Jim is choosing between two exercise routines.In Routine #1, he does only running, burning 15.5 calories per minute.In Routine #2, he burns 26 calories walking. He then runs at a rate that burns 10.3 calories per minute.For what amounts of time spent running will Routine #1 burn more calories than Routine #2?Use t for the number of minutes spent running, and solve your Inequality for t.

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.

In this polynomial, we have:

Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)

Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)

Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)

Term 4: -1 (This is a constant term with a degree of 0.)

We can see that there are four distinct terms separated by addition and subtraction operations:

18x³, -2x², 4x, and -1.

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The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

\( \dfrac{2}{x} - 9\)

Step-by-step explanation:

the quotient of 2 and x:

\( \dfrac{2}{x} \)

9 less than the quotient of 2 and x:

\( \dfrac{2}{x} - 9\)

The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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(0.4n)(16n) = (0.4)(16)(n)(n) = 6.4n²

Answer: 6.4n²

Hope this helps!! plz mark brainliest??

The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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During the morning rush hour, there are 6,400 junior and high school students, 3,400 adults, and 5,800 senior citizens riding the subway.

Let's assume the number of junior and high school students riding the subway during the morning rush hour is J, the number of adults is A, and the number of senior citizens is S.

From the given information, we can set up a system of equations based on the number of riders and the revenue generated.

Equation 1: J + A + S = 15,600 (total number of riders)

Equation 2: 1.04J + 2.20A + 1.04S = 32,464 (revenue equation with original ticket prices)

Equation 3: 1.24J + 2.60A + 1.04S = 38,264 (revenue equation with new ticket prices)

We can start by subtracting Equation 2 from Equation 3 to eliminate the J and S terms:

0.2J + 0.4A = 3,800

Next, we can multiply Equation 1 by 0.2 and subtract it from the above equation to eliminate the J term:

0.4A - 0.2J - 0.2A = 3,800 - 3,120

0.2A = 680

A = 680 / 0.2 = 3,400

Now, we can substitute the value of A back into Equation 1 to find the values of J and S:

J + 3,400 + S = 15,600

J + S = 15,600 - 3,400

J + S = 12,200

We have two equations with two variables (J + S = 12,200 and 1.04J + 1.04S = 12,264). By solving these equations simultaneously, we find J = 6,400 and S = 5,800.

Therefore, during the morning rush hour, there are 6,400 junior and high school students, 3,400 adults, and 5,800 senior citizens riding the subway.

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To find the number of subway riders in each category, we set up a system of equations based on the total number of passengers and the total revenue. Solving this system will give us the number of junior and high school students, adults, and senior citizens. The number of riders doesn't change with the increase of ticket prices.

To solve this problem, we set up a system of equations based on the information given in the question.

Let's denote the number of junior and high school students as J, adults as A, and senior citizens as S. We know that there's total of 15,600 passengers, so:

J + A + S = 15,600

We also know that the total revenue was $32,464. Given the ticket prices for each group, we can write:

$1.04J + $2.20A + $1.04S = $32,464

Solving this system of equations (possibly with the help of a calculator or computer software), we can find the number of riders in each category.

The number of riders for each category would only change if the number of riders changes, not the price of the tickets, so when the prices increase, the number of riders remains the same.

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

Slope is the change in Y over the change in x:

Slope = (42 - 18) / (8-2)

Slope = 24/6

Slope = 4

The answer for blanks in statements are, an x-intercept of 1 , -3, x>1 , increasing , 7.5.

Many mathematical and real-world phenomena are described by functions. Modeling real-world occurrences like population increase, interest rates, or physical motion is frequently done using them. There are many distinct features that functions can have, including continuity, differentiability, and periodicity. Functions can also be linear or nonlinear.

The domain and range of functions are crucial components. The set of all potential input values makes up the domain of a function, whereas the set of all possible output values makes up the range. The behaviour of a function, such as whether it is increasing, decreasing, or constant, can also be used to categorize it. A function's graph shows the relationship between its input and output values graphically.

