The dual bar chart below shows the results of a survey asking a group
of 140 people about their favourite pet.
Given that 40 people said
that cats were their favourite
pets, complete the table.
Favourite pet Frequency
Cat
40
Frequency
Dog
Hamster
Other
Cat
Dog Hamster Other
Favourite pet​

Answer:

After 10 hours, Jared is the most expensive sitter

Explanation:

Given that Kathy babysits for $7.25 an hour, plus $5.75 in transport cost, and

Jared babysits $7.50 an hour, plus $3.25 in transport cost.

We want to know after how many hours is Jared the most expensive sitter.

In an equation form, we write the cost of babysitting for x hours for

Kathy as: 7.25x + 5.75

Jared as 7.50x + 3.25

We want to know at what value of x is

7.50x + 3.25 > 7.25x + 5.75

Solving for x in the above inequality

Subract 7.25x from both sides:

7.50x + 3.25 - 7.25x > 5.75

0.25x + 3.25 > 5.75

Subtract 3.25 from both sides

0.25x > 5.75 - 3.25

0.25x > 2.5

Divide both sides by 0.25

x > 2.5/0.25 = 10

x > 10

Therefore, after 10 hours, Jared is the more expensive sitter.

Thus, the third-order Taylor polynomial for f(x) = cos(x) at a = 0 is: \(P_3(x) = 1 - x^2 / 2! + x^4 / 4!\).

Taylor Polynomials:

We have f(x) = cos(-5x) = cos(0 - 5x), so we can use the Taylor series for cos(x) centered at a = 0:

cos(x) = Σ\((-1)^n * x^(2n) / (2n)!\)

Thus, we have:

\(P_1(x) = cos(0) + (-5x) * (-sin(0)) = 1\\P_2(x) = 1 + 0 + (-5x)^2 / 2! = 1 + 12.5x^2\\P_3(x) = 1 + 0 + (-5x)^2 / 2! + 0 + (-5x)^4 / 4! = 1 + 12.5x^2 + 52.0833x^4\\P_4(x) = 1 + 0 + (-5x)^2 / 2! + 0 + (-5x)^4 / 4! + 0 + (-5x)^6 / 6! = 1 + 12.5x^2 + 52.0833x^4 + 136.7188x^6\)

Interval of Convergence:

The power series given is:

Σ\((2k+1)*(x-2)^k\)

Using the ratio test, we have: limit:

\(|(2k+3)(x-2)^(k+1) / ((2k+1)(x-2)^k)| = |x-2| lim |2k+3| / |2k+1| = |x-2|\)

So, the series converges for |x - 2| < 1, or 1 < x < 3. Thus, the interval of convergence is (1, 3).

Polar Coordinates:

Using the Pythagorean theorem, we have:

r = \(\sqrt{(x^2 + y^2)\\\\\sqrt{(5^2 + 73.5^2) }\\\)

r= 73.790

Using trigonometry, we have:

θ = arctan(y/x) = arctan(73.5/5) = 1.493 rad = 85.758°

In the range 0 ≤ θ < 2π, this point can be expressed in polar coordinates as (73.790, 85.758°) or (73.790, 445.242°).

In the range -π < θ ≤ π, this point can be expressed in polar coordinates as (73.790, -94.242°).

Third-Order Taylor Polynomial:

The Taylor series for cos(x) centered at a = 0 is:

cos(x) = \(1 - x^2 / 2! + x^4 / 4! - x^6 / 6! + ...\)

Taking the first four terms, we have:

\(P_3(x) = 1 - x^2 / 2! + x^4 / 4! = cos(x) + x^6 / 6!\)

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The expression that is equivalent to 27x² - 72x/9x is 3x - 8

