the product of 5 and the number k is less than 60

Step-by-step explanation:

Given that

To find

So, according to the question

we have,

         (0,40) and (15,70)

We have to find the equation of line

So, we know that

               y = mx + c, ---------------(1)

From graph,

           c = 40 and

           m = slope (we have to find it)

We kwon the slope of any two point

      m = \(\frac{y_2-y_1}{x_2-x_1}\)

Where,

        x₁ = 0 , and y₁ = 40

        x₂ = 0 , and y₂ = 40        

So,

      m = \(\frac{y_2-y_1}{x_2-x_1}\)

      m = \(\frac{70-40}{15-0}\)

      m = \(\frac{30}{15}\)

      m = 2

Now putting the all values in equation (1)

We will get,

               y = mx + c, ---------------(1)

               y = 2x + 40

Answer:

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Answer:

1.39

Step-by-step explanation:

Given the quadratic equation :

2x^2+3x-8 = 0

We could apply the quadratic equation formula :

a = 2 ; b = 3, c = - 8

The formula is stated as :

-b±sqrt(b² - 4ac)/2a

To save computation tune, we could use a calculator :

The roots are : - 2.886 ; 1.386

The positive solution rounded to the nearest hundredth is : 1.39

Step-by-step explanation:

here is how you work the answer out

They should use 6 cup of Noah's measuring cup

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the number of cup the should use:

Number of cup = Recipe call / Noah's cup

Number of cup = (3/4) / (1/8)

Number of cup = 3*8 / 4*1

Number of cup = 24/4

Number of cup = 6

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Correctly written question:

Melanie and Noah are baking a birthday cake for Francesca. The recipe call for 3/4 measuring cup and Noah has a 1/8 measuring cup. Which cup should they use?

The odds ratio is 2.48

Population odds ratio Confidence Interval, upper bound = 1.03

Population odds ratio Confidence Interval, lower bound = 0.42

Given information: Arwin suggested that plants pollinated by long tongued insects would benefit by having long flowers. To measure the advantaged of having long flowers, Johnson and Steiner (1997) experimentally shortened 119 of 239 flowers.

The remaining flowers were control. One week later, 50 out of the 119 shortened flowers had received pollen, whereas 87 out of the control flowers had received pollen.

We need to estimate the odds ratio of not receiving pollen after flower shortening, as compared to control flowers. To calculate the odds ratio, we first need to calculate the probability of not receiving pollen after flower shortening and probability of not receiving pollen in the control flowers.

We know that: Total number of flowers in the experiment = 239

Flowers Shortened = 119

Control flowers = 239 - 119 = 120

Number of shortened flowers that did not receive pollen = 69

Number of control flowers that did not receive pollen = 33

Probability of not receiving pollen after flower shortening (p1) = Number of shortened flowers that did not receive pollen / Total number of shortened flowers= 69/119= 0.58 (rounded to 2 decimal spaces)

Probability of not receiving pollen in control flowers (p2) = Number of control flowers that did not receive pollen / Total number of control flowers= 33/120 = 0.28 (rounded to 2 decimal spaces)

The odds ratio of not receiving pollen after flower shortening, as compared to control flowers is calculated using the below formula: odds ratio (OR) = (p1 / 1 - p1) / (p2 / 1 - p2)

Substituting the values, we get: OR = (0.58 / 0.42) / (0.28 / 0.72)= 2.48 (rounded to 2 decimal spaces)

Therefore, the odds ratio is 2.48.Round the values in the answer to two decimal spaces and do not add any units to your answer.

