3.) Fill in the blank.
___ + 1 = sec^2 0
A.) 1
B.) tan^2 0
C.) -cos^2 0
D.) 0
E.) sec^2 0

To find the value of b in the exponential function, we can use the given data points for the years 2010 and 2012. By substituting the values into the equations, we can solve for b.

To find the value of b in the exponential function, we can use the given data points for the years 2010 and 2012. Let's start by setting up two equations:

p(0) = ab0 = a = 425

p(2) = ab2 = 612

From the first equation, we know that a = 425. Substituting this value into the second equation:

425b2 = 612

Divide both sides of the equation by 425:

b2 = 612/425

Take the square root of both sides:

b = √(612/425)

Simplifying the expression gives us the value of b.

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Answer: E) 1/5

Step-by-step explanation:

The probability of any member being selected for each of the 3 posts is 1/10 that is they have equal probabilities of being selected for any of the posts.

The probability that harry would be selected for;

Secretary Ps= 1/10

Treasurer Pt = 1/10

So the probability of being selected for either secretary or treasurer is

P = Ps + Pt

P = 1/10 + 1/10

P = 2/10

P = 1/5

Note: ignore the sequence of selection

Answer:

So such system with fewer equations than unknowns can never have a unique solution.

Step-by-step explanation:

Linear equations are equations which contain variable with degree 1.

The variables can be 1 or 2 or any other number

say there are n varaibles

Then to solve this we must have n independent equations.

If number of equations are less than number of variables we can have parametric solutions only with infinite points lying on it.

There is no chance for this to have a unique solution.

For unique solutions, there must be equal number of equations with the variables and the determinant formed by the coefficients should not be 0.

So such system with fewer equations than unknowns can never have a unique solution.

Answer:

2.233444444e62 is the answer

Answer: It will take the largest pipe 5.5 hours to fill the swimming pool alone.

It will take the smallest pipe 16.5 hrs to fill the swimming pool alone.

It will take the other pipe 11 hours to fill the pool alone.

Step-by-step explanation: let time needed to fill the swimming pool by the largest pipe be x ... eq (1)

Let time needed to fill the swimming pool by the smallest pipe be 3x ... eq(2)

Let time needed to fill the swimming pool by the other pipe be 2x ...eq(3)

The job to be done (to fill a swimming pool) be 3/x +3/3x+3/2x=1 ... eq(4)

Multiply 6x on both sides you will get:

6(3)+2(3)+3(3)=6x

18+6+9=6x

33=6x

33/6=x

X=5.5hours

Substitute x=5.5 into EQ 2 and 3

3x=3×5.5=16.5hours

2x=2×5.5=11hours

Check: substitute the value of x into eq3/5.5+3/16.5+3/11

0.545+0.182+0.273=0.9997=1

Answer: c. The mean is much larger than the median

Step-by-step explanation:

A dataset is skewed to the right when the peak of the dataset is located in the left( left of the mean), and it has a long right tail. It is also call positive skewed distribution. One of the characteristics of right skewed dataset is that the mean of the dataset is always greater/larger than the median and mode.

Therefore, for the case above if the mean is much larger than the median, it indicates that the dataset is skewed to the right.

A dataset is skewed to the right when the mean is much larger than the median. Therefore, the correct answer is option c.

When a dataset is skewed to the right, it means that the distribution of data is not symmetric, and it is stretched out more towards the higher values (right side) than the lower values (left side). This can be due to the presence of outliers or a natural characteristic of the data.

Now, let's look at why option "c" indicates right skewness:

c. The mean is much larger than the median.

The mean is the arithmetic average of all the values in the dataset, while the median is the middle value when the data is arranged in order. When a dataset is positively skewed (skewed to the right), it means that there are some significantly larger values in the right tail of the distribution that pull the mean to the right (towards higher values).

In this situation:

The mean gets pulled toward the larger values because the larger values have a greater impact on the mean due to their magnitude.

The median remains closer to the bulk of the data because it is not affected by extreme values as much as the mean.

So, when the mean is much larger than the median, it is an indication that there are significant outliers or a longer right tail in the dataset, which is a characteristic of a right-skewed distribution.

Therefore, the correct answer is option c.

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Answer:

knowledge base

Step-by-step explanation:

Knowledge base is a database used to retrieve information both in structured and unstructured form. It is like an online library.

