  2.999

(b) We have to find the value of P'(25)

When we differentiate equation (1) and we get

P'(t) = 0.00236×0.0953\(e^{0.0953t}\)....(2)

When t = 25

Now we put the value of t in equation (2) and we get

P'(25) = 0.00236×0.0953\(e^{0.0953(25)}\)

P'(25) = 0.0024

We have to find the value of P'(50)

When t = 50

Now we put the value of t in equation (2) and we get

P'(50) = 0.00236×0.0953\(e^{0.095350)}\)

P'(50) = 0.026

We have to find the value of P'(75)

When t = 75

Now we put the value of t in equation (2) and we get

P'(75) = 0.00236×0.0953\(e^{0.0953(75)}\)

P'(75) = 0.286

(c) Let P(t) = 100

100 = 0.00236 \(e^{0.0953t}\)

t = 112

Hence, The percentage of people in each of the age groups that die in a given year is creasing The formula implies that even one will be dead by age 112.

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The formula suggests that even at age 112, there will be some mortality rate within the population.

The given formula, P(t) = 0.00236, represents the percentage of people in any particular age group who will die in a given year.

(a) To find the value of P(25), we substitute t = 25 into the equation:

P(25) = 0.00236

Therefore, P(25) = 0.00236 or approximately 0.026.

Similarly, for P(50):

P(50) = 0.00236 or approximately 0.277.

And for P(75):

P(75) = 0.00236 or approximately 2.999.

(b) To find the value of P'(25), we differentiate the equation P(t) = 0.00236:

P'(t) = 0.00236 × 0.0953

Substituting t = 25:

P'(25) = 0.00236 × 0.0953

Therefore, P'(25) = 0.0024.

Similarly, for P'(50):

P'(50) = 0.00236 × 0.0953 or approximately 0.026.

And for P'(75):

P'(75) = 0.00236 × 0.0953 or approximately 0.286.

(c) If we set P(t) = 100, we can solve for t:

100 = 0.00236

Solving for t, we find:

t = 112

This implies that according to the given formula, the percentage of people in each age group dying in a given year, even one person will be dead by the age of 112.

Therefore, the formula suggests that even at age 112, there will be some mortality rate within the population.

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To make a cake and frosting, you typically need different ingredients for each component.

For a basic cake recipe, you will need ingredients such as flour, sugar, eggs, butter or oil, baking powder or soda, and milk or water. The specific recipe may vary depending on the type of cake you are making, but these are some common ingredients.

For the frosting, you will typically need ingredients such as powdered sugar, butter or shortening, vanilla extract, and milk or heavy cream. Additional flavorings or colors may be added based on the desired taste and appearance of the frosting.

Overall, the cake and frosting are distinct components with their own set of ingredients. While some ingredients may overlap, such as butter or sugar, the quantities and ratios can differ between the two. So, in total, you would need a combination of ingredients for the cake and frosting to create a complete and delicious dessert.

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Answer:

he should save $70 each week

Step-by-step explanation:

1200 - 640 = 560

560/8 = 70

The value of y when the value of x is 1, can be found to be 60 miles.

As depicted in the graph, an augmented consumption of gallons of fuel by the hybrid vehicle concomitantly correlates to an increase in mileage capacity.

Concretely, according to our research data, we confirm that for every gallon expended, there is a mileage expansion rate of 60 units. Hence, when the quantity x equals 1, it implies usage of one gallon only.

Accordingly, empirical evidence suggests that traveling precisely sixty miles remains possible on utilization of one gallon which thus confirms the efficiency of using hybrid cars as a viable option.

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Answer:

27.8miles

first we add 37 and 17=54

then multiple it with 20 and divide by 100 so we can change it to percent

so it will be 10.8 miles and then we add it with 17 miles =27.8 miles

Answer:

  D.  a[1] = 12; a[n] = 33·a[n-1]

Step-by-step explanation:

You can make the correct choice by seeing what you get with n=1 and n=2 in the various expressions.

In general,

  an = a1·r^(n-1)

For n=1, the value of this is ...

  a1 = a1·r^(1-1) = a1·r^0 = a1 . . . . as you expect.

That is, the a1 term of the recursive formula is the leading coefficient in the explicit formula.

__

For n=2, you have ...

  a2 = a1·r(2-1) = a1·r

That is, the previous term was multiplied by r. In the given explicit formula, r=33, so the recursive formula will tell you ...

  a[n] = 33·a[n-1]

__

Altogether, we have ...

