Which pair of ratios will make a proportion?

A. 1/3 and 12/36
B. 1/3 and 5/14
C. 1/3 and 1/2
D. 1/3 and 4/16​

If the null hypothesis that two means are equal is true, 97% of the computed z values lie between 2.17.

Any variation between the selected characteristics that you observe in a set of data is thought to be the result of chance, according to the null hypothesis. For instance, any difference between the average earnings in the data and zero is caused by chance if the expected earnings for the gambling game are actually equal to zero. An assertion that there is no correlation between two population parameters is referred to as a null hypothesis. To prepare the ground for additional experimentation or research that explains the position of interest, researchers reject or refute the null hypothesis.

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The probability that the lifetime of at least one component exceeds 2 is 0.135.

Given that the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image.

We want to find the probability that the lifetime of at least one component exceeds 2.

The probability that the lifetime of at least one component exceeds 2 is P(X>2).

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}f(x,y)dydx\end[/tex]

Now, we will substitute the given function, we get

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}xe^{-x(1+y)}dydx\end[/tex]

Further, we will simplify this, we get

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\left[-e^{-x(1+y)\right]_{0}^{\infty}dx\\ &=\int_{x=2}^{\infty}e^{-x}dx\\ &=\left[-e^{-x}\right]_{2}^{\infty}\\ &=e^{-2}\\ &=0.135\end[/tex]

Hence, the probability that the lifetime of at least one component exceeds 2 for the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image is 0.135.

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Answer:

----------------------------

Given is the right triangle.

The two angles are complementary, so their sum is 90°:

The angles are:

Answer:

Step-by-step explanation:

Now we have to,

→ find the value of each angle.

Forming the equation,

→ 90° + (p - 10°) + (p + 50°) = 180°

Now the value of p will be,

→ 90° + (p - 10°) + (p + 50°) = 180°

→ (90° - 10° + 50°) + (p + p) = 180°

→ 130° + 2p = 180°

→ 2p = 180° - 130°

→ p = 50°/2

→ [ p = 25° ]

Then the value of other angle is,

→ p - 10° || → p + 50°

→ 25° - 10° || → 25° + 50°

→ 15° || → 75°

Hence, these are the angles.

The set of coordinates after the reflection is (c) M' = (-3, -4) N' = (2, -3) O' = (1, -1) P' = (-2, -2)

The graph represents the given parameter

On the graph, we have the following coordinate points

M = (-3, 4)

N = (2, 3)

O = (1, 1)

P = (-2, 2)

The rule of the reflection is given as:

Reflection across the x-axis

Mathematically, this is represented as

(x, y) ⇒ (x, -y)

When this is applied to the points, we have the following representation

M' = (-3, -4)

N' = (2, -3)

O' = (1, -1)

P' = (-2, -2)

Hence, the set of coordinates is (c)

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The sentence, using the rational root theorem, is completed as follows:

If a polynomial function f has integer coefficients, then every rational solution of f(x) = 0 has the format p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational root theorem states that a polynomial with integer coefficients will have every rational solution following the format p/q.

The variables p and q are defined as follows:

Hence the blanks in this problem are completed, respectively, by:

Constant term and leading coefficent.

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The expression for tension in the string is T = [(L/2)×(m1×g) + (x)×(m2×g)]/d.

We are a diagram that shows two blocks with masses m1 and m2.There are two strings, A and B. Everything is in equilibrium. Equilibrium is a condition of rest or balance caused by opposing forces acting equally. We need to find the tension in string A. Let the tension in the strings A and B be denoted by the variables "Ta" and "Tb", respectively. The net torque at point B must be zero as everything is in equilibrium. The diagram is attached below.

Στ(B) = 0

τ(a) + τ(b) + τ(m1) + τ(m2) = 0

τ = r×F×sin(θ)

d×(Ta)×sin(90°) + 0 - (L/2)×(m1×g)×sin(90°) - (x)×(m2×g)×sin(90°) = 0

d×(Ta) - (L/2)×(m1×g) - (x)×(m2×g) = 0

Ta = [(L/2)×(m1×g) + (x)×(m2×g)]/d

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The amount that will be spent on the cupcakes is $48.

From the information, Luisa plans to prepare cupcakes for her daughter's birthday and spends $15 on 25 units.

Let the amount spent on 80 cupcakes be x.

This will be illustrated as:

25/80 = 15/x

Cross multiply

25x = 15 × 80

25x = 1200

Divide

x = 1200/25

x = 48

The amount will be $48.

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System of equations that models the situation is Option C . 2x+3y = 7.20 , 4x+3y = 8.80 and the price per pound for oranges is $1.40.

Given:

Part A

Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80.

Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges.

2x + 3y = 7.20

4x + 2y = 8.80

Part B

on solving two equations:

2x + 3y = 7.20 and 4x + 2y = 8.80

2(2x + 3y) - 4x - 2y = 2*7.20 - 8.80

4x + 6y - 4x - 2y = 14.40 - 8.80

4y = 5.60

y = 5.60/4

= $1.40

hence price of oranges per pound is $1.40.

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The consecutive integers such 4 that times the smaller integer is 50 less than 6 times the larger integer are 22 and 23.

Let the consecutive integers be x and x + 1.

In this case, the integers are such 4 that times the smaller integer is 50 less than 6 times the larger integer.

This will be:

4(x) = 6(x + 1) - 50

4x = 6x + 6 - 50

Collect like terms

4x - 6x = -44

-2x = -44

Divide

x = 44/2

x = 22

Also, x + 1 = 22 + 1 = 23

The numbers are 22 and 23.

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Answer:

65

Step-by-step explanation:

Since 39 is 60%, 100/60= 1 2/3

39*1 2/3 is 65

The answer to the given question is -4/3 or 1/2

The product of 6 and the square of a number is increased by 5 times the number, the result is 4.

Firstly, let's write the algebraic expression for the above statement and represent the number as x.

The algebraic expression can be written as:

(6 x x²) + 5x = 4

6x² + 5x = 4

The other expression can also be written as:

6x² + 5x - 4 = 0

Secondly, we must factorize the algebraic expression to solve for x.

6x² - 3x + 8x - 4 = 0

3x (2x - 1) + 4 (2x + 1) = 0

(3x + 4)(2x - 1) = 0

Thirdly, we need to solve for x.

3x + 4 = 0

3x = -4

Now, we need to divide both sides by 3.

3x/3 = -4/3

x = -4/3

or

2x - 1 = 0

2x = 1

Now, we need to divide both sides by 2.

2x/2 = 1/2

x = 1/2

Hence, the values that the number could be is -4/3 or 1/2.

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solve 1/3 x= -4/5

1/3 * -4/5 = -4/15

-2 2/5

4/15

2 2/5

-4/15

Answer:

first option

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] x = - [tex]\frac{4}{5}[/tex]

multiply both sides by 15 ( the LCM of 3 and 5 ) to clear the fractions

5x = - 12 ( divide both sides by 5 )

x = - [tex]\frac{12}{5}[/tex] = - 2 [tex]\frac{2}{5}[/tex]

Answer:

Step-by-step explanation:

2

The Answer is Han will cover 2.5 miles distance

What is distance ?

Distance is the total path covered by a object or person. As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.

Han and Tyler both started running toward each other from opposite ends of a 10 mile path along a river.

We need to find the distance run by Han after a half hour.

Han will cover a distance in 12 minutes=1 mile

Han will cover a distance in 1 minute= 1/12mile

Han runs distance in 30 minutes=30*1/12 miles

Hence, Han runs 2.5 miles after half hour.

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As per the given ratio, the four numbers are 27, 33, 81 and 99.

Ratio:

Ratio means a mathematical expression written in the form of a:b, where a and b are any integers. It expresses a fraction.

Give,

Here we have the ratio 9: 11.

And the difference is 6.

And we need to find the four numbers to it.

Let us consider both the number be 9x, 11x since their ratio is 9:11

And we have assume that our expected answer to be positive (since we are dealing with ratios)

So, their difference can be written as,

=> 11x-9x = 6

When we simplify it, then we get,

=> 2x = 6

Here we need the value of x,

=> x= 3

Now that we know the value of ‘x’ is, we can find required numbers through it,

=> 9x = 9 * 3= 27

=> 11x = 11*3 = 33

=> 27x = 27*3 = 81

=> 33x = 33*3 = 99

Thus, the four numbers are 27, 33, 81, 99.

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Answer:

11?

Step-by-step explanation:

since 8+3 = 11 won't each student get 11 because they equally share it and in total 11 x 8 = 88 so they have to share 11 blocks of clay.

The probability of getting a sum greater than 10 is 1/12.

From the question, we have

total outcomes = 6 ×6 = 36

Number of events of sum greater than 10: {5, 6}, {6, 5}, {6, 6} = 3

Probability = 3/36

=1/12

The probability of getting a sum greater than 10 is 1/12.

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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Answer:210

Step-by-step explanation:

The equation is 51 = x + 120 × 0.30 that can find the monthly base fee charged by Chitchat wireless.

The equation representing the scenario will be formed through following components.

Total bill = monthly base fee + number of minutes × cost per minute

In the above mentioned equation, let us assume the monthly base fee to be x. Now, keep the values in formula to find the value of x.

51 = x + 120 × 0.30

Performing multiplication on Right Hand Side of the equation

51 = x + 36

Rewriting the equation according to x

x = 51 - 36

Performing subtraction on Right Hand Side of the equation

x = 15

Thus, the monthly base fee is $15.

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Answer:

Step-by-step explanation:

right i think?

The dimensions of the box are (S-2x)by(S-2x)byS =  2S/3 by 2S/3 S by S/6 to obtain a box with largest possible volume

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

Let S = length of the sides of the square cardboard sheet.  Let x = the side of each square cut from the corners.  The volume, V, of the box when the sheet is folded up is:

V = (S-2x)(S-2x)x = 4x3 - 4Sx2 + S2x

To find the maximum value, take the derivative of V wrt x, set it to zero, and solve for x:

V ' = dV/dx = 12x2 - 8Sx + S2

0 = 12x2 - 8Sx + S2

0 = (6x-S)(2x-S)

x = S/6 and S/2

To determine which is the max and which is the min, take the second derivative of V wrt x.

V'' = d2V/dx2 = 24x - 8S

At x = S/2, V'' = 24(S/2) - 8s = 4S. Since S>0, the point x=S/2 is a minimum. This makes sense because you have cut away the entire cardboard square.

At x = S/6, V'' = 24(S/6) - 8S = -4S < 0, so x = S/6 is the maximum

The dimensions of the box are (S-2x)by(S-2x)byS =  2S/3 by 2S/3 S by S/6

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Answer:

below

Step-by-step explanation:

y = 3 * 2^x          plug in the values of x (first column) to get the values in the second column

Step-by-step explanation:

3900 if by hundreds

If by thousands 4000

The number of solutions of the system of equations is given by:

Zero.

The number of solutions of a system of equations is obtained considering the coefficients and the constants of each side of the expression.

If the sides have different coefficients, then it will guarantee that the solution has only one solution, as there will be a division by a term different of zero.

If the sides have the same coefficients and then different constants, as is the case in this problem, the number of solutions is of zero, as a number different of zero will be divided by zero.

If the sides have the same coefficients and the same constants, then the number of solutions is of infinity, as the equivalent solution will be obtained with a division of zero by zero, that can be any value.

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Percentage Change = (ΔV/IV₁I) × 100

Constant rate of Change = (y₂ - y₁)/ (x₂ - x₁)

Constant Percentage Change:

This means that after t period the something has grown to [tex]g^{t} = 1.10^{t}[/tex] it original value .

percentage change formula equals the change in value divided by the absolute value of the original value multiplied by 100.

Constant rate of Change:

In which the rate does not change between different points in the function. in short, constant rate of change refers to the comparison of the way two quantities changes. in equation, the constant rate of change can be seen as a slope.

An exponential function is a function that changes at a constant percentage rate.

An exponential function y of t is characterized by the following property:

when t increases by 1 to find the new value of y the current value by the base.

                 y- value for t +1 = Base of y - value for t

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The graph of the exponential function f(x) = (3/4)ˣ is attached below and this is also option A in the question given

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.

In the given function

f(x) = (3/4)ˣ,

we can use a graphing calculator to plot the graph while applying the values from the table of function.

Comparing the graph plotted and the options given, the answer is option A

Kindly find the attached graph below

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The system of equation for each condition will be; 2a + 3c = 325.94 and

2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and

c = $46.99

A linear equation is an algebraic equation of the form y = mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.

At an amusement park, the cost for an adult admission is a and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95 and all ticket prices include tax.

According to question,

2a + 3c = $325.94

4a + 2c = $256.95

2a + c = $162.97

Solving the equation by using elimination method, we get,

a = $57.99 and c = $46.99

Hence, The system of equation for each condition will be; 2a + 3c = 325.94 and 2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and c = $46.99

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The screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.

What is the area of a rectangle?

If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be calculated as

                  Area = Length * Breadth

The length of the screen is 11 in. and the breadth of the screen is 7 in.

Then the area of the screen,

            Area = length * breadth

                     =  11 * 7

                     = 77 square inches.

Hence, the screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.

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If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, this phenomenon is called random phenomenon.

A phenomenon is random if individual outcomes are uncertain, but there is in spite of that, a regular distribution of outcomes in a great number of repetitions.

The probability of any outcome of a random phenomenon can be

described as the proportion of times the outcome would happen in a very lengthy chain of repetitions.

The outcome of any individual coin toss is random. But the outcome over many tosses is foreseeable, as long as the trials are individualistic (i.e., the outcome of a new coin flip is not impacted by the outcome of the preceding flip).

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