These systems evaluate user input which can be keywords or phrases in English via artificial intelligence algorithms and return the desired output.

Knowledge management systems utilize a database management system (DBMS) to help users find information through natural language queries, facilitating the handling of large datasets and information retrieval across various fields.

Knowledge management systems use a large database called a database management system (DBMS) that allows users to find information by entering keywords or questions in normal English phrases. A DBMS is a software package that enables the creation, storage, maintenance, manipulation, and retrieval of large datasets distributed over one or more files.

For instance, systems like Microsoft Access, Oracle, FileMaker Pro, and Avanquest MyDataBase provide such functionalities that help in managing data efficiently.

These systems are crucial in handling vast amounts of information and assist in translating user queries into actionable data through a friendly interface designed to interpret natural language input. They are critical in various fields including personal, business, government, and scientific endeavors, facilitating a seamless flow of information.

Answer:

A

Step-by-step explanation:

p = 25 + 5s

s = amount of shoes sold

Rich sold 7 shoes. Plug in 7 for s

p = 25 + 5(7)

p = 25 + 35

p = 60

Answer: the correct answer is a. $60

Step-by-step explanation:

Using the formula that states Rich's weekly salary

P= 25 + 5s , where p is the salary and s the number of pairs sold, then

P= $25 + $5*7

P=$25 + $ 35

P= $ 60

Answer:

$309.18

Step-by-step explanation:

To pay off in 12 months = 12 * 657.80 = $7,893.6

To pay off in 18 months = 18 * 455.71 = $8202.78

If he takes the lower monthly payments, he will end up paying 8202.78 - 7893.6 = $309.18

Answer:

A. Esmeralda converted the mixed number to the wrong improper fraction.

D. Esmeralda did not divide –24 by 6 correctly.

E.  Esmeralda did not use the reciprocal of the divisor.

Step-by-step explanation:

Evaluating Esmerald's simplified expression, the errors in her evaluation are :

The appropriate evaluation procedure should be :

[tex]\frac{-5\frac{1}{4}}{\frac{3}{2}}[/tex]

Convert the Numerator to an improper fraction

[tex]\frac{\frac{21}{4}}{\frac{3}{2}}[/tex]

Take the reciprocal of the denominator

[tex]\frac{3}{2} = \frac{2}{3} [/tex]

Multiply the Numerator by the reciprocal of the denominator

[tex](-\frac{21}{4} )(\frac{2}{3}) = - \frac{42}{12} = -3 \frac{1}{2}[/tex]

Therefore, Esmeralda made three errors in her simplification procedure.

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Answer:

The diameters of circles that could fit completely inside circle O are 25, 36, 42, 48 and 54.

Step-by-step explanation:

The actual diameter of the circle:

[tex]\pi r^{2} = 16 x \\2\pi r = x\\\\16(2\pi r)=16x\\\\32\pi r= \pi r^{2} \\\\\frac{32\pi r}{\pi r} = \frac{\pi r^{2} \\}{\pi r} \\\\r = 32[/tex]

Since the radius is equal to 32 units, the diameter is equal to 64 units.

Therefore, the diameters of circles that could fit completely inside circle O must be smaller than or equal to 64.

Answer: the number of single-crust cherry pies that was sold is 16

the number of double-crust apple pies that was sold is 20

Step-by-step explanation:

Let x represent the number of single-crust cherry pies that was sold.

Let y represent the number of double-crust apple pies that was sold.

The total number of pies sold on a busy Friday was 36. This means that

x + y = 36

Grandma's Bakery sells single-crust apple pie for $6.99 and double-crust cherry pie for $10.99. If the amount collected for all the pies that day was $331.64, it means that

6.99x + 10.99y = 331.64 - - - - - - - - -1

Substituting x = 36 - y into equation 1, it becomes

6.99(36 - y) + 10.99y = 331.64

251.64 - 6.99y + 10.99y = 331.64

- 6.99y + 10.99y = 331.64 - 251.64

4y = 80

y = 80/4 = 20

x = 36 - y = x = 36 - 20

x = 16

Answer:

1 3 5

Step-by-step explanation:

Answer:

Condition 1:   y>0

Condition 2:  x+y>-2

Step-by-step explanation:

We are told that we have a set of points in the Cartesian system (i.e. x-y coordinate), so we can define our point as:

[tex](x,y)[/tex]

We are given two conditions and we want to create a system of inequalities. Now, generally speaking, inequalities are expressions relating mathematical expressions through 'comparison' (i.e. less than, greater than, or less/greater and equal to) usually recognized by [tex]<[/tex], [tex]>[/tex], [tex]\leq[/tex] and [tex]\geq[/tex], respectively.

