Andre is running in an 80-meter hurdle race. There are 8 equally-spaced hurdles on the race track. The first hurdle is 12 meters from the start line and the last hurdle is 15.5 meters from the finish line.
Estimate how far the hurdles are from one another. Explain your reasoning.

The door of the ramp must begin at a distance of 25.72ft in order to raise the ramp by 5ft.

Data;

To solve this problem, this is a right angle triangle and we can use trigonometric ratio SOHCAHTOA here.

Since we have the value of angle and opposite and solving only for adjacent, we can use tangent of the angle.

\(tan \theta = \frac{opposite}{adjacent} \\\)

Let's substitute the values into the formula above and solve

\(tan 11 = \frac{5}{x} \\x = \frac{5}{tan 11} \\x = 25.72ft\)

The door of the ramp must begin at a distance of 25.72ft in order to raise the ramp by 5ft.

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Where variable r is the correlation coefficient.

1) In the scatter plot, when r is closer to 1 it means there is a strong evidence of positive association between the variables.

The scatter plot would be described as a strong positive relationship.

2) When r is near -1, in a scatter plot it indicates there is a strong evidence of negative association between the variables.

Therefore, when r is near -1, the scatter plot will look like a a downward slope, starting from the left.

3) In a scatter plot when r is close to 0, it indicates there is a weak or no relationship between the variables.

The graph when the r is near 0 the graph would be described as no linear relationship( there is weak evidence of relationship between the variables)

Step-by-step explanation:

the more likely an event the closer it is to being certain

the more unlikely an event the closer it is to being impossible

Answer:

15

Step-by-step explanation:

multiply -3 x 5. then find distance from -15 from 0

Answer:

Step-by-step explanation:

\(\sqrt{14}/\sqrt{18}\)= \(\sqrt{14*18} /18=\sqrt{2*7*2*3*3} /18=\)6\(\sqrt{7} /18\)=\(\sqrt{7}/3\)

Answer:

54 in³

Step-by-step explanation:

9×3×2 = 54 in³

_______

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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Answer: 20

Step-by-step explanation: it is 20 because 2 negative numbers multiplied by each other will always be positive

The correct expression is  \($(150 \cdot 1.15)^7$\) (Choice A).

The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).

To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.

If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.

Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.

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Answer: 300a^3cb

Step-by-step explanation:

\($$Simplify the following:$$15 \times 4 \times 5 a^{2} c a b$$$$\begin{aligned}&15 a^{2} \times 4 c \times 5 a b=15 a^{2+1} \times 4 c \times 5 b: \\ \\&15 \times 4 \times 5 a^{2+1} c b\end{aligned}$$$$\begin{aligned}&2+1=3 \\ \\&15 \times 4 \times 5 a^{3} c b \end{aligned}$$$$\begin{aligned}&15 \times 4=60 \\ \\&60 \times 5 a^{3} c b\end{aligned}$$$$60 \times 5=300$$Answer:$$300 a^{3} c b$$\)

The higher R-squared value of the multiple regression model with the higher order independent variable implies that the linear model is not the best fit and that a more complex model is needed to better explain the data

1. Multiple regression models involve fitting a model that includes one or more independent variables to predict a dependent variable.

2.A value of X to a higher power, such as X squared, for an independent variable in a multiple regression model indicates that the relationship between the independent and dependent variables is not linear.

3. If this model produces a higher value of R-squared than a linear model, it means that it is a better fit for the data.

4. However, it does not necessarily imply that the linear model's residual plot is not randomly distributed around the zero line.

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Answer:

3/5

Step-by-step explanation:

um 3/5+2/5 = 1

9514 1404 393

Answer:

  (b)  m∠1 = 67.4°, m∠2 = 104.5°

Step-by-step explanation:

It is easiest to find angle 2 first, then make your answer selection based on that.

The exterior angle 121.8° is the sum of the remote interior angles 17.3° and angle 2. Then ...

  angle 2 = 121.8° -17.3° = 104.5° . . . . . . . matches the second choice

__

Angle 2 is an exterior angle of the top triangle. It, too, is the sum of the remote interior angles:

  104.5° = angle 1 + 37.1°

  angle 1 = 104.5° -37.1° = 67.4°

Answer:

C!

Step-by-step explanation:

m∠1 = 75.5°, m∠2 = 67.4°

Answer:

-4b3 + 7b - 7        (the three is supposed to be in the upper side of the b but i cant do it on a keyboard)

Step-by-step explanation:

The unit rate would be

(3/4 gal) / (1/5 min)

because the machine is filled with 3/4 gal of water in 1/5 of a minute. Do the arithmetic to get the unit rate of

(3/4 gal) / (1/5 min) = (3/4 • 5) gal/min = 15/4 gal/min

Don's mistake was to multiply 3/4 by 1/5 to get 3/(4•5) = 3/20, but he should have divided by 1/5 instead.

