Select the correct answer.
Which number line represents the solution to |x - 5] <3?

In a dice, there is a six side

Probability of occurring a score = 1/18

                                           = 1*2/18*2

                                               = 2/36

                                        =   preferred outcome/ Total outcome

Only 5 is a number that has occurred twice

The score that has a probability of occurring of 1/18 is 5.

The two dice having different values 30/36 = 5/6 (because the probability of the two dice having equal values is 6/36 = 1/6.)

The probability of the second dice being less than the first dice is the same as the probability of the first dice is less than the second dice: (5/6) / 2 = 5/12.

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Answer:

x = 1          y = 0

Step-by-step explanation:

-8x + y = -8

6x - y = 6

y have the same coefficient but one is negative and the other is positive therefore we add both the equations

we get:

-2x = -2

divide both sides by -2

x = 1

now as we have the value of x we can input this into any one of the starting equations

-8x + y =-8

-8(1) +y = -8

-8 + y = -8

add 8 to both sides

y = 0

Answer:

(1, 0 )

Step-by-step explanation:

- 8x + y = - 8 → (1)

6x - y = 6 → (2)

adding (1) and (2) term by term will eliminate y

- 2x + 0 = - 2

- 2x = - 2 ( divide both sides by - 2 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

- 8(1) + y = - 8

- 8 + y = - 8 ( add 8 to both sides )

y = 0

solution is (1, 0 )

Answer: Least 1/2

Step-by-step explanation: Middle 2/3

Greatest 5/6

Answer:

Least 1/2

Middle 2/3

Greatest 5/6

Step-by-step explanation:

First,5 divided by 6,is 0.83(in to 1 decimal point)

Then 2 divided by 3 is 0.67(in to 1 decimal point)

Last 1 divided by 2 is 0.5(in to 1 decimal point)

So is 5/6 is greatest and 2/3 is in the middle and the least is 1/2.

Answer:

  40%

Step-by-step explanation:

You want to know what percent of $70 is $28.

The question can be written as an equation, using a variable for the unknown percentage:

  x% · $70 = $28

The percent sign can be considered to be fully equivalent to "/100". Dividing by dollars on both sides, we can rewrite the equation as ...

  x/100 · 70 = 28

Dividing by the coefficient of x gives ...

  x = 28/0.70

  x = 40

The complete statement is ...

  40% of $70 = $28

__

Additional comment

If you're comfortable with writing decimal fractions as percentages, and vice versa, you can do without the %, and simply write ...

  x · 70 = 28

  x = 28/70 = 0.40 = 40%

This tells you 40% of $70 is $28, which is what you want to know.

The charge on the 150 nF capacitor is 3200 nF, the charge on the 120 nF capacitor is 3200 nF, the total energy stored in the network is [tex]76.8 \times 10^{-6} \mathrm{~J}[/tex], the energy stored in the 150 nF capacitor is [tex]34.1 \times 10^{-6} \mathrm{~J}[/tex], the energy stored in the 120 nF capacitor is [tex]42.67 \times 10^{-6} \mathrm{~J}[/tex], the potential difference across the 120 nF and 150 nF capacitor is 21.33V, 26.67 V.

The equivalent capacitance when the capacitors are connected in series is,

[tex]$$C_{\text {eq }}=\left(\frac{1}{C_1}+\frac{1}{C_2}\right)^{-1}=\left(\frac{1}{150 \mathrm{nF}}+\frac{1}{120 \mathrm{nF}}\right)^{-1}=66.67 \mathrm{nF}$$[/tex]

the charge on each capacitor remains the same because they connected in series. Hence, the charge on each capacitor is,

Q=C V=(66.67 nF) (48 V)=3200 nC

the charge on the 150 nF capacitor is  [tex]Q_{150}[/tex]=3200 nC

the charge on the 120 nF capacitor is [tex]Q_{120}[/tex]=3200 nC

the total energy stored in the network is,

[tex]$$$U=\frac{Q^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(66.67 \times 10^{-9} \mathrm{~F}\right)}=76.8 \times 10^{-6} \mathrm{~J}$$[/tex]

the energy stored in the 150 nF capacitor is,

[tex]$U=\frac{Q_{150}{ }^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(150 \times 10^{-9} \mathrm{~F}\right)}=34.1 \times 10^{-6} \mathrm{~J}$$[/tex]

the energy stored in the 120 nF capacitor is,

[tex]$U=\frac{Q_{150}{ }^2}{2 \mathrm{C}}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(120 \times 10^{-9} \mathrm{~F}\right)}=42.67 \times 10^{-6} \mathrm{~J}$$[/tex]

the potential difference across the 150 nF capacitor is,

[tex]$$V_{150}=\frac{Q_{150}}{C_{150}}=\frac{3200 \times 10^{-9} \mathrm{C}}{150 \times 10^{-9} \mathrm{~F}}=21.33 \mathrm{~V}$$[/tex]

the potential difference across the 120 nF capacitor is,

[tex]$$V_{120}=\frac{Q_{100}}{C_{120}}=\frac{3200 \times 10^{-9} \mathrm{C}}{120 \times 10^{-9} \mathrm{~F}}=26.67 \mathrm{~V}$$[/tex]

