Oliver works 5 days a week. He drives 53 kilometres each day and walks a total of 25 kilometres over the week: He uses the following formula to calculate how far he travels in a working week.
Distance travelled = (53 km + 5 km) x number of days. How far does he travel in total? ​

Answer:

63.90 is greater than63.990

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Hello!

No 63.90 is not greater than 63.990

(I fixed this)

Answer:

12/19

Step-by-step explanation:

19/19 - 7/19 = 12/19

The table and graph is mentioned below.

In mathematics, a graph is a visual representation of a set of objects, often referred to as vertices or nodes, and the connections or edges that exist between them. Graphs are used to represent a wide range of mathematical concepts, such as functions, equations, and data sets.

A graph can be thought of as a collection of points or vertices that are connected by lines or edges. The way these vertices and edges are arranged can convey important information about the relationships between the objects being represented.

Graphs can be classified into different types, such as directed or undirected graphs, weighted or unweighted graphs, and cyclic or acyclic graphs. They can also be used to model real-world systems, such as social networks, transportation systems, and computer networks.

a)Table for Members:

Number of Movies (n) Cost (C1)

               0                 $75.00

               10                 $95.00

               20                 $115.00

               30                 $135.00

               40                 $155.00

               50                 $175.00

Table for Non-members:

Number of Movies (n) Cost (C2)

                0                 $5.75

                10                 $60.75

                20                 $115.75

                30                 $170.75

                40                 $225.75

                50                 $280.75

b) On the same set of axes, the graph is attached below.

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Different kinds of graphs, including directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs, can be distinguished.

In mathematics, a graph is a picture of a collection of things, also known as vertices or nodes, and the links or edges that join them. Numerous mathematical ideas, including functions, formulae, and data sets, are represented by graphs.

A collection of vertices or points linked by lines or edges is referred to as a graph. The arrangement of these vertices and edges can reveal crucial details about the connections between the things being represented.

Different kinds of graphs, including directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs, can be distinguished. Additionally, they can be used to simulate real-world systems like computer networks, transit systems, and social networks.

a)Table for Members:

Number of Movies (n) Cost (C1)

0                 $75.00

10                 $95.00

20                 $115.00

30                 $135.00

40                 $155.00

50                 $175.00

Table for Non-members:

Number of Movies (n) Cost (C2)

0                 $5.75

10                 $60.75

20                 $115.75

30                 $170.75

40                 $225.75

50                 $280.75

b) On the same set of axes, the graph is attached below.

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Answer:

Step-by-step explanation:

a. Variables:

D0 = Demand for nurses in 2000 = 2,000,000

S0 = Supply of nurses in 2000 = 1,890,000

D2020 = Projected demand for nurses in 2020 = 2,810,414

S2020 = Projected supply of nurses in 2020 = 2,001,998

Equations:

For 2000: D0 = S0

For 2020: D2020 = S2020

b. Using substitution, we can set the two equations equal to each other:

D0 = S0

2,000,000 = 1,890,000 + m(S0 - 1,890,000) (where m is the rate of increase in supply)

m = 0.063

Now we can use this value of m to find out during which year the supply of nurses was equal to the demand:

2,000,000 = 1,890,000 + 0.063(S - 1,890,000)

S = 2,013,008

Therefore, the supply of nurses was equal to the demand in the year 2013.

Answer:

Option 3: -2

Step-by-step explanation:

The slope of the graph is negative, and the only option with a negative term for the slope is -2.

So the slope of the graph is -2.

Answer:

wish i could herlp sorry have a great day

Step-by-step explanation:

Answer:

x > -2

Step-by-step explanation:

Answer:

{14,28,39}

Step-by-step explanation:

By the Triangle Inequality Theorem, if given side lengths \(a\), \(b\), and \(c\), where \(c\) is the longest side of the triangle, then \(a+b\geq c\) holds true.

For the first set of numbers, \(12+16\ngeq29\), so it doesn't represent the three sides of a triangle

For the second set of numbers, \(14+21\ngeq36\), so it doesn't represent the three sides of a triangle

For the third set of numbers, \(14+28\geq39\), so it does represent the three sides of a triangle

For the fourth set of numbers, \(8+14\ngeq24\), so it doesn't represent the three sides of a triangle

Answer:

Step-by-step explanation:

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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Answer:

36

Step-by-step explanation:

9x is equal to 9 multiplied by x.

x=4 so it is 9 x 4

9 x 4=36

The second term in the binomial expansion of (2r - 3s)¹² is -73728 r¹¹ s option (A) is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

(2r - 3s)¹²

Using nth term of the binomial expansion is:

= C (12, 2-1) (2r)¹²⁻²⁺¹ (-3s)²⁻¹

After solving

= -73728 r¹¹ s

Thus, the second term in the binomial expansion of (2r - 3s)¹² is -73728 r¹¹ s option (A) is correct.

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The given expression is equivalent to \($(1215)^{x/5}\).

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following equation -

\($(\sqrt[5]{1215})^{x}\)

For \($\sqrt[a]{x} = x^{1/a}\)

Using the rule, we can write -

\($(\sqrt[5]{1215})^{x}\) = \($(1215)^{x/5}\)

Therefore, the given expression is equivalent to \($(1215)^{x/5}\).