Answer:

-343

Step-by-step explanation:

(-7)(-7)=49

(49)(-7)= -343

Answer:

Step-by-step explanation:

Answer:

There are different combinations you can do.... for example

10 tables of 4 and 20 tables of 6

or

25 tables of 4 and 10 tables of 6

so Im not sure which :/ but the equation would be:

10x+20y=160

or

25x+10y=160

there are different combinations of the two so im  not sure T_T

This question is based on the concept of linear equation. Therefore, the equation would be, 10x+20y=160 or  25x+10y=160 to represent the situation.

Given:

He wants to have only tables for 4 and tables for 6. The total number of tables is 160.

And x represent the number of 4 seat tables and y represent the number of 6 seat tables.

We need to determined an equation to represent the situation.

Let x represent the number of 4 seat tables and y represent the number of 6 seat tables.

According to the question,

There are different combinations we can make as below,

For example :

10 tables of 4 and 20 tables of 6

or

25 tables of 4 and 10 tables of 6

Therefore, the equation would be, 10x+20y=160  or  25x+10y=160 to represent the situation.

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Using the Factor Theorem, the equation of h(x) is given as follows:

h(x) = -2(x³ - 2x² - 5x + 6)

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

Looking at the table, considering the values of x when h(x) = 0, the roots of h(x) are given as follows:

\(x_1 = -2, x_2 = 1, x_3 = 3\)

Then the rule is:

h(x) = a(x + 2)(x - 1)(x - 3)

h(x) = a(x² + x - 2)(x - 3)

h(x) = a(x³ - 2x² - 5x + 6)

The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:

6a = -12

a = -12/6

a = -2.

Hence the function is given by:

h(x) = -2(x³ - 2x² - 5x + 6)

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The probability that 35 or more people from the sample of 215 customers are concerned about the digital environment is 0.7043.

To calculate the probability that 35 or more people from the sample of 215 customers are concerned about the digital environment, we can use the binomial distribution formula.

The binomial distribution is applicable here because we have a fixed sample size (215 customers) and each customer can be categorized as either concerned or not concerned.

Let's denote p as the probability that a randomly selected customer is concerned about the digital environment.

From the given information, we know that 29% of technology experts believe our lives will be more harmed than helped, so p = 0.29.

The formula for the probability mass function of the binomial distribution is:

\(P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)\)

Where:

P(X = k) is the probability of k successes (in this case, customers concerned about the digital environment)

C(n, k) is the number of combinations of n items taken k at a time

\(p^k\) is the probability of k successes

\((1 - p)^{(n - k)\) is the probability of (n - k) failures

Now, let's calculate the probability of having 35 or more customers concerned:

P(X ≥ 35) = P(X = 35) + P(X = 36) + ... + P(X = 215)

Using this formula, we can calculate the probability using a cumulative approach:

P(X ≥ 35) = 1 - P(X ≤ 34)

Calculating this probability requires summing up a large number of individual probabilities, which can be time-consuming.

Therefore, it is more practical to use statistical software or calculators to obtain an accurate answer.

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Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer: 5 cm and 12 cm

Step-by-step explanation:

Answer:

7).39

8).40

Step-by-step explanation:

Answer:

$1,679.62

Step-by-step explanation:

129.60*12=$1,555.20

You then do 1,555.2*.08, and get:124.416

You then add the 2 together to find the amount needed to be paid back.

a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer:

15 in

Step-by-step explanation:

LxH

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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Answer: 10

Step-by-step explanation:

The measures, using the Law of Sines, are given as follows:

The law of sines states that the ratio between the sine of each angle and the side length opposite to this angle has to be equal for all the angles in the problem.

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is given as follows:

m < B + 25 + 36 = 180

m < B = 180 - (25 + 36)

m < B = 119º.

Then the length BC is obtained as follows:

sin(25º)/BC = sin(36º)/28

BC = 28 x sin(25º)/sin(36º)

BC = 20.13.

The length AC is obtained as follows:

sin(119º)/AC = sin(36º)/28

AC = 28 x sin(119º)/sin(36º)

AC = 41.62.

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There are no restrictions in the Domain of this expression.

1) Simplifying that expression

Combining like terms we have:

2) Since this function presents no undefinition, then we can state that any value within the Real set is valid for that. So the Domain of that function is:

D = (-∞, ∞) or simply put D = R