Four students wrote statements about cosecant, secant, and cotangent values as shown below.


Anik

The cosecant, secant, and cotangent of an acute angle may be greater than 1 or less than 1.

Isabella

The cosecant, secant, and cotangent of an acute angle are always greater than 1.

Kayla

The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.

Morris

The cosecant and secant of an acute angle may be greater than or equal to 1, but the cotangent of an acute angle is always less than 1.

Which student is correct?
Anik
Isabella
Kayla

Just multiplying the amount of possibilities in each category together will give us the total number of meals that can be made using the options provided.

This is known as the Fundamental Counting Principle. Using this principle, the total number of possible meals is:

6 main courses × 4 vegetables × 2 salads × 3 beverages = 144 possible meals

Therefore, there are 144 possible meals that can be made by choosing from the given options.

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Using the conversion formula,

In Australia on the country roads the speed is 60mph and on the motorways is 66mph.

In South Africa on the country roads the speed is 60mph and on the motorways is 72mph.

In Great Britain on the country roads the speed is 58mph and on the motorways is 67mph.

In Turkey on the country roads the speed is 54mph and on the motorways is 54mph.

To translate the number to miles per hour, we must multiply it by the conversion factor of 0.6214. As an illustration, 50 km/h is equivalent to 31.07 mph.

In the question,

By multiplying each speed limits with the conversion factor = 0.6214,

we can get the speed limits in miles per hour.

Therefore,

In Australia on the country roads the speed is 60mph and on the motorways is 66mph.

In South Africa on the country roads the speed is 60mph and on the motorways is 72mph.

In Great Britain on the country roads the speed is 58mph and on the motorways is 67mph.

In Turkey on the country roads the speed is 54mph and on the motorways is 54mph.

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The complete question is:

The table at right shows speed limits in some foreign countries in kilometers per hour. One kilometer is equal to miles. What are these speed limits in miles per hour?

The number from oldest to youngest is - 5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3 , the layer 5 is older than the layer 3 and line "B" represent - Fault .

How to do ordering of rock layers ?

Ordering of rock layers, also known as stratigraphy, is a process of arranging rock layers in a specific order based on their age and location. There are several principles that geologists use to determine the relative ages of rock layers:

Law of superposition: In an undisturbed sequence of rocks, the oldest rocks are at the bottom and the youngest rocks are at the top.

Principle of original horizontality: Layers of sediment are originally deposited horizontally, and any deformation of these layers must have occurred after deposition.

Principle of cross-cutting relationships: Any feature that cuts across a rock or rock layer is younger than the rock or layer that it cuts across.

Principle of inclusions: Any rock fragments included in another rock layer must be older than the rock layer that contains them.

Ordering of given rock layers :

The number from oldest to youngest is given below -

5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3

The age of layer 5 is older than the layer 3 .

The line "B" represent - Fault . A fault in rock is a fracture or break in the Earth's crust where rock on either side has moved relative to the other side.

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Answer: To find how much Godwin owes Aidan, we first need to calculate the total cost of the items Aidan purchased:

10 cans of soup for $8.69, so the cost per can of soup is $8.69/10 = $0.869 per can.

1 case of chili for $19.20, so the cost per can of chili is $19.20/24 = $0.80 per can.

Godwin takes 4 cans of soup at $0.869 per can, which is a total of 4 x $0.869 = $3.476 for the soup.

Godwin takes 12 cans of chili at $0.80 per can, which is a total of 12 x $0.80 = $9.60 for the chili.

Therefore, Godwin owes Aidan $3.476 + $9.60 = $13.076.

The unit rate of the soup is $0.869 per can.

The unit rate of the chili is $0.80 per can.

Step-by-step explanation:

There are 64 different two-digit numbers that can be formed using the digits 3,9,4,7,6,1,2 and 8 with repetition.

To see why, note that there are 8 possible choices for the first digit (any of the 8 given digits can be used) and 8 possible choices for the second digit (again, any of the 8 given digits can be used). Therefore, by the multiplication principle of counting, there are 8x8=64 possible two-digit numbers that can be formed.

To find all possible two-digit numbers, simply list all possible combinations of the given digits, allowing repetition. One example would be: 11, 12, 13, ..., 98, 99.

Alternatively, you can use the formula for counting with repetition, which is n^k where n is the number of choices for each digit and k is the number of digits. In this case, n=8 (since there are 8 possible digits) and k=2 (since we want two-digit numbers). Therefore, the total number of possible two-digit numbers is 8^2=64.

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Answer: 3, 5, and 7

Step-by-step explanation:

Vertical angles, corresponding angles, and alt. ext. angles

a)c = (31.5 - 17.5)/(31.5/7 + 17.5/7)

b)4 mph.

The equation to solve for the speed of the river's current is c = (31.5 - 17.5)/(31.5/7 + 17.5/7) = 4 mph. Therefore, the speed of the river's current is 4 miles per hour.

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The solution to this system of linear equations is x = 11/3, y = -3/13, and z = 1/12.

The augmented matrix of a system of linear equations is [[1,0,5,-(11)/(3)],[-4,1,-23,(68)/(3)],[5,0,25,-(43)/(3)]]. To solve this system, we can use the process of elimination.

Step 1: Add 4 times row 1 to row 2.

[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[5,0,25,-(43)/(3)]]

Step 2: Subtract 5 times row 1 from row 3.

[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[0,0,15,-(32)/(3)]]

Step 3: Divide row 2 by -13.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,15,-(32)/(3)]]

Step 4: Add 3 times row 2 to row 3.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,12,-(1)/(13)]]

Step 5: Divide row 3 by 12.

[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,1,(1)/(12)]]

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There are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.

To perform long division, we need to follow these steps:

Set up the long division problem with the dividend on the inside and the divisor on the outside of the division symbol.
Determine how many times the divisor can go into the first digit or group of digits of the dividend.
Write the result above the division symbol and multiply it by the divisor.
Subtract the result from the first digit or group of digits of the dividend.
Bring down the next digit or group of digits from the dividend and repeat the process until there are no more digits to bring down.
The final result is the quotient with any remainders.

For the first problem, 32.156 / 100, we can set it up like this:

```
100 | 32.156
```

Since 100 cannot go into 32, we need to bring down the next group of digits, which is 156. Now we have:

```
100 | 3215.6
```

100 can go into 3215 a total of 32 times, so we write 32 above the division symbol and multiply it by 100:

```
32
100 | 3215.6
  -3200
   -----
     15.6
```

Now we bring down the next group of digits, which is 6:

```
32.1
100 | 3215.6
  -3200
   -----
     156
```

100 can go into 156 a total of 1 time, so we write 1 above the division symbol and multiply it by 100:

```
32.16
100 | 3215.6
  -3200
   -----
     156
    -100
   -----
      56
```

Since there are no more digits to bring down, we are left with a remainder of 56. So the final result is 32.156 with a remainder of 56.

For the second problem, 174.787 / 0.01, we can set it up like this:

```
0.01 | 174.787
```

Since 0.01 cannot go into 174, we need to bring down the next group of digits, which is 787. Now we have:

```
0.01 | 17478.7
```

0.01 can go into 17478 a total of 1747800 times, so we write 1747800 above the division symbol and multiply it by 0.01:

```
1747800
0.01 | 17478.7
   -17478
    -----
        0.7
```

Since there are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.

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The possible numbers of hours Yolanda could rent the boat is 6 hours.

The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().

Here the given boat cost per hour = $7.

Offer he gets = $3.

Now writing a inequality then, t represent number of hours,

=> 7t-3[tex]\le[/tex]39

Now solving this inequality for t then,

=> 7t[tex]\le[/tex]39+3

=> 7t[tex]\le[/tex]42

=> t[tex]\le[/tex]42/7

=>t[tex]\le[/tex]6

Hence the possible numbers of hours Yolanda could rent the boat is 6 hours.

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Answer: x^3+x^2y–4y–4x  = (x-2)(x+2)(x+y)

The number of means is 13. Option B

We can use the formula for the nth term of an arithmetic sequence to solve the problem. Let d be the common difference and n be the number of terms between -65 and 125.

Then we have:

a + (n-1)d = 125 (1)

a + nd = -113 (2)

Subtracting equation (2) from equation (1), we get:

(n-1)d + 238 = 0

Solving for d, we get:

d = -238/(n-1)

Using the formula for the twelfth term, we have:

a + 11d = -113

Substituting the expression for d, we get:

a - 11(238/(n-1)) = -113

Multiplying both sides by n-1, we get:

a(n-1) - 11(238) = -113(n-1)

Substituting a = -65 and simplifying, we get:

n = 13

Therefore, the number of means is 13

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The probability that a person who tests positive actually has the

the disease is, 10%.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Given, A certain disease has an incidence rate of 0.8%.

Therefore, The probability that a person who tests positive actually has the disease is,

= (8/0.8)%.

= 10%.

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Answer:

(0,4)

Step-by-step explanation:

Your coordinates of your Y-intercept is where the line crosses over the Y line (the vertical line). This means your x (x,y) is always going to be 0 and your y is going to be the number in which the line crosses over your Y-line.

Answer: The flat rate cost is $25.70 and the cost per item is $2.30, so the total cost (y) can be represented as:

y = 2.30x + 25.70

This is in slope-intercept form, where the slope is 2.30 and the y-intercept is 25.70.

Step-by-step explanation:

For an expression 2(3a+2b−7), an equivalent expression is 6a + 4b - 14

The correct answer is an option (D)

Consider an expression 2(3a+2b−7)

We simplify this expression.

2(3a+2b−7)

To simplfy this expression, multiply each term of (3a+2b−7) by 2

2(3a+2b−7)

= 2 × (3a + 2b - 7)

= (2 × 3a) + (2 × 2b) - (2 × 7)

= 6a + 4b - 14

So, we get 2(3a+2b−7) = 6a + 4b - 14

Therefore, 6a + 4b - 14 is an equivalent expression to 2(3a+2b−7)

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The complete question is:

Which expression is equivalent to the given expression? 2(3a+2b−7) ​

A 5a+4b−5

B 6a+2b−7

C 6a+4b−7

D 6a+4b−14

a. The variable is the type of communication preference: postal service or email.

b. The population is the adult population in Puerto Rico.

c. The parameter being estimated is the percentage of adults who prefer postal mail to electronic mail.

d. The parameter being estimated is the percentage of adults who prefer postal mail to electronic mail.

e. The sample is the 600 adults that the graduate student surveyed.

a. The variable in this research project is the preferred method of communication for adults in Puerto Rico (postal mail or email).

b. The population in this research project is the adult population in Puerto Rico.

c. The sample in this research project is the 600 adults that the graduate student surveyed.

d. The parameter in this research project is the percentage of adults in Puerto Rico who prefer postal mail to email.

e. The statistic in this research project is the 250 adults who indicated their preference for the postal service out of the 600 adults surveyed. This statistic was used to estimate the parameter of 48% of adults in Puerto Rico preferring the postal service to email.

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Answer: See attached.

Step-by-step explanation:

     First, we will find the unit rate by dividing.

18 hours / 3 lawns = 6 hours per lawn

     Then, we can fill out the other values using this unit rate.

1 lawn * 6 hours = 6

12 hours / 6 hours = 2

       Lastly, we will use these two equivalent ratios we found above to fill out the table and then plot the points. See attached.

For a=7 the quadratic equation have no real roots. (4)

For a quadratic equation y=ax^(2)-6x+3 to have no real zeroes, the discriminant of the equation must be less than zero. The discriminant of a quadratic equation is given by the formula b^(2)-4ac, where a, b, and c are the coefficients of the equation. In this case, a=a, b=-6, and c=3.

Plugging these values into the formula for the discriminant, we get:

(-6)^(2)-4(a)(3)<0

36-12a<0

12a>36

a>3

Therefore, the values of a that will make the quadratic equation have no real zeroes are those that are greater than 3. This means that the correct answer is (4) a=7, since this is the only value of a that is greater than 3.

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Answer:

a) experimental : 4 ÷ 20 = 1/5 or 20%

Theoretical : 1/6

b) experimental: 18÷20= 9/10 or 90%

Theoretical : 5/6 or 83%

c) experimental: 2÷20 = 1/10 or 10%

Theoretical : 1/6

Answer: C (17)

Step-by-step explanation: We need to make the equation true so we take

2x times 17 to get 34  and so 34-22=12

After performing multiplication or division and simplify we get 2x2 − xy − 3y2 as the answer of this question.

The question is asking you to perform the multiplication or division and simplify:

x2 + 2xy + y2 ÷ x2 − y2 =

(x2 + 2xy + y2)(3x2 − xy − 2y2) ÷ (x2 − y2) =

3x4 − x3y − 2x2y2 − 3xy2 + 2xy3 + 2y4 ÷ (x2 − y2) =

3x4 − x3y − 2x2y2 − 2y4 ÷ (x2 − y2)

= 2x2 − xy − 3y2

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$x_1 = \frac{7}{2}, \ x_2 = \frac{11}{2}, \ x_3 = -\frac{1}{2}, \ x_4 = \frac{9}{2}$.

To solve this system of equations, first use the array method to organize the equations.

Array Method:

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 1 & 5 & 6 & 9 & 0 \\ 1 & 17 & 13 & 20 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Now, use row operations to solve the system. Begin by combining the first and third equations by adding them together.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 1 & 5 & 6 & 9 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Next, combine the second and fourth equations by subtracting the fourth equation from the second equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 7 & 2 & 9 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Then, combine the second and third equations by adding the second equation to the third equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 0 & 14 & 36 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Now, combine the first and third equations by subtracting the third equation from the first equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 0 & 14 & 36 & 0 \\ 0 & 0 & -2 & -9 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Finally, use back substitution to solve for the variables. Starting with $x_4$, use the fourth equation to solve for it:

$x_4 = \frac{9}{2}$

Then, use the third equation to solve for $x_3$:

$x_3 = -\frac{1}{2}$

Continuing this process, we can also solve for $x_2 = \frac{11}{2}$ and $x_1 = \frac{7}{2}$.

Therefore, the solution to the system is:

$x_1 = \frac{7}{2}, \ x_2 = \frac{11}{2}, \ x_3 = -\frac{1}{2}, \ x_4 = \frac{9}{2}$.

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The first step in solving by elimination is (4) Multiply top equation by 2

From the question, we have the following parameters that can be used in our computation:

5x + y = 9

10x - 7y = -18

To eliminate x the coefficient of x in both equations muet be the same i.e 10

Using the above as a guide, we have the following:

Multiply (1) by 2

So, we have

10x + 2y = 18

10x - 7y = -18

Hence, the first step is (4)

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By following the 6 steps explained, you can find the quotient of a multiple of 10 and any number.

To use place value to find the quotient of a multiple of 10 and a number, you can use the following steps:

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The statement, "Only datasets having a linear relationship between variables can be assessed using regression analyses" is False, because Non-Linear relationships also can be assessed, the correct option is (b)False.

The Regression Analysis can be used to assess the relationship between variables, including non-linear relationships.

There are various types of regression models that can capture non-linear relationships, such as polynomial regression, exponential regression, and logarithmic regression.

The interpretation of the regression coefficients and other statistics may be different in non-linear regression models compared to linear regression models.

Therefore, the given statement is (b)False.

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The axis of symmetry of a quadratic function can be found by taking the negative of the coefficient of the x term, and then dividing it by 2. In this case, the coefficient of the x term is -2, so the axis of symmetry is located at x = -1.

The key features of the quadratic function are the vertex, the y-intercept, and the x-intercepts. To find the vertex, substitute the x-value for the axis of symmetry into the equation. In this case, the vertex is located at (x, y) = (-1, 27).

The y-intercept is found by setting x = 0 and solving for y. This gives us y = -24, so the y-intercept is located at (0, -24).

To find the x-intercepts, set y = 0 and solve for x. In this case, the x-intercepts are located at (2, 0) and (6, 0).

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In response to the supplied query, we may state that Therefore, the area of the circle is approximately 113.1 cm² (rounded to one decimal place).

A circle is created in the plane by each point that is a specific distance from another point (center). Hence, it is a curve made up of points that are separated from one another by a defined distance in the plane. Moreover, it is rotationally symmetric about the centre at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "centre." A circular symmetry line is made by drawing a line through the circle. Moreover, it is rotationally symmetric about the centre at every angle.

We must make certain assumptions because the diagram was not created precisely. Assume that the quarter circle is a perfect quarter circle and that its radius is 12 cm (as given in the question).

A = r2, where r is the radius, is the formula for calculating a circle's surface area. Due to the fact that we only have a quarter of a circle, we must divide the outcome by 4. Hence, the quarter circle's area is:

[tex]A = (1/4)\pi r^2\\A = (1/4))\pi(12^2)\\A = (1/4))\pi(144)\\A = 36)\pi[/tex]

Therefore, the area of the shape is approximately 113.1 cm² (rounded to one decimal place).

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Answer:

the account balance will be $15, 485.41

Step-by-step explanation:

Compound interest, can be calculated using the formula FV = P*(1+R/N)^(N*T), where FV is the future value of the loan or investment, P is the initial principal amount, R is the annual interest rate, N represents the number of times interest is compounded per year, and T represents time in years.

5890*(105.61/100)*17

=15485.41

ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

We can use the logarithmic property that states that ln(a * b) = ln(a) + ln(b) to rewrite ln(144) in terms of ln(3) and ln(4).

First, we can find the prime factorization of 144:

[tex]144 = 2^4 * 3^2[/tex]

Using the property above, we can rewrite ln(144) as:

[tex]ln(144) = ln(2^4 * 3^2) = ln(2^4) + ln(3^2)[/tex]

Now, we can use another logarithmic property that states that ln(aᵇ) = b * ln(a) to simplify ln(2⁴) and ln(3²):

ln(144) = 4 ln(2) + 2 ln(3)

Therefore, ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

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