POPULATION ODDS RATIO CONFIDENCE INTERVAL: To calculate the population odds ratio confidence interval, we can use the below formula: ln (OR) ± Zα/2 √ ( (1/p1) - 1/n1 + (1/p2) - 1/n2)

Here,α/2 = (1 - confidence level) / 2 = (1 - 0.95) / 2 = 0.025Z0.025 = 1.96 (for 95% confidence level)

Substituting the values, we get: ln (2.48) ± 1.96 √ ( (1/0.58) - 1/119 + (1/0.28) - 1/120)ln (2.48) ± 0.81

Upper Bound = ln (2.48) + 0.81 = 1.03

Lower Bound = ln (2.48) - 0.81 = 0.42

Therefore, Population odds ratio Confidence Interval, upper bound = 1.03

Population odds ratio Confidence Interval, lower bound = 0.42

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If E= Emily's homeroom class students, and S = Santiago's homeroom class students then

Answer:

19g^2

Step-by-step explanation:

Answer:

144 I think????? ????????

Answer:

y = 1/3x - 19/3

Step-by-step explanation:

3y = x -3

y = 1/3x -3

Slope = 1/3

Point= (1,-6)

y-intercept = -6 - (1/3)(1) = -6 - 1/3 = -19/3

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Answer:

2.88x=7.2

x=7.2/2.88

x=2.5

=)

Answer:

x=4

Step-by-step explanation:

btw that's what M a t h w a y.

(a) To evaluate (x^2) for the ground state of the Harmonic Oscillator, we need to integrate x^2 multiplied by the square of the absolute value of the wavefunction ψ0(x).

(b) The expectation value of p^2 for the ground state of the Harmonic Oscillator is simply the eigenvalue corresponding to the momentum operator squared.

(c) By calculating the uncertainties in position (Δx) and momentum (Δp) for the ground state, we can verify that their product satisfies Heisenberg's uncertainty principle, Δx · Δp ≥ ħ/2.

(a) In the ground state of the Harmonic Oscillator, the wavefunction is given by \(\psi_0(x) = \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{2\sigma^2}}\), where \(\sigma\) is the standard deviation.

To evaluate \((x^2)\), we need to find the expectation value of \(x^2\) with respect to the wavefunction \(\psi_0(x)\). Using the formula for the expectation value, we have:

\((x^2) = \int_{-\infty}^{\infty} x^2 \left|\psi_0(x)\right|^2 dx\)

Substituting the given wavefunction, we have:

\((x^2) = \int_{-\infty}^{\infty} x^2 \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{\sigma^2}} dx\)

Evaluating this integral gives us the value of \((x^2)\) for the ground state of the Harmonic Oscillator.

To evaluate \(\sigma_2\), we can simply take the square root of \((x^2)\) and subtract the expectation value of \(x\) squared, \((x)^2\).

(b) To evaluate \((p^2)\), we need to find the expectation value of \(p^2\) with respect to the wavefunction \(\psi_0(x)\). However, in this case, it is clear that the ground state of the Harmonic Oscillator is an eigenstate of the momentum operator, \(p\). Therefore, the expectation value of \(p^2\) for this state will simply be the eigenvalue corresponding to the momentum operator squared.

(c) The Heisenberg's uncertainty principle states that the product of the uncertainties in position and momentum (\(\Delta x\) and \(\Delta p\)) is bounded by a minimum value: \(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\).

To show that the uncertainty product satisfies the uncertainty principle, we need to calculate \(\Delta x\) and \(\Delta p\) for the ground state of the Harmonic Oscillator and verify that their product is greater than or equal to \(\frac{\hbar}{2}\).

If the ground state wavefunction \(\psi_0(x)\) is a Gaussian function, then the uncertainties \(\Delta x\) and \(\Delta p\) can be related to the standard deviation \(\sigma\) as follows:

\(\Delta x = \sigma\)

\(\Delta p = \frac{\hbar}{2\sigma}\)

By substituting these values into the uncertainty product inequality, we can verify that it satisfies the Heisenberg's uncertainty principle.

Regarding the statement \((x) = 0\) and \((p) = 0\) for this problem, it seems incorrect. The ground state of the Harmonic Oscillator does not have zero uncertainties in position or momentum. Both \(\Delta x\) and \(\Delta p\) will have non-zero values.

