Here is part of a timetable for the Paris to Montpellier express train service.
The average speed of the 20 07 train from Paris is 224 km/h. Work out the distance this train travels from Paris to Montpelli

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

\(\cfrac{x}{48}=\cfrac{48}{64}\implies \cfrac{x}{48}=\cfrac{3}{4}\implies 4x=144\implies x=\cfrac{144}{4}\implies \boxed{x=36}\)

An essential concept in mathematics and can be applied to a variety of fields such as physics, economics, and engineering.

The slope of a line in a Cartesian plane is a numerical representation of its steepness and inclination relative to the x-axis.

The slope of a straight line refers to the rise or fall of the y-coordinate as it moves from left to right along the x-axis.

There are a few different ways to interpret the slope of a line, but generally it can be thought of as the rate at which the dependent variable changes with respect to the independent variable.
When the slope is positive, the line rises from left to right, indicating that the dependent variable is increasing as the independent variable increases.

In other words, there is a direct relationship between the two variables.

Conversely, when the slope is negative, the line falls from left to right, indicating that the dependent variable is decreasing as the independent variable increases.

This means that there is an inverse relationship between the two variables.
The magnitude of the slope can also provide information about the relationship between the variables.

If the slope is close to zero, then the relationship between the two variables is weak or nonexistent.

However, if the slope is large in magnitude (i.e. close to 1 or -1), then there is a strong relationship between the variables.

A slope of zero indicates that there is no change in the dependent variable as the independent variable changes, while a slope of undefined means that the line is vertical and has no slope.
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Answer:

2.23kg

Step-by-step explanation:

If you can get 1 kg for $4.50. You can perform a ratio to find out how much you get for $10.

1/4.50=x/10

.2222222=x/10

multiply the 10 on both sides

x=2.23 kg for $10

There are 24 hostel rooms, because the histogram has 24 bars. Each bar represents the number of guests in one hostel room. Since the bars range from 0 to 23, that means there are 24 hostel rooms total.

A histogram is a graphical representation of a data set that shows the frequency of data points within a given range. It is similar to a bar graph, but is used to display the distribution of numerical data. The x-axis typically represents the data points, while the y-axis shows the number of occurrences of these data points. Histograms are used to provide a visual representation of data that can be used to identify patterns and trends. Histograms can also be used to compare different data sets and determine if they are similar or different.

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Answer: 25 rooms!

Step-by-step explanation:

if you use khan np!

Answer:

6 days

Step-by-step explanation:

2 boys that each work half as fast as the men is equivalent to having one extra man. So instead of 3 men we have 4. 4/3 the manpower means 3/4 the time. 3/4 of 8 is 6.

Answer:

6 days.

Step-by-step explanation:

The 3 men can build 1/8 of a wall in 1 day.

So 1 man can build 1/24 wall in 1 day.

So 1 boy can build  1/48 in 1 day and 2 boys can build 1/24 wall in 1 day.

So we have the equivalent of  4 men working and they can build 4 * 1/24

= 1/6 of a wall per day

So the answer is 6 days.

In linear regression, the variance around the regression line represents the variability of the dependent variable (response variable) that is not explained by the regression model.

It measures the dispersion of the actual data points around the predicted values from the regression line.

The variance around the regression line can vary with different values of the predictor variable. This is because the relationship between the predictor variable and the response variable may not be constant across the entire range of the predictor variable. In other words, the spread or dispersion of the data points around the regression line may change as the predictor variable changes.

By examining the residuals (the differences between the observed values and the predicted values from the regression line) and calculating their variances, you can assess the variability of the data points around the regression line. This variability is an important aspect of understanding the goodness of fit of the regression model and the accuracy of the predictions.

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The price of one adult ticket is $15 and the price of one child ticket is $8.

Two sets of equations can be derived from this question:

14a + 14c = 322 equation 1

12a + c = 188 equation 2

These equations are known as simultaneous equations and they can be solved to determine the cost of each ticket using the elimination method.

In order to determine the cost of the adult's ticket multiply equation 2 by 14

168a + 14c = 2632 equation 3

Subtract equation 1 from 3

2310 = 154a

Divide both sides by 154

a = $15

To determine the cost of the children's ticket substitute for a in equation 1

14(15) + 14c = 322

210 + 14c = 322

322 - 210 = 14c

112 = 14c

c = $8

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Answer:

\(v = u + at \\ u = 6 \\ a = 10 \\ t = 2 \\ then \\ v = 6 + 10 \times 2 \\ = 6 + 20 = 26 \\ thank \: you\)

Entry of 1.00 in the diagonal of the matrix indicate that it is a correlation matrix .

