Which ordered pair is a solution of
y=1/2x-3
A.(1, 4)
B.(2, -1)
C.(3, 12)
D.(4, -1)

The experimental probability of landing on a number greater than 4 is 0.25 or 25%.

To find this probability, we need to determine the number of successful outcomes (landing on a number greater than 4) and divide that by the total number of trials (60).

The successful outcomes are 5 and 6, with a frequency of 10 and 8 respectively. To add these two frequencies together, we can use 10 + 8 = 18.

So, the experimental probability is 18/60 = 0.3 or 25%.

It's important to note that experimental probability is based on the outcomes of an experiment or a sample and it may not be the same as a theoretical probability which is based on the ratio of favorable outcomes to the total number of outcomes in a theoretical model.

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the answer in fraction form is 18/60

if thats what you are looking for.

Answer:

Annually cumulating interest can be determined by the following formula:

W=P(1+r)^y

r represents the interest rate as a decimal, and P represents the starting amount of money.

Step-by-step explanation:

Answer:

x = 23

y = 119

Step-by-step explanation:

Line m is parallel to line n and the angle given as 61 and the angle that is represented with 4x - 31 are alternate angles and have equal measurement.

We can write the following equation based on this information:

4x - 31 = 61 add 31 to both sides

4x = 92 divide both sides by 4

x = 23

now onto y,

the angle represented with y and the angle that is represented with 4x - 31 are supplementary and their measures add up to 180:

4x - 31 + y = 180 replace x with 23

4*23 - 31 + y = 180

92 - 31 + y = 180 subtract like terms

61 + y = 180 subtract 61 from both sides

y = 119

\( \frac{1}{3} .( \frac{2x - 6}{5} ) = \frac{4}{9} .( \frac{x + 1}{3} )\)

\( \frac{2x - 6}{15} = \frac{4x + 4}{27} \)

\(54x - 162 = 60x + 60\)

\( - 222 = 6x\)

\(x = - 37\)

I guess it's right.We learnt this way in Turkey.

Answer:

The expression representing the perimeter of the platter will be:

P = 10/3x units

Hence, option (D) is true.

Step-by-step explanation:

Let the length l of a rectangular platter will be =  x

As the width of a rectangular platter is 2/3 its length.

so the width w of a rectangular platter will be = 2/3x

As the perimeter of the platter is defined as:

P=2(l+w)

where l is the length, and w is the width

substituting length l = x and width w = 2/3x

\(P=2\left(x\:+\:\frac{2}{3}x\right)\)

    \(=2\cdot \frac{5}{3}x\)             ∵ \(x\:+\:\frac{2}{3}x=\:\frac{5}{3}x\)

    \(=\frac{10x}{3}\) units

Therefore, the expression representing the perimeter of the platter will be:

P = 10/3x units

Hence, option (D) is true.

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There are 5 11 pointer questions and 15 3 pointer questions

We are given that total points of the test is 100

The test contains questions of two markings 3 points and 11 points

It is given that the total number of questions is 20

Let the number of three pointer questions be 'x' and the number of 11 pointer questions be 'y'

Thus total number of questions=x + y =20

Now the total sum of all the points comes to 100

Therefore,

3x+11y =100

x + y =20

x= 20-y

Now putting the value of x in the other question,

3(20-y) +11y =100

60-3y +11y=100

8y=100-60

8y=40

y=5

Thus x=20-y=20-5=15

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Given:

A deck of 52 cards is given.

To find- the probability of drawing the Ace of spades.

Explanation-

We know that there are only four aces in a deck.

Every suit has its own ace. Thus, we have one ace of spades.

The probability is given by th ratio of the total number of favorable outcomes to the total possible outcomes.

Mathematically, we get

The probability as a percent will be-

Thus, the probability of drawing the Ace of spades is 1.92%.

The answer is 1.92%.

Answer:

40.95

Step-by-step explanation:

P = 1500 + 75 = 1575

I = Prt

I = 1575(1.3%)(2)

I = 40.95

The solution to the quadratic equation x² + 7x + 5 = 0 is x = [7 ± √29]/2

From the question, we have the following equation that can be used in our computation:

x^2 + 7x -5 = 0

To start with, we need to properly represent the equation

So, we have the following representation

The equation is given as

x² + 7x + 5 = 0

The equation can then be calculated using the following quadratic formula

So, we have

x = [-b ± √(b² - 4ac)]/[2a]

In the equation x² + 7x + 5 = 0, we have the variables

a = 1, b = -7 and c = 5

Substitute a = 1, b = -7 and c = 5 in the equation

x = [-(-7) ± √((-7)² - 4 * 1 * 5)]/[2 * 1]

Evaluate the products and exponents

This gives

x = [7 ± √(49 - 20)]/[2]

Evaluate the difference

So, we have

x = [7 ± √29]/2

Hence, the solution is x = [7 ± √29]/2

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To determine the discard date of the dish, we need to consider the use-by dates of both the beef and the pork.

