Use the minimum and maximum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 14, max = 121, 8 classes

Answer:

[tex] a = 2.7 [/tex]

Step-by-step explanation:

Distributive property can be used to solve the equation, by multiplying [tex] \frac{2}{3} [/tex] with [tex] 6a, [/tex] and [tex] 9 [/tex]

Thus,

[tex] (\frac{2}{3}*6a) + (\frac{2}{3}*9) = 16.8 [/tex]

[tex] 2*2a + 2*3 = 16.8 [/tex]

[tex] 4a + 6 = 16.8 [/tex]

Subtract 6 from both sides.

[tex] 4a + 6 - 6 = 16.8 - 6 [/tex]

[tex] 4a = 10.8 [/tex]

Divide both sides by 4 to solve for a

[tex] \frac{4a}{4} = \frac{10.8}{4} [/tex]

[tex] a = 2.7 [/tex]

F is conservative if we can find a scalar funciton f such that grad(f) = F.

This would entail

[tex]\dfrac{\partial f}{\partial x}=10yz[/tex]

[tex]\dfrac{\partial f}{\partial y}=10xz[/tex]

[tex]\dfrac{\partial f}{\partial z}=10xy[/tex]

Integrate both sides of the first equation with respect to x :

[tex]f(x,y,z)=10xyz+g(y,z)[/tex]

Differentiate both sides with respect to y :

[tex]\dfrac{\partial f}{\partial y}=10xz=10xz+\dfrac{\partial g}{\partial y}[/tex]

[tex]\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)[/tex]

Differentiate both sides with respect to z :

[tex]\dfrac{\partial f}{\partial z}=10xy=10xy+\dfrac{\mathrm dh}{\mathrm dz}[/tex]

[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C[/tex]

So we have

[tex]f(x,y,z)=10xyz+C[/tex]

that satisfies

[tex]\nabla f(x,y,z)=\mathbf F(x,y,z)[/tex]

and so F is indeed conservative.

Answer:

x+2y=12-------(1)

x-2y=3---------(2)

Adding equations 1 and 2

we get

2x=18

x=9

Equation 1

9+2y=15

2y=15-9

2y=6

y=3

The solution of the given system is x=9, y=3

Step-by-step explanation

Answer:

x = {9, -3}

Step-by-step explanation:

Or it can be shown as:

Answer:

60%

Step-by-step explanation:

We need convert 3/5 into a percent in order to find the answer.

We can convert by first dividing 3 by 5 to find the decimal value.

3/5= .6

Now we need to multiply by 100 to make it a percentage

.6 x 100= 60

60%

Answer:

6

Step-by-step explanation:

10 - 4 = 6

16 - 10 = 6

22 - 16 = 6

Answer:6

Step-by-step explanation:

1) 10-4=6

2) 16-10=6

3) 22-16=6

Answer:

200,000

Step-by-step explanation:

The current population: 50,000

Doubling time:70

Population after 280 years=?

280/70=4

50,000*4=200,000

Hope this helps ;) ❤❤❤

Answer: 800,000

Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.

Answer:

$14.4

Step-by-step explanation:

From the question;

There are 300 strands of light each containing 150 light bulbs. Altogether, there are;

300 x 150 light bulbs = 45000 light bulbs.

Also;

Each bulb consumes 4 watts of power. Since there are 45000 light bulbs, the total power consumed by all the bulbs is;

45000 x 4 watts = 180000watts

Next convert the total power consumed to kW by dividing by 1000. i.e

180000watts = 180kW

Therefore, total power consumed is 180kW

He lights up for 5 hours a day for 30 days. This means that the total number of hours he lights his home for those 30 days is:

30 x 5 hours = 150 hours.

Now since power in his area sells for $0.08/kWh, this means that;

1kWh costs $0.08

Then;

180kWh will cost [180kWh x $0.08 / 1kWh] = $14.4

Therefore, he will end up paying $14.4 to light his home for the holidays.

Answer:

80 ft

Step-by-step explanation:

in similar triangles sides are proportional.

[tex]\frac{176}{h} =\frac{120+100}{100} =\frac{220}{100} =\frac{22}{10} \\h=\frac{10}{22} \times 176=80[/tex]

h=80 ft

Answer:

Range { 2,6,8}

Step-by-step explanation:

The domain is the input and the range is the output

Range { 2,6,8}

Answer:

2, 6, 8

Step-by-step explanation:

The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.