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QN:-- For the capacitor network shown in (Figure 1) , the potential difference across ab is 48 V .

Find the charge on the 150 nF capacitor.

Find the charge on the 120 nF capacitor.

Find the total energy stored in the network.

Find the energy stored in the 150nF capacitor.

Find the energy stored in the 120nF capacitor.

Find the potential difference across the 150 nF capacitor.

Find the potential difference across the 120 nF capacitor.

Answer: The distance between the two parallel lines is 11/12.

Step-by-step explanation:

The distance between two parallel lines can be found by calculating the difference between the y-intercepts of the two lines. In this case, the y-intercept of the first line is (-1/4,0), and the y-intercept of the second line is (-7/6,0). The difference between these y-intercepts is (-1/4 - (-7/6)) = 11/12. Therefore, the distance between the two parallel lines is 11/12.

Answer:

0.4 x 10^-1

Step-by-step explanation:

4 x 10^0

=> 4

=> 0.4 x 10^-1

The complete table is

Length of fencing(feet)   1             3          6            9            10

cost($)                               9         27         54          81           90

What is fencing of a wall?

A fence is a building used to enclose a space, usually outdoors. It is often made of posts joined by boards, wire, rails, or nets. In contrast to a wall, a fence lacks a firm basis over its whole length.

The cost of fencing 3 feet is $27.

Applying unitary method:

The cost of fencing 1 feet is $27/3 = $9.

The  cost of fencing 6 feet is $(6×9) = $54

The  cost of fencing 10 feet is $(10×9) = $90.

$27 needs to make a fencing with length 3 feet.

$1 needs to make a fencing with length 3/27 feet = 1/9

$9 needs to make a fencing with length (1/9)× 9 = 1 feet.

$81 needs to make a fencing with length (1/9)× 81 = 9 feet.

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Step-by-step explanation:

photo is not clear post again.

The tip of man's shadow moving with speed of 25/3 ft/sec, when he is 40 feet from the pole.

We have, height of street light on pole,

AB = 15ft.

Height of man , BC = 6 ft.

Speed of man walks away from the pole.

= 5 ft/sec

This problem is look like a time rate problem , Let us consider x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole, i.e,

length of Shadow, CE =( y -x) ft

We assume the man and pole are standing straight up, which means the 2 triangles are similar. By similarity of triangles, (y − x)/y = 6/15

=> 15(y-x) = 6y

=> 15y - 15x = 6y

=> 15y - 6y = 15x

=> 9y = 15x

=> y = (15/9)x = (5/3)x

differentiate the above equation with respect to t or time.

dy/dt = (5/3)dx/dt

We know that, dx/dt = 5 ft/sec because the man is walking that speed away from the pole. We want to calculate dy/dt, how fast the tip of the shadow is moving when y = 40 feet

dy/dt = (5/3) (5) = 25/3 ft/sec.

We see actually, the man's distance from the pole doesn't matter since only his speed affects how fast his shadow moves. Hence, the tip of the shadow is moving with speed of 25/3 ft/sec.

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Parameters are values that describe the entire population, while statistics are values that describe only a sample of the population. Since there is no way to know the exact values of the parameters, they cannot be calculated from a sample of data.

Parameters are values that describe the characteristics of the entire population. They are used to make inferences about the population and provide a basis for making decisions. On the other hand, statistics are values that describe only a sample of the population. They are used to estimate the parameters of the population. Since it is not possible to know the exact values of the parameters, they cannot be calculated from a sample of data. Instead, we use statistics to estimate the parameters. This is why it is important to use a representative sample when collecting data, as it provides a better estimate for the population parameters

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Answer:

X = add 25  Y =add 3 see 3 ,3+3=6  so i think y is 3

Step-by-step explanation:

The length of the wall in her drawing is given as follows:

5.6 inches.

A scaling measurement represents the proportion of a total dimension, as it is the ratio between the length of the drawing with the actual length of the object.

