Una arquitecta va a construir un puente con un arco parabólico bajo tablero. Si la luz del puente es de 10 metros y la altura máxima del arco es de 5 metros. Determine las longitudes de las columnas sabiendo que, sobre el eje central del arco, el tablero está a una distancia de 1 metro del arco y la separación entre ellas es la misma

Answer:

answer is 1

Step-by-step explanation:

\(-\frac{9}{12} - (-\frac{7}{4}) = -\frac{3}{4} - (-\frac{7}{4})\\=\frac{4}{4} = 1\)

The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.

Based on the regression table provided, we can answer this question. The following is the regression table:Regression output table for night street fair variableNameCoefficientStandard Errort-StatP-ValueConstantb0.340.1402.430.023Number of male visitorsb10.6130.51320.750.462Number of female visitorsb10.9070.57918.830.000Number of retail standsb0.1160.0452.570.016Number of food (and beverage) standsb0.3160.0575.500.000Number of performanceb0.1460.1071.360.184The null hypothesis is rejected if p-value < 0.1; that is, there is a significant difference between the independent and dependent variables. The p-value of the Number of male visitors, the Number of female visitors, the Number of retail stands, the Number of food (and beverage) stands, and the Number of performances variables are 0.462, 0.000, 0.016, 0.000, and 0.184, respectively. As a result, the variables that are significant at the 10% level are the Number of female visitors, the Number of retail stands, and the Number of food (and beverage) stands. Therefore, the organizer should consider removing the Number of male visitors and Number of performance variables from the regression model. The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.

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Answer:

The slope of the line = m = 3/4

Step-by-step explanation:

We know that the slope-intercept of line equation is  

\(y=mx+b\)

Here:

Given the equation of line L

\(3x - 4y = 24\)

Writing the equation in the slope-intercept form

\(3x - 4y = 24\)

Add -3x to both sides

\(3x\:-\:4y+\left(-3x\right)=\:24+\left(-3x\right)\)

\(-4y=\:-3x+24\)

Divide both sides by -4

\(-\frac{4y}{4}=\:\frac{\left-3x+24\right}{-4}\)

\(y=\frac{3}{4}x-6\)

Comparing the equation with \(y=mx+b\)

Therefore, the slope of the line = m = 3/4

Answer:

To solve for x,  I would use Cosine.

This is because cosine holds the ratio of adjacent/hypotenuse. Based on the diagram, we can see that HYPOTENUSE = x, so we are solving for x. We know the angle, is 17 degrees. Lastly, we know the triangle leg ADJACENT to the angle is 10 units long. So we would use cosine, implementing the ratio adjacent/hypotenuse. Solving this, we would use cos(17)=10/x. Then our goal is to isolate x, so cos(17)=10/x becomes cos(17)*x=10, we are still trying to isolate x, so, x=10/cos(17). Therefore, our answer  x = 10.457 units. cosine would be the best way to go.

Step-by-step explanation:

The right answer is -8/3

please see the attached picture for full solution

hope it helps

Answer:

\(slope = \frac{8}{ - 3} \)

Step-by-step explanation:

\((4 \: \: \: ,\: \: 18) = > (x1 \: \: ,\: \: y1) \\ (7 \: , \: \: \: \: \: 10) = > (x2 \: \: \: ,\: \: y2)\)

\(slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{18 - 10}{4 - 7} \\ = \frac{8}{ - 3} \)

hope this helps

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good luck! have a nice day!

The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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Answer:

The letter E

Answer:

All you have to do is image flipping the triangle on the right over and then you'll see they are equal. You can also look at AB and DE and see they both are right angles.

Step-by-step explanation:

Answer:

5x+6

Step-by-step explanation:

x-3+7x+21-3x-12

5x+6

\( =\tt x - 3 + 7(x + 3) - 3x - 12\)

\( =\tt x - 3 + 7x + 21 - 3x - 12\)

\( =\tt 7x + x - 3x - 3 - 12 + 21\)

\( =\tt 8x - 3x - 15 + 21\)

\( \color{plum}=\tt\bold{ 5x + 6}\)

\(\color{hotpink} =\tt x - 3 + 7(x + 3) - 3x - 12 \color{plum}=\tt\bold{ 5x + 6}\)

Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

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

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Answer:

River C: 2,600 miles

River D: 3,000

Step-by-step explanation:

Since beside a 400 mile difference they are the same just subtract 400 and divide it by 2 then add 400 to find river d

Answer:

Equation A) y = \(x^{3} + 2x^{2} - 1\) is Graph E

Equation B) y = \(2x^{2} - x -3\) is Graph A

Equation C) y = \(\frac{1}{x} +1\) is Graph B

Equation D) y = \(2-3x^{2} -x^{3}\) is Graph D

Answer:

$61.50

Step-by-step explanation:

14.25(4) + 4.50

= 57.00 + 4.50

= 61.50

Answer:

0

Step-by-step explanation:

positive numbers are always bigger than negative numbers

Answer:

Step-by-step explanation:

10 percent of 3000 = 300

3000+300=3300

3300+300=3600

3600+300=3900

interest = 3900-3000

= R900

he will pay R900 interest over 3 years.

i think this is the answer.

The value of f(4) is approximately 10.790 (a).

Given, f'(x)=√x^2 + 2 cos x + 3.