For example :

              A₁                 A₂             A₃             A₄                A₅

A₁            1

A₂           2                  1

A₃           3                 4                  1

A₄           5                 6                  7               1

A₅           8                 9                 10              11                  1

Diagonal values is always equal to 1 as the relation between A₁ to A₁ is always equal to one.

Therefore, the entry of one on the diagonal of the given matrix represents it is a correlation matrix.

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Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The probability that the randomly selected patient had a blood test requested during their visit is approximately 0.120

In this case:

We can calculate the overall probability as the weighted average of the probabilities from each doctor:

Probability = (Probability from Dr. Sarabia) * (Percentage of patients seen by Dr. Sarabia) + (Probability from Dr. Tran) * (Percentage of patients seen by Dr. Tran) + (Probability from Dr. Jackson) * (Percentage of patients seen by Dr. Jackson)

Probability = (0.10 * 0.27) + (0.10 * 0.32) + (0.15 * 0.41)

Probability ≈ 0.027 + 0.032 + 0.061

Probability ≈ 0.12

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The volume of the cone that has a height of 9 yards and a base diameter of 10 yards will be 235.5 cubic yards.

Let h be the height of the cone and A be the base area of the cone.

Then the volume of the cone will be

Volume = (1/3) × A × h

The diameter of the base circle is 10 yards. Then the area of the base circle is given as,

A = (π/4) d²

A = (3.14 / 4)(10)²

A = 0.785 x 100

A = 78.5 square yards

The height of the cone is 9 yards. Then the volume of the cone is given as,

V = (1/3) x 78.5 x 9

V = 78.5 x 3

V = 235.5 cubic yards

The volume of the cone that has a height of 9 yards and a base diameter of 10 yards will be 235.5 cubic yards.

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(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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Answer:

-1 and 4/3

Step-by-step explanation:

So first we want to find the equation for the linear function g(x):

We know that it is linear, so it will follow the equation

y = mx + b

m is the slope, and b is the y-intercept

First, find the slope:

We can see that every time the x increases by 1, the output value is increased by 2

This means that the slope will be 2

Then, find the y-intercept:

The y-intercept is when the x value is equal to 0, so in this table, when the x value is 0, the output is 7

So putting these number into the equation will give us:

y = 2x + 7

Now to find the solutions:

You have to set these equations equal to each other and solve for x

The set up should look like this:

\(3x^{2} + x +3 = 2x+7\)

Put all of the values on one side:

\(3x^{2} -x-4 = 0\)

And then solve for x by factoring:

\(3x^{2} +3x-4x-4\) = 0

\((3x^{2} +3x)+(-4x-4)\) = 0

\(3x(x+1)-4(x+1)\) = 0

(x+1)(3x-4) = 0

Finally, to get the x values:

x + 1 = 0

x = -1

and

3x - 4 = 0

3x = 4

x = 4/3

So the answers are:

x = -1 and 4/3

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).

A polynomial function is a relation where a dependent variable is equal to a  polynomial expression. A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.

The general form of a polynomial expression is:

a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ.

The highest power to a variable is the degree of the polynomial expression.

When degree = 2, the function is a quadratic function.

When degree = 1, the function is a linear function.

The quadratic function is given to us:

f(x) = 3x² + x + 3.

We need to determine the linear equation g(x). Since it's a linear equation we use the two-point method to determine the equation.

The two-point formula is:

y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(2) = 11, g(1) = 9

g(x) - g(1) = ((g(2)-g(1))/(2-1))*(x-1)

or, g(x) - 9 = ((11-9)/(2-1))*(x-1)

or, g(x) - 9 = 2(x-1)

or, g(x) = 2x - 2 + 9 = 2x + 7

∴ g(x) = 2x +7, is the linear function g(x)

We are asked to find the solution to the system of equations f(x) and g(x).

To find the solution we need to check what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).

