Claudia’s skis are 150 centimeters long. How many millimeters is this?

Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

Answer:

x= −  8 /13  = −1  8 /5  = −1.625

Step-by-step explanation:

either one is the answer

<3 Enjoy,

    Dea

Answer:

x=-1.625  Decimal form  

x= -13/8    Fraction form

Step-by-step explanation:

3(-2x-1)=2(x+5)

Use distributive property to solve-

-6x-3=2x+10

Now add like terms

-6x-3=2x+10

    +3       +3

   -6x=2x+13  (get the x by itself)

  -2x    -2x

-8x=13     Divide

x= -1.625   Decimal form

x=-13/8   Fraction form

The values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.

The given number is 123,000 which is the mth number in the nth row.

The rows contain two more numbers than the previous row.

Let us assume that the first row has m1 numbers.

Therefore, the second row has m1 + 2 numbers, the third row has m1 + 4 numbers, and so on.

We can represent the above information in a general formula as;

m1 + 2 (n - 1) = m

where m1 is the number of elements in the first row and n is the row number in which 123,000 is present.

By solving the above equation, we get

m1 = m - 2 (n - 1)

Now, we can calculate the value of n as;

n = (m - m1) / 2 + 1

Substituting the values of m and m1, we get

n = (123,000 - m1) / 2 + 1

Therefore, the values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.

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Answer:

\(the \: time \: will \: be \: \boxed{1.8 \: hrs} \to \: \\ this \: is \: true \: since \: the \: car \: traveled \: with \: lower \: speed : \\ it \: will \: then \: cover \: the \: same \: distance \\ \: with \: mor e\: time. \: this \: is \: true \:s ince \to \boxed{1.8 \: hrs \: > 1.6 \: hrs}\)

Explanation:

\(since \: velocity \: is \: given \: as \to \\ v = \frac{d}{t} \\ then \: the \: time \: is \to \\ t = \frac{d}{v} \: since \: (d) \: is \: constant \: in \: this \: case \to \\ when \: (v\: is \: 100 \: km {(h)}^{ - 1} ) \: then \: the \: time \: is \to \\ t = \frac{160}{100} = 1.6 \: hrs \\ \\ when \: (v\: \: is \: 90 \: {km(h)}^{ - 1}) \: then \: the \: time \: is \to \\ t = \frac{160}{90} = 1.7777777778 \\ hence \: the \: time \: will \: be \: \boxed{1.778 \: hrs}\)

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Given data:

The first coordinate is (-21, -64).

The second coordinat is (-15, -48).

The expression for the equation of the line passing through the given points is,

Substitute 0 for y to get x intercept.

Thus, the x-intercept is (3,0).

Answer:

Step-by-step explanation:

This is a reflection over a horizontal line.

Let's find the line by calculating the difference of the y-coordinates of corresponding points:

The middle line is:

The solutions of the quadratic equation with the given values are:

x = (-13 + √149) / 2

x = (-13 - √149) / 2

To find the solutions of the quadratic equation using the given values of a=1, b=13, and c=5, we can plug them into the quadratic formula:

\(x = (-b \pm \sqrt{(b^2 - 4ac)) / (2a)}\)

Plugging in the values:

\(x = (-(13) \pm \sqrt{((13)^2 - 4(1)(5))) / (2(1))}\)

Simplifying further:

\(x = (-13 \pm \sqrt{(169 - 20)) / 2}\)

\(x = (-13 \pm \sqrt{149} ) / 2\)

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Answer:

31 days

Step-by-step explanation:

155/5=31

Answer: 31

Step-by-step explanation:

155 divided by 5 equals 31

Answer: number 3

Step-by-step explanation:

The number of centilitres which is equivalent to 0.00005 liters as required to be expressed in standard form is; 5 × 10-² cL.

Recall that; it follows from metric systems that;

100 centilitres = 1 litres.

On this note, it follows from proportion that the number of centilitres present in 0.00005 litres as required is;

= 0.00005 × 100 centilitres

= 0.005 centilitres.

Ultimately, when expressed in standard form, it follows that the number of centilitres in 0.00005 liters is; 5 × 10-² cL.

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Approximately 37.5% of the data are greater than 28, 33.3% of the data are less than 23, 91.7% of the data are greater than 17.5, and 62.5% of the data are between 17.5 and 28.

To answer the questions, we can analyze the given data set.

First, let's count the number of data points that satisfy each condition:

Greater than 28:

There are 9 data points greater than 28 (29, 29, 29, 30, 29, 29, 28, 28, 28).

Less than 23:

There are 8 data points less than 23 (20, 18, 15, 17, 17, 15, 17, 19).

Greater than 17.5:

There are 22 data points greater than 17.5.

Between 17.5 and 28:

There are 15 data points between 17.5 and 28.

Now, let's calculate the approximate percentage for each condition:

Percent greater than 28:

The total number of data points is 24. Approximately, 9 out of 24 data points are greater than 28.

Percentage =\((9 / 24) \times 100 = 37.5\)%.

Percent less than 23:

Approximately, 8 out of 24 data points are less than 23.

Percentage = \((8 / 24) \times 100 = 33.3\)%.

Percent greater than 17.5:

Approximately, 22 out of 24 data points are greater than 17.5.

Percentage = \((22 / 24) \times 100 = 91.7\)%.

Percent between 17.5 and 28:

Approximately, 15 out of 24 data points are between 17.5 and 28.

Percentage = \((15 / 24) \times 100 = 62.5\)%.

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The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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The answer is C

A is a circle so no.