The beef has a use-by date of September 1, which means it should not be consumed after that date for safety reasons.

The pork, on the other hand, has a use-by date of September 15, indicating it should not be consumed after that date.

Since the dish includes both beef and pork, we must follow the earliest use-by date to ensure food safety. In this case, the beef has the earlier use-by date of September 1.

Therefore, the discard date of the dish would be September 1, as it should not be consumed or kept beyond that date.

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Answer:

True

Step-by-step explanation:

Answer:

  A.  True

Step-by-step explanation:

The graph passes the horizontal line test, so the inverse relation is a function.

__

The horizontal line test requires any horizontal line intersect the graph in at most one place.

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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Answer: So zero represents the point when locating a point on the number line like negatives and positives

Answer:

684 in^2

Step-by-step explanation:

SA = 2 ( l*w + l*h+ w*h)

SA = 2( 6*15 + 6*12+ 15*12)

     = 2( 90+72+180)

    = 2(342)

    = 684 in^2

Answer:

The least amount of fencing needed for the rectangular pen is 72.19 feet.

Step-by-step explanation:

The area and perimeter equations of the pen are, respectively:

\(p = 2\cdot (x + y)\) (1)

\(A = x\cdot y\) (2)

Where:

\(p\) - Perimeter, in feet.

\(A\) - Area, in square feet.

\(x\) - Width, in feet.

\(y\) - Length, in feet.

Let suppose that total area is known and perimeter must be minimum, then we have a system of two equations with two variables, which is solvable:

From (2):

\(y = \frac{A}{x}\)

(2) in (1):

\(p = 2\cdot \left(x + \frac{A}{x}\right)\)

And the first and second derivatives of the expression are, respectively:

\(p' = 2\cdot \left(1 -\frac{A}{x^{2}} \right)\) (3)

\(p'' = \frac{4\cdot A}{x^{3}}\) (4)

Then, we perform the First and Second Derivative Test to the function:

First Derivative Test

\(2\cdot \left(x - \frac{A}{x^{2}} \right) = 0\)

\(2\cdot \left(\frac{x^{3}-A}{x^{2}} \right) = 0\)

\(x^{3} - A = 0\)

Given that dimensions of the rectangular pen must positive nonzero variables:

\(x^{3} = A\)

\(x = \sqrt[3]{A}\)

Second Derivative Test

\(p'' = 4\)

In a nutshell, the critical value for the width of the pen leads to a minimum perimeter.

If we know that \(A = 169\,ft^{2}\), then the value of the perimeter of the rectangular pen is:

\(x = \sqrt[3]{169\,ft^{2}}\)

\(x \approx 5.529\,ft\)

By (2):

\(y = \frac{A}{x}\)

\(y = \frac{169\,ft^{2}}{5.529\,ft}\)

\(y = 30.566\,ft\)

Lastly, by (1):

\(p = 2\cdot (5.529\,ft + 30.566\,ft)\)

\(p = 72.19\,ft\)

The least amount of fencing needed for the rectangular pen is 72.19 feet.

The length of AB of the right-angle triangle will be 8.626 centimeters.

It's a condition of a triangle with one 90-degree gradient that obeys Pythagoras' theorem and can be unraveled using the trigonometry role.

The triangle ΔABC is a right-angle triangle.

The one angle of the right-angle triangle is 27° which is opposite to the side AB and the hypotenuse of the right-angle triangle is 19 cm.

The length of AB of the right-angle triangle is given as,

sin 27° = AB / 19

AB = 19 × sin 27°

AB = 19 × 0.45399

AB = 8.626

The length of AB of the right-angle triangle will be 8.626 centimeters.

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The growth rate given by value of dR / dc at C = 2 is 0.0021 (approx).

The given formula is, R(C) = 1.35c / (0.29 + c)

=> R(C) = 1.35c / 0.29 + 1.35c / c

Take the derivative of R with respect to c: R(C) = 1.35c / 0.29 + 1.35c / c

Differentiating with respect to c, dR / dc = 1.35(0.29 + c) - 1.35c / (0.29 + c)2dR / dc

= 1.35(0.29 + c - c) / (0.29 + c)2dR / dc

= 1.35(0.29) / (0.29 + c)2

At C = 2,dR / dc = 1.35(0.29) / (0.29 + 2)2= 0.002129

A bacterial growth rate is given by the equation R(C) = 1.35c / (0.29 + c).