  \(\boxed{a_1=12,\ a_n=33a_{n-1}}\)

Answer:

60%

Step-by-step explanation:

Answer:

2 \(\frac{1}{20}\)

Step-by-step explanation:

for question a)

It would be easier if you converted these to improper fractions (currently it is in the form of a proper fraction)

to convert to improper fraction, you would multiply the denominator (bottom no. of fraction) by the whole number , then add that with the numerator (top no. of fraction) and put the whole thing over the denominator.

E.g.

7 \(\frac{1}{4}\) = 7x4 + 1 = 29

Thus, improper fraction would be \(\frac{29}{4}\)

do same thing  for other one

thus , \(\frac{26}{5}\)

now,

\(\frac{29}{4}\) - \(\frac{26}{5}\)

however, you can't do this as the denominators are not the same, so multiply them by a number which would give the a common denominator (20 would be the best option for common denominator)

\(\frac{145}{20} -\frac{104}{20}\) = \(\frac{41}{20}\)

convert back to mixed number

2 \(\frac{1}{20}\)

Answer:

Step-by-step explanation:

a) Step1 : write in improper form

Step 2 : Find least common denominator

Step 3: Find equivalent fractions and then subtract

\(7\frac{1}{4}-5\frac{1}{5} = \frac{29}{4}-\frac{26}{5}\\\)

            \(= \frac{29*5}{4*5}-\frac{26*4}{5*4}\\\\=\frac{145}{20}-\frac{104}{20}\\\\=\frac{145-104}{20}\\\\=\frac{41}{20}\\\\=2\frac{1}{20}\)

b) Keep Change Flip method

\(4\frac{1}{4}\) ÷ \(2\frac{1}{5} = \frac{17}{4}\) ÷ \(\frac{11}{5}\)

            \(=\frac{17}{4}*\frac{5}{11}\\\\=\frac{85}{44}\\\\=1\frac{41}{44}\)

Answer: 12

Step-by-step explanation:

Area of trinagle = b * h /2

8*3= 24/2= 12

Answer:

  £225

Step-by-step explanation:

The relationship between the cost price (cp) and the selling price (sp) is ...

  cp + 5% × cp = sp

  cp(1.05) = sp . . . . . . collect terms

  cp = sp/1.05 . . . . . . divide by 1.05

  cp = £236.25/1.05 = £225

The original wholesale price was £225.

Answer:

y = -4/3 x - 1/3

Step-by-step explanation:

y = -4/3 x + b

5 = -4/3 (-4) + b

15 = 16 + 3b

b = -1/3

y = -4/3 x - 1/3

The equation of line b, parallel to line a and passing through the point (-4,5), is y = (3/4)x + 8.

To find the equation of line b, which is parallel to line a and passes through the point (-4,5), we need to use the fact that parallel lines have the same slope.

Given that line a has the equation y = (3/4)x - 3, we can determine its slope. The slope of line a is the coefficient of x, which is 3/4.

Since line b is parallel to line a, it will also have a slope of 3/4.

Using the slope-intercept form of a linear equation (y = mx + b), we can substitute the slope and the coordinates (-4,5) into the equation to solve for the y-intercept, b.

5 = (3/4)(-4) + b

Simplifying, we have:

5 = -3 + b

Adding 3 to both sides, we find:

b = 8

Therefore, the equation of line b, parallel to line a and passing through the point (-4,5), is y = (3/4)x + 8.

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Answer:

cos 25° = X/11

and

sin 65° = X/11

is this good enough or do you need more workings?

Answer:

C = 90°

Step-by-step explanation:

The interior angles in every triangle are equal to 180 degrees. So, this means that

\( \alpha + \beta + \gamma \\ = 180 \: degrees\)

Which means that A + B +C = 180 degrees

A=25°

B = 65°

C =?

C = 180° - (A + B)

C = 180° - (25° +65°)

C = 180° - 90°

C = 90°

Answer:

plot between 1/3 and 2/3 or 1/2.

Box plots present the shape of the distribution (density curve), Box plots can involve a categorical variable and a continuous numerical variable, Box plots show where the peak of the distribution is are the correct statement.

Instead of showing the raw data points, Box Plots takes the sample data and then present the ranges of values based on the quartiles and also display the asterisks for outliers that generally falls outside the whiskers.

Yes, the shape of distribution can be understood from a Box Plot. It can show whether a statistical data set is normally distributed or skewed.

A Box plot is a graph of the distribution that has Continuous variables. It is also applicable for Categorical variables.

Box Plot generally shows the below parameters: Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.

A size can be determined by using these parameters but is not directly seen in a Box Plot

Generally a Standard Deviation is not visualized by Box Plot. It mainly visualizes Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.

Yes, the peak of the distribution can be analyzed from Box Plot

Generally for Normal Distribution, Mean = Median and this is the point where the peak is seen.