The expression whose equivalence is to be determined is given as

27x^2-72x/9x

The above expression can be properly expressed as follows

27x² - 72x/9x

Introduce the use of brackets

So, we have

(27x² - 72x)/9x

Factor out x from the numerator

This gives

(27x² - 72x)/9x = x(27x - 72)/9x

Cancel out the common factor

(27x² - 72x)/9x = (27x - 72)/9

Factor out 9 from the numerator

This gives

(27x² - 72x)/9x = 9(3x - 8)/9

Cancel out the common factor

(27x² - 72x)/9x = 3x - 8

Hence, the equivalent expression is 3x - 8

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Answer:

In 256 ways

Step-by-step explanation:

The number of answer choices will be; 4 * 3 = 12 answer choices

Okay, so per question we have 4 choices

The number of ways we can answer the first question is 4 ways since there are 4 choices

For the second question, 4 ways also

For the third 4 ways

And for the last question, four ways too

So the number of ways to correctly answer the question will be ;

4 * 4 * 4 * 4 = 256 ways

Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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Answer:

false

Step-by-step explanation:

7x2=14

14-28= -14

Answer:

x = 2

x = -2

Step-by-step explanation:

Answer:

Due to having 24 divisors.

Step-by-step explanation:

360 has many factors which might be the reason it was chosen for the number of degrees in a full turn. There are total 24 divisors of 360 number which make it the highest factors among all numbers. All circles are divided into 360 even parts so that the Sun would move through 1 part each day. Each of these parts was describes 1 degree and this division give us the idea that a circle contains 360 degrees so we can say that this is the reason that 360 is chosen in degrees.

Answer:

x = 14

Step-by-step explanation:

5(22 - x) = 40

Distribute the 5 into the parenthesis.

110 - 5x = 40

Subtract 110 from both sides.

-5x = -70

Divide both sides by -5.

x = 14.

Proof:

5(22 - x) = 40

Substitute variable.

5(22 - 14) = 40

Subtract inside parenthesis.

5(8) = 40

Multiply 5 and 8.

40 = 40.

Answer: 4/9 < 7/12 is true. 4/9 = 16/36 while 7/12 = 21/36. Please mark me brainliest!

Answer:

4x - 7 = 13

4x = 13 + 7

4x = 20 (divide both sides by 4 to get x)

4x/4 = 20/4

x = 5

Step-by-step explanation:

The probability that no two consecutive heads will occur is 13/32.

It should be noted that probability simply means the likelihood of the occurence of an event based on chance.

In this case, the fair coin is tossed 5 times and we simony want it find the probability that no two consecutive heads will occur.

This will be:

Let n be the number of strings of h

Let t be the length n with two adjacent H's.

Therefore, the probability will be:

= (8+5)/2^5

= 13/32

In conclusion, the probability that no two consecutive heads will occur is 13/32.

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Because both 2 and 72 under the radical are positive numbers, we can apply this rule:

     \(\sqrt{2}\cdot\sqrt{72} = \sqrt{2\cdot72}\)

Now that new version, \(\sqrt{2\cdot 72}\) is the same thing as \(\sqrt{144}\), because \(2\cdot72=144\).

And \(\sqrt{144}=12\).

12 is your answer.

The rule we used is \(\sqrt{a}\cdot\sqrt{b} = \sqrt{a\cdot b}\), but it only works if both \(\sqrt{a}\) and \(\sqrt{b}\) are real numbers (AKA if a and b are both non-negative).

Answer:

A

Step-by-step explanation:

The other values are lesser than 5.63

Answer:

5.658-A

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

1 is in the hundreds place

9 is in the tens place

4 is in the ones place

6 is in the tenths

Answer:

The constant of proportionality is 2.

Step-by-step explanation:

z^2 = kW   where k is a constant.

When z = 4 , W = 8 so

4^2 = 8k

k = 4^2/8

= 16/8

= 2.