We know that R(C) = 1.35c / (0.29 + c) dR / dc = 1.35(0.29 + c - c) / (0.29 + c)2dR / dc = 1.35(0.29) / (0.29 + c)2dR / dc = 1.35(0.29) / (0.29 + 2)2dR / dc = 0.002129

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The Average Variable Cost (AVC) Formula is a fundamental concept in economics and business management. It is used to calculate the average cost of producing one unit of a good or service, taking into account only the variable costs of production.

Variable costs are those costs that change with the level of production, such as raw materials and labor. Fixed costs, on the other hand, do not change with the level of production and include expenses such as rent and equipment.

The AVC formula is calculated by dividing the total variable costs of production by the number of units produced. This gives the average cost of producing each unit of the good or service, taking into account only the variable costs.

The value of the AVC formula lies in its ability to help managers and business owners understand the cost structure of their operations. By calculating the average variable cost, they can determine the minimum price they need to charge for their product or service in order to cover their costs and make a profit.

In addition, the AVC formula can be used to compare the efficiency of different production methods. By calculating the AVC for each method, managers can determine which method is the most cost-effective, taking into account only the variable costs.

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the proportion of products that exhibit edge roughness is 0.035 (rounded to four decimal places).

To determine the proportion of products that exhibit edge roughness, we can use the law of total probability. We'll calculate the probability of rough edges for each category of blade sharpness and then sum them up, weighted by the proportion of blades in each category.

Let's denote:

A: Product has rough edges

N: Blade is new

A_N: Product has rough edges given new blade (probability = 0.02)

A_A: Product has rough edges given average sharpness blade (probability = 0.04)

A_W: Product has rough edges given worn blade (probability = 0.04)

P(N) = 0.25 (proportion of new blades)

P(A) = ?

We need to calculate P(A), the proportion of products that exhibit edge roughness.

Using the law of total probability:

P(A) = P(A_N) * P(N) + P(A_A) * P(A) + P(A_W) * P(W)

We know that P(N) = 0.25, P(A_A) = 0.60, and P(A_W) = 0.15. Let's substitute these values into the equation:

P(A) = 0.02 * 0.25 + 0.04 * 0.60 + 0.04 * 0.15

P(A) = 0.005 + 0.024 + 0.006

P(A) = 0.035

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Answer:

34 degrees

Step-by-step explanation:

sin(x) = opp/hyp = 9/16

So, x = 34.22 degrees

After rounding to the nearest degree, x = 34 degrees

The following probability which  is true: P(1.5 - .02 < X < 1.5 + .02) = 0.68 for the distribution of log-cell counts of red blood cells for women.

Given that the distribution of log-cell counts of red blood cells for women age 25-30 is approximately normally distributed with µ = 1.5 cells/microliter and σ = 0.1 cells/microliter.

In this, the probability of the Z score for a range is asked.

The value of Z is given by:

Z = (X - µ)/σZ

= (1.5 - 1.5)/0.1

= 0

In the Z table, the value of 0 is 0.5.

So, the following probability will be found:

P(1.5 - .02 < X < 1.5 + .02) = P(-0.2 < Z < 0.2)

We know that 0.2 value is in between 0 and 0.25 in the Z table.

P(1.5 - .02 < X < 1.5 + .02) = P(-0.2 < Z < 0.2)

= P(Z < 0.2) - P(Z < -0.2)

= 0.5793 - 0.4207

= 0.1586

≈ 0.16

Therefore, the option which is true is: P(1.5 - .02 < X < 1.5 + .02) = .68.

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Answer:

It is not possible to determine the local maximum of the graphed function over the interval [-3, 1.5] based on the given information. The maximum value of the curved line occurs at (negative 1.6, 56) and (2, 0), but these points do not fall within the interval [-3, 1.5]. Similarly, the minimum value of the curved line occurs at (0.8, negative 11.4), but this point also does not fall within the interval [-3, 1.5]. The curve crosses the x-axis and y-axis at (negative 2.5, 0), (0, 0), and (2, 0), but these points do not correspond to local maxima or minima of the curve.

To determine the local maximum over the interval [-3, 1.5], it would be necessary to have additional information about the shape of the curve and its values at points within the given interval.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

edge 23

Answer: i am almost positive its (A)

i really hope im not wrong because this answer is the only one that has a stable rising action going up by the same number it did with the number before it. if its not right then your other option is (D)

Step-by-step explanation:

Answer:

the guy above me is right. i had this question and i was confused to and i just guessed that it goes by the way the numbers rise. therefore the answer is indeed (A)

Step-by-step explanation:

give him brainliest cause i just confirmed that he is right but i didn't actually know this. he put more effort in the question than me

The given initial value problem is a second-order linear homogeneous differential equation. To solve it, we first find the characteristic equation by substituting y = e^(rx) into the equation. This leads to the characteristic equation r^2 - 10r + 50 = 0.