On her drawing a 10-foot wall is 8 inches, hence the scale measurement for this problem is given as follows:

8 inches/10 feet = 0.8 inches per feet.

The scale means that each feet of an actual object is represented by a length of 0.8 inches on the drawing.

Audrey wants to add a 7 foot wall to the drawing, meaning that the length of the drawing is given as follows:

7 x 0.8 = 5.6 inches.

(applying the proportion found from the scale measurement).

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Answer:

Step-by-step explanation:

81.64

Answer:

There are several measurements that a professional engineer would need to make in order to design and construct a bridge over a stream for a farmer's sheep to graze. These measurements may include:

Width and depth of the stream: The engineer will need to determine the width and depth of the stream in order to determine the size and type of bridge that is needed.

Soil composition and stability: The engineer will need to assess the soil composition and stability of the area surrounding the stream in order to determine the foundation and support structure needed for the bridge.

Water flow: The engineer will need to measure the water flow in the stream in order to determine the load-bearing capacity of the bridge and to ensure that it is able to withstand the forces of the water.

Distance between the two banks: The engineer will need to measure the distance between the two banks of the stream in order to determine the length of the bridge and ensure that it is long enough to span the stream.

Height of the banks: The engineer will need to measure the height of the banks of the stream in order to determine the height of the bridge and ensure that it is tall enough to allow the sheep to pass under it.

The value of TC = 5.9

According to the given figure of the triangle ABC, (refer to the attached figure)

The length of perpendicular bisector AC is = m

The length of perpendicular bisector BC is = n

The point at which line m and line n are intersecting = T

Given the value of TA = 5.9

According to the corner theorem.

AC = CF

So, ΔTFA ≅ ΔTFC

⇒ TA = TC = 5.9

Therefore, The value of TC = 5.9

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Answer:

y = -1

Step-by-step explanation:

y = 4 · -2 + 7

y = -8 + 7

y = -1

Although part of your question is missing, you might be referring to this full question: What are the vertex and range of y = |2x + 6| + 2?

(0, 2); 2 < y < ∞

(0, 2); −∞ ≤ y < ∞

(−3, 2); 2 < y < ∞

(−3, 2); −∞ ≤ y < ∞

The vertex of the function is (–3, 2) and the range of the function is 2 < y < ∞.

The given modulus function:

y = |2x + 6| + 2

Now, we get two equations out of the absolute value function:

y = 2x + 6 + 2

y = 2x + 8

and

y = –2x – 6 + 2

y = –2x – 4

The vertex of the function will be at a point where these two equations are equal. So, we can calculate the vertex as follows:

2x + 8 = –2x – 4

2x + 2x = –4 – 8

4x = –12

x = –3

If x = –3, then y = 2(–3) + 8 = –6 + 8 = 2

Thus, the vertex of the function is (–3, 2).

Now, the values that y can take will range from 2 to infinity as y cannot take values below the vertex.

Thus, the range of the function is 2 < y < ∞.

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Answer:

$3.02

Step-by-step explanation:

You just subtract 97.98-94.96.

Answer:

3.02

Step-by-step explanation:

you subtract 94.96 from 97.98

The given statement is true for tabulation method representing the variable different categories and summarize it in tabulation method makes the calculation simple.

As given in the question,

Therefore, the given statement of representing the variable different categories and summarize it in tabulation method makes the calculation simple is a true statement.

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Answer: 52,000

Step-by-step explanation: Because we are rounding to the nearest hundred, we only need to focus on the #'s 4, 3, and 7 in 52,437. So, 3 is less than 5, so we have to round down to 3 (stays the same) and 4 is less than 5 so, we round down to 4 (also stays the same), and since 7 is greater than 5, we can round up to 440. But, 440 is still less than 500, so your final answer should be 52,000.

The approximate probability that at least 45 of 50 patients can be cured with the drug is 0.788.

To find the approximate probability that at least 45 of 50 patients can be cured with the drug, we can use the binomial formula. The binomial formula allows us to calculate the probability of a certain number of success out of a set of trials given a certain probability of success for each trial. In this case, we have a probability of success of 0.9 and 50 trials. Therefore, the probability of at least 45 of the 50 patients being cured with the drug is 0.788. This can be calculated using the binomial formula or a binomial probability calculator.

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Answer:

2.64 square meters.

Step-by-step explanation:

To find the surface area of a cuboid, you need to find the area of each of the six faces and add them together. A wooden cuboid with an open flame base that has a square surface with 1.2 meter sides and a height of 0.25 meters would have a surface area of 1.2 * 1.2 + 4 * (1.2 * 0.25) = 1.44 + 1.2 = 2.64 square meters. This is because the base of the cuboid has an area of 1.2 * 1.2 = 1.44 square meters, and each of the four sides has an area of 1.2 * 0.25 = 0.3 square meters. The total surface area of the cuboid is therefore the sum of these areas: 1.44 + 4 * 0.3 = 2.64 square meters.

The value of the old fare to the nearest cent will be $423.08. Then the correct option is B.

Any product's quantity is presented as if it were a percentage of one hundred. The proportion can be written as 1/4 of 100. One hundred percent is symbolized by the symbol %. The sign for it is the letter "%".

The cost of an aircraft ticket from New Orleans to Boston expanded to $550. This is a 30% expansion.

Let 'x' be the old fare. Then the equation is given as,

(1 + 0.30) x = $550

Simplify the equation, then we have

(1 + 0.30) x = $550

1.30 x = $550

x = $550 / 1.30

x = $423.08

The worth of the old admission to the closest penny will be $423.08. Then the right choice is B.

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Yes, the starting position of these players form a perpendicular line.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Using Trigonometry

sin [tex]\theta[/tex] = 33.33/100

sin [tex]\theta[/tex] = 0.3333

[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)

[tex]\theta[/tex] = 19.469

cos 19.469 = B/ 100

0.9428 = B/ 100

B= 94.28

tan  [tex]\theta[/tex] = P/B

tan  [tex]\theta[/tex] = 94.28/ 33.33

[tex]\theta[/tex] = 70.5

Using Angle Sum property

< 3= 180 - (70.5 + 19.5)

<3 = 180 - 90

<3 = 90

Hence, they form perpendicular line.

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Triangle A and Triangle B are right triangle. Triangle A ha a height of 8 meter and a bae of 6 meter. then The length of one of the legs of the triangle is 10 units.

An isosceles triangle has a base length of 126 units and a height of 16 units. We need to find out the length of one of the legs of the triangle.

First of all, we will consider a perpendicular bisector of the triangle. This divides the given triangle into two equal right-angled triangles. Now, in the smaller triangle, we will use the Pythagorean theorem.

Let the length of the leg be represented by the variable "x". The length of the base of the right-angled triangle is half the length of the base of the original triangle.

x² = (6)² + (8)²

x = sqrt ( 36+64)

x = √100

x = 10

Hence, the length of one of the legs of the triangle is 10 units.

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[tex]-4w+ 2 = 14[/tex]

Subtract 2 from both sides:

[tex]-4w+2-2=14-2[/tex]

[tex]-4w=12[/tex]

Divide both sides by -4:

[tex]\dfrac{-4w}{-4} =\dfrac{12}{-4}[/tex]

[tex]= \fbox{w = -3}[/tex]

Answer:

w = -3

Step-by-step explanation:

-4w + 2 = 14

-4w + 2 - 2 = 14 - 2 (Subtract 2 from both sides)

-4w = 12

-4w/-4 = 12/-4 (Divide -4 from both sides)

w = -3

18 inches is not a possible length for the third side of a triangle

What is the triangle inequality theorem?

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.

By triangle inequality theorem:

This theorem states that the sum of any two sides of a triangle must be greater than the third side.

As per the statement:

A triangle has two sides of lengths 8 inches and 10 inches.

Let the third side be x.

The Sum of the two sides is:

8 + 10 = 18

By triangle inequality theorem:

18 > x

or

x < 18

⇒ the length of the third side must be less than 18

From the given options:

Length of third sides 12, 16, and 17 which are less than 18.

the value which could the length of the third side be are: 12, 16, and 17.

Hence, 18 inches is not a possible length for the third side of a triangle

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The number of different ways of distributing the scholarships is 32,760.


consider the situation: fifteen students are competing for 4 Rotary scholarships.
consider each scholarship  is to be a position In which a student assigned.
This is a permutation problem as:
   

A) each student selected from the same set.  
b) No students can be selected twice.
c) The order in which students are assigned to three scholarships.  

Four students  are assigned in 4 activities For scholarships.

Activity A1: select a student from the set of 15 students for giving away the first scholarship.

Activity A2: select a student from remaining 14 students for giving away the second scholarship.

Activity A3: select a  student from remaining 13 students for giving away the third scholarship.

Activity A4: Select a student from remaining 12 students for giving away the forth scholarship.

According to multiplication rule of accounting the number of different arrangements is  A1 X A2 X A3 X A4  
15 X 14 X 13 X 12=32760  

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