help please !
ence ivices fue unit IN IS Newton's): 30 W Assume that Tension 1 is 108 N, Tension 2 is 132 N. Write the component form of the two tension vectors (for example< 2,4>) using the magnitudes and angles g

You have a bag of 10 marbles. Three of them are red, five are blue, and two are green. The probability of randomly picking a green or blue marble out of the bag is 0.7 or 70%.

The given information is that there is a bag of 10 marbles, among which three are red, five are blue, and two are green. We are required to find out the probability of randomly picking a green or blue marble out of the bag.

So, the probability of randomly picking a green or blue marble out of the bag can be determined using the formula of probability.

The formula is:

P(E) = Number of Favorable Outcomes / Total Number of Possible Outcomes

Where,

P(E) is the probability of the event and E is the event.

For the given problem,

the event is picking a green or blue marble from the bag.

The total number of possible outcomes is the total number of marbles in the bag, which is 10.

Number of Favorable Outcomes

There are five blue marbles and two green marbles in the bag.

So, the number of favorable outcomes is

5 + 2 = 7.

P(E) = Number of Favorable Outcomes / Total Number of Possible Outcomes

P(E) = 7 / 10

P(E) = 0.7

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To find the limit of cos(x)/(1-sin(x)) as x approaches (π/2)+, we can use l'Hospital's Rule.

First, we can take the derivative of both the numerator and denominator with respect to x: lim cos(x)/(1 − sin(x)) x → (π/2)+ = lim [-sin(x)/(cos(x))] / [-cos(x)] x → (π/2)+ = lim sin(x) / [cos(x) * cos(x)] x → (π/2)+

Now, plugging in (π/2)+ for x, we get: lim sin(π/2) / [cos(π/2) * cos(π/2)] x → (π/2)+ = 1 / (0 * 0) = undefined

Since the denominator approaches 0 as x approaches (π/2)+, and the numerator is bounded between -1 and 1, the limit does not exist.

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Option D, the function is graphed. And the condition is y = {x² +4,x<2

                                                                                            -x+4, x >2

In a mathematical function from a set X to a set Y, exactly one element of Y is assigned to each element of X. The function's codomain and domain are respectively referred to as the sets X and Y as a whole.

Functions were initially thought of as the relationship between varying quantities and other variables. The impact of time on a planet's position serves as an example of this. The concept was historically developed with the development of infinitesimal calculus at the end of the 17th century, and up until the 19th century, the functions taken into consideration were differentiable.

Let us check option A first

y={x² +4, x≤ 2

    -x+4, x<2

For, x² +4, x≤ 2

x   2     1     0     -1      -2

y   3     5    4      5       8

Here, the condition is satisfied

Now, we have to check the condition

-x+4, x<2

The condition is not satisfied.

Similarly, we have to check all the options.

And finally by checking all the conditions,

Option D is correct and the conditions are

y = {x² +4,x<2

      -x+4, x >2

Therefore, the option D function is graphed.

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Answer:   \(\frac{x^8}{256y^{20}}\)

If the font is too small, it says x^8 all over top 256y^20 as one big fraction.

========================================================

Work Shown:

\(\left(\frac{5x^3}{20xy^5}\right)^4\\\\\\\left(\frac{x^2}{4y^5}\right)^4\\\\\\\frac{\left(x^2\right)^4}{(4^1)^4\left(y^5\right)^4}\\\\\\\frac{x^{2*4}}{4^{1*4}y^{5*4}}\\\\\\\frac{x^{8}}{4^{4}y^{20}}\\\\\\\frac{x^{8}}{256y^{20}}\\\\\\\)

Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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The amount accumulated after investing a principal P for t years at an interest rate compounded annually is  $46,057.58.

Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Therefore, let's find the amount accumulated after investing a principal P for t years at an interest rate compounded annually.

\(A = p(1 + \frac{r}{n} )^{nt}\)

where

p = 15,500

r = 9.5%

t = 12

n = 1

\(A = 15500(1 + \frac{0.095}{1} )^{1(12)}\)

A = 15,500.00(1 + 0.095)¹²

A = $46,057.58

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$46,057.58, answer for acellus

Answer:

The distance between points A and B is 3 units

Step-by-step explanation:

We need to find distance between points on the number line.

The points given are:

A = -1 , B = 2

The formula used is: \(Distance = |b-a|\)

Putting values of a and b and finding answer:

\(Distance = |b-a|\\Distance = |2-(-1)|\\Distance=|2+1|\\Distance=|3|\\Distance = 3\)

So, The distance between points A and B is 3 units

Answer: the answer to this is true

Answer:

The value of b is 21

Step-by-step explanation:

29=√20^2+b^2

or, 29=√400+b^2

or, 841=400+b^2

or, 841-400=b^2

or, √441=b

b=21

An inequality is a relationship that compares two numbers or other mathematical expressions in an unfair manner. When comparing the sizes of two numbers on the number line, it is most frequently used. The graph of each equation or inequality is given the attachment.

