Find the volume of a rectangular prism with a height of 18 if the base has a length of 9 and a width of 17.
Select one:
O a. 2678 units cubed
O b. 2049 units cubed
O c. 2754 units cubed
O d. 2957 units cubed

Answer:

Step-by-step explanation:

Equation of the line using point (0, 1) and slope 4/5 is

[tex]y - 1 = \frac{4}{5} (x - 0) \\ \\ 5y - 5 = 4x \\ \\ 5y - 4x = 5[/tex]

Hope this helps you

Answer:

D. [tex]\boxed{5y-4x=5}[/tex]

Step-by-step explanation:

Slope = m = 4/5

y - intercept = b = 1 (As from the point (0,1) , y-intercept is when x = 0)

So, the equation becomes

=> [tex]y = mx+b[/tex]

=> [tex]y = \frac{4}{5} x +1[/tex]

=> [tex]y - \frac{4}{5} x = 1[/tex]

Multiplying both sides by 5

=> [tex]5y-4x = 5[/tex]

Answer: Eli’s age is 24 years and Cora’s age is 74 years

Step-by-step explanation:

To find Eli’s age and Cora’s age, use the following condition.

Eli’s age is represented by term ‘x’

Cora’s age is represented by term ‘3x + 2’

x + 3x + 2 = 98

Add x and 3x

4x + 2 = 98

Subtract 2 from both sides

4x = 96

Divide by 4 on both sides

x = 24

Therefore Eli’s age is 24 years

To find Cora’s age, plug in 24 for x

3(24) + 2 = 72 + 2 = 74

Answer:

Cora is 74 years old

Eli is 24 years old

Step-by-step explanation:

Cora’s age = x

Eli’s age = y

x = 3y + 2

x + y = 98

x = 98 - y

98 - y = 3y + 2

98 - 2 = 3y + y

96 = 4y

24 = y

x + 24 = 98

x = 98 - 24

x = 74

Answer:

( x+2)^2 + ( y+2) ^2 = 9

Step-by-step explanation:

The center is at (-2,-2)

The radius is 3  which is the number of units from the center to the circles edge

The equation of a circle can be written as

( x-h) ^2 + (y-k) ^2 = r^2  where ( h,k) is the center and r is the radius

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

( x+2)^2 + ( y+2) ^2 = 9

Answer:

Graph A.

Step-by-step explanation:

Given the inequality: [tex]y\leq \dfrac{1}{4}x-3[/tex]

Since the sign is "less than or equal to", the line cannot be dotted. Therefore, Options C and D are incorrect.

Since the sign is a "less than" sign, the required region must be below the line. Therefore, the graph which shows the given inequality is Graph A.

Answer:

B

Step-by-step explanation:

The line from the vertex to the base is a perpendicular bisector and divides the isosceles triangle into 2 right triangles with hypotenuse x

Using Pythagoras' identity in either of the 2 right triangles, then

x² = 12² + 5² = 144 + 25 = 169 ( take the square root of both sides )

x = [tex]\sqrt{169}[/tex] = 13 → B

Answer:

6c1;   [tex]Area = 81.12m^2[/tex]

6cii:  See Explanation

Step-by-step explanation:

Given

[tex]A = 3p^2[/tex]

[tex]0 \leq p \leq 6[/tex]

Where A represents Area and P represents Width

Required

Solve 6c

Please note that because you only need 6c, I'll solve using calculations;

Solving 6ci:

Area of the cage, when width is 5.2m

Substitute 5.2m for p in[tex]A = 3p^2[/tex]

[tex]A = 3 * 5.2m^2[/tex]

[tex]A = 3 * 27.04m^2[/tex]

[tex]A = 81.12m^2[/tex]

Hence, the area of the cage is 81.12m²

Solving 6cii:

Area of the cage, when width is 40m

From the range of value of p:   [tex]0 \leq p \leq 6[/tex], 40m is out of range of the values of p

However, if the range is extended; the value of Area is as follows;

Substitute 40m for p

[tex]A = 3 * 40m^2[/tex]

[tex]A = 3 * 1600m^2[/tex]

[tex]A = 4,800m^2[/tex]

The answer is B.) (-1 1/5, 4 3/5)  /  [tex]\left(-1\:\frac{1}{5},\:4\frac{3}{5}\right)[/tex]

Answer:

11.3, or 12 if you need a whole number

Step-by-step explanation:

1 L = 1,000 mL. After adding all of your mL, you get 11,300. Divide that by 1,000 to get 11.3. To fully refill all of her fish tanks, she would need to refill it 12 times, but if you're looking for an exact number, 11.3.

