The measure of angle ABC is 36° ⇒ 1st answer

Step-by-step explanation:

Let us revise some important facts in the circle

The measure of the center angle is equal to the measure of its subtended arc

The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc

The vertex of a central angle is the center of the circle and its sides are radii in the circle

The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle

In circle D

∵ D is the center of the circle

∵ A and C lie on the circle

- DA and DC are radii

∴ ∠ADC is a central angle subtended by arc AC

∴ m∠ADC = m of arc AC

∵ m∠ADC = (7x + 2)°

∵ m of arc AC = (8x - 8)°

- Equate them to find x

∴ 8x - 8 = 7x + 2

- subtract 7x from both sides

∴ x - 8 = 2

- Add 8 to both sides

∴ x = 10

Substitute the value of x in the measure of ∠ADC

∵ m∠ADC = 7(10) + 2 = 70 + 2

∴ m∠ADC = 72°

∵ AB and BC are two chords in circle D

∴ ∠ABC is an inscribed angle subtended by arc AC

∵ ∠ADC is a central angle subtended by arc AC

- By using the 2nd fact above

∴ m∠ABC = m∠ADC

∴ m∠ABC = × 72

∴ m∠ABC = 36°

Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60

Step-by-step explanation:

Answer:

y = 2/3.

Step-by-step explanation:

y = constant nunber × x,

6 = constant number × 72,

Constant number is 1/12.

y = 1/12 × 8 = 2/3.

Thus the answer is 2/3.

Answer:

250

Step-by-step explanation:

The total of the ratios is

2+5 = 7

Take the total amount and divide by 7

350 / 7 = =50

Multiply each amount by 50

2*50  : 5 * 50

100 : 250

The larger portion is 250

Answer:

Step-by-step explanation:

350 is total

2 parts : 5 parts (2+5 = 7 parts in all)

350 : 7 parts = $50 for each part

2parts = 2·50= $100

5 parts = 5·50 =$250

$100: $250

the larger portion is $250

Answer:

Height A = [tex]12\frac{3}{4}[/tex] inches

Step-by-step explanation:

Height A = Sum of widths of all sections of the cabinet + thickness of the wood

Height A = [tex]1\frac{1}{4}+\frac{1}{4}+4\frac{1}{2}+\frac{1}{4}+4\frac{1}{2}+2[/tex]

               = [tex](1+4+4+2)+(\frac{1}{4}+\frac{1}{4}+\frac{1}{2}+\frac{1}{4}+\frac{1}{2})[/tex]

               = [tex]11+(\frac{1+1+2+1+2}{4} )[/tex]

               = [tex]11+\frac{7}{4}[/tex]

               = [tex]11+1\frac{3}{4}[/tex]

               = [tex]11+1+\frac{3}{4}[/tex]

               = [tex]12\frac{3}{4}[/tex] inches

Given:

x-intercepts of the hyperbola are ±4.

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

Center of the hyperbola is at origin.

To find:

The equation of the hyperbola.

Solution:

The general equation of a hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]            ...(i)

Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.

Center of the hyperbola is at origin. So, h=0 and k=0.

x-intercepts of the hyperbola are ±4. So,

[tex]\pm a=\pm 4[/tex]

[tex]a=4[/tex]

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

[tex]\pm c=\pm 2\sqrt{5}[/tex]

[tex]c=2\sqrt{5}[/tex]

We know that,

[tex]a^2+b^2=c^2[/tex]

[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]

[tex]16+b^2=20[/tex]

[tex]b^2=20-16[/tex]

[tex]b^2=4[/tex]

Taking square root on both sides, we get

[tex]b=\sqrt{4}[/tex]                    [b>0]

[tex]b=2[/tex]

Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get

[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]

[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]

Therefore, the correct option is (d).

Answer:

false

Step-by-step explanation:

standard form cannot contain fractions or decimals

Answer:

x=6.25 and y=1.5

Step-by-step explanation:

Given equation

2x+5y=20

y=0.4x-1

Putting the value of y in above equation

2x+5(0.4x-1)=20

2x+2x-5=20

4x-5=20

4x=20+5

4x=25

x=6.25

Now,

y=0.4x-1( Given)

Putting the value of x=6.25 in above equation y

y=0.4(6.25)-1

y=2.5-1

y=1.5

Answer:

3.141

Step-by-step explanation:

3 decimals is .xxx, and you round the last digit up, so it becomes 3.141

Answer:

3.141

Step-by-step explanation:

since the forth number behind the decimal place is bigger than 5 we round up the third number.

I hope this helps in anyway.

9514 1404 393

Explanation:

This is a self-answering question: you solve it by graphing the equations.

The solution is where the lines intersect. The point of intersection of the lines is the point that satisfies all the equations for the lines, hence is a solution to the system. If they do not intersect, there are no solutions. If the lines are coincident, there are an infinite number of solutions.