Answer:

The answer is D. You can confirm this from the graph down below

Step-by-step explanation:

Answer:

x<3

Step-by-step explanation:

Answer:

[tex]\boxed{x\leq 3}[/tex]

Step-by-step explanation:

[tex]4x \leq 12[/tex]

[tex]\sf Divide \ both \ parts \ by \ 4.[/tex]

[tex]\displaystyle \frac{4x}{4} \leq \frac{12}{4}[/tex]

[tex]x\leq 3[/tex]

Answer:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Step-by-step explanation:

First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.

Now let's get started on the problem. Cosine functions generally take the form

[tex]y=a\cos(b(x-c))+d[/tex]

Where:

[tex]|a|[/tex] is the amplitude

[tex]\frac{2\pi}{b}[/tex] is the period, or the time it takes to go one full rotation around the circle (ferris wheel)

[tex]c[/tex] is the horizontal displacement

[tex]d[/tex] is the vertical shift

Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find [tex]b[/tex] to put into our function:

[tex]\frac{2\pi}{b}=2[/tex]

[tex]2\pi=2b[/tex]

[tex]\pi=b[/tex]

I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:

[tex]\frac{\max-\min}{2}[/tex]

[tex]\frac{54-4}{2}[/tex]

[tex]\frac{50}{2}=25=a[/tex]

Our vertical transformation is given by [tex]\min+a[/tex] or [tex]\max-a[/tex], which is the height of the center of the ferris wheel, [tex]4+25=29=d[/tex]

Because cosine starts at the minimum, [tex]c=0[/tex].

The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Answer:

Step-by-step explanation:

cot (x)=2/3

we know csc^2(x)-cot^2(x)=1

csc^2(x)=1+cot^2(x)=1+4/9=13/9

csc (x)=±√13/3

Answer:

1) y=⅚x -2⅓

2) y=8/3x -5

Step-by-step explanation:

Point-slope form:

y=mx+c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient.

Gradient of given line= [tex] \frac{5}{6} [/tex]

Thus, m=⅚

Susbt. m=⅚ into the equation,

y= ⅚x +c

Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.

When x=4, y=1,

1= ⅚(4) +c

[tex]1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3} [/tex]

Thus the equation of the line is [tex]y = \frac{5}{6} x - 2 \frac{1}{3} [/tex].

The gradients of perpendicular lines= -1.

Gradient of given line= -⅜

-⅜(gradient of line)= -1

gradient of line

= -1 ÷ (-⅜)

= -1 ×(-8/3)

= [tex] \frac{8}{3} [/tex]

[tex]y = \frac{8}{3} x + c[/tex]

When x=3, y=3,

[tex]3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5[/tex]

Thus the equation of the line is [tex]y = \frac{8}{3} x - 5[/tex].

7km/ 4km per hour = 1 3/4 hours

3/4 hour = 45 minutes

Total time = 1 hour and 45 minutes.

Answer:

Step-by-step explanation:

6x - y = 3

4x + 3y = 1

Solve the equation for y

y = -3 + 6x

4x + 3y = 1

Substitute the given value of y into the equation

4x + 3y = 1

plug the value

[tex]4x + 3( - 3 + 6x) = 1[/tex]

Distribute 3 through the parentheses

[tex]4x - 9 + 18x = 1[/tex]

Collect like terms

[tex]22x - 9 = 1[/tex]

Move constant to R.H.S and change its sign

[tex]22x = 1 + 9[/tex]

Calculate the sum

[tex]22x = 10[/tex]

Divide both sides of the equation by 22

[tex] \frac{22x}{22} = \frac{10}{22} [/tex]

Calculate

[tex]x = \frac{5}{11} [/tex]

Now, substitute the given value of x into the equation

y = -3 + 6x

[tex]y = - 3 + 6 \times \frac{5}{11} [/tex]

Solve the equation for y

[tex]y = - \frac{3}{11} [/tex]

The possible solution of the system is the ordered pair ( x , y )

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

Check if the given ordered pair is the solution of the system of equations

[tex]6 \times \frac{5}{11} - ( - \frac{3}{11} ) = 3[/tex]

[tex]4 \times \frac{5}{11 } + 3 \times ( - \frac{3}{11} ) = 1[/tex]

Simplify the equalities

[tex] 3 = 3[/tex]

[tex]1 = 1[/tex]

Since all of the equalities are true , the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Answer:

X= 3

Y= 18

Each side of the triangle= 10 units

Step-by-step explanation:

LMN is equilateral so

LM = MN

3x+1= 4x-2

3x-4x = -2-1

-x = -3

X= 3

MP is the perpendicular bisector of line LN

so definitely angle lpm =90.