Answer:

[tex]125m {}^{3}n {}^{6} [/tex]

Step-by-step explanation:

Since

[tex]a {}^{b} \times a {}^{c} = a {}^{b + c} [/tex]

[tex](5mn {}^{3} ) {}^{3} = (5) {}^{3}(m) {}^{3} (n {}^{3}) {}^{3} = 125m {}^{3}n {}^{3 + 3} = 125m {}^{3}n {}^{6} [/tex]

Hope this helps :) ❤❤❤

Answer:

[tex]125m^3n^9[/tex]

Step-by-step explanation:

[tex](a*b)^n=a^nb^n\\\\(5mn^3)^3=5^3m^3(n^3)^3\\\\125m^3(n^3)^3\\\\(a^b)^c=a^{bc}\\\\\rightarrow (n^3)^3=n^{3*3}=n^9\\\\\boxed{125m^3n^9}[/tex]

Brainilest Appreciated.

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

[tex]-5(x-2)=-25[/tex]

Expand the brackets on the left side of the equation.

[tex]-5(x)-5(-2)=-25[/tex]

[tex]-5x+10=-25[/tex]

Add -10 on both sides.

[tex]-5x+10-10=-25-10[/tex]

[tex]-5x=-35[/tex]

Divide both sides by -5.

[tex]\displaystyle \frac{-5x}{-5} =\frac{-35}{-5}[/tex]

[tex]x=7[/tex]

Answer:

[tex] \boxed{\sf x= 7} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: x: \\ \sf \implies - 5(x - 2) = - 25 \\ \sf Divide \: both \: sides \: of \: - 5 (x - 2) = - 25 \: by \: - 5: \\ \sf \implies \frac{ - 5(x - 2)}{ - 5} = \frac{ - 25}{ - 5} \\ \\ \sf \frac{ \cancel{ - 5}}{ \cancel{ - 5}} = 1 : \\ \sf \implies x - 2 = \frac{ - 25}{ - 5} \\ \\ \sf \frac{ - 25}{ - 5} = \frac{5 \times \cancel{ - 5}}{ \cancel{ - 5}} = 5 : \\ \sf \implies x - 2 = \boxed{ \sf 5} \\ \\ \sf Add \: 2 \: to \: both \: sides: \\ \sf \implies x + ( \boxed{ \sf 2} - 2) =5 + \boxed{ \sf 2} \\ \\ \sf 2 - 2 = 0 : \\ \sf \implies x = 5 + 2 \\ \\ \sf 5 + 2 = 7 : \\ \sf \implies x= 7[/tex]

Answer:

1.35 meters

Step-by-step explanation:

Let the original length of the string be x.

So, we started out with x centimeters. Rachel used 2/3 of it (the original amount) to tie some books together. Therefore, we now have:

[tex]x-\frac{2}{3}x[/tex]

centimeters of string left. This represents the original minus the amount she used.

Next, she used 1/3 of the remaining string. In other words:

[tex]x-\frac{2}{3}x-\frac{1}{3}(x-\frac{2}{3} x)[/tex]

The newly added terms is 1/3 of the remaining string length.

And she ends up with 30 centimeters. Therefore, we need to solve the equation for x:

[tex]x-\frac{2}{3}x-\frac{1}{3}(x-\frac{2}{3} x) =30\\\frac{1}{3}x-\frac{1}{3}x+\frac{2}{9}x=30\\\frac{2}{9}x=30\\ x=30\cdot \frac{9}{2}=135 \text{ centimeters}[/tex]

Therefore, the original length of the string was 135 centimeters or 1.35 meters (move the decimal two places to the left).