The graph, visual depiction of statistical information or a functional relationship between variables. Graphs serve a predictive purpose because they can highlight broad trends in the quantitative behaviour of data. However, they can be inaccurate and occasionally deceptive as mere approximations.

Most graphs have two axes: a horizontal axis for a set of independent variables and a vertical axis for a set of dependent variables. A broken-line graph is the most typical type of graph, with time usually acting as the independent variable.

16. 2y – 4x < 8

=  2y < 4x + 8

= y < 2x + 4

17. -4y > -x + 12

= y > x/4 + -3

18. | x + 3 |= y

y = | x + 3 |

19.  |2x – 6| + 2 = y

y = |2x – 6| + 2

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Answer:

1.5

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Answer:

y = -4x + 2

Step-by-step explanation:

y = mx + b ( slope-intercept)

1. Find Slope:

\(\frac{y^2 - y^1}{x^2 - x^1}\)

Lets name 2 as y2 and 10 as y1. And 0 as x2 and 2 as x1.

\(\frac{2-10}{0-2}\)  =  \(\frac{-8}{2}\) = -4

m/slope = -4

2. Find y-intercept:

\(y = mx +b\)

2 = -4(0) + b

= 2 = b

Y-intercept/b = 2

3. Put into slope-intercept form:

y = mx + b

= y = -4x + 2

Hope that helps! :D

Answer:

0?

Step-by-step explanation:

i looked it up.

Answer: -7/2 +- (Squareroot)6i/2

The perimeter of the rectangle, in simplest expression form, is 10x + 14.

To find the perimeter of a rectangle, we need to know either the length and width of the rectangle or the area and one side length.

In this case, we are given the area of the rectangle as \(6x^2 + 17x + 12\) square feet.

To find the length and width, we can factor the given area expression:

\(6x^2 + 17x + 12\)

= (2x + 3)(3x + 4)

From the factored form, we can see that the length is (3x + 4) and the width is (2x + 3).

To find the perimeter, we use the formula:

Perimeter = 2(length + width).

Substituting the values, we get:

Perimeter = 2(3x + 4 + 2x + 3)

         = 2(5x + 7)

         = 10x + 14

Therefore, the perimeter of the rectangle, in simplest expression form, is 10x + 14.

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Answer:

57

Step-by-step explanation:

.85n = 51

n = 51/0.85

n = 60

10% of 60 is 6

.95 x 60 = 57

95% of the number 60 = 57.

Addition is an operation used in math to add numbers. The result that is obtained after addition is known as the sum of the given numbers.

For example, if we add 2 and 3, (2 + 3) we get the sum as 5.

Given,

85% of a number is 51 and 10% of the same number is 6

95 % of number = 85% of a number + 10% of the same number

                           = 51 + 6

                           = 57

0.95 × number = 57

number = 60

Hence, 57 is the 95% of the number 60.

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After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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The given problem is a 0-1 integer programming problem, which involves finding the maximum value of a linear objective function subject to a set of linear constraints, with the additional requirement that the decision variables must take binary values (0 or 1).

To solve this problem by implicit enumeration, we systematically evaluate all possible combinations of values for the decision variables and check if they satisfy the constraints. The objective function is then evaluated for each feasible solution, and the maximum value is determined.

In this case, there are three decision variables: x1, x2, and x3. Each variable can take a value of either 0 or 1. We need to evaluate the objective function 2x1 - x2 - x3 for each feasible solution that satisfies the given constraints.

By systematically evaluating all possible combinations, checking the feasibility of each solution, and calculating the objective function, we can determine the solution that maximizes the objective function value.

The explanation of the solution process, including the enumeration of feasible solutions and the calculation of the objective function, can be done using a table or a step-by-step analysis of each combination.

This process would involve substituting the values of the decision variables into the constraints and evaluating the objective function. The maximum value obtained from the feasible solutions will be the optimal solution to the problem.

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Answer:

3 months

Step-by-step explanation:

120 + 40m = 180 + 20m

Collect like terms

40m - 20m = 180 - 120

20m = 60

Divide

m = 60/20

m = 3

It will take them 3 months before Jaclyn and Pedro have saved the same amount of money.

The probability that the second card is a king given that the first card is not a king is 4/51.

This is because there are 4 kings in the deck and 51 cards left after the first card is drawn that are not kings.

To understand this problem, we need to use conditional probability. The event that the first card is not a king is our condition and we want to find the probability that the second card is a king given this condition. We know that there are 4 kings in the deck & 51 cards left after the first card is drawn that are not kings.. So the probability that the second card is a king given that the first card is not a king is 4/51.

The order in which the cards are drawn does not matter since we are not replacing the first card.

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Answer:

it 102

Step-by-step explanation:

I hope it works

Answer:

x = -1

Step-by-step explanation:

you try to get x by itself in this case I devided x/2 and -2/2

For {K} = 12, the image will remain preserved.