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Answer:

857.96

Step-by-step explanation:

964/100=9.64

9.64x11=106.04

964-106.04=857.96

Answer:

Concept:

Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!

The values are given below as

The image below shows how to calculate the mean

By substituting values, we will have

Hence,

The mean = 10

To calculate the variance, we will use the formula below

Hence

The variance = 21

To calculate the standard deviation,

Hence,

The standard deviation is = 4.58

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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The infant's weight is 7 pounds and 10 ounces using weight conversion.

To convert the weight of the newborn from grams to pounds, we need to divide the weight by the number of grams in one pound, which is 453.59. So, 3,459 grams divided by 453.59 grams per pound is equal to 7.628 pounds.

To find the weight in ounces, we need to multiply the decimal part of the pounds by 16 (since there are 16 ounces in one pound). So, 0.628 x 16 = 10.048 ounces.

Therefore, the infant's weight is 7 pounds and 10 ounces.

It is important to note that weight conversion is often used in the medical field to monitor the health and growth of newborns. By tracking their weight in pounds and ounces, doctors can ensure that they are gaining weight at a healthy rate and are meeting their developmental milestones.

This information can also be used to make adjustments to their feeding or treatment plans if necessary. It is crucial for healthcare professionals to accurately convert weight measurements to ensure the best possible care for their patients.

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Answer:

16

Step-by-step explanation:

8 questions

2 answers on each question

8*2=16

Answer:

180 - 55 = angle 1

80 - 55 = 25 so 180 - 55 = 125

angle 1 = 125 degrees

The given box plot answers are,

a) 6

b) 5

c)3

d) 5

What is box plot?

   A suitable graphical representation of the concentration of the data is provided by box plots, often known as box-and-whisker plots or box-whisker plots. They also demonstrate how remote the extreme numbers are from the bulk of the data. Five numbers are used to create a box plot: the minimum value, first quartiles, median, third quartile, and maximum value.

Here in the given box plot middle line value is called median .Then ,

Median = 6

Now the maximum quartile = 8

The minimum quartile = 3

Now IQR is difference between the minimum and maximum quartile.

Then ,

=> IQR = 8-3 =5

Therefore the answers are

a) 6

b) 5

c)3

d) 5

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Answer:

well 1/3 is red

Step-by-step explanation:

Answer:

44/51

Step-by-step explanation:

1 5/6 ÷ 2 1/8

Change to improper fractions

1 5/6 = (6*1+5)/6 = 11/6

2 1/8 = (8*2 +1) /8 = 17/8

11/6 ÷17/8

Copy dot flip

11/6 * 8/17

11/17 * 8/6

11/17 *4/3

44/51

Answer:

perimeter is 36 cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

-Start by distributing the 2, -2(3m+1/2).

-Getting -6m-1, your equation should look like -40-6m-1=7m-2

-Combine -40 and -1 to get -41, and then add the -6m to the other side.

-The equation should look like -41=13m-2. Add the 2 to the -41 to get -39.

-Now, we have -39=13m. divide both sides by 13 to get m=-3.

Logarithms are a useful tool in determining the acidity or basicity of a solution. pH is a measure of the concentration of hydrogen ions in a solution and is calculated using the formula pH = -log[H+].

A solution with a pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.

Using logarithms, we can determine the pH of 7 solutions ranging from strong acid to neutral to strong base. To do this, we need to measure the concentration of hydrogen ions in each solution and then use the formula above to calculate the pH.

For example, if we have a solution with a hydrogen ion concentration of 0.001 M, we can calculate the pH as follows:

pH = -log(0.001) = 3

This solution would be considered a strong acid, as it has a pH below 7. Similarly, a solution with a hydrogen ion concentration of 10^-7 M (which is the same as a concentration of 1x10^-7 M) would have a pH of 7 and would be considered neutral.

Finally, a solution with a hydrogen ion concentration of 10^-11 M would have a pH of 11 and would be considered a strong base.

In summary, using logarithms, we can determine the acidity or basicity of a solution by calculating its pH. A pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.

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The quality control engineer will test the parts every 3 minutes.

To determine how often the quality control engineer tests the parts, we need to find the least common multiple (LCM) of the time it takes for the first machine to make a part and the time it takes for the second machine to make a part.
The first machine makes a part every 12 seconds, while the second machine makes a part every 45 seconds.
To find the LCM, we can list the multiples of each number and look for the smallest number that appears in both lists:
Multiples of 12: 12, 24, 36, 48, 60, 72, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, ...
From the lists above, we can see that the smallest number that appears in both lists is 180.
Therefore, the quality control engineer will test the parts every 180 seconds.
To express the answer in minutes, we can convert 180 seconds to minutes:
180 seconds ÷ 60 = 3 minutes

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