So in our case let set up our inequalities.

Condition 1: the y-coordinate is positive

This can be mathematically translated as

[tex]y>0[/tex]

(i.e. [tex]y[/tex] is greater than 0, therefore positive)

Condition 2: the sum of the coordinates is more than -2

This can be mathematically translated as

[tex]x+y>-2[/tex]

(i.e. the summation of the two coordinates is greater than -2 but not equal to).

The system of inequalities described by the two conditions is:

[tex]y>0\\x+y>-2[/tex]

Final answer:

The two conditions given translate to the system of inequalities y > 0 and x + y > -2, which describe a specific region in the xy-coordinate plane.

Explanation:

The two conditions given by the student describe a certain region in the xy-coordinate plane. To translate these conditions into a system of inequalities, we first establish the inequality representation of each condition:

Condition 1 states that the y-coordinate is positive, which means any y value must be greater than zero. Therefore, this can be written as y > 0.

Condition 2 requires that the sum of the coordinates (x + y) is more than -2. Therefore, this inequality is x + y > -2.

Together, these two conditions form the following system of inequalities to describe the set of points in the xy-coordinate plane:

y > 0

x + y > -2

Answer:

[tex]\displaystyle -11 = x[/tex]

Step-by-step explanation:

3x + 15 = x - 7

- 3x + 7 - 3x + 7

____________

[tex]\displaystyle \frac{22}{-2} = \frac{-2x}{-2} \\ \\ -11 = x[/tex]

I am joyous to assist you anytime.

Answer:

the rise of the center of the rail will be given by =[tex]\sqrt{hypotenuse^{2}\hspace{0.15cm} -\hspace{0.15cm} base^{2} }[/tex]

= [tex]\sqrt{1500.065^{2} \hspace{0.15cm} -\hspace{0.15cm}1500^{2} }[/tex] m = 13.964 m

Step-by-step explanation:

i) the normal length of the railroad is 3 km = 3000 m.

ii) on a hot day day the railroad rail expands by 13cm  = 0.13m

iii) the center of the railroad is at 1500 m which is half of the total length.

iv) the expansion of the railroad in either half of the road is 0.065m which is half of the total expansion.

v) each half of the railroad can be represented by a right angled triangle whose base will be = 1500 m and hypotenuse will be = 1500.065 m .

vi) the rise of the center of the rail will be given by =[tex]\sqrt{hypotenuse^{2}\hspace{0.15cm} -\hspace{0.15cm} base^{2} }[/tex]

= [tex]\sqrt{1500.065^{2} \hspace{0.15cm} -\hspace{0.15cm}1500^{2} }[/tex] m = 13.964 m

The center of the rail would rise about 16.06 meters above the ground.

To find out how much the center of the rail rises above the ground due to expansion:

we can consider that the rail expands uniformly along its length.

If it expands by 13 cm over a length of 3 km, we can calculate the rise at the center using trigonometry, considering that the expansion causes the rail to form a very shallow arc.

The expansion forms a segment of a circle, where the rail length is the arc length, and the rise at the center is the height of the segment. We can use the formula for the height of a segment of a circle:

[tex]\[ h = r - \sqrt{r^2 - \left(\frac{l}{2}\right)^2} \][/tex]

Where:

h is the height of the segment (the rise at the center),

r  is the radius of the circle (which we can approximate as the radius of the Earth, as the rail is very long compared to its curvature),

l is the arc length of the segment (the expansion of the rail).

Given that the Earth's radius is approximately 6371 km, we need to convert all lengths to meters:

[tex]\[ r = 6371 \times 1000 \text{ meters} \][/tex]

[tex]\[ l = 3 \times 1000 \times 100 \text{ meters} \][/tex]

[tex]\[ h = 6371 \times 1000 - \sqrt{(6371 \times 1000)^2 - \left(\frac{3 \times 1000 \times 100}{2}\right)^2} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{(6371000)^2 - (150000)^2} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{40641464900000 - 22500000000} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{40641442400000} \][/tex]

[tex]\[ h \approx 6371000 - 6370983.94 \][/tex]

[tex]\[ h \approx 16.06 \text{ meters} \][/tex]

Answer:

The Subtraction equation use to find the age of his oldest relative is [tex]x-79=5[/tex].

