What two positive real numbers whose product is 86 have the smallest possible sum? The numbers are and (Type exact answers, using radicals as needed.)

Answer:

Step-by-step explanation:

son age be x

Aman age is 3x

ten years ago

son age x-10

aman age 3x -10

A.T.Q

5(x-10) = 3x -10

5x -50 = 3x - 10

2x = 40

x =20

3x=60

son present age =20

aman present age = 60

Answer:

If the first card drawn is green and not replaced before the second draw, then there are a total of 51 cards left, of which 19 are green.

Therefore, the probability of drawing two green cards is:

(19/51) * (18/50) = 171/850

The answer as a fraction in lowest terms is:

171/850

The study of statistics rests on two major​ concepts probability which  is the branch of mathematics that deals with the likelihood of events occurring and Data Analysis is the process of examining and interpreting data in order to gain insights and make better decisions

Probability theory is based on the idea that, given enough data, the frequency of an event can be predicted and allows for the formulation of mathematical models that can quantify the likelihood of particular outcomes. Probability is the foundation of statistics and helps to explain the behavior of chance events.It involves the collection, organization, and analysis of data from a variety of sources, such as survey responses, observations, experiments, or existing databases.

Data analysis is used to identify patterns and relationships in data, draw conclusions, and make decisions. It is an important part of statistics, as it helps to uncover insights that would otherwise remain hidden. Data analysis tools, such as statistical models, can be used to gain greater insight into the data.

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Answer: x=-1

Step-by-step explanation:

3x+2(2x+8)=9

Answer:

3x+2y=9

3x+2(2x+8)=9

3x+4x+16=9

7x=-7

x=-1

y=2(-1)+8

y=-2+8

y=6

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The solubility product constant (Ksp) for calcium carbonate (CaCO3) is \(2.802 \times10^{-13}.\)

To calculate the solubility product constant (Ksp) for calcium carbonate (CaCO3), we need to know the balanced chemical equation for its dissolution in water. The balanced equation is:

CaCO3(s) ⇌ Ca2+(aq) + CO32-(aq)

The solubility of calcium carbonate is given as \(\frac{5.3\times10^{-5} g}{L}\). This means that at equilibrium, the concentration of calcium ions (Ca2+) and carbonate ions (CO32-) in the solution will be:

[Ca2+] = x (where x is the molar solubility of CaCO3)

[CO32-] = x

Since 1 mole of CaCO3 dissociates to form 1 mole of Ca2+ and 1 mole of CO32-, the equilibrium concentrations can be expressed as:

[Ca2+] = x

[CO32-] = x

The solubility product constant (Ksp) expression for CaCO3 is:

Ksp = [Ca2+][CO32-]

Substituting the equilibrium concentrations:

Ksp = x * x

Now, we can substitute the given solubility value into the equation. The solubility is given as \(\frac{5.3\times10^{-5} g}{L}\), which needs to be converted to moles per liter \((\frac{mol}{L}\)):

\(\frac{5.3\times10^{-5} g}{L}\) * (\(\frac{1 mol}{100.09 g}\)) = \(\frac{5.297\times10^{-7} mol}{L}\)

Now, we can substitute this value into the Ksp expression:

Ksp = (\(\frac{5.297\times10^{-7} mol}{L}\)) * (\(\frac{5.297\times10^{-7} mol}{L}\))

= \(2.802\time10^{-13}\)

Therefore, the solubility product constant (Ksp) for calcium carbonate (CaCO3) is \(2.802\times10^{-13}\).

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Step-by-step explanation:

2+3=5

58+62=120

120÷5=24

so 24 carbohydrates are in one glass of milk

The area of each of the missing faces is 40 m².

The length of each of the missing faces is 10 m.

The missing dimension is 10 m by 4 m.

Area is the region bounded by a plane shape.

To calculate the area of each missing face, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

And the length of each of the missing edge can be calculated using the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute into equation 2

Hence, the length is 10 m.

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Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975% in the compound interest.

When interest is earned on a loan or investment, it is earned on both the principal and any accumulated interest, which is known as compound interest. In other words, interest is added to the principal, and the resulting sum is then used to determine future interest. Compounding causes an investment or loan to increase more quickly than it would with simple interest, where just the principal is charged interest. Compounding may occur daily, monthly, quarterly, annually, or at any other interval.

To compare the plans of the two accounts we have:

Rate = ( 1 + rate / n)ⁿ - 1

where, n is the compounded period.

For plan A:

Effective annual interest rate = (1 + (0.5%/4))⁴ - 1 ≈ 0.5025%

For Plan B, we have:

Effective annual interest rate = (1 + 3.5%)¹- 1 = 3.5%

Comparing the two we see that Plan B offers higher rates by:

3.5% - 0.5025% ≈ 2.9975%.

