20 POINTS. PLEASE HELP FAST. FIRST ANSWER GETS BRAINLIEST.

Answer:

158m^3

Step-by-step explanation:

First, let's figure out the total amount of water in the tank.

It measures 4.5m by 6m by 8m. The volume of a rectangular prism is V=lwh.

Therefore, the volume is:

[tex]V=(4.5)(6)(8)=216 m^3[/tex]

We are told is it filled to the brim, so we can conclude that there are 216 cubic meters of water in the tank.

We used 58 cubic meters of water, so we simply need to subtract that from 216:

[tex]216m^3-58m^3=158m^3[/tex]

There is still 158 cubic meters of water left in the tank.

Answer:

158 m^3

Step-by-step explanation:

Volume of the tank

= 4.5 * 6 * 8

= 216 m^3.

So amount left in the tank

= 216 - 58

= 158 m^3.

Answer:

D

Step-by-step explanation:

cas if x =1

then 1^2>or=1

1is not >or=1

Answer:

A. z/y

Step-by-step explanation:

Because the trig ratios are; tangent : opp/adj cos : adj/hyp sin : opp/hyp

because tan of x is z/10, z must be opposite

and because cos of x is 10/y, then y must be the hypotenuse

this means sin of x must be z/y

Answer:

A. sin x = z/y

Step-by-step explanation:

Answer:

Equation:  87 + 91 + 86 + x = 360

Solution: 264 + x = 360

x = 360 - 264

x = 96

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

First three Kelsea's test grades : 87, 91 and 86

2. What score must she get on her fourth test to receive at least an A- ?

Define variable:  x that represents the grade needed by Kelsea on her fourth test to receive at least an A-

Equation:  87 + 91 + 86 + x = 360

Solution: 264 + x = 360

x = 360 - 264

x = 96

Now you can understand if the previous work you did is correct

Answer:

x=10

Step-by-step explanation:

The triangles are similar so we can use ratios to solve

6.5      (6.5+6.5)

------ = -----------------------

5              x

6.5      (13)

------ = -----------------------

5              x

Using cross products

6.5x = 65

Divide by 6.5

6.5x/6.5 = 65/6.5

x = 10

Explanation:

The area of a semicircle is given by ...

  A = πr^2/2

where r is the radius. Here, we're given diameters, so in terms of diameter, the area of a semicircle is ...

  A = π(d/2)^2/2 = (π/8)d^2

__

The area of the semicircle with diameter AC is ...

 white area = (π/8)AC^2

The area of the semicircle with diameter BC is ...

  left semicircle area = (π/8)BC^2

And the area of the semicircle with diameter AB is ...

  right semicircle area = (π/8)AB^2

__

We can use the relationship between the areas to find the shaded area:

  triangle area + left semicircle area + right semicircle area =

     white area + shaded area

Then the shaded area is ...

  shaded area = triangle area + left semicircle area + ...

     right semicircle area - white  area

__

Filling in the values for area from above, we have ...

  shaded area = triangle area+ (π/8)BC^2 +(π/8)AB^2 -(π/8)AC^2

  shaded area = triangle area + (π/8)(BC^2 +AB^2 -AC^2)

From the Pythagorean theorem, we know that ...

  AC^2 = BC^2 +AB^2

Substituting this into the above equation gives ...

  shaded area = triangle area + (π/8)((Bc^2 +AB^2 -(BC^2 +AB^2))

  shaded area = triangle area + 0 . . . . simplify

  shaded area = triangle area

Answer: 5.34

Step-by-step explanation: 18 - 12.66 = 5.34

Answer:

b

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Open box is in rectangular shape. cuboid that is open in the top

l = length = 30 - (2.5 + 2.5 ) = 30 - 5 = 25 cm

h = 2.5 cm

w = width = 30 - (2.5 + 2.5) = 30 - 5 = 25 cm

Surface Area = 2lh + 2wh + lw

                     = 2*25*2.5 + 2* 25*2.5 + 25*25

                    =125 + 125 + 625

                   = 875 square cm

Volume = lwh

             = 25*25*2.5

             = 1562.5 cubic cm

Answer:

(4,-1)

Step-by-step explanation:

The required coordinate of J is (1, 4). Hence the option c is correct.

Rectangle JKLM is rotated 90° clockwise about the origin.
On a coordinate plane, rectangle J K L M has points (negative 4, 1), (negative 1, 1), (negative 1, negative 1), (negative 4, negative 1).

Rectangle is four sided polygon whose opposites sides are equal and has angle of 90° between its sides.

While rotating the rectangle about origin clock wise, the new coordinates forms of  rectangle J K L M has points  ( 4, 1), (1, 1), (negative 1,  1), (negative1 ,  4).