The general solution of the differential equation is y(x) = e^(5x)(C₁cos(5x) + C₂sin(5x)), where C₁ and C₂ are constants determined by the initial conditions.

To determine the particular solution, we differentiate y(x) to find y'(x) = e^(5x)(5C₁cos(5x) + 5C₂sin(5x) - C₂cos(5x) + C₁sin(5x)), and then differentiate y'(x) to find y''(x) = e^(5x)(-20C₁sin(5x) - 20C₂cos(5x) - 10C₂cos(5x) + 10C₁sin(5x)).

Substituting the initial conditions y(0) = 1 and y'(0) = 5 into the general solution and its derivative, we obtain the following equations:

1 = C₁,

5 = 5C₁ - C₂.

Solving these equations, we find C₁ = 1 and C₂ = 4.

Therefore, the particular solution to the initial value problem is y(x) = e^(5x)(cos(5x) + 4sin(5x)).

To find the value of y when x = 1.52, we substitute x = 1.52 into the particular solution and evaluate it. The result will depend on the rounding instructions provided.

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Answer:

x = 10

Step-by-step explanation:

The segment parallel to the third side of the triangle and intersecting the other 2 sides, divides those sides proportionally, that is

\(\frac{2x-5}{10}\) = \(\frac{28-8}{8}\) = \(\frac{20}{8}\) ( cross- multiply )

8(3x - 5) = 200 ← distribute left side

24x - 40 = 200 ( add 40 to both sides )

24x = 240 ( divide both sides by 24 )

x = 10

From the given data value of function f ' (- 10) is,

⇒ f ' (- 10) = 0.035

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.

Given that;

Table for the given data is shown.

Now, We have to find the value of f ' (- 10).

Since, - 10 is in between - 11 and - 9.

Hence, The slope given the value of f ' (- 10) as;

⇒ f ' (- 10) = (1.12 - 1.05) / (- 9 - (- 11))

⇒ f ' (- 10) = (0.07/2)

⇒ f ' (- 10) = 0.035

Thus, From the given data value of f ' (- 10) is,

⇒ f ' (- 10) = 0.035

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Given:

Radius of circle is 13 cm

Height of triangle is 5 cm

To find:

Value of 'a' and 'b'

Steps:

To find value of 'a', we will use Pythagoras theorem as the triangle is a right angle triangle,

A² + B² = C²

\(a^{2} + 5^{2} = 13^{2}\)

\(a^{2} + 25 = 169\)

\(a^{2} = 169 - 25\)

\(a^{2} = 144\)

\(\sqrt{a^{2}}=\sqrt{144}\)

\(a = 12\)

Now to find the value of 'b', i will use law of cosine,

\(c=\sqrt{a^{2}+b^{2}-2ab(cos\beta ) }\)

\(12 = \sqrt{13^{2}+5^{2}-2(5)(13)(cos\beta )}\\12=\sqrt{169 + 25-130(cos\beta )}\\12=\sqrt{194-130(cos\beta )}\\144 = 194 - 130(cos\beta )\\50 = 130(cos\beta )\\cos\beta = 0.3846\\\beta = cos^{-1}(0.3846)\\\beta = 67.38\)

Therefore, the values of 'a' and 'b' is 12 and 67.38 respectively

Happy to help :)

If u need any help feel free to ask

The differential equation dy/dx = 3x² - 2 with f(-1) = 2 is y = x³ - 2x + 1To solve this differential equation, we need to integrate both sides with respect to x.

dy/dx = 3x² - 2

Integrating both sides:

∫dy = ∫(3x² - 2)dx

y = x³ - 2x + C

Here, C is the constant of integration that we need to find. To do that, we can use the initial condition f(-1) = 2.

Substituting x = -1 and y = 2 in the equation:

2 = (-1)³ - 2(-1) + C

2 = -1 + 2 + C

C = 1

Therefore, the solution to the differential equation is:

y = x³ - 2x + 1

To overlay this solution on a slope field for the differential equation, we need to first draw the slope field. We can do this by calculating the slopes at different points in the x-y plane.

Using the differential equation, we know that the slope at any point (x, y) is given by:

dy/dx = 3x² - 2

We can draw arrows with slopes equal to 3x² - 2 at various points in the plane to get the slope field.

Once we have the slope field, we can overlay the solution y = x³ - 2x + 1 on it by plotting the curve y = x³ - 2x + 1 and checking if the direction of the curve matches the arrows in the slope field.

Overall, the solution to the differential equation dy/dx = 3x² - 2 with f(-1) = 2 is y = x³ - 2x + 1, and we can overlay this solution on the slope field to visualize the behavior of the solution at different points in the plane.

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