Answer:

135 cm or 1.35 m

Step-by-step explanation:

2/3(135) = 90

1/3(90) = 30

Explanation:

We'll use the tangent ratio to connect the opposite and adjacent sides with the reference angle

tan(angle) = opposite/adjacent

tan(A) = 14/7

Then use the arctangent function (aka inverse tangent) to fully isolate A

A = arctan(14/7)

A = 63.4349 degrees approximately; make sure your calculator is in degree mode

Round this to the nearest whole number to get 63.

Answer:

3/4

Step-by-step explanation:

Explanation:

List out the total number of outcomes = {1,2,3,4,5,6,7,8,9,10,11,12}

We have 12 items in this list.

From this list, highlight the outcomes that are less than 9. So we will have this smaller list of {1,2,3,4,5,6,7,8} which has 8 items in it.

There are 8 ways to get what we want (a number less than 9) out of 12 outcomes total

The probability is therefore 8/12 = 2/3

Answer:

[tex]y = \frac{5x}{2} - 5[/tex]

Step-by-step explanation:

Given the equation 5x - 2y = 10, to write the equation in slope-intercept form, we need to write it in the standard format y = mx+c where m is the slope/gradient and c is the intercept.

From the equation given  5x - 2y = 10, we will make y the subject of the formula as shown;

[tex]5x - 2y = 10\\\\subtract \ 5x \ from \ both \ sides\\\\5x - 2y - 5x = 10 - 5x\\\\-2y = 10-5x\\\\Dividing \ both \ sides\ by \ -2;\\\\\frac{-2y}{-2} = \frac{10-5x}{-2}\\ \\[/tex]

[tex]y = \frac{10}{-2} - \frac{5x}{-2} \\\\y = -5 + \frac{5x}{2}\\\\y = \frac{5x}{2} - 5[/tex]

Hence the equation that represents the first equation written in slope-intercept form is [tex]y = \frac{5x}{2} - 5[/tex]

Answer:

Step-by-step explanation:

Let the unknown number = x

[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]

x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]

[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]

Answer:

Other equation: y = 1/3x + 5

Solution: (3, 6)

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Identify tables

1st table is the unknown equation

2nd table is the known equation (found using y-intercept 7)

Step 2: Find missing equation

m = (6 - 5)/(3 - 0)

m = 1/3

y = 1/3x + b

5 = 1/3(0) + b

5 = b

y = 1/3x + 5

Step 3: Find solution set using substitution

1/3x + 5 = -1/3x + 7

2/3x + 5 = 7

2/3x = 2

x = 3

y = 1/3(3) + 5

y = 1 + 5

y = 6

Answer:

Hey there!

The solution is where the lines intersect, and here we see that would be (-4,3)

Hope this helps :)

Hey there!

"8x = 25"

In order for you to solve for "x-value" (or the equation) we have to DIVIDE both of your sides by 8

8x/8 = 25/8

Cancel out: 8x/8 because that gives you the value of 1 and you don't need it at the moment (in that equation that is)

Keep: 25/8 Because it solves for your equation

Your x equals: 25/8 aka 1 1/8 aka 3.125 (you could choose any one of these as your answer because they are all correct)

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer with  explanation:

Given: An airline company advertises that 100% of their flights are on time after checking 5 flights from yesterday and finding that these 5 were on time.

a) population: A large group of observations have characteristics related to the point of the study.

Here, population: "All flights operated by the company"

b) Sample: It is a subset of the population.

Here, Sample: "5 flights from yesterday"

(c)

Since the number of flights per day operated by an airline company is much larger than 5 ( generally in hundreds).

i.e. the sample is too small to be able to assure that the results are true.

Hence, this is not a representative sample.

(d) To determine the percentage of their flights that are on time we use the following formula:

(Number of flights are on time) ÷ (Total flights) x 100

Answer:

y=2/3x-2

Step-by-step explanation:

All of the given options are in slope intercept form.

Slope intercept form is y=mx+b

This is where m is the slope fo the line and b is the y intercept

That said, we can simply plug the given values into the form.

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

Simplify

y=2/3x-2

Answer:

A. y= 2/3x-2

Step-by-step explanation:

The slope of a line is written in slope-intercept form, which is:

y= mx+b

where m is the slope and b is the y-intercept.