__

The equations can be graphed by any of a number of methods. (My favorite is to let a graphing calculator do it.) The method of choice depends on the coefficients and the form the equations are given in. Methods of graphing are a topic for a more lengthy discussion.

Answer:

0.0005729

Step-by-step explanation:

since the exponent is negative, move the decimal four units to the left to get:

0.0005729

Answer:

C 8

Step-by-step explanation:

the number cube has six sides and the coin has 2 sides

Answer:

x=8

Step-by-step explanation:

5-x=13

5-5=0

13-5=8

x stays because its a variable

x=8

one solution

Given:

Consider the dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft.

To find:

The volume of rectangular prism.

Solution:

The volume of a cuboid or rectangular prism is:

[tex]V=l\times b\times h[/tex]

Where, l is length, b is breadth and h is height of the prism.

The dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft. So, the volume of the prism is:

[tex]V=3.4\times 0.8\times 0.6[/tex]

[tex]V=1.632[/tex]

Therefore, the volume of the rectangular prism is 1.632 cubic feet ​.

Answer and Step-by-step explanation:

Write down everything that is being asked into the math form of it.

[tex](4+9)^3 * \frac{x}{(5x)(x-1)}[/tex]

(I think that is what it is asking, how they word it is kind of weird).

Now solve.

[tex]36^3*\frac{x}{5x^2-5x}[/tex]

[tex]46656*\frac{1}{5(x-1)}\\\\\frac{46656}{5(x-1)}[/tex]<- I think this should be the answer.

#teamtrees #PAW (Plant And Water)

Answer:

dvide 54 by 6 then the answer you get  subrtact it by 3 then the answer you get multiply iy by 2 then thats will be your answer

Step-by-step explanation:

remember always use PEMDAS always add or subract wich ever comes first and if theres none of that then do Multiply or devide wich ever comes first  ( btw your answer is   ( 3 )

Answer:

0.39375 = 39.375% probability that the next book by this publisher captures at most 6.15% of the market

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Randomly between 3 and 11% of the market.

This means that [tex]b = 11, a = 3[/tex]

What is the probability that the next book by this publisher captures at most 6.15% of the market?

[tex]P(X < 6.15) = \frac{6.15 - 3}{11 - 3} = 0.39375[/tex]

0.39375 = 39.375% probability that the next book by this publisher captures at most 6.15% of the market

Complete Question

A sensor output was acquired for 32 seconds at a rate of 200 Hz and spectral analysis was performed using FFT. If the data set was split into 5 segments (each 6.4 seconds long), what is the resulting:

a)F minimum

b) F maximum

c) Frequency resolution

Answer:

a) [tex]Fmax=100Hz[/tex]

b) [tex]Fmin=0Hz[/tex]

c) [tex]F_r=0.0313[/tex]

Step-by-step explanation:

From the question we are told that:

Time [tex]t=32sec[/tex]

Frequency[tex]F=200Hz[/tex]

Segments [tex]\mu=5[/tex]

Generally the equation for Frequency Range is mathematically given by

[tex]Fmax=\frac{F}{2}[/tex]

[tex]Fmax=100Hz[/tex]

Therefore

a) [tex]Fmax=100Hz[/tex]

b) [tex]Fmin=0Hz[/tex]

c)

Generally the equation for Frequency Resolution is mathematically given by

[tex]F_r=\frac{F}{N}[/tex]

Where

N=The Total dat points

N=Sampling Frequency *Time

[tex]N=200*32[/tex]

[tex]N=6400[/tex]

Therefore

[tex]F_r=\frac{200}{6400}[/tex]

[tex]F_r=0.0313[/tex]

Answer: Chad Makes $1.50 more

Step-by-step explanation:

You have to divide 30 from 4 to see Horatio’s hourly rate which is 7.5 and then you will see that 9 - 7.5 is 1.5. I hope this helped

Answer:

[tex](-14,4)[/tex]

Step-by-step explanation:

Given

[tex](-14,12)[/tex]   [tex]\to[/tex]    [tex]y =f(x)[/tex]

[tex]g(x) = \frac{1}{3}f(x)[/tex]

Required

The corresponding point on [tex]y = g(x)[/tex]

[tex](-14,12)[/tex]   [tex]\to[/tex]    [tex]y =f(x)[/tex] means:

[tex]12 = f(-14)[/tex]

or

[tex]f(-14)=12[/tex]

[tex]g(x) = \frac{1}{3}f(x)[/tex] is calculated

[tex]g(-14) = \frac{1}{3} * f(-14)[/tex]

[tex]g(-14) = \frac{1}{3} * 12[/tex]

[tex]g(-14) = 4[/tex]

So, the corresponding point on [tex]y = g(x)[/tex] is: [tex](-14,4)[/tex]

9514 1404 393

Answer:

  ∠2 = 92°

Step-by-step explanation:

The angles marked with expressions in x are "alternate interior" angles, so are congruent.

  -8x +144 = 2x +74

  70 = 10x . . . . . . . . . . add 8x-74 to both sides

  7 = x . . . . . . . . . . . . . divide by 10

The angles adjacent to angle 2 are ...

  2x +74 = 2(7) +74 = 88 . . . . degrees

Angle 2 is the other angle of the linear pair with angle 2x+74 (or angle 1), so is ...

  ∠2 = 180° -88°

  ∠2 = 92°

Answer:

Step-by-step explanation:

Answer:

1205.76 m^3

Step-by-step explanation:

given:

radius = 8m

height = 18 m

volume of a cone = πr2h/3

=3.14 * (8)^2 * 18/3

=3.14 *64 *18/3

=3617.28/3

=1205.76 m^3

Answer:

The longer piece is 15 feet long and the shorter piece is 3 feet long.

Step-by-step explanation:

Create a system of equations where x is the length of the longer piece and y is the length of the shorter piece:

x + y = 18

x = 5y

Solve by substitution by substituting 5y as x into the first equation:

x + y = 18

5y + y = 18

Solve for y:

6y = 18

y = 3

So, the shorter piece is 3 feet long. Since the longer piece is 5 times longer, find its length by multiplying this by 5:

3(5)

= 15

So, the longer piece is 15 feet long.

The longer piece is 15 feet long and the shorter piece is 3 feet long.

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

the first option (1,3) and (1,-2)

Step-by-step explanation:

it is unusual to have neighboring corners of a rectangle called A and C. normally the neighbors of A are B and D. but ok.

A and C have the same x coordinate (-3). so, A is directly above C. the distance between them is therefore only the difference between their y coordinates.

AC = 3 - -2 = 3 + 2 = 5

the area of the rectangle is length × width, so

20 = AC × AB = 5 × AB

AB = 20/5 = 4

in a rectangle all angles are 90 degrees.

so, to find B we need to draw a line of 4 units from A to the right, perpendicular to AC. that means that now the y coordinate is the same as for A (3), and the distance to A is just the difference in the x coordinate :

4 = Bx - -3 = Bx + 3

Bx = 1

=> B = (1, 3)

to maintain the rectangle shape now D has to be right under B and to the right of C with the same distances

DB = AC = 5

DC = AB = 4

due to the special orientation of the rectangle (the sides are all parallel to the x- and y-axis) we can simply add the distances to the corresponding coordinates, or just deduct from the other points :

D has to have the same x coordinate as B (1).

D has to have the same y coordinate as C (-2).

so, D = (1, -2)

Answer:

Step-by-step explanation:

Answer:

73

Step-by-step explanation:

-9+84+(-2) =

-9+82 =

= 73

Hope this helps

Answer:

[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]

Step-by-step explanation:

Rate of Water Fill [tex]R=\frac{dv}{dt}=70cm^3[/tex]

Length [tex]l=8cm[/tex]

Height [tex]H=15cm[/tex]

Water level [tex]L_w= 4cm[/tex]

Generally the equation for relationship b/w h and a is mathematically given by

Since by the properties of similar triangles

 [tex]k=\frac{h}{1/2}[/tex]

Let

 [tex]h=15cm \\\\a=8cm[/tex]

 [tex]k=\frac{h}{1/2a}[/tex]

 [tex]k=\frac{15}{4}[/tex]

Therefore

 [tex]\frac{h}{1/2a}=\frac{15}{4}[/tex]

 [tex]a=\frac{8h}{15}[/tex]

Generally the equation for volume of Pyramid is mathematically given by

 [tex]V=\frac{1}{3}ah^2h[/tex]

Subsitute a

 [tex]V=\frac{1}{3}(\frac{8h}{15})h^2h[/tex]

Therefore

 [tex]\frac{dv}{dt}=\frac{(\frac{1}{3}(\frac{8h}{15})h^2h)}{dt}[/tex]

 [tex]\frac{dv}{dt}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]

Since

 [tex]\frac{dv}{dt}=70cm^3s^{-1}[/tex]

Therefore

 [tex]70cm^3s^{-1}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]

 [tex]\frac{dh}{dt}=\frac{70}{169}*\frac{225}{64}[/tex]

 [tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]

Answer:

20% chance of h

40% chance of p

Answer:

[tex]\% = 11.96\%[/tex]

Step-by-step explanation:

Given

See attachment for box plot

Required

Percentage greater than or equal to 233

From the box plot, the maximum is:

[tex]Max = 244[/tex]

The minimum is:

[tex]Min = 152[/tex]

Percentage greater than 233 is calculated as:

[tex]\% = \frac{Max - 233}{Max - Min}[/tex]

[tex]\% = \frac{244 - 233}{244-152}[/tex]

[tex]\% = \frac{11}{92}[/tex]

Express as percentage

[tex]\% = \frac{11}{92}*100\%[/tex]

[tex]\% = \frac{1100}{92}\%[/tex]

[tex]\% = 11.96\%[/tex]