Step-by-step explanation:

Given:

Age of youngest  relative = 5 years

We need to write a subtraction equation that could be used to find the age of his oldest relative.

Solution:

Let the age of the oldest relative be 'x'.

Now given:

Age of youngest  relative is 79 years less than the age of his oldest relative.

So we can say that;

Age of oldest relative minus 79 is equal to Age of the youngest relative.

framing in equation form we get;

[tex]x-79=5[/tex]

Hence the Subtraction equation use to find the age of his oldest relative is [tex]x-79=5[/tex].

Final answer:

The subtraction equation to find the age of Curry's oldest relative, based on the given information, is x - 5 = 79. Solving this equation reveals that the oldest relative is 84 years old.

Explanation:

The question involves setting up a subtraction equation to find the age of Curry's oldest relative, given that the youngest relative is 5 years old and this is 79 years less than the age of the oldest relative. We can represent the age of the oldest relative as x. The equation is based on the information that the difference in age between the oldest and youngest relatives is 79 years. Therefore, the equation can be set up as x - 5 = 79.

To solve for x, which represents the age of the oldest relative, you would add 5 to both sides of the equation to isolate x on one side. This results in x = 84. So, the oldest relative is 84 years old.

Answer:

  1.685·10^-1 inches

Step-by-step explanation:

To find the total thickness, multiply the thickness of each sheet by the number of sheets and add the values for the different kinds of sheets:

  (15)(4.3·10^-3) +(20)(5.2·10^-3) = (64.5 +104.0)·10^-3 = 168.5·10^-3

  = 1.685·10^-1 . . . inches

Option A:

Hence, x ÷ 4 > x – 12 is true for x = 20.

Solution:

To find which is the suitable inequality is true for the value x = 20.

Option A: x ÷ 4 > x – 12

⇒ [tex]\frac{x}{4}>x-12[/tex]

Multiply 4 on both sides of the inequality,

⇒ x > 4x – 48

Subtract 4x on both sides of the inequality,

⇒ –3x > – 48

⇒ 3x > 48

Divide 3 on both sides,

⇒ x > 16

If x = 20, then 20 > 16 is true.

Option B: 2x < x +22

Subtract x on both sides of the inequality,

⇒ x < 22

If x = 20, then 20 < 22 is false.

Option C: x + 30 > 3x

Subtract x on both sides of the inequality,

⇒ 30 > 2x

Divide by 2 on both sides of the inequality,

⇒ 15 > x

If x = 20, then 15 > 20 is false.

Option D: x – 5 < 2x – 35

Subtract x on both sides of the inequality,

⇒ – 5 < x – 35

Add 35 on both sides of the inequality,

⇒ 30 < x

If x = 20, then 30 < 20 is false.

Hence, x ÷ 4 > x – 12 is true for x = 20.

Final answer:

A person can talk for at most 19 minutes on a long-distance call without exceeding a $2 limit, accounting for the initial charge and the cost of additional minutes.

Explanation:

To find out at most how many minutes a person can talk on a phone without exceeding $2, considering the initial charge is 40 cents for the first three minutes, and 10 cents for each additional minute, we need to calculate the total cost based on the number of minutes.

The problem can be broken down as follows:

The cost for the first 3 minutes is 40 cents.

After the initial 3 minutes, each additional minute costs 10 cents.

We have a budget of $2 (or 200 cents) to not exceed.

First, subtract the initial 40 cents from the total budget:

200 cents - 40 cents = 160 cents

With 160 cents left and each additional minute costing 10 cents:

160 cents[tex]\(\div\)[/tex] 10 cents = 16 additional minutes

Therefore, adding the initial 3 minutes:

3 + 16 = 19 minutes

A person can talk for at most 19 minutes without exceeding a $2 limit.

The student uses Census sampling, a technique where every individual in a chosen population is surveyed. This method is reasonable for small populations, but can be impractical for larger groups.

The sampling technique used by the community college student in his statistics class is called Census sampling. This is because the student is collecting data from every individual in the total population of his statistics class. In other words, the student is not selecting a random or specific subset of the class; he is including everyone in his study. This can be useful for small populations, like a single class, as it provides data from all members, but it can be time-consuming and impractical for larger groups or populations.

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Answer:

9.6.

Step-by-step explanation:

Because DE || AC:

x/12 = 8/10

10x = 96

x = 9.6.

Answer:

Part 1) The slopes are negative reciprocals of one another.

Part 2) There is no relationship.

Step-by-step explanation:

Part 1)

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

Part 2)

The y-intercept is the value of y when the value of x is equal to zero

Two linear functions that are perpendicular, could have the same y-intercept (the y-intercept would be the point of intersection between both lines)

so

There is no relationship

Yes, it is possible to get three different values for the same statistic when sampling from a set population due to sampling variation.

Yes, it is possible to get three different values for the same statistic when sampling from a set population.

For example, let's consider a population of students' test scores. If three different samples are taken from this population, each sample may have different scores, resulting in different values for the same statistic such as the mean.

This variability in sample statistics is due to sampling variation, which is a natural occurrence when selecting different samples from the same population.

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Answer: C. 225

Step-by-step explanation:

To get the total population (x), we will take the 40% of the total population and equate to 90

40%× x = 90

40/100 × x = 90

40x/100= 90

Cross multiplying,

40x = 100 × 90.

x = 9000/40

x =225 C

Answer:

The Inequality modelling the equation is [tex]425\leq x\leq 523[/tex].

The cafeteria typically serve lunch for students between 425 to 523.

Step-by-step explanation:

Given:

Each students pays for lunch = $2.75

Cafeteria brings between $1168.75 and $1438.25.

We need to find the number of students cafeteria typically serve.

Solution:

Let the number of student served be 'x'.

Now we can say that;

Total money make is equal to Each students pays for lunch multiplied by number of students served.

But total money made is in the form of range so we can say that;

[tex]1168.75\leq 2.75x\leq 1438.25[/tex]

Now Dividing all sides by 2.75 we get;

[tex]\frac{1168.75}{2.75}\leq \frac{2.75x}{2.75}\leq \frac{1438.25}{2.75}\\\\425\leq x\leq 523[/tex]

Hence the Inequality modelling the equation is [tex]425\leq x\leq 523[/tex].

Hence we can say that, The cafeteria typically serve students between 425 to 523.

Answer:

Hallie ride 62 miles on bicycle.

Step-by-step explanation:

Given:

Let the number of miles Samantha rode be 'x'.

Hallie rode her bicycle 7 miles less than 3 times the number of miles Samantha rode.

It means that number of miles Hallie ride is equal to 3 multiplied by number of miles Samantha rode and then subtracting by 7.

framing in equation form we get;

number of miles Hallie ride = [tex]3x-7[/tex]

But Given:

number of miles Samantha rode =23 miles.

Now by substituting the value of [tex]x=23[/tex] in above equation we get;

number of miles Hallie ride = [tex]3x-7 = 3\times23-7 = 69-7 = 62 \ miles[/tex]

Hence Hallie ride 62 miles on bicycle.

Answer:

Step-by-step explanation:

a)

p(d) - probability of a rivet being defective

p(r) - probability of seam needing to be reworked

The probability of the seem needing to be reworked is equal to the probability that ANY of 24 rivets is defective

Thus the probability that none of the 25 rivets is defective is 1-p(r)

p(r) = 16%, thus 1-p(r) = 84%

1-p(r) = (1-p(d))^24

0.84 = (1-p(d))^24

0.84^(1/24) = 1-p(d)

==> 1-p(d) = 0.9927615998

==> p(d) = 1-0.9927

==> p(d) = 0.0073

b) given p(r) = 8%, thus 1-p(r) = 92%

1-p(r) = (1-p(d))^24

0.92 = (1-p(d))^24

0.92^(1/24) = 1-p(d)

==> 1-p(d) = 0.99653179446

==> p(d) = 1-0.9965

==> p(d) = 0.0035

Answer:

36

Step-by-step explanation:

Pretty simple

Multiply the numbers of different type of wood by the different type of length by the different type of width which is 4x3x3 = 36

4 wood type A B C D

3 length type L1 L2 L3

3 width type 1 2 3

So for wood A we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)

for wood B we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)

for wood C we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)

for wood D we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3) if we count the combinations together we will arrive at 36