The line has a slope of 2/3 and a y-intercept of -2. Therefore,

m= 2/3

b= -2

Substitute these values into the slope intercept form.

y= mx+b

y=2/3x+(-2)

Adding a negative number (+-) can be simplified to just a negative(-)

y= 2/3x-2

Therefore, the equation of the line is A. y= 2/3x-2

Answer:

[tex]\frac{77\pi }{3}[/tex] cm³

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )

Here diameter = 4 cm , hence r = 4 ÷ 2 = 2 cm

V = [tex]\frac{4}{3}[/tex]π × 2³ = [tex]\frac{4}{3}[/tex]π × 8 = [tex]\frac{32\pi }{3}[/tex] cm³

Thus

combined volume = [tex]\frac{32\pi }{3}[/tex] + 15π = [tex]\frac{32\pi }{3}[/tex] + [tex]\frac{45\pi }{3}[/tex] = [tex]\frac{77\pi }{3}[/tex] cm³

Answer:

Step-by-step explanation:

Draw the solid line y = 3x.  Now shade the region below this line.

I will simply invent a point:  (2, -1).  Here y = -1 and x = 2.  Either this point is in the shaded region or it is not.  Substituting 2 for x in y  ≤ 3x, we get

y ≤ 3(2), or y ≤ 6.  Is -1 less than 6?  YES.  So the (arbitrarily chosen) point (2, -1) is a solution of the given inequality.

Answer:

Step-by-step explanation:

Let L be the length of this rectangle

The length of a rectangle is 2 feet less than four times the width

● L+2 = 4w

The area of this rectangle is 38.2 ft^2

● L*w = 38.2

The system of equations is

L+2 = 4w => L-4w =2

L*w = 38.2 => L= 38.2/w

Replace L by 38.2/w in L-4w =2

● L-4w = 2

● (38.2/w)-4w = 2

●(38,2-4w^2)/w = 2

● 38.2-4w^2 = 2w

● 38.2-4w^2-2w = 0

● -4w^2-2w+38.2 =0

Multiply by -1 to reduce the - signs

● 4w^2+2w-38.2 =0

This is a quadratic equation so we will use the discriminant

□□□□□□□□□□□□□□□□□

The discriminant is b^2-4ac

● b= 2 (2w)

● a= 4 (4w^2)

● c= -38.2 (the constant term)

b^2-4ac =2^2-4*4*(-38.2) = 615.2 > 0

The discriminant is positive so we have two solutions w and w' :

●●●●●●●●●●●●●●●●●●●●●●●●

w= (-2-24.8)/8 = -3.35

24.8 is the root square of 615.2(the discriminant)

●w is negative

● a distance is always positive so this value isn't a solution

w'= (-2+24.8)/8 =2.85 > 0

So this value is a solution for our equation

■■■■■■■■■■■■■■■■■■■■■■■■■■

w= 2.85 feet

Answer:

w=3.35

Step-by-step explanation:

The length of a rectangle is two feet less than four times the width:

length=4W-2

A=L*W

A=(4W-2)(W)

38.2=4W^2-2W

4W^2-2W-38.2=0  complete the square to find the solution add term(b/2)²

4W²-2W+1/4=38.2+1/4

4(W²-W/2+1/16)=38.45

4(w-1/4)^2=38.45

(w-1/4)²=38.45/4=9.6125

w-1/4=+ or -√9.6125 ( since it is width it has to be positive

w=√9.6125+1/4 = 3.35

Answer:

(x*(1+a))*0.8 = 400; x = 500/1+a

Step-by-step explanation:

First, increase the number (which we will call x) by a%

x*(1+a) -> You do 1 + a because if you wanted to increase let's say 5 by 20% you would do 5 + 5*0.2 and if you factor that out it becomes 5(1+0.2)

Next, decrease it by 80%.

(x*(1+a))*0.8

Finally, make it into an equation.