Answer:

z² = 2W

Step-by-step explanation:

Assuming you require the equation of proportionality

Given z² is directly proportional to W then the equation relating them is

z² = kW ← k is the constant of proportion

To find k use the condition z = 4 when W = 8

4² = 8k

16 = 8k ( divide both sides by 8 )

2 = k

z² = 2W ← equation of proportionality

Answer:

The no. are 11 and 12

Step-by-step explanation:

n(n+1)=17+5(2n+1)

n^2 +n=17+10n+5

n^2 -9n-22

Splitting the middle term

n^2 -11n+2n -22

n(n-11)+2(n-11)

(n-11)(n+2)

As n cannot ne negative,

n=11 and 12(consecutive no.)

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The two of the consecutive positive integers whose product is 17 more than 5 times their sum are 11 and 12.

An integer is a complete number, therefore, not including the decimals and fractions. And it that can be either positive, negative, or zero.

Integer examples include -5, 1, 5, 8, 97, and 3,043.

Non-integer numbers include: -1.43, 1 3/4, 3.14, and more.

Let the first of the two consecutive integers be represented by x. Then, the other number can be written as (x+1).

Now, the product and the sum of the two numbers can be written as,

Product = x(x+1) = x² + x

Sum = x + (x+1) = 2x + 1

Further, it is given that the product of two consecutive positive integers is 17 more than 5 times their sum. Therefore, we can write,

x² + x = 17 + 5(2x + 1)

x² + x = 17 + 10x + 5

x² + x - 17 - 10x - 5 = 0

x² - 9x - 22 = 0

x² - 11x + 2x - 22 = 0

x(x - 11) + 2(x - 11) = 0

(x - 11)(x + 2) = 0

x = -2, 11

Thus, there are two numbers that can fulfil the given condition but since it is mentioned that we only need two positive consecutive integers. Therefore, the two numbers are 11 and 12.

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Answer:

(4, -1)

Hope you can understand what I did

Answer:

50 squirrels, 60 inches, A'(3,0), B'(9,0), C'(9,6)

Step-by-step explanation:

Given that the ratio of birds to squirrels is 4:5 and there are 90 altogether, define a variable \(x\), and \(4x + 5x = 90\), and \(x = 10\). Since squirrels are the \(5x\) part, \(5\cdot10 = 50\) squirrels.

1/5 of her total height is 12 so let's say her total height is \(h\) and \(\frac{1}{5}h = 12\).

Solve for \(h\) to get 60 inches.

Translating this triangle to the right 3 units just means adding 3 to all the x coordinates of the vertices. This gives you A'(3,0), B'(9,0), C'(9,6).

The most goals the team scored in a game is 8

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

The box plot

The most goals the team scored in a game is the maximum of the box plot

From the box plot, we have

Maximum = 8

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

Most goal = 8

Hence, the most goal is 8

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I'm sorry, but I don't see a question or any context for your statement. Could you please provide more information or clarify your request?

To find the parametric equations for the line through point P(1, 4, 5) that is parallel to the plane x + y + z = 2 and perpendicular to another line, we need to determine the direction vector of the line and use it to construct the parametric equations.

The direction vector is obtained by taking the cross product of the normal vector of the plane and the direction vector of the given line. By using the point-slope form of the line equation, we can then write the parametric equations.

The given plane has the equation x + y + z = 2. The normal vector of the plane is (1, 1, 1), as the coefficients of x, y, and z represent the normal vector components. We also have a line for which we want to find a line parallel to the plane and perpendicular to it. To determine the direction vector of the line, we take the cross product of the normal vector of the plane and the direction vector of the given line.

Let's assume the direction vector of the given line is represented by vector v = (a, b, c). Taking the cross product of (a, b, c) and (1, 1, 1) will give us the direction vector of the line parallel to the plane and perpendicular to the given line.

Next, we can write the parametric equations for the line using the point-slope form. Since we have the point P(1, 4, 5) on the line and the direction vector obtained from the cross product, we can express the equations as follows:

x = 1 + at

y = 4 + bt

z = 5 + ct

where t is a parameter that varies along the line. These equations represent the parametric equations for the line passing through point P(1, 4, 5) that is parallel to the plane x + y + z = 2 and perpendicular to the given line.

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Answer:

The correct option is commutative property.

Step-by-step explanation:

The expression that Renee is simplifying is:

\((7)\cdot(\frac{13}{29})\cdot(\frac{1}{7})\)

It is provided that, Renee recognizes that 7 and \(\frac{1}{7}\) are reciprocals, so she would like to find their product before she multiplies by \(\frac{13}{29}\).

The associative property of multiplication states that:

\(a\times b\times c=(a\times b)\times c=a\times (b\times c)\)

The commutative property of multiplication states that:

\(a\times b\times c=a\times c\times b=c\times a\times b\)

The distributive property of multiplication states that:

\(a\cdot (b+c)=a\cdot b+a\cdot c\)

The identity property of multiplication states that:

\(a\times 1=a\\b\times 1=b\)

So, Renee should use the commutative property of multiplication to find the product of 7 and \(\frac{1}{7}\),

\((7)\cdot(\frac{13}{29})\cdot(\frac{1}{7})=(7\times\frac{1}{7})\times\frac{13}{29}=\frac{13}{29}\)

Thus, the correct option is commutative property.

Answer:

The correct option is commutative property.

Step-by-step explanation:

i took the test and got it right thx to the person ontop of mehn give him credit :p

Answer:

1.59

Step-by-step explanation:

Divide 2,787 by 1,750

An "event" is an outcome of a population that has some probability of being selected.

In statistics, an event refers to a specific outcome or combination of outcomes of an experiment or random process. It represents a subset of the sample space, which is the set of all possible outcomes.

For example, let's consider rolling a fair six-sided die. The sample space consists of the numbers 1, 2, 3, 4, 5, and 6. An event could be rolling an even number, which consists of the outcomes 2, 4, and 6. Each of these outcomes has an equal probability of 1/6.

Events can also be combined using logical operators. For instance, the event of rolling a number greater than 3 and less than 6 would consist of the outcome 4 and 5. The probability of this event would be 2/6 or simplified, 1/3.

In summary, an event is a specific outcome or combination of outcomes from a population, and it has a certain probability of being selected.

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An "outcome" is an outcome of a population that has some probability of being selected.

An "outcome" refers to a specific result or observation that can occur in a given situation or experiment. In the context of a population, an outcome represents one possible result that could be selected or observed.

When we talk about a population, we are referring to a group of individuals or items that share a common characteristic. For example, a population could be all the students in a school, all the trees in a forest, or all the cars in a city.

In statistics, we often take samples from populations to make inferences or draw conclusions about the entire population. When selecting a sample from a population, each individual or item in the population should have some probability of being chosen. This ensures that the sample is representative of the population and provides reliable information.

For example, if we want to study the average height of all students in a school, we might randomly select a sample of students from the population (all students in the school). Each student in the population has some chance of being selected, which means each student represents a potential outcome of the sample.

In summary, an outcome in the context of a population refers to a specific result or observation that has some probability of being selected from the population.

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The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.

The importance of the hydrologic cycle can be understood by considering its various functions:

Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.

Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.

Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.

Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.

Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.

It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.

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On solving the provided question we can say that the equation gives us  101.77 mi S; 63.59 mi W and S 39.4° W; 131.7 nautical miles

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.

The ship will have traveled 120 nautical miles in the six hours between noon and six o'clock using the formula distance = speed time distance (20 nm/h) (6 h).

The location of the ship will be in (S, W) coordinates.

\(120(cos(32), sin(32)) ≈ 120(0.848048, 0.529919) ≈ (101.77, 63.59)\)

The ship will have traveled 101.77 miles south and 63.59 miles west.

83.59). The distance from port will be ...

\(d = √(101.77^2 +83.59^2) = 131.7\\ arctan(83.59/101.77) ≈ 39.4\)

The bearing and distance are ...

S 39.4° W

131.7 nautical miles

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Answer:

d

Step-by-step explanation: