Need help with my math please. 31-41.

Answer:

x=1.08 (3SF)

Step-by-step explanation:

hope it helps!!!!

Answer:

y = 5x - 7

Step-by-step explanation:

y = mx + c

y = 5x + c

to find c, input given coordinates

8 = 5 x 3 + c

8 = 15 + c

-c = 15 - 8

-c = 7

c = -7

put that all together and you get:

y = 5x - 7

The equation of the line with a slope of 5 that contains the point (3,8) is

The equation of a line in slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept.

Given that the slope is 5 and the line contains the point (3,8), we can substitute these values into the equation and solve for the y-intercept (b).

Using the point-slope form of the equation:

y - y₁ = m(x - x₁)

We have:

y - 8 = 5(x - 3)

Expanding and simplifying:

y - 8 = 5x - 15

Now, let's isolate y:

y = 5x - 15 + 8

y = 5x - 7

Therefore, the equation of the line with a slope of 5 that contains the point (3,8) is y = 5x - 7.

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Voluntary sampling is one type of sampling method that is not probability based this means that the survey's findings cannot be reliably extrapolated or generalized.

What is voluntary sampling?

A sample made up of people who freely decided to take part in the sample group is known as a voluntary sampling. Those who want to participate in a voluntary sampling typically do so because they are passionate about the topic of the survey. According to definitions, a sample with self-selected individuals is one that includes voluntary responses.

Researchers who wanted to be able to generalize their findings to the entire community would not choose volunteer sampling because it does not produce a representative sample.

A convenience sample is one that the researcher can use at their discretion, such as voluntary sampling.

However, because only those who have strong opinions about the poll will typically agree to participate, voluntary sampling can result in bias.

The survey's findings cannot be confidently extrapolated or generalized because of the possibility of bias.

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A graph for the data (time and distance) shown in the given table is plotted in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, the data of a linear graph are directly proportional and as such as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.

In this exercise, you're required to plot a graph for the data (time and distance) that are recorded for an object that is starting from rest.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 67.814x

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The area of  the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.

For given question,

We need to find the area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2]

The region bounded by given curves is as shown below.

The area of this region would be,

[tex]\Rightarrow A=\int\limits^\frac{1}{2} _0 {y-\frac{4}{\sqrt{1-x^{2}}}} \, dx \\\\\Rightarrow A=\int\limits^\frac{1}{2} _0 {4e^{-x}-\frac{4}{\sqrt{1-x^{2}}}} \, dx[/tex]

Now we evaluate above integral.

[tex]\Rightarrow A=4\int\limits^\frac{1}{2} _0 {e^{-x}-\frac{1}{\sqrt{1-x^{2}}}} \, dx\\\\\Rightarrow A=4[\int\limits^\frac{1}{2} _0 {e^{-x}}\,dx -\int\limits^\frac{1}{2} _0{\frac{1}{\sqrt{1-x^{2}}}} \, dx]\\\\\Rightarrow A=4([e^{-x}]_0^{\frac{1}{2} } -[sin^{-1}(x)]_0^{\frac{1}{2} })\\[/tex]

[tex]\Rightarrow A=4([1-\frac{1}{\sqrt{e} } ] -[\frac{\pi}{6} ])\\\\\Rightarrow A=4(1-\frac{1}{\sqrt{e} } -\frac{\pi}{6} )\\\\\Rightarrow A=|4~\times (-0.13013)|\\\\\Rightarrow A=0.521[/tex]

Therefore, the area of  the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.

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The annual rate of inflation is 35560.86%.

To find the annual rate of inflation:

Now, sub in 4 and 0.099

Therefore, the annual rate of inflation is 35560.86%.

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The correct question is given below:

The rate of inflation in the fictional land of Sardinia is such that the price of a car costing 24,000 dollars in U.S. currency will double in seven years. What is the annual rate of inflation? what will be the price of this car in four years?

The length of the line segment of octagon which is AB equal to 3.4 cm.