And lpm = 5y = 90

5y = 90

Y= 90/5

Y = 18°

For the side of the triangle

3x+1

But x= 3

3(3)+1

9+1

10

Each side of the triangle= 10 units

Answer:

2064 cm squared

Step-by-step explanation:

First I will try to solve for the area of each side:

Side #1(trapezoid): Area of a Trapezoid = half of sum of bases*height

A= (6+27)/2*8 = 33/2 *8 =132

Side #2(opposite trapezoid): Same area as theother one...

A= 132

Side#3(Top):

A=6*30=180

Side #4(Bottom):

A=27*30=810

Side #5(Left side):

A=10*30=300

Side #6(Right Side):

A=30*17=510

After solving for all the areas we just need to add them all up:

SA=132+132+180+810+300+510=2064 cm squared

Hope this helps!

Answer:

total surface area = 2064 cm^2

Step-by-step explanation:

Given prism with trapezoidal bases.

H=8

B1 = 27

B2 = 6

slant sides = 10, 17 cm

H = 30

Area of bases

A1 = 2 * (B1+B2)/2 * h

= 2* ( (27+6)/2 * 8 )

= 264

Area of sides

A2 = perimeter * H

= (6+17+27+10)*30

= 1800

Total area = A1+A2 = 264+1800 = 2064 cm^2

Answer:

the correct answer is 45°

Answer:

45 degrees.

Explanation: This is the correct answer on Edge 2021, just took the Unit test and made a 100%. Hope this helps ^-^.

Answer:

The third side of the triangle is 10x + 3

Step-by-step explanation:

x + 1 + 2x + 4 = 3x + 5

( 13x + 8 ) - ( 3x + 5 ) = 13x + 8 - 3x - 5

= 10x + 3

Answer:

A: 15

Step-by-step explanation:

The angles are opposite to each other.

Vertically opposite angles are equal in size.

Put up an equation and solve for a.

6a + 10 = 3a + 55

Subtract 3a and 10 on both sides.

6a - 3a = 55 - 10

Combining like terms.

3a = 45

Divide both sides by 3.

a = 45/3

a = 15

The value of a is 15.

Answer:

a = 15

Step-by-step explanation:

=> 6a + 10 = 3a + 55 (Vertically Opposite Angles are congruent)

Combining like terms

=> 6a - 3a = 55 - 10

=> 3a = 45

Dividing both sides by 3

=> a = 15

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.

Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.

Learn more about Triangle:

https://brainly.com/question/2773823

#SPJ5

Answer:

$17

Step-by-step explanation:

data:

In statistics, the range is the difference between the highest value and the lowest value of the data set.

Highest value = $147

Lowest value = $130

Range = $17

Answer:

a. 0.04

b. 0.9772

Step-by-step explanation:

Please check attachment for complete solution and step by step explanation

Answer:

Step-by-step explanation:

From the Given data in the above question it can be said that the experiment is a Binomial experiment because there is a success rate and a failure rate involved and the success rate is about 30% of the babies recovering from the ailment while the failure rate is about 70% of the babies not recovering from the ailment

The number of babies (n) = 5

success rate (p) = 30% = 0.3

failure rate (q) = 100% - 30% = 70% = 0.7

The possible values of the random value x = from 0 to 5

Answer:

j = 44/3

Step-by-step explanation:

j varies jointly as g and v. This can be represented mathematically as:

[tex]j \alpha gv\\j = kgv[/tex].............(1)

Where k is a constant of proportionality

j = 2 when g = 4 and v = 3

Substitute these values into equation (1)

2 = k * 4 * 3

2 = 12 k

k = 1/6

when g = 8 and v = 11:

j = (1/6) * 8 * 11

j = 44/3

Answer:

Step-by-step explanation:

32,256,2048,16384,......,2⁵⁰

32=2⁵

256=2⁸

2048=2¹¹

16384=2¹⁴

2⁵, 2⁸, 2¹¹,2¹⁴, ….,2⁵⁰

[tex]t_{1}[/tex]=2⁵; [tex]t_{2}[/tex]=2⁸

r=2⁸:2⁵=2³

[tex]t_{n}[/tex]=[tex]t_{1}[/tex]*[tex]r^{n-1}[/tex]

2⁵*[tex]2^{3(n-1)}[/tex] =2⁵⁰

5+3(n-1)=50

3n-3=45

3n=48

n=48:3

n=16

So, 16 terms