Thus, the required coordinate of J is (1, 4).

Learn more about rectangles here:
https://brainly.com/question/16021628

#SPJ2

Answer:

x = (3 +/- sqrt(17) / 4.

Step-by-step explanation:

x = [-(-3) +/- sqrt((-3)^2 - 4*2*-1)] / 4

x = (3 +/- sqrt(17) / 4.

Answer:

5 pounds of miniature chocolate and 2 butterscotch hard candies

Step-by-step explanation:

5 x $1.80 =$9 for 5 pounds of candy

2 x $1.00 =$2 for 2 pounds of candy

2 + 5 =7 pounds

7 pounds of candy using $11.00

Answer:

9 ft

Step-by-step explanation:

a²+b²=c²

20²+b²=25²

400=b²=625

b²=625-400

b²=225

b=15 (the distance up the wall the ladder is to begin with)

20-13=7

7²+b²=25²

49+b²=625

b²=625-49

b²=576

b=24 (The distance up the wall the ladder is after moving it)

24-15=9

Answer:

Ok so im in 7thgrade so ima try to help answer is x= 8x9

Answer:

Step-by-step explanation:

Hello,

a. The area of region P is the area of the rectangle 1 * e minus the

[tex]\displaystyle \int\limits^0_1 {e^x} \, dx=[e^x]^{1}_{0}=e-1[/tex]

So this is e - (e-1) = e - e + 1 = 1

b. The area of region P is the area of the rectangle 1 * e minus P and minus the

[tex]\displaystyle \int\limits^0_1 {e^{-x}} \, dx=[-e^{-x}]^{1}_{0}=-e^{-1}+1[/tex]

So this is

[tex]e - 1 - (-e^{-1}+1) = e-1+e^{-1}-1=e+e^{-1}-2[/tex]

This is around 1.08616127...

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Hey there!

Original Equation

-5x-4y=-8

Multiply by -1

5x+4y=8

Subtract 4y

5x=8-4y

Divide by 5

x=(8-4y)/5

Let me know if this helps :)

Answer:

x = -4/5y + 8/5

Step-by-step explanation:

So to single out x we use the communicative property,

its the moving of numbers and variables to each side of the equation.

So we have,

-5x - 4y = -8

+4y

-5x = 4y - 8

Divide -5 by both sides,

x = -4/5y + 8/5

Thus,

the equation rearanged is x = -4/5y + 8/5.

Hope this helps :)

Answer:

Step 2: addition property of equality

Step 4: multiplication property of equality

Step-by-step explanation:

=>In step 2, from step 1, where you have [tex] -\frac{y}{2} - 6 = 15 [/tex] , to make -6 cross over to the other side of the equation, the addition property of equality was applied. That would ensure the equation remains balanced. Thus, 6 is added to both sides of the equation.

[tex] -\frac{y}{2} - 6 + 6 = 15 + 6 [/tex]

[tex] = -\frac{y}{2} = 21 [/tex]

=>In step 4, the multiplication property of equality was used as both sides of the equation were multiplied by -2, to balance the equation and also solve for y.

Answer:

Step 2 > addition

Step 4 > multiplication

Step-by-step explanation:

Answer:

Domain: (-5,-4,-3,-2,-1,0,1,2,3,4,5)

Range: (0,1,2,3,4, -1, -2)

Step-by-step explanation:

Domain means all of the x-axis values on the graph, so for example in (-2,0), -2 would be part of the domain and 0 part of the range. Therefor, what you would do would be take all of the plots and put all x values as the domain and all y values as the range. Hope this helped!

Answer:

V = 32 in^3

Step-by-step explanation:

The area of the triangle is (1/2)(base)(height), which here comes to:

                                                (1/2)(4 in)(8 in) = 16 in^2.

The volume is (16 in^2)(height) =  (16 in^2)(2 in) = 32 in^3

Answer:

9

Step-by-step explanation:

because the angle is 45 deg, it is 1/8 of the full circle

the arc it intercepts will also be 1/8 the circumference of the full circle

72*1/8=9

Answer:

Consecutive angles in a parallelogram are, D supplementary.

Step-by-step explanation:

Consecutive angles in a parallelogram will always sum to 180 degrees.

Answer:

Supplementary

Step-by-step explanation:

Correct answer in Ap3x. Just took the quiz.

Answer:

The answers are as follows.

Step-by-step explanation:

Expressions:

Computation:

Product of 2 and x is 14

2(x) = 14

x = 7

6 added with a number gives 14

6+x = 14

x = 8

The product of six and a gives 12

6(a) = 12

a = 2

12 divided by y gives 2

12 / y = 2

y = 6

6 subtract from a number and get 12

x - 6 = 14

x = 20

Answer:

C. [tex](5-\frac{1}{2})^6[/tex]

Step-by-step explanation:

Given

[tex]15(5)^2(-\frac{1}{2})^4[/tex]

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

[tex]Sum = 2 + 4[/tex]

[tex]Sum = 6[/tex]

Each term of a binomial expansion are always of the form:

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

Where n = the sum above

[tex]n = 6[/tex]

Compare [tex]15(5)^2(-\frac{1}{2})^4[/tex] to the above general form of binomial expansion

[tex](a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]

Substitute 6 for n

[tex](a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]

[Next is to solve for a and b]

From the above expression, the power of (5) is 2

Express 2 as 6 - 4

[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]

By direct comparison of

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

and

[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]

We have;

[tex]^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4[/tex]

Further comparison gives

[tex]^nC_r = 15[/tex]

[tex]a^{n-r} =(5)^{6-4}[/tex]

[tex]b^r= (-\frac{1}{2})^4[/tex]

[Solving for a]

By direct comparison of [tex]a^{n-r} =(5)^{6-4}[/tex]

[tex]a = 5[/tex]

[tex]n = 6[/tex]

[tex]r = 4[/tex]

[Solving for b]

By direct comparison of [tex]b^r= (-\frac{1}{2})^4[/tex]

[tex]r = 4[/tex]

[tex]b = \frac{-1}{2}[/tex]

Substitute values for a, b, n and r in

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

[tex](5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

Solve for [tex]^6C_4[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......[/tex]

Check the list of options for the expression on the left hand side

The correct answer is [tex](5-\frac{1}{2})^6[/tex]

Answer:

583.33 cm³

Step-by-step explanation:

From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:

[tex]\frac{b}{H-h}=\frac{B}{H}\\ b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm[/tex]

The volume of the frustrum is given by:

[tex]V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3[/tex]

Answer:

Step-by-step explanation:

First, we can figure out how many additional inches of rope are needed.  If there are 8 knots, 16 additional inches will be needed. Peter would need 9 feet 4 inches of rope, or 112 inches.

The formula for finding the length of the rope needed would be 8+2n.

Hope this helps!

Answer:

112 inches

Step-by-step explanation:

Each knot needs 2 inches of rope

There are 2 knots

2*8 = 16 inches

He wants 8 ft from the ground, but he wants it in inches

8 ft* 12 inches per foot = 96 inches for the rope

96+ 16 =112 inches of rope

Answer:

7.06

Step-by-step explanation:

17/8 = 15/DF

DF = 7.06

Answer:

The upper bound on the length of a randomly chosen nail from all nails manufactured by the company is 2.004 cm.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\bar x[/tex]

And the standard deviation of the sample means (also known as the standard error) is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

In this case the sample of nails selected is quite large, i.e. n = 100 > 30.

So, the sampling distribution of sample mean length of nails will be approximately normal.

Then according to the Empirical rule, 95% of the normal distribution is contained in the range,

[tex]\mu\pm 2\cdot \frac{s}{\sqrt{n}}[/tex]

Compute the upper bound as follows:

[tex]\text{Upper Bound}=\mu\pm 2\cdot \frac{s}{\sqrt{n}}[/tex]

                     [tex]=2+(2\times\frac{0.002}{\sqrt{100}})\\\\=2+0.0004\\\\=2.004[/tex]

Thus, the upper bound on the length of a randomly chosen nail from all nails manufactured by the company is 2.004 cm.

Answer:

Given that 1 and 4 are vertical asymtotes we have;

(a) -∞

(b) +∞

(c) +∞

(d) -∞

Step-by-step explanation:

(a) For the function;

[tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]

We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)

Therefore, as the function approaches 4 from the left [lim (x → 4⁻)] gives;

[tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(3.999 - 1)\cdot (3.999 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(2.999)\cdot (-0.001)} \right )[/tex][tex]=- \infty[/tex]

(b) Similarly, we have;

[tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]

We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)

Therefore, as the function approaches 4 from the right [lim (x → 4⁺)] gives;

[tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(4.0001 - 1)\cdot (4.0001 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(3.0001)\cdot (0.0001)} \right )[/tex][tex]= +\infty[/tex]

(c)

[tex]\lim_{x\rightarrow 1^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]

We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)

Therefore, as the function approaches 1 from the left [lim (x → 1⁻)] gives;

[tex]\lim_{x\rightarrow 1 ^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 1^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(0.999 - 1)\cdot (0.999 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(-0.001)\cdot (-3.001)} \right )[/tex][tