The square of a number, x, is 16 less than eight times the number. What is the number?

Answer:

(a) 2 white & 1 red ball = 42 ways

(b) All 3 white balls =  4 ways

(c) All 3 red balls = 35 ways

Step-by-step explanation:

An urn contains 4 white balls and 7 red balls. Three balls are selected.

In how many ways can the 3 balls be drawn from a total of 11 ​balls:

​(a) If 2 balls are white and 1 is​ red?

The 2 white balls can be selected in ⁴C₂ ways

The 1 red ball can be selected in ⁷C₁ ways

2 white & 1 red ball = ⁴C₂ × ⁷C₁

2 white & 1 red ball = 6 × 7

2 white & 1 red ball = 42 ways

​(b) If all 3 balls are​ white?

The 3 white balls can be selected in ⁴C₃ ways

The 0 red ball can be selected in ⁷C₀ ways

All 3 white balls = ⁴C₃ × ⁷C₀

All 3 white balls =  4 × 1

All 3 white balls =  4 ways

​(c) If all 3 balls are​ red?

The 3 red balls can be selected in ⁷C₃ ways

The 0 white ball can be selected in ⁴C₀ ways

All 3 red balls = ⁷C₃ × ⁴C₀

All 3 red balls = 35 × 1

All 3 red balls = 35 ways

Check the picture below.

since we know that x = 3/7, we can then plug that on either of the twin legs, since it's an isosceles, and get the length of each leg, so say let's plug it in 5x + 16

\(5x + 16\implies 5\left( \cfrac{3}{7} \right)+16\implies \cfrac{38}{7}+16\implies \cfrac{38+112}{7}\implies \cfrac{150}{7}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\stackrel{\textit{both legs}}{\cfrac{150}{7}+\cfrac{150}{7}}+\stackrel{\textit{base}}{6}\implies \cfrac{150+150+42}{7}\implies \cfrac{342}{7}\implies 48\frac{6}{7}\impliedby \textit{perimeter}\)

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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Step-by-step explanation:

x = number of cards

the production costs (PC) per day are

PC(x) = 264 + 1.1x

the sales (S) are

S(x) = 5.1x

the profit (P) per day is sales minus costs

P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =

= 5.1x - 264 - 1.1x = 4x - 264

we need to find the value of x, so that P(x) = 52.

52 = 4x - 264

316 = 4x

x = 316/4 = 79

79 cards must be delivered daily to make a profit of $52.

The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.

According to the problem, two equations can be set up:

If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:

A + n = 7(B - n)

If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:

A - n = 2(B + n)

We can rearrange these equations to make them easier to solve:

8n = 7B - A

3n = A - 2B

Setting these equal to each other, since they are both equal to 24n, gives:

21B - 3A = 8A - 16B

37B = 11A

A / B = 37 / 11

= 3. 36

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The charge density that must be glued to the surface of an insulating, cubical box  is\(σ = dq / dA = Q / a^2\)

Gauss's law can be applied to determine the charge density on the box's surface. According to Gauss's law, the charge enclosed by a closed surface determines how much electric flux passes through it.

Take into account a box-centred spherical Gaussian surface with radius r. By virtue of symmetry, the electric field must be radial and have a constant strength over the entire sphere. The flux through the sphere is therefore given by:

\(Φ = E(r) * 4πr^2\)

where E(r) is the electric field's strength at radius r.

The point charge Q in the box's centre is now equal to the charge contained within the sphere. So, according to Gauss's law:

\(Φ = Q / ε0\)

When the permittivity is 0

where 0 represents the free space permittivity.

The electric field outside the box should be the same as the electric field created by a point charge Q in the middle of the box. In order to ensure that the flux through any spherical surface outside the box is equal, we must choose the charge density on the box's surface.

Take into account a tiny element with surface area dA on the box's surface. The electric field caused by this element of charge at point P outside the box can be expressed as:

\(dE = (1 / 4πε0) * dq / r^2\)

where r is the distance between the element and point P and dq is the charge on the tiny surface-area element.

We integrate across all the minor components of the surface area of the box to determine the total electric field at point P caused by the entire surface of the box:

\(E = dE = (1 / 4.0)*dq / r2\)

Now, we want this electric field to match the electric field caused by point charge Q in the box's centre, which is determined by:

\(E' = Q / (4πε0r^2)\)

As a result, we have:

\(E = E': (1 / 4 0) * dq / r2 = Q / (4 0 r2)\)

To solve for dq, we obtain:

\((Q / a2)*dA = dq\)

therefore, the charge density on the box's surface is given by:

\(σ = dq / dA = Q / a^2\)

To produce the same electric field outside the box as that caused by a point charge Q at the centre of the box, we must glue a uniform charge density of Q / a2 on the box's surface.

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Answer:

36

Step-by-step explanation:

1/2 × b× h

= 1/2 × 9×8

= 9×4

= 36 sq. in

33/64 cups of sugar does snoopy scoop out.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The amount of sugar needed = 2 3/4 cups

Amount of sugar per scoop = 5 1/3 cups/scoop

So, number of cups of sugar scoops

= cups of sugar needed/ cups of sugar per scoop                                                                              

                                   =11/4 /16/3

                                     =11/4 *3/16

                                     =33/64

Hence, 33/64 cups of sugar does snoopy scoop out.

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Answer:

see explanation

Step-by-step explanation:

Given

x² , then when x = - 4

x² = - 4 × - 4 = + 16

[ the product of a negative and a negative results in a positive ]

Answer:

  both functions have the same graph

Step-by-step explanation:

The first function is described in terms of its slope and y-intercept, so can be written in slope-intercept form as ...

  y = mx + b . . . . m = slope (-7/9); b = y-intercept (3)

  y = -7/9x +3

__

The second function is written in point-slope form:

  y -k = m(x -h) . . . . m = slope (-7/9), point = (h, k) = (18, -11)

  y +11 = -7/9(x -18)

If we rearrange the second equation to the form of the first, we get ...

  y = -7/9x +14 -11 . . . . eliminate parentheses, subtract 11

  y = -7/9x +3 . . . . . . . matches the equation of the first function

__

Both functions describe the same relation.

The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3

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

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations intersect is when both equations are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is factored, we have

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

So, we have

x = -1 and x = 3

Hence, the x-coordinates are x = -1 and x = 3

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Question

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

The reading on the scale in part (a) is 11.0 kg, in part (b) is 5.5 kg, and in part (c) is 16.5 kg.

a) The reading on the scale will be 11.0 kg. This is because the mass of the salami is supported by the cord, which is then measured by the spring scale. The force exerted by the salami on the spring is equal to the weight of the salami, which is equal to the mass times the acceleration due to gravity (F = ma = mg). Therefore, the reading on the scale will be equal to the mass of the salami (11.0 kg).

b) The reading on the scale will be half of 11.0 kg, or 5.5 kg. This is because the weight of the salami is being supported by two cords, one running from the salami to the pulley and one running from the pulley to the wall. The force exerted by the salami on the scale is equal to the weight of the salami (F = mg). Since the force is now being shared between two cords, the force exerted on the scale is only half the weight of the salami (F = mg/2). Therefore, the reading on the scale will be 5.5 kg.

c) The reading on the scale will be 16.5 kg. This is because the two salamis are now being supported by one cord, which runs from one salami to the other and then to the scale. The force exerted by the salamis on the scale is equal to the sum of the weights of both salamis (F = mg₁ + mg₂). Therefore, the reading on the scale will be equal to the sum of the masses of both salamis (16.5 kg).

The reading on the scale in part (a) is 11.0 kg, in part (b) is 5.5 kg, and in part (c) is 16.5 kg.

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The simplified version of the expression would be 31-w

The numerical part of the expression given is :

Simplifying using Subtraction operation:

Adding the alphabetical part :

Therefore, the simplified form of the expression is 31-w.

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Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

Answer:

1-20: Make it 1 unit tall

21-40: Make it 5 units tall

41-60: Make it 2 units tall

61-80: Make it 2 units tall

81-100: Make it 4 units tall

Step-by-step explanation:

1-20: 8 (1 number)

21-40: 22, 25, 31, 36, 38 (5 numbers)

41-60: 46, 50 (2 numbers)

61-80: 62, 69 (2 numbers)

81-100: 84, 84, 87, 90 (4 numbers)

Answer:

13)

Given:

x = 3

y = 1.5

We exchange these values into our equation (2x + 4y + 3x);

2x + 4y + 3x

Altered, would be:-

2(3) + 4(1.5) + 3(3)

6 + 6 + 9

= 21

15) First, we need to find the volume of the cube;

1/2(one side), but since all sides to a cube are equal we multiply that length by itself 3 times.

So;

1/2 x 1/2 x 1/2 = 1/8 is the volume of one cube.

Now we find the rectangular prism's volume, using the formula;

V(volume) = W x H x L

Where 'W' represents the width, 'H' represents the height, and 'L' represents the length.

Substitute these values in our formula:

V = W x H x L

V = 2 1/2 x 8 x 1/2

V = 5/2 x 8 x 1/2

V = 5/2 x 8/2

V = 5/2 x 4

V = 10

So now, we divide the total volume by the volume of one cube to get the total of how many cubes would be needed to fill this prism.

10 ÷ 1/8

10 x 8/1

10 x 8

= 80

Answer: (1/3) = (4/12)

Step-by-step explanation:

I got this answer by taking (1/3) and multiplying the denominator and numerator by 4 --> (1 * 4/ 3 * 4) == (4/12)

Answer:

1/3 = 4/12 is true

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When a point (x,y) lies on a unit circle, the following equation holds true:

We are given

and need to find x.

Let's put it into the equation and figure out x. Shown below:

We can simplify the square root of 8 by using the radical property:

Thus, square root of 8 becomes:

Thus, the simplest form of x is:

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Answer:

ye ye

Step-by-step explanation:

sin ti no me va bien

Answer:

\(\boxed{\frac{3}{56} }\)

Step-by-step explanation:

\(\frac{1}{7} /\frac{8}{3} =\frac{1}{7} *\frac{3}{8} =\frac{3}{56}\)

Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

Answer:

The cost of a chicken shawarma wrap = $10.99

The cost of an order of spiced potatoes=$4.99

Equations needed

3x+2y =42.95

5x + 4y=74.91

Step-by-step explanation:

x = the cost of a chicken shawarma wrap

y = the cost of an order of spiced potatoes

Ms. Ironperson

3x+2y =42.95

Mr. Thoro

5x + 4y=74.91

3x+2y =42.95 (1)

5x + 4y=74.91 (2)

Multiply (1) by 2

6x + 4y=85.9 (3)

5x + 4y=74.91. (2)

Subtract (2) from (3)

6x - 5x= 85.9 - 74.91

x=$10.99

Substitute the value of x into (1)

3x+2y =42.95 (1)

3(10.99) + 2y =42.95

32.97 + 2y = 42.95

2y = 42.95 - 32.97

2y=9.98

Divide both sides by 2

y=9.98/2

=4.99

y=$4.99

Therefore,

The cost of a chicken shawarma wrap = $10.99

The cost of an order of spiced potatoes=$4.99

The ratios will be equal if the theorem that the product of the extremes equals the product means follows.

Let us understand the equality of ratios through example. The example ratio will be -

7:10 = 21:30

In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.

Product of extremes = 7 × 30

Extremes product = 210

Product of means = 21 × 10

Means product = 210

Since the products are equal, the ratios are also equal.

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The complete question is -

Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.

Ratio = 7:10 and 21:30.

Answer: 1 hour 38 minutes

Step-by-step explanation:

From 11:51 AM to 12:00 PM (noon)

9 minutes

from 12:00 PM to 1:00 PM

1 hour

1:00 PM to 1:29 PM

29 minutes

______________________________

9 minutes + 1 hour + 29 minutes

1 hour 38 minutes

The following information regarding a dependent variable (Y) and an independent variable (X) is provided in the following blanks in the image below.

A dependent variable is the variable that changes as a result of the independent variable manipulation. It's the outcome you're interested in measuring, and it “depends” on your independent variable. In statistics, dependent variables are also called: Response variables (they respond to a change in another variable) a) least square estimate of the Y intercept  =2 b)least squares estimate of the slope is =1 c)coefficient of determination is  1-SSE/SST =0.625 d)coefficient of correlation is =(0.625)1/2 =0.7906 e) MSE =SSE/(n-2) =6/(5-2) =2

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Answer:

A certain shade of pink us created by adding 3 cups of red paint to 7 cups of white paint

Step-by-step explanation:

Constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.

To make color pink,

for every 3 cups of red , we need 7 cups of white.

Let 'r' be the cups of red required

let 'w' be the cups of white required

so , as per the question

for 3 r we need = 7 w

r = 7/3 w

so, 7/3 is constant of proportionality

The domain of the graph is, { x | - 3 ≤ x ≤ 5 }

The range of the graph is, {y | 10 ≤ y ≤ 60 }

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The graph is shown in figure.

We know that;

The domain of the graph is shown on x - axis, and range of the graph is shown y - axis by graph.

Hence, Domain of graph is,

⇒ { x | - 3 ≤ x ≤ 5 }

And, Range of graph is,

⇒ {y | 10 ≤ y ≤ 60 }

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Yes, because it is a graph of a straight line with y = 1.625x, y changes for every value of x.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, Value set for x and y.

Since it asked if the given equation is linear or not

The general formula for the line:

y = mx +c

where,

m is slope

and c is constant

m = (y₂ - y₁)/(x₂ - x₁)

in our case

m = 26 - 13 / 16 -8

m = 13/8

Thus the equation of a line:

y = 13/8x + c

putting any of the given coordinates in the given equation:

c = 0

Thus, the equation of a line

y = 1.625x

Therefore, yes, y varies for every value of x since it is a graph of a straight line y = 1.625x

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