Function h has an x-intercept of 1 and a y-intercept of -3.  The function is positive for x>1 and increasing on all intervals of x. The average rate of change for the function on the interval [0, 2] is 7.5

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ANSWER:

21 sides

STEP-BY-STEP EXPLANATION:

We can calculate the number of sides by means of the following equation

Replacing and solving for n:

Therefore this polygon has a total of 21 sides

Answer:

2/3 book/hour

Step-by-step explanation:

1/2 multiplied by 4/3= 2/3

9514 1404 393

Answer:

  66.5 cm²

Step-by-step explanation:

A horizontal line at the "knee" on the right will divide the figure into a 4 cm by 2 cm rectangle, and a trapezoid with bases 4 cm and 9 cm, and height 11-2 = 9 cm. Then the total area of the figure is ...

  A = LW + 1/2(b1 +b2)h

  A = (4 cm)(2 cm) + (1/2)(4 cm +9 cm)(9 cm) = 8 cm² +58.5 cm²

  A = 66.5 cm² . . . . area of the figure

Answer:

2x^3-2x^2+x

Step-by-step explanation:

Just trust me!

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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The null and alternative hypotheses can be stated as follows:

c. H0: µ = 12, Ha: µ ≠ 12

The null hypothesis (H0) assumes that the population mean content of the bottles is 12 ounces, indicating perfect adjustment of the filling machine. The alternative hypothesis (Ha) states that the population mean content is not equal to 12 ounces, suggesting that the machine is not in perfect adjustment.

The rejection region for α = 0.01 can be specified as:

c. |t| > 2.68

This means that we would reject the null hypothesis if the absolute value of the calculated t-statistic is greater than 2.68.

To calculate the p-value, we need the t-statistic corresponding to the sample mean and standard deviation. With a sample mean of 11.88 ounces, a standard deviation of 0.35 ounces, and a sample size of 49, we can calculate the t-statistic. The p-value represents the probability of observing a sample mean as extreme as the one obtained, assuming the null hypothesis is true.

The p-value cannot be determined without the t-statistic value or the corresponding degrees of freedom.

Without the p-value, we cannot draw a definitive conclusion. To make a conclusion, we would compare the calculated t-statistic to the critical t-value based on the chosen significance level (α = 0.01). If the calculated t-statistic falls within the rejection region (|t| > 2.68), we would reject the null hypothesis. If the calculated t-statistic falls outside the rejection region, we would fail to reject the null hypothesis.

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Step-by-step explanation:

Triangle X with vertices (−2, 4), (2, 4), and (−2, 2)

Two similar triangles have the same corresponding ratio thus the triangle similar to{ (−1, 2), (1, 2), and (−1, 1) } is { (−2, 4), (2, 4), and (−2, 2) } thus option (A) will be correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

As per the given vertices of a triangle (−1, 2), (1, 2), and (−1, 1).

The plot of the triangle using the above vertices plotted below,

The triangle with vertices (−2, 4), (2, 4), and (−2, 2) also has been plotted.

The ratio of the corresponding length of the blue triangle to purple is 4/2 = 2.

Hence "Two similar triangles have the same corresponding ratio thus the triangle similar to{ (−1, 2), (1, 2), and (−1, 1) } is { (−2, 4), (2, 4), and (−2, 2)". }

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Answer:

Make the -4 exponent in the denominator positive.

Answer: B.1.50

Step-by-step explanation:

22.50 divided by 5 = 4.5

21.00 divided by 3.5 = 6.0

           6 - 4.5 = 1.50

This will tell us the differences in

  how much money they made.

9514 1404 393

Answer:

  C. Division: (x^2-5x+3)÷(x-2)=x-3+-3/x-2

Step-by-step explanation:

The set of polynomials is closed under all basic arithmetic operations except division. The reciprocal of a (non-constant) polynomial is not a polynomial.

The division example shown in choice C illustrates the set is not closed under division.

Answer:

3.65

Step-by-step explanation:

Answer:

50.2 in.³

Step-by-step explanation:

Volume of cylinder, V = πr²h.

V = πr²h

V = 3.14 × (2 in.)² × 4 in.

V = 50.2 in.³

Answer:

10 I think that is right.