Integrating both sides with respect to x, we get:

f(x) = ∫(√x^2 + 2 cos x + 3) dx

Using substitution method, let u = x^2 + 1, then du/dx = 2x

Substituting in the above equation, we get:

f(x) = ∫(√u^2 + 1) du/2

Applying trigonometric substitution, let u = tanθ, then du = sec^2θ dθ

Substituting in the above equation, we get:

f(x) = ∫(secθ) dθ

f(x) = ln|secθ + tanθ| + C

Using the initial condition f(1) = 2, we get:

ln|secθ + tanθ| + C = 2

Substituting u = tanθ and x = 1, we get:

ln|√(1 + u^2) + u| + C = 2

C = 2 - ln|√2 + 1|

Substituting x = 4, we get:

ln|√(1 + 15) + 4| + 2 - ln|√2 + 1|

f(4) = ln(4√4) + 2 - ln(√2 + 1)

f(4) = ln8 + 2 - ln(√2 + 1)

f(4) = ln(8(√2 + 1)^-1) + 2

f(4) = ln(8/√2 + 1) + 2

f(4) = ln(4√2 + 4) + 2

f(4) = ln(4(√2 + 1)) + 2

f(4) = ln(4) + ln(√2 + 1) + 2

f(4) = 2ln2 + ln(√2 + 1) + 2

f(4) ≈ 10.790 (Option a).

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Answer:

A=6a2=6×(5)2=6×25=150cm2.

Step-by-step explanation:

The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2

Experimental probability of 3

From the table of values, we have

n(3) = 1

Total = 12

So, we have

P(3) = 1/12

Experimental probability of 6

From the table of values, we have

n(6) = 3

Total = 12

So, we have

P(6) = 3/12

P(6) = 1/4

Experimental probability of less than 4

From the table of values, we have

n(Less than 4) = 6

Total = 12

So, we have

P(Less than 4) = 6/12

P(Less than 4) = 1/2

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Answer:

18

Step-by-step explanation24/0.75 is 18

Answer:

18

Explanation:

Not sure what you mean by AGONSA but the method to get 18 is;

\(\frac{24}{1} *\frac{3}{4} = \frac{72}{4} = 18\)

The three true statements about the two triangles are:
- Î"xyz is similar to Î"x'y'z'
- Angle xzy is congruent to Angle y'z'x'.
- The length of yx is twice the length of y'x'

1. Î"xyz ~ Î"x'y'z': The two triangles are similar because the reflection preserves the shape and the dilation with a scale factor of one-half changes the size proportionally.
2. Angle xzy ≅ Angle y'z'x':

Since the triangles are similar, their corresponding angles are congruent.

The reflection and dilation transformations do not affect the angle measures.
3. yx = 2y'x':

Due to the dilation with a scale factor of one-half, the corresponding side lengths of the triangles have a ratio of 2:1. So, the length of yx is twice the length of y'x'.

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Answer:

1 5/12

Step-by-step explanation:

subtract 3 3/4 - 2 1/3 and you get 1 5/12

Answer:

17/12

Step-by-step explanation:

I turned the two fractions into improper fractions and made them have the same denominators. Then I subtracted.

Answer:

x = 3

Step-by-step explanation:

\( (3x,\: x +1)=(x_1, \:y_1) \)

\( (11,\: 12)=(x_2, \:y_2) \)

\(slope = \frac{y_2 - y_1}{x_2 - x_1} \\ \\ 4 = \frac{12 - (x + 1)}{11 - 3x} \\ \\ 4 = \frac{12 - x - 1}{11 - 3x} \\ \\ 4 = \frac{11 - x}{11 - 3x} \\ \\ 4(11 - 3x) = 11 - x \\ \\ 44 - 12x = 11 - x \\ \\ 44 - 11 = 12x - x \\ \\ 33 = 11x \\ \\ x = \frac{33}{11} \\ \\ \huge \red{ \boxed{x = 3}}\)

Answer:

1, 3 and 5

Step-by-step explanation:

You can formulate the postulate as:

x² + (x + 2)² + 15 = (x + 4)²

Which simplifies to x² - 4x + 3 = 0, with solutions x=1 and x=3

so 1, 3 and 5 must be the other tuple.

Squares are the numbers that are produced when a value is multiplied by itself.

If expression be \($9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$\) then the value exists \($11 \sqrt{2}-5 \sqrt{7}$\).

The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.

The original number can be attained by multiplying the square root of an integer by itself.

Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.

Let the expression be \($9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$\)

Now, \($\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$\)

\($\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$\)

therefore \(9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$\)

simplifying the given expression, we get

\($=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$\)

\($=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$\)

\($=11 \sqrt{2}-5 \sqrt{7}$\)

Therefore, the correct answer is option a) \($11 \sqrt{2}-5 \sqrt{7}$\)

The complete question is:

Simplify \($9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$\)

a) \($11 \sqrt{2}-5 \sqrt{7}$\)

b) \($11 \sqrt{4}-5 \sqrt{14}$\)

c) \($6 \sqrt{5}$\)

d) \($6 \sqrt{9}$\)

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The system of inequalities that is represented by the graph is given as follows:

The system of linear inequalities is defined with linear functions, which have the slope-intercept format given as follows:

y = mx + b.

In which the parameters are given as follows:

For the upper bound of the inequality, we have that the linear function:

Then the upper bound of the inequality has the definition given by:

y ≤ -x + 1.

For the lower bound of the inequality, we have that the linear function:

Hence the lower bound of the inequality has the definition given by:

y ≥ -0.75x + 0.5.

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The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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Answer:

TR is the smallest side.

RS is in the middle.

ST is the largest side.

Step-by-step explanation:

Angle R is the biggest angle, so it is opposite from the biggest side (not R) side ST.

Angle S is the smallest angle so it is opposite from the smallest side (not S) side TR.

The third angle is in between, so the opposite side is in between.