Given is the scale factor of {K} = 12.

We can write the scale factor as -

reduction  {for K < 1}

enlargement  {for K > 1}

preserved  {for K = 1}

For {K} = 12, the image will remain preserved.

Therefore, for {K} = 12, the image will remain preserved.

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Answer: 15

Step-by-step explanation:

 4-7+9=8

  +7     +7

  4+9=15

    15=15

Answer:

Step-by-step explanation:

Answer:

I believe the quiz had 18 questions, with a 14:4 ratio

Answer

The constant of variation is

k = 6

Since the direct variation equation is

y = kx

We can just substitute the value of k

y = 6x

Explanation

We are told that y varies directly as x, which can be written as

y ∝ x

Introducing the constant of variation, k, we have

y ∝ x

y = kx

We can then solve for k knowing that

y = 1 when x = (1/6)

y = kx

1 = (k) (1/6)

1 = (k/6)

We can rewrite this as

(k/6) = 1

we can then multiply both sides by 6

(k/6) × 6 = 1 × 6

k = 6

Hope this Helps!!!

The slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.

The slope of a line (m) = change in y/change in x = y2 - y1/x2 - x1 or rise/run of the line.

Given the following points on the line:

(-4, 2) = (x1, y1)

(-5, 0) = (x2, y2)

Substitute the values into m = y2 - y1/x2 - x1:

Slope (m) of the line = (0 - 2) / (-5 - (-4))

Slope (m) of the line = (-2) / (-5 + 4)

Slope (m) of the line = -2/-1

Slope (m) of the line = 2

Thus, the slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.

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The total number of roots for the given polynomial is for f(x) = 3x⁶ + 2x⁵ + x⁴ - 2x³ is 6.

What is the polynomial function?

A polynomial function is a function that may be written as a polynomial. A polynomial equation definition can be used to obtain the definition. P(x) is the general notation for a polynomial. The degree of a variable of P(x) is its maximum power. The degree of a polynomial function is particularly important because it tells us how the function P(x) behaves as x becomes very large. A polynomial function's domain is full real numbers (R).

Here, we have

Given:  polynomial function: f (x) = 3x⁶ + 2x⁵ + x⁴ - 2x³

We have to find the number of roots of a polynomial function.

For finding the number of roots, we just need to see what is the degree fro the given polynomial, where the degree of the polynomial is nothing but the highest exponent.

For the function f (x) = 3x⁶ + 2x⁵ + x⁴ - 2x³, here the degree is 6, and the respective function is having 6 numbers of roots, which be real roots and complex roots too.

Hence, the total number of roots for the given polynomial is for f(x) = 3x⁶ + 2x⁵ + x⁴ - 2x³ is 6.

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The surface area is increasing at a rate of approximately 2513.274 square centimeters per second.

The problem provides us with the rate of change of the radius, which is 2 cm/sec. We are asked to find how fast the surface area is increasing when the radius is 10 cm.

To find the rate at which the surface area is increasing, we can use the formula for the surface area of a sphere, which is 4πr^2.

First, we differentiate the formula with respect to time (t) to find the rate of change of the surface area, which is dA/dt:

dA/dt = d/dt(4πr^2)

Next, we substitute the given rate of change of the radius into the equation:

dA/dt = d/dt(4π(10)^2)

Simplifying further:

dA/dt = d/dt(400π)

Since the radius is increasing at a constant rate, its derivative is simply the constant rate itself, which is 2 cm/sec.

Therefore:

dA/dt = 2(400π)

Simplifying the expression:

dA/dt = 800π

Rounding to the nearest thousandths:

dA/dt ≈ 2513.274

So, when the radius of the sphere is 10 cm, the surface area is increasing at a rate of approximately 2513.274 square centimeters per second.

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The solution to the differential equation dz/dt = z^2 - 16 is z(t) = 4/tan(4t + C), where C is an arbitrary constant.

Explanation:

To solve the given differential equation dz/dt = z^2 - 16, we can separate the variables and integrate. Rearranging the equation, we have dz/(z^2 - 16) = dt. Now we integrate both sides.

Integrating the left side involves partial fraction decomposition, which leads to the integral of dz/((z - 4)(z + 4)). This can be expressed as (1/8) * (1/(z - 4) - 1/(z + 4)). Integrating the right side gives us t + D, where D is a constant of integration.

Now, we have (1/8) * (1/(z - 4) - 1/(z + 4)) = t + D. Multiplying both sides by 8 and simplifying, we get (z - 4) - (z + 4) = 8(t + D). Combining like terms, we have -8 = 8t + 8D. Rearranging the equation, we get 8t = -8 - 8D.

Dividing by 8, we obtain t = -1 - D. Letting C = -1 - D, we have t = C.

Finally, we can rewrite the solution as z(t) = 4/tan(4t + C), where C is an arbitrary constant. This represents the general solution to the given differential equation.

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