B has a curve so no.

D isn't connected so obviously no.

Answer:

8

Step-by-step explanation:

plug in the values of x and y into the equation

4(4) / (2)

16 / 2 = 8

To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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The strategy that will help to eliminate the variable and solve the equation easily is (D) multiply the second equation by 3 and add it to the first equation.

So, to cancel the variable that will make the equation easy to solve:
Let,

So, calculate as follows:

This addition of the (2) equation to the (1) equation will give the answer:

Hence, variable x has been canceled.

Therefore, the strategy that will help to eliminate the variable and solve the equation easily is (D) multiply the second equation by 3 and add it to the first equation.

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The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

To do this, we add and subtract a constant term to the quadratic expression to make it a perfect square.

In this case, we use the formula x² + 2bx + b² = (x + b)² to rewrite the quadratic expression as a perfect square trinomial, and then we solved for the variable by isolating the squared term and taking the square root.

Here we have

- 3x² + 33 = 48x

Keep 'x' terms on one side and constant terms sides on another side

=> - 3x² - 48x = - 33

Divide by - 3 on both sides

=> -3(x² + 4x)/3 = - 33/3  

=> x² + 16x = 11      

Take half of the 'x' term and square it and add on both sides

=> x² + 2(8x) (x) + (8)² = 11 + (8)²  

Which is in the form of x² + 2bx + b² = (x + b)²

=> [x + 8]² = 75

Therefore,

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

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A linear equation can have one or more variables.

A linear equation of one variable is represented as:

\(Ax + B = C\)

Where

A linear equation of two variables is represented as:

\(y = mx + b\)

Where

There are several ways to solve a linear equation; one of these ways is by using the distributive property of equality.

The distributive property of equality states that:

\(a(b + c) = ab + ac\)

Now; for example

\(3(x + 1) = 2\)

The first step is to distribute the left-hand side, as follows

\(3 \times x + 3 \times 1 = 2\)

Then you evaluate all products

\(3x + 3 = 2\)

Apply subtraction property of equality

\(3x +3 - 3= 2 -3\)

\(3x = -1\)

Apply division property of equality

\(\frac{3x}3 = -\frac 13\)

\(x = -\frac 13\)

Hence, the value of x for \(3(x + 1) = 2\) is \(-\frac 13\)

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Answer:

$17

Step-by-step explanation:

Multiply 3 and 3 + Multiply 4 and 2

3 x 3 = 9

4 x 2 = 8

Add them up --

Final Result = 9 + 8 = ($)17 in total, for the bouquets that Penny buys--

Hope you understand !

From the given figure

Since AC intersects EH at point F, then

Since AC // BD, and EH is the transversal

Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.

To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.

First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.

Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.

To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).

(1/3) * 69 ≈ 23

Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.

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The score that is two standard deviations above the mean is; x' = 140

The empirical rule of normal distribution which is the 68 - 95 - 99.7 rule, is a statistical rule which states that almost all the given observed data for a particular normal distribution will definitely fall within three standard deviations ( σ) of the mean or (µ).

In a normal distribution, approximately 68% of scores are within 1 standard deviation of the mean.

Approximately 95% of scores are within 2 standard deviations of the mean.

Approximately 99.7% of scores are within 3 standard deviations of the mean.

We are given;

Mean; µ = 100

Standard deviation; σ = 20

Thus, the score that is two standard deviations above the mean is;

x' = μ + 2σ

x' = 100 + 2(20)

x' = 140

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Answer:

\(\sqrt{7}\)

Step-by-step explanation:

Law of cosines

c^2 = a^2 + b^2 - 2abcosC

c^2 = 2^2 + 3^2 - 2(2)(3)cos60

c^2 = 4 + 9 - 12 * 0.5

c^2 = 7

c = \(\sqrt{7}\)

Lets find f(n) formula

\(\boxed{\sf f(n)=\dfrac{1680}{n}}\)

Now

\(\\ \sf\longmapsto f(10)=\dfrac{1680}{10}=168\)

\(\\ \sf\longmapsto f(12)=\dfrac{1680}{12}=140\)

\(\\ \sf\longmapsto f(16)=\dfrac{1680}{16}=105\)

\(\\ \sf\longmapsto f(14)=\dfrac{1680}{14}=120\)

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².

From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.

It should be noted that 15% of the material will be:

= 15% × 115.4

= 17.31 ft²

It should be noted that 20% of the material will be:

= 20% × 115.4

= 23.08 ft²

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Money Matters is the best value for money for £750 they are giving 806.25 euros.

Customers can exchange one currency for another at a currency exchange, which is a licensed business.

The three agents are giving the money at different rates:-

Travel Exchange   =  750  x   1.1065  =   798.75 Euros

Phoenix Financial =   1.1050  x  750  =   787.5 Euros

Money Matters      =  1.1075  x   750  =    806.25 Euros

We can see that Money Matters is giving the best value for money.

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Answer:

The length, in feet, of the side of the garden that is against the wall is(60 - x - CD) ft.

Step-by-step explanation:

Consider the diagram below.

The wall is labelled as AD, the side perpendicular to the wall is labelled as AB and the side against the wall is labelled as CB.

It is provided that the rectangular garden is enclosed by  60 feet of fencing on three sides.

That is,

AB + CB + CD = 60 ft.

⇒ x + CB + CD = 60 ft.

Then the length, in feet, of the side of the garden that is against the wall is:

x + CB + CD = 60 ft.

⇒ CB = (60 - x - CD) ft.

Answer: 60-2x

Step-by-step explanation:

Answer:

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