Given that the area of the regular octagon is 54 [tex]cm^{2}[/tex], apothem of regular octagon is 4 cm. Line segment AB is side of the octagon.

We are required to find the length of the line segment AB.

A regular octagon has eight equal sides.

Area of regular octagon=Perimeter*apothem/2-----------1

We have to put the value of area and apothem in equation 1.

54=perimeter*4/2

Perimeter=(54*2)/4

=27 cm

Perimeter=27 cm.

Now we know that the perimeter is equal to the sum of the lengths of all sides of figure. So,

Perimeter=8*side

27=8*AB

AB=27/8

=3.375 cm

After rounding off it will be equal to 3.4 cm.

Hence the length of line segment is equal to 3.4 cm.

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Answer:

A

Step-by-step explanation:

The midpoint between A and E is (0,1)

The coordinates of the cities are given as:

A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).

From the above, we have:

A = (-2,3)

E = (2,-1)

The midpoint between A and E is calculated using

Midpoint = 1/2 * (x1 + x2, y1 + y2)

Substitute the known values in the above equation

Midpoint = 1/2 * (-2 + 2, 3 - 1)

This gives

Midpoint = 1/2 * (0, 2)

Evaluate the product

Midpoint = (0, 1)

Hence, the midpoint between A and E is (0,1)

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The rate of  VAT is 10%.

In the question, we are asked to find the VAT rate, given that the market price of an article is Rs. 10000, the rate of discount and the rate of VAT are equal, and the price after VAT is Rs. 9900.

We assume the rate of discount and the rate of VAT to be r%.

Thus, discount = r% of Rs. 10000 = Rs. r/100 * 10000 = Rs. 100r.

Thus, the price after discount = Rs. 10000 - 100r = Rs. 100(100 - r)

Then, VAT = r% of (Rs. 100(100 - r)) = Rs. r/100 * 100(100 - r) = Rs. r(100 - r).

Thus, the price after VAT = Rs. 100(100 - r) + Rs. r(100 - r) = Rs. (100 + r)(100 - r).

The price after VAT is given to be Rs. 9900.

Thus, (100 + r)(100 - r) = 9900,

or, 100² - r² = 9900,

or, r² = 100² - 9900,

or, r² = 10000 - 9900 = 100,

or, r = ±√100 = ±10.

Since r is the rate of VAT, it cannot be negative, making r = 10.

Thus, the rate of  VAT is 10%.

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Step-by-step explanation:

3×5×2 = 30 lorry trips to deliver 2,500 crates.

3 lorries, 5 trips per day, 2 days

that means that one lorry trip transports

2,500 / 30 = 250/3 = 83.33333... crates = 83 1/3 crates.

now we need x lorries each making 6 trips per day in 1 day (so, 6 trips, period) to transport 10,000 crates.

that looks like

x × 6 × 83.33333... = 10,000

x × 6 × 83 1/3 = 10,000

x × (6×83 + 6 × 1/3) = 10,000

x × (498 + 2) = 10,000

500x = 10,000

x = 20

so, we need 20 lorries each doing 6 trips in one day to transport 10,000 crates in one day.

these are altogether 20×6 = 120 lorry trips.

that is 4 times the number of the original scenario (30 trips).

and logically, when doing 4 times the work, we achieve 4 times the result (10,000 crates instead of 2,500).

Considering that a fraction is not defined when the denominator is zero, the equation is not defined for an angle of 90º.

A fraction is not defined when the denominator is zero.

In this problem, the expression is given by:

cos(θ)/(1 - sin(θ)) + cos(θ)/(1 + sin(θ)) = 4.

The denominators are zero in two cases:

Hence the equation is not defined for an angle of 90º.

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Step-by-step explanation:

Total Angle in a triangle is 180°

so D = 140 + 25 = 165°

D = 190° - 165° = 15°

Your answer is 15°.

Answer:

angle d = [tex]\boxed{15}^ {\circ}[/tex]

Step-by-step explanation:

The angles in a triangle add up to 180°.

∴ ∠d + 25° + 140° = 180°

⇒ ∠d + 165° = 180°

⇒ ∠d = 180° - 165°

⇒ ∠d = 15°

Answer:

Answer:

They are all true except for D

Step-by-step explanation:

What they are asking you to do, is take your rectangle and flip it over the top.  QR would stay right where it is and line ST would now be on top and line QR would be the bottom.  If you can picture that, you can see that all the statements would be true but D.

Expected value of playing the game  = $0.8

What is cost ?

Cost of playing = $2

Expected return

10% chance to win $1 = $1  10% = $0.1

25% chance to win back $2 = $2  25% = $0.5

50% chance to win $5 = $5  50% = $2.5

15% chance to lose $2 (being cost) = $2  15% = ($0.3)

= $0.1 + $0.5 + $2.5 - $0.3 = $2.8

Now for this we have to pay fixed cost $2

Thus, expected value of playing game = $2.8 - $2 = $0.8

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Answer: Choice D

[tex]\frac{-19}{\text{x}-5}[/tex]

=================================================

Work Shown:

[tex]\frac{\text{x}^2+10\text{x}+25}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}+5)}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}+5}{1} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}-5)}{1(\text{x}-5)} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\[/tex]

[tex]\frac{\text{x}^2-25}{\text{x}-5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-(\text{x}^2-6)}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-\text{x}^2+6}{\text{x}-5}\\\\\\\frac{-19}{\text{x}-5}\\\\\\[/tex]

This matches with choice D as the final answer.

Keep in mind that we can only subtract fractions when the denominator is the same. The rule is [tex]\frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}[/tex]

Answer:

Step-by-step explanation:

13

The name of the polygon is (B) hexagon.

To find the name of the polygon:

Therefore, the name of the polygon is (B) hexagon.

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The complete question is given below:

A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. What is the name of the polygon?

A) Octagon

B) Hexagon

C) Heptagon

D) Quadrilateral

Step-by-step explanation:

180(n-2)/n=90 ( this is the solution for the 90)

cross multiplying

180n-360=90n

180n-90n=360

90n=360

90n/90=360/90

n=4, the number of sides for the polygon with 90° is 4 sides

Solution for 100°

180(n-2)/n=100

180n-360=100n

180n-100n=360

80n=360

80n/80=360/80

n=4.5

Same applies to the rest 110°,125° ,150°,175°

The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

According to the statement

we have given that the radius of the clock face is 10 inches and the face of a clock is divided into 12 equal parts.

And we have to choose the three statements which are correct from the given options.

So,

Check the all given options to find the correct options.

So, OPTION A :

360/12=30 degrees between each number

3-1 = 2 2*30 = 60 degrees so A is FALSE

Now, OPTION B:

C=2 x π x r

r=10

using 3.14 for PI = 10*3.14 =31.4 x 2 = 62.8 so B is TRUE

Now OPTION C:

30 x 4 = 120 degrees = TRUE

Now, OPTION D:

10-3 = 7

7/12 x 62.8 = 0.5833*62.8 = 36.63 inches = FALSE

Now, OPTION E:

1/12=0.0833 x 62.8 = 5.23 rounded to 5.2 = TRUE

So, The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

Disclaimer: This question was incomplete. Please find the full content below.

Questions:

The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle.

Which statements about the clock are accurate? Check all that apply.

A. The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.

B. The circumference of the clock is approximately 62.8 inches.

C.The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

D. The length of the major arc between 3 and 10 is approximately 31.4 inches.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

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Answer:

Q₃ = 185

Step-by-step explanation:

the first step is to find the median of the data set

the median is the middle value of the data arranged in ascending order

112 , 130 , 132 , 140 , 149 , 151 , 163 , 172 , 185 , 190 , 200

                                            ↑ middle value

median = 151

the upper quartile Q₃ is the middle value of the data to the right of the median

163 , 172 , 185 , 190 , 200

                   ↑ middle value

upper quartile Q₃ = 185

Answer:

H:182000

L=28000

Step By Step

H=House

L=Lot

H+L=210000

H(6.5)=L

L+(L(6.5)=210000

L=28000

28000(6.5)=H

H:182000

Answer: x = 52 m

Step-by-step explanation:

     The formula we will use, which solves for the area of a trapezoid, is [tex]a=\frac{a+b}{2} h[/tex] where a is a base, b is a base, and h is the height.

    We will input the known values, then solve for x.

         [tex]\displaystyle a=\frac{a+b}{2} h[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=\frac{36\;\text{m}\;+x}{2}*27\;\text{m}[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=(18\;\text{m}+\frac{x}{2})*27\;\text{m}[/tex]

         [tex]\displaystyle 1,188\;\text{m}^2=486\;\text{m}+\frac{27x}{2}[/tex]

         [tex]\displaystyle 702\;\text{m}^2=\frac{27x}{2}[/tex]

         [tex]\displaystyle 1,404\;\text{m}^2=27x[/tex]

         [tex]\displaystyle x=52\;\text{m}[/tex]

Answer:

-1.8

Step-by-step explanation:

its bigger than -9 and -4.2

Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.

Given: 4x - 8y = 9 ............(1)

8x - 7y = 9 ............(2)

To be the same line, the equations have to be multiples of each other.

Multiplying (1) by 2, we get

2(4x - 8y = 9) = 8x - 16y = 18

From (1) solve the value of y, we get

4x - 8y = 9 ............(1)

-8y = -4x + 9

The value of y = (1/2)x - 9/8

From (2),

8x - 7y = 9

solve the value of y, we get

-7y = -8x + 9

The value of y = (8/7)x - 9/7

To be the exact line, the equations would be exact. Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.

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Answer:

14

Step-by-step explanation:

Subtract 3 from both sides to isolate g / make g the subject :

g + 3( -3 ) = 17 (-3)

g = 17-3

g = 14

Substituting this into the equation gives us :

14 + 3  = 17

17 = 17

So our final answer is 14

Hope this helped and have a good day

Answer:

x^2/ 16 + y^2/4 = 1

Step-by-step explanation:

The major axis is 4 and that goes with the x variable.  It is the major axis because 4 is a larger value than 2.

4 x 4 = 16

2 x 2 = 4

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

In this problem we know the coordinates of a vertex, a co-vertex and the center of an ellipse. Based on this information, we find an ellipse whose major axis is parallel to the x-axis. whose formula in standard form is:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

The major semiaxis has a length of 4 units and the minor semiaxis has a length of 2 units. If we know that (h, k) = (0, 0), a = 4 and b = 2, then the equation of the ellipse is:

x² / 16 + y² / 4 = 1

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

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Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C

Common ratio, r = second minutes / first minutes

= 95.1 / 97

= 0.98041237113402

Approximately,

r = 0.98

nth term of the sequence, Tn = ar^n -1

Tn = 97 × 0.98^(n-1)

Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)

= 97 × 0.98^(15-1)

= 97 × 0.98^14

= 97 × 0.7536419414749019520643907584

= 73.1032683230654893502459035648

Approximately,

T15 = 73.1°C

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Answer:

1.89

Step-by-step explanation:

34 ÷ (14 − 5) × 2

34 ÷ (9) × 2

34 ÷ 18

1.89

Numerical expression:

numerical expression is a phrase involving numbers.

In mathematics, a numerical expression is a set of numbers that have been written together by utilizing arithmetic operators addition, subtraction, multiplication, and division.

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By  evaluating  the expression 34 ÷ (14 − 5) × 2  we get = 1.89

Children can use the acronym BODMAS to help them remember the proper sequence to carry out mathematical operations when solving problems. The abbreviation BODMAS stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction.

A numerical expression is a sentence that uses numbers. A numerical expression in mathematics is a group of integers that have been combined using the addition, subtraction, multiplication, and division arithmetic operators.

Appling the BODMAS

= 34 ÷ (14 − 5) × 2

= 34 ÷ (9) × 2

= 34 ÷ 18

= 1.89

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