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Answer:

No

Step-by-step explanation:

they are not equivalent

Answer:

4x-53

Step-by-step explanation:

Boy=x

sis = x-53

father = 4x-53

Answer:

P=0

Step-by-step explanation:

-7+7(2+ p) = 8p +7

-7+14+7p=8p+7

-7+14+7p=8p+7

7+7p=8p+7

7+7p=8p+7

(Add/Subtract Like terms)

Subtract 7 from the left to the right.

It will become:

7p=8p+7-7

It will become:

7p=8p

Subtract 8p from both sides.

-1p=0

Or:

-p=0.

Since its still a negative, make it a positive.

p=0

Answer: (-3, 1)

explanation: I drew a graph and translated it!

The perimeter of the rhombus in this problem is given as follows:

19.8 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The diagonal length can be obtained as follows:

RU + UT = 7.

Applying the Pythagorean Theorem, the side length is obtained as follows:

x² + x² = 7²

2x² = 49

\(x = \sqrt{\frac{49}{2}}\)

x = 4.95.

Then the perimeter is given as follows:

P = 4 x 4.95

P = 19.8 units.

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The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.

Part A:

The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

Part B:

An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5.

Part C:

Simply, the domain is constrained by x=0.

We are obliged at x=6 .

This is because we have to avoid a negative profit.

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Answer:

if breadth is in cm then area is 4000cm^2

Step-by-step explanation:

if breadth is in meter area is 40m^2

formula

area =lb

Answer:

–59

Step-by-step explanation:

f(x) = -2x - 7

f(x) = -2(-4x + 6) - 7

f(x) = 8x - 12- 7

f(x) = 8x - 19

f(x) = 8(-5) - 19

f(x) = -40 - 19

f(x) = -40 - 19

f(x) = - 59

Answer: √74 is as simple as it can get. It factors to 37·2, both of which are prime numbers and neither of which is a perfect square. If you plug it into your calculator √74 ≈ 8.6.

An 86% confidence interval for the difference in age to leave mother is -3.10091

What is confidence Interval?

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given, Gorilla Baby sample

x means x bar here so, \(x_{1}\) = 3.21

\(s_{1}\) = 0.81

\(n_{1}\) = 64

Human Baby sample

x means x bar here so, \(x_{2}\) = 19.1

\(s_{2}\) = 2.16

\(n_{2}\) = 200

Confidence interval needs t score

t score = 1.18

86% confidence interval = \(x_{1}\) - \(x_{2}\) ± tc \(\sqrt{s^{2} {1} / n_{2} + s^{2} {2} / n_{2}\)

= 3.21 - 19.1 ± 1.18 √0.81²/64 +2.16²/200

= 3.21 - 19.1 ± 1.18 √0.033

= -3.10091

An 86% confidence interval for the difference in age to leave mother is -3.10091

The detail question is here,

A study based on the Association primate Ebmarah looked at the average age a baby gorilla leaves it’s mother versus the average age the human baby leaves it’s mother . Naturally they are different , so we don’t want a hypothesis test. Instead, find an  86% confidence interval  for the difference in age to leave mother.

Gorilla:

Sampled 64 babies

Stayed with mother on average 3.21 years

Standard deviation:  0.81

Human:

Sampled  200 babies

Stayed with mother on average 19.1 years

Standard deviation:  2.16

Matched  pairs  standard deviation :0.23

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1.

The question requires you to find csc of angle thetha

The formula to apply is;

So, First find sin of the angle theta, then its reciprocal

Sin theta= opposite side length / hypotenuse

Answer

0.7071

Or

Using surds

Cancel 8 both in the denominator and numerator to remain with

T

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

Hello!

We have two different scenarios that we have to solve in the question. We will be solving for both the x and y variable.

We were given the equation: -3y + 2x = -18

To solve for our variables, we will use the values given in our question.

Solve:

Lets solve for the value "y", where our x = 0

Plug in 0 to x and solve:

-3y + 2(0) = -18

-3y = -18

y = 6

Lets now solve for the value "x", where our y = 0

Plug in 0 to y and solve:

-3(0) + 2x = -18

2x = -18

x = -9

Therefore, our answers would be: y = 6, x = -9

Answer:

y = 6

x = -9

Answer:

10 feet

Step-by-step explanation:

Given,

Volume of right cylinder = 2000 π cubic feet.

Length ( l ) = 20 feet

To find : Radius ( r )

Formula : -

Volume of right cylinder = πr²h

πr²h = 2000 π

Divide π on both sides,

r²h = 2000

r² = 2000 / h

r² = 2000 / 20

r² = 100

= 10 x 10

r²= 10²

r = 10 feet

Hence,

the radius is 10 feet.

Answer:

Step-by-step explanation:

We have to follow these rules:

+/+ = +

-/- = +

+/- = -

-/+ = -

so

positive numbers:

+2/+3 ; -2/-3 ; -1/-3 ; +1/+3

negative numbers:

+2/-3 ; -2/+3 ; -1/+3 ; +1/-3