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Answer: If you want to know what x = it's 0

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable. x = 0

Answer:

-10 = b

Step-by-step explanation:

y=mx+b    substitute numbers for the variables

5= -3(-5)+b

5=15+b

-15 -15

-10= b

Answer:

y = - 3x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3, thus

y = - 3x + c ← is the partial equation

To find c substitute (- 5, 5) into the partial equation

5 = 15 + c ⇒ c = 5 - 15 = - 10

y = - 3x - 10 ← equation of line

Answer: 42 gallons

Step-by-step explanation:

given data:

average gas mileage/day = 29miles/gallon

distance travelled each day by James = 87miles

How much gas does he use in 14days drive.

solution:

james drives 87miles daily, so in 14 days he would have travelled

= 87miles * 14

= 1218miles travelled.

gas used in 14days

1218miles distance traveled in 14 days

29miles/gallon

= 1218miles / 29miles

= 42gallons of gas have been used by janew to fuel his truck in 14days.

Answer:

Teodolindo obtuvo 22 respuestas correctas y 8 respuestas incorrectas o no contestadas.

Step-by-step explanation:

Un sistema de ecuaciones lineales, también conocido como sistema lineal de ecuaciones o simplemente sistema lineal, es un conjunto de ecuaciones lineales (es decir, un sistema de ecuaciones en donde cada ecuación es de primer grado), en el cual se relacionan dos o más incógnitas.

En los sistemas de ecuaciones, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones.

En este caso se debe establecer un sistema de ecuaciones, donde las variables son:

Siendo 30 preguntas en el examen, se tiene la ecuación:

x + y= 30

Por cada respuesta correcta se obtenían 5 puntos y por cada respuesta incorrecta o pregunta no contestada, se perdían 2 puntos. Teodolindo obtuvo 94 puntos en este examen. Entonces se representa esta situación mediante la expresión:

5*x - 2*y= 94

Entonces el sistema de ecuaciones a resolver es:

\(\left \{ {{x+y=30} \atop {5*x-2*y=94}} \right.\)

El método de sustitución consiste en despejar o aislar una de las incógnitas (por ejemplo,  x ) y sustituir su expresión en la otra ecuación. De este modo, obtienes una ecuación de primer grado con la otra incógnita,  y . Una vez resuelta, calculas el valor de  x  sustituyendo el valor de  y  calculado.

Entonces, despejando el valor de x de la primer expresión obtienes:

x= 30 -y

Reemplazando en la segunda ecuación obtienes:

5*(30 -y) - 2*y= 94

Resolviendo:

5*30 - 5*y - 2*y= 94

150 - 5*y - 2*y= 94

- 5*y - 2*y= 94 -150

-7*y= -56

y= (-56)÷(-7)

y= 8

Reemplazando el valor de y obtenido en la expresión x= 30 -y se obtiene:

x= 30 - 8

x=22

Teodolindo obtuvo 22 respuestas correctas y 8 respuestas incorrectas o no contestadas.

Hello!

7r/3s + 3r/4s =

= 4×7r/4×3s + 3×3r/3×4s =

= 28r/12s + 9r/12s =

= 28r+9r/12s =

= 37r/12s

Good luck! :)

The results tell us that jersey numbers on a football team vary much more than expected, as evidenced by the large range and standard deviation. The sample variance is also relatively high, indicating that there is a fair amount of variability among the jersey numbers in the sample. These statistics are meaningful and can provide insight into the distribution of jersey numbers on the team.

To find the range, we need to subtract the smallest number from the largest number in the sample. So, the range is:

94 - 15 = 79

To find the sample variance and standard deviation, we first need to find the mean of the sample. We can do this by adding up all the numbers and dividing by the total number of players:

(33 + 74 + 70 + 65 + 56 + 47 + 39 + 72 + 57 + 94 + 15) / 11 = 54.18

Next, we need to find the difference between each number and the mean, square them, and add them up. This gives us the sum of squares:

[(33 - 54.18)^2 + (74 - 54.18)^2 + (70 - 54.18)^2 + (65 - 54.18)^2 + (56 - 54.18)^2 + (47 - 54.18)^2 + (39 - 54.18)^2 + (72 - 54.18)^2 + (57 - 54.18)^2 + (94 - 54.18)^2 + (15 - 54.18)^2] = 15864.4

The sample variance is then calculated by dividing the sum of squares by the total number of players minus one:

15864.4 / 10 = 1586.44

Finally, we can calculate the sample standard deviation by taking the square root of the variance:

√1586.44 ≈ 39.83

The results tell us that jersey numbers on a football team vary much more than expected, as evidenced by the large range and standard deviation. The sample variance is also relatively high, indicating that there is a fair amount of variability among the jersey numbers in the sample. These statistics are meaningful and can provide insight into the distribution of jersey numbers on the team.

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Answer:

Step-by-step explanation:

The input of an inverse trigonometric function is an angle

The output of an inverse trigonometric function is a number, the same as the regular sine function. This is the same for ALL Trigonometric functions.

Answer:

i do not know is this is the right answer but i hope i will help you.

if the unswer is incorrect pls let me know

Answer: 2.25 x 10^18

Step-by-step explanation:

When dividing with exponents you subtract

56-38= 18

10 cancels out

(9 x 10^18) / 4

= 2.25 x 10^18

To reverse the order of integration, we need to rewrite the limits of integration in terms of the other variable.
The value of the given integral by reversing the order of integration is (5/12)(\(e^{24}\) - 1).

The given integral is ∫∫ \(5e^{(2x)}\) dx dy, where the limits of x are from 0 to 4 and the limits of y are from 0 to 3y.
To integrate with respect to y first, we need to express the limits of y in terms of x.
From the limits of y given, we have 0 ≤ y ≤ 3y, which simplifies to 0 ≤ y.
Now we need to find the upper limit of y. To do this, we set the expression for the upper limit equal to the constant 12, which is the upper limit of x.
So we have 3y = 12, which gives y = 4.
Thus, the limits of integration become ∫∫ \(5e^{(2x)}\) dy dx, where the limits of y are from 0 to 4 and the limits of x are from 0 to 3y.
Now we can integrate with respect to y:

∫∫ \(5e^{(2x)}\) dy dx = ∫ 0^4 ∫ 0^(3y) \(\int\limits^4_0 \int\limits^{(3y)}_0 5e^{(2x)} dx dy\)
= \(\int\limits^4_0  [5/2 e^{(2x)}]_0^{(3y)} dy\)
= \(\int\limits^4_0  [5/2 (e^{(6y)} - 1)] dy\)
= \([5/12 (e^{(6y)} - 1)]_0^4\)
= \((5/12)(e^{24} - 1)\)
Note that the order of integration can be reversed if the integrand is continuous on a rectangular region that contains the original region of integration.

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Answer:

<3 = 40 degrees

Step-by-step explanation:

90 + 58 + <1 = 180

148 + <1 = 180

<1 = 32

<1 = <2

32 = <2

<2 + <3 + 108 = 180

32 + <3 + 108 = 180

<3 + 140 = 180

<3 = 40

Answer: 3/4 granola bars

Step-by-step explanation:

From the question, we are given the information that Davita brought 6 granola bars for herself and the 7 other girls in her camp group.

The fraction of a granola bar that each girl gets if they agree it equally would be the number of granola bars bought divided by the total number of girls which is 8. Therefore, the calculation would be:

= 6 ÷ 8.

= 3/4 granola bars

Each person gets 3/4 granola bars.

The fraction of a granola bar that each girl will get is 3/4

To get the fraction of a granola bar will each girl get, we will take the ratio of the total granola to total number of girls.