(x*(1+a))*0.8 = 400

If you solve it, you get:

x(1+a) = 500

x = 500/1+a

Answer:

We accept H₀, with CI = 90 %, porcentage of O blood type in college students does not differ from the world population porcentage

Step-by-step explanation:

The test is a proportion  two-tail test ( note: differs)

p₀ = 45 %      or  p₀ = 0,45

n = 1000

p =  47 %        or  p  = 0,47

Test Hypothesis

Null hypothesis                                H₀                   p  =  p₀

Alternative hypothesis                    Hₐ                   p  ≠ p₀

CI  we assume 90 %  then  α = 10 %    α  =  0,1    α/2  = 0,05

z score  from z-table   z(c) = 1,64

To calculate z(s) = ( p - p₀ ) / √ p₀q₀/ n

z(s)  = ( 0,47  -  0,45 )/ √( 0,45)*(0,55)/1000

z(s)  =  0,02/√( 0,2475)/1000

z(s)  =  0,02/0,01573

z(s) = 1,2714

Now we compare z(s) and z(c)

z(s) < z(c)      1,2714 < 1,64

Then z(s) is in the acceptance region we accept H₀

Answer:

[tex]\sqrt{16}[/tex] = 4

[tex]\sqrt{25}[/tex] = 5

16x^2 - 40x + 25

= (4x - 5)^2

Hope this helps!

Answer:

4x-5, B

Step-by-step explanation:

EDGE 2020

Answer:

About 11 (10.9955742876...)

Step-by-step explanation:

Circumference=(pi) (diameter) or C=πd

Hope this helps!

The circumference of the circle is about 11 inches.

We are given that the diameter of a circle is 3.5 inches.

Noted that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

Therefore circumference of the circle = 2πr

Circumference=(2πr)

The diameter or C = πd

diameter = 3.5 inches

Circumference=(3.5 x 3.14)

Circumference = (10.99) inches

Learn more about circumference here;

brainly.com/question/12512221

#SPJ2

Answer:

[tex]P(A\ and\ B) = \frac{3}{7}[/tex]

Step-by-step explanation:

Your question is not well presented; (See Attachment for complete details)

Required

Find P(A n B)

where

A = Event that the place is a city

B = Event that the place is in North

The first step is to get the sample space;

Let S represent the sample space;

[tex]S = \{India,\ Tokyo,\ Houston,\ Peru,\ New York,\ Tijuana,\ Canada \}[/tex]

[tex]n(S) = 7[/tex]

The next is to list events A and B

A = City

[tex]A = \{Tokyo,\ Houston,\ New York,\ Tijuana\}[/tex]

B = North America

[tex]B = \{Houston,\ New York,\ Tijuana,\ Canada\}[/tex]

The next is to list common elements in A and B

[tex]A\ n\ B = \{Houston,\ New York,\ Tijuana\}[/tex]

[tex]n(A\ and\ B) = 3[/tex]

The probability of A and B is calculated as follows;

[tex]P(A\ and\ B) = \frac{n(A\ and\ B)}{n(S)}[/tex]

Substitute [tex]n(A\ and\ B) = 3[/tex] and [tex]n(S) = 7[/tex] in the expression above

[tex]P(A\ and\ B) = \frac{3}{7}[/tex]

Answer:

11.95

Step-by-step explanation:

435 divided by 8 is 54.375

650 divided by 54.375 is 11.95 (Rounded)

Answer:  11.95 hours

Step-by-step explanation:

[tex]\dfrac{435\ miles}{8\ hrs}=\dfrac{650\ miles}{x}\\\\\\435x=8(650)\\\\\\x=\dfrac{8(650)}{435}\\\\\\x=\large\boxed{11.95}[/tex]

Answer:

y = 250

Step 1:

To solve, we plug in 50x for y.

[tex]50x=200+10x[/tex]

Then, we subtract the 10x from the right side. Our goal is to get the x by itself first.

[tex]40x=200[/tex]

Then, we divide both sides by 40, since we have to get the x by itself.

[tex]\frac{40x}{40}=x\\\\\frac{200}{40} =5[/tex]

x = 5

Step 2:

Now that we found x, we plug in 5 to the original equation and solve from there.

[tex]y=200+10(5)\\y=200+50\\y=250[/tex]

y = 250