Hence, Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975%.

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Occupants are 10 times more likely to be killed in a crash when not buckled in. option c.

Wearing a seatbelt is one of the simplest ways to protect oneself while in a vehicle. When properly worn, it decreases the likelihood of being seriously injured or killed in a collision by as much as 50%. When an individual is not wearing a seatbelt, they are putting their lives at risk. Wearing a seatbelt should be a routine habit whenever an individual sits in a vehicle.

Buckling up is the easiest and most effective way to prevent injuries and fatalities on the road. If drivers, passengers, and children buckle up every time they travel in a vehicle, the likelihood of being killed or injured in a collision is greatly reduced. When occupants of a vehicle do not buckle up, they are 10 times more likely to be killed in a crash. This means that the likelihood of being killed is significantly higher when not wearing a seatbelt.

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Let the two numbers be x and y. Then, x + y = 11 and 2xy = 48. Solving these equations, x = 3 and y = 8.

Let the two numbers be x and y. Then, we need to solve the following two equations:

x + y = 11

2xy = 48

Subtracting y from both sides of the first equation, we get

x = 11 - y

Substituting the value of x in the second equation, we get

2(11 - y)y = 48

Simplifying the left side of the equation, we get

22 - 2y = 48

Subtracting 22 from both sides of the equation, we get

-2y = 26

Dividing both sides of the equation by -2, we get

y = -13

Substituting the value of y in the first equation, we get

x = 11 - (-13)

Simplifying the right side of the equation, we get

x = 24

Therefore, the two numbers are x = 24 and y = -13.

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Answer:

20mph

Step-by-step explanation:

because you have to divide 240 by 12 and the answer is 20

The given system of equations do not have a solution since their related line equations have the same slope.

The given system of equations is:

-x + 5y = 3   .......... (1)

2x - 10y = 4   ........(2)

In Equation (1), add both sides by (-5y)

-x + 5y + (-5y) = 3 + (-5y)

-x = -3 - 5y

Multiply by (-1)

x = 3 + 5y

Substitute x = 3 + 5y into equation (2)

2x - 10y = 4

2.(3 + 5y) - 10y = 4

6 + 10y - 10y = 4

6 = 4 (False)

Since the last equation is false, we might suspect that the given system of solution does not have solutions.

We need to check the slope of both equations:

-x + 5y = 3

⇒ 5y = x + 3

⇒ y = 1/5 x + 3/5

2x - 10y = 4

⇒ -10 y = -2x + 4

⇒ y = (2/10) x - 4/10

⇒ y = 1/5 x - 2/5

We can see that both equations have the same slope, i.e. 1/5.

Hence, they do not have solutions since the lines are parallel to each other.

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

plug 2 in for x and solve.

5(2)-7=3

Answer:

80%

Step-by-step explanation:

100% is full so you do 100%-20%=80% so thats the answer

False; Side-by-side box plots may not be the most appropriate plot to explore the data in a two-way design with one factor having three levels and the other factor having two levels

In a two-way design with one factor having three levels and the other factor having two levels (3x2 design), side-by-side box plots of the first factor separated by levels of the second factor may not be the best plot to explore the data. Box plots are useful for visualizing the distribution of a single variable, but they may not effectively display the interactions between the two factors in a two-way design.

To explore the data in a two-way design, it is often more informative to use interaction plots or interaction effects plots. These plots show the relationship between the two factors and how their effects interact. An interaction plot displays the mean or median of the response variable for each combination of the two factors, and it includes separate lines or bars for each level of one factor within each level of the other factor.

By examining the interaction plot, you can assess whether the effects of one factor differ depending on the level of the other factor. This provides insights into the interaction between the two factors and helps identify any significant differences or patterns in the data.

Using side-by-side box plots in a two-way design may not adequately capture the interaction effects and may overlook important insights about the relationship between the factors. Therefore, alternative plots, such as interaction plots, are more suitable for exploring the data in a 3x2 design.

Side-by-side box plots may not be the most appropriate plot to explore the data in a two-way design with one factor having three levels and the other factor having two levels (3x2 design). Interaction plots or interaction effects plots are better suited for visualizing the interaction effects between the two factors and capturing the relationships in the data.

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volume of sphere is increasing at a rate of  62,832 mm3/s.

 The volume of a three-dimensional space can be determined. It is frequently numerically expressed in terms of several imperial units or SI-derived units. Volume and length are dependent on one another.

Step 1: Define an equation that relates the volume of a sphere to its radius.

V = 4/3*π*r3

Step 2: Take the derivative of each side with respect to time (we will define time as "t").