3x² + x + 3 = 2x + 7

or, 3x² - x - 4 = 0

or, 3x² + 3x - 4x - 4 = 0

or, 3x(x+1) -4(x+1) = 0

or, (3x-4)(x+1) = 0

∴ Either 3x-4=0 ⇒ x = 4/3

or, x+1=0 ⇒ x = -1.

g(-1) = 5 (from the table)

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

g(4/3) = 2(4/3) + 7 = 8/3 + 21/3 = 29/3

f(4/3) = 3*(4/3)² + (4/3) + 3 = 16/3 + 4/3 + 9/3 = 29/3

∴ f(-1) = g(-1) and f(4/3) = g(4/3), so

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).

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M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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multiply Start Fraction 5 Over 7 End Fraction by 3.

What do math fractions mean?

An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                                Whether it is in the numerator or denominator, a complex fraction contains a fraction.

                             The numerator and denominator of a correct fraction are opposite each other.

What is basic fraction theory?

Every fraction has two components: the numerator, which is the actual number of parts, and the denominator, which is the total number of parts.

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Answer:

c is the answer i took the test

Step-by-step explanation:

Answer:

Divide

Step-by-step explanation:

When you see something say "how many times larger than __ is __" You will Divide

(e.g. how many times larger is 6 than 3? divide 6 by 3 and you'll find out that 6 is 2 times as large as 3)

Hope this helps!

Times= multiplication

How many times larger means how many times that numner can get multiplied by the smaller number.

Hope it helped! :)

Answer:

\( \sqrt{(12) {}^{2} } + (7) {}^{2} \\ = 13.89\)

Answer: x = 14

Step-by-step explanation:

\(h^2 = p^2 + b^2 \\x^2 = 12^2 + 7^2\\x^2 = 144+49\\x^2 = 193\\x = \sqrt{193} \\x = 13.89\\so, x = 13.9 \\so, x = 14\)

Answer:

6-3x

x=-1

6-3(1)

6-3

3

Step-by-step explanation:

Answer:

t = 6.29 years

Step-by-step explanation:

The general formula of an exponential function is

\(y=ab^x\), where a is the initial value (i.e., value of y when x = 0), b is the base, and x is the exponent.

We can express rabbit population as a function of time in years, which means in our formula, r is like y and t is like x:

\(r=ab^t\)

Because at time t = 0, the rabbit population is 20, we know that our a value for the equation is 20.

We can find b by simply plugging in 20 for a and any point for r and t like (1, 60):

\(60=20b^1\\3=b\)

Thus, the equation we will need to use to find the rabbit population is

\(r < 20(3)^t\)

It's helpful to use an inequality where the equation is greater than r since we want to know how many years it will take for the population to exceed 20000:

\(20000 < 20(3)^t\\\\1000 < 3^t\\\\log(1000) < log(3)^t\\\\log(1000) < t*log(3)\\\\log(1000)/log(3) < t\\\\6.287709823 < t\\6.29 < t\)

We can check our answer by plugging in 6.29 for t and check whether the answer we get is greater than 20000:

\(20000 < 20(3)^6^.^2^9\\20000 < 20*1002.519185\\20000 < 20050.38369\\20000 < 20050.38\)

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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To find the expected number of sixes appearing on three die rolls, we can calculate the probability of rolling a six on each individual roll and then multiply it by the number of rolls.

The probability of rolling a six on a single roll of a fair die is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a six.

Since the rolls are independent events, we can multiply the probabilities together to find the probability of rolling a six on all three rolls:

(1/6) * (1/6) * (1/6) = 1/216

Therefore, the probability of rolling a six on all three rolls is 1/216.

To find the expected number of sixes, we multiply the probability by the number of rolls:

Expected number of sixes = (1/216) * 3 = 1/72

So, the expected number of sixes appearing on three die rolls is 1/72.

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Step-by-step explanation:

Hope it helped

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If Ariana removes the $4,800 rent from the set, the mean and median of the remaining rents will decrease because $4,800 is a very high value compared to the other rents.

Before removing the $4,800 rent, the mean can be calculated by adding up all the rents and dividing by the total number of rents (5):

Mean = (1,000 + 1,200 + 1,300 + 1,400 + 4,800) / 5 = 2,540

The median is the middle value in the set, which is 1,300.

After removing the $4,800 rent, the new mean can be calculated by adding up the remaining rents and dividing by the new total number of rents (4):

New Mean = (1,000 + 1,200 + 1,300 + 1,400) / 4 = 1,225

The new median is still 1,300 because it is the middle value in the remaining set.

Therefore, removing the $4,800 rent will decrease both the mean and median of the remaining rents.

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Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.