Given the following parameters

Total number of 6 granola bars

Total number of girls plus Davita is 8

Taking the required ratio;

Ratio = number of granola: total number of girls

Ratio = 6:8

Ratio = 3:4

Hence the fraction of a granola bar that each girl will get is 3/4

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Answer: 6 times 10 less than a number

Step-by-step explanation:

      This question is asking us to give a written description for the expression given.

6(n - 10)​

6 times 10 less than a number

The difference between the 51st term of a and the 51st term of b is 1000.

the nth term of an arithmetic series is given by \(a_{n}= a_{0}+(n-1)*d\)

where \(a_{0}\) is the first term of the arithmetic series, \(a_{n}\) is the nth term of the series and d is the common difference

Given that,

\(a_{0}=b_{0}=30\)

Common difference of both series that have absolute value = 10

common difference of series a is 10 as this series is increasing

similarly, the common difference of series b is -10 as it is decreasing

Putting the values in the above equation we get:

\(a_{51}= a_{0}+(n-1)*d\\\)

=> 30 + (51-1)*10

=> 30 + 500 = 530

Thus, the value of \(a_{51}\) is 530.

\(b_{51}= b_{0}+(n-1)*d\\\)

=> 30 + (51-1)*-10

=> 30 -500 = -470

Thus, the value of \(b_{51}\) is -470.

so we have to find the value of \(a_{51}-b_{51}\) which is 530 - (-470) =530 +470 =1000

Therefore, The difference between the 51st term of a and the 51st term of b is 1000.

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Answer:

2334

Step-by-step explanation:

The 1-tree lower bound is a valid lower bound on the solution to the Traveling Salesman Problem (TSP) because it provides a lower limit on the optimal solution's cost.

To understand why the 1-tree lower bound is valid, let's consider the definition of the TSP. In the TSP, we are given a complete graph with vertices representing cities and edges representing the distances between the cities. The goal is to find the shortest Hamiltonian cycle that visits each city exactly once and returns to the starting city.

In the context of the 1-tree lower bound, we start with a given vertex v and compute a minimum spanning tree (MST) T on the graph G excluding the vertex v. An MST is a tree that spans all the vertices with the minimum total edge weight. It ensures that we have a connected subgraph that visits each vertex exactly once.

Adding the two shortest edges from v to T creates a 1-tree. This 1-tree connects the vertex v to the MST T. By construction, the 1-tree includes all the vertices of the original graph G and has a total weight that is at least as large as the weight of the optimal solution.

Now, let's consider the Hamiltonian cycle of the TSP. Any Hamiltonian cycle must contain an edge that connects the vertex v to the MST T because we need to return to the starting vertex after visiting all other cities. Therefore, the optimal solution must have a cost that is at least as large as the cost of the 1-tree.

By using the 1-tree lower bound, we have effectively obtained a lower limit on the optimal solution's cost. If we find a better solution with a smaller cost, it means that the 1-tree lower bound was not tight for that particular instance of the TSP.

In summary, the 1-tree lower bound is a valid lower bound on the TSP because it constructs a subgraph that includes all the vertices and has a cost that is at least as large as the optimal solution. It provides a useful estimate for evaluating the quality of potential solutions and can guide the search for an optimal solution in solving the TSP.

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Answer:

t = - 65

Step-by-step explanation:

- \(\frac{t}{13}\) - 2 = 3 ( add 2 to both sides )

- \(\frac{t}{13}\) = 5 ( multiply both sides by 13 to clear the fraction )

- t = 65 ( multiply both sides by - 1 )

t = - 65

Answer:

wheres the table

Step-by-step explanation:

I dont see a picture so I cant help u sorry

The percentage of the total hours did Andrea work is,

⇒ 27.1%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Total number of hours to work is,

⇒ 5.8 + 8.1 + 7.3 + 8.7 hours

⇒ 29.9 hours

Here, Andre work 8.1 hours.

Hence, The percentage of the total hours did Andrea work is,

⇒ 8.1 / 29.9 × 100

⇒ 27.1%

Thus, The percentage of the total hours did Andrea work is,

⇒ 27.1%

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