(d/dt)V = (d/dt)(4/3*π*r3)

dV/dt = 4πr2*dr/dt

Step 3: We are told in the problem statement that diameter is 100m, so therefore r = 50mm. We are also told the radius of the sphere is increasing at a rate of 2mm/s, so therefore dr/dt = 2mm/s. We are looking for how fast the volume of the sphere is increasing, or dV/dt.

dV/dt = 4π(50mm)2*(2mm/s)

dV/dt = 62,832 mm3/s

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Answer:

17.72\(\frac{miles}{hr}\)

Step-by-step explanation:

If you are trying to take 26 ft/s to being miles per hour this is how you do it.

26 \(\frac{ft}{s}\) * \(\frac{mile}{5280ft}\) *\(\frac{3600s}{hr}\)

so

17.72\(\frac{miles}{hr}\)

Answer:

b) is the correct option

The correct term for a sample obtained in such a way that every element in the population has an equal chance of being selected is a "random sample."

In a random sample, each member of the population has an equal probability of being chosen, providing a representative subset of the population. This sampling method helps to reduce bias and ensures that the sample is more likely to accurately reflect the characteristics of the entire population.

Random sampling is a fundamental principle in statistics and research, allowing for generalizations and inferences to be made about the population based on the characteristics observed in the sample. It is widely used in various fields, such as social sciences, market research, and opinion polls, to draw meaningful conclusions about a larger population.

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The distance traveled in the first 5.2 seconds when the speed dropped from the rest as v(t) = 9.8t is equal to 132.496 meters.

'v' is the speed of the object in meter per second

't' is the time in seconds.

Speed dropped from rest 'v(t) = 9.8t '

Distance traveled in the first 5.2 seconds is equal to

= \(\int_{0}^{5.2}\)9.8t dt

= ( 9.8 / 2 )t² \(|_{0}^{5.2}\)

Substitute the lower and upper limit to get the required distance we have,

= 4.9 [ ( 5.2)² - 0² ]

= 4.9 × 27.04

= 132.496 meters

Therefore, the distance traveled for the given first 5.2 seconds is equal to 132.496 meters.

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The above question is incomplete, the complete question is:

Free fall the speed v of an object dropped from rest is given by v(t)=9.8t where v is meters per second and time 't' is in seconds.

(a) Express the distance traveled in the first 5.2 seconds as an integral.

The solution to the quadratic equation x² + 4x + 4 = 0 is x = -2 and x = -2

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The standard form of a quadratic equation is:

y = ax² + bx + c

Where a, b and c are constants

Given the quadratic equation:

x² + 4x + 4 = 0

x² + 2x + 2x + 4 = 0

x(x + 2) + 2(x + 2) = 0

(x + 2)(x + 2) = 0

x + 2 = 0; and x + 2 = 0

x = -2 and x = -2

The solution to the quadratic equation is x = -2 and x = -2

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Answer:

Median 1.5

Step-by-step explanation:

Answer:

Median is the most appropriate and the value is 1.5

Step-by-step explanation:

The survey designers can help ensure that they are getting accurate and representative responses from their participants.

The way questions are worded or the order in which they are asked can significantly impact people's responses and ultimately influence the accuracy of the survey results. Here are two specific ways in which this can happen:
1. Question Wording Effect: This refers to the impact of the specific wording of the survey questions on people's responses.

This effect is especially pronounced for questions that are complex, sensitive, or controversial.
2. Question Order Effect: This refers to the impact of the order in which the survey questions are presented on people's responses.

Similarly, if a survey question asks about a person's level of satisfaction with a product before asking about their experience with the product, it may influence their overall satisfaction rating.
Overall,

It is important to carefully consider the wording and order of questions when designing a survey to ensure accurate and reliable results.

By avoiding biased or leading questions and carefully considering the order in which questions are presented.

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The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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where y_1(x) = x^(-1/2) * cos((√21/2) * ln(x)) and y_2(x) = x^(-1/2) * sin((√21/2) * ln(x)), and u_1(x) and u_2(x) are obtained from the integration and variation of parameters of u_1'(x) and u_2'(x) as explained below.

To find a particular solution to the given differential equation using the method of variation of parameters, we follow these steps:

Step 1: Write the differential equation in standard form:

5xy" - 10y + 25y = (81 + x^2) - (1/2e^(5x)ln(x^2 + 81)) + (xe^(5x))

Step 2: Determine the complementary solution by solving the homogeneous equation:

5xy" - 10y + 25y = 0

The homogeneous solution can be found by assuming y = x^r and solving for the characteristic equation:

5r(r-1) + 10r - 25 = 0

5r^2 + 5r - 25 = 0

r^2 + r - 5 = 0

Solving the quadratic equation, we find two roots: r = (-1 ± √21i)/2. Therefore, the homogeneous solution is:

y_c(x) = C_1x^(-1/2) * cos((√21/2) * ln(x)) + C_2x^(-1/2) * sin((√21/2) * ln(x))

where C_1 and C_2 are arbitrary constants.

Step 3: Determine the particular solution using the method of variation of parameters. We assume the particular solution has the form:

y_p(x) = u_1(x)*y_1(x) + u_2(x)*y_2(x)

where y_1(x) and y_2(x) are the linearly independent solutions of the homogeneous equation. In our case, y_1(x) = x^(-1/2) * cos((√21/2) * ln(x)) and y_2(x) = x^(-1/2) * sin((√21/2) * ln(x)).

We need to find u_1(x) and u_2(x). To do this, we use the following formulas:

u_1'(x) = (g(x)*y_2(x)) / (W(y_1, y_2))

u_2'(x) = (-g(x)*y_1(x)) / (W(y_1, y_2))

where g(x) = (81 + x^2) - (1/2e^(5x)ln(x^2 + 81)) + (xe^(5x)) and W(y_1, y_2) is the Wronskian of y_1(x) and y_2(x).

The Wronskian of two functions is given by:

W(y_1, y_2) = y_1(x)*y_2'(x) - y_1'(x)*y_2(x)

Differentiating y_1(x) and y_2(x):

y_1'(x) = (-1/2)*x^(-3/2)*cos((√21/2) * ln(x)) + (√21/2)*x^(-1/2)*sin((√21/2) * ln(x))

y_2'(x) = (-1/2)*x^(-3/2)*sin((√21/2) * ln(x)) - (√21/2)*x^(-1/2)*cos((√21/2) * ln(x))

Now, we can calculate u_1'(x) and u_2'(x):

u_1'(x) = [(81 + x^2) - (1/2e^(5x)ln(x^2 + 81)) + (xe^(5x))] * [(-1/2)*x^(-3/2)*sin((√21/2) * ln(x)) - (√21/2)*x^(-1/2)*cos((√21/2) * ln(x))] / [x^(-1/2)cos((√21/2) * ln(x))(-1/2)*x^(-3/2)*sin((√21/2) * ln(x)) - (-1/2)*x^(-3/2)*cos((√21/2) * ln(x))*x^(-1/2)*sin((√21/2) * ln(x))]

u_2'(x) = [(81 + x^2) - (1/2e^(5x)ln(x^2 + 81)) + (xe^(5x))] * [(-1/2)*x^(-3/2)*cos((√21/2) * ln(x)) + (√21/2)*x^(-1/2)*sin((√21/2) * ln(x))] / [x^(-1/2)cos((√21/2) * ln(x))(-1/2)*x^(-3/2)*sin((√21/2) * ln(x)) - (-1/2)*x^(-3/2)*cos((√21/2) * ln(x))*x^(-1/2)*sin((√21/2) * ln(x))]

Integrating u_1'(x) and u_2'(x) will give us u_1(x) and u_2(x).

Finally, the particular solution is given by:

y_p(x) = u_1(x)*y_1(x) + u_2(x)*y_2(x)

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The 3 × 3 matrix that translates a point in r 2 by (3, 1) then rotates the result 45 degrees about the origin is

M = | 1/√2    -1/√2    3/√2- 1/√2 |

      | 1/√2    1/√2     1/√2 + 1/√2 |

       | 0           0                1 |

To find the 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates, we can follow these steps:

Translation Matrix:

The translation matrix for a 2D translation by (3, 1) is:

T = | 1 0 3 |

| 0 1 1 |

| 0 0 1 |

This matrix translates a point (x, y) by adding the translation vector (3, 1) to it.

Rotation Matrix:

The rotation matrix for a 2D rotation by 45 degrees counterclockwise is:

R = | cos(theta) -sin(theta) 0 |

| sin(theta) cos(theta) 0 |

| 0 0 1 |

Since we want to rotate by 45 degrees, theta = 45 degrees = π/4 radians. Therefore, the rotation matrix becomes:

R = | cos(π/4) -sin(π/4) 0 |

| sin(π/4) cos(π/4) 0 |

| 0 0 1 |

Simplifying, we have:

R = | 1/√2 -1/√2 0 |

| 1/√2 1/√2 0 |

| 0 0 1 |

Combine Translation and Rotation:

To obtain the combined transformation matrix, we multiply the translation matrix T by the rotation matrix R:

M = T * R

Performing the matrix multiplication:

M = | 1 0 3 | | 1/√2 -1/√2 0 |

| 0 1 1 | * | 1/√2 1/√2 0 |

| 0 0 1 | | 0 0 1 |

Simplifying, we have:

M = | 1/√2 -1/√2 3/√2 - 1/√2 |

| 1/√2 1/√2 1/√2 + 1/√2 |

| 0 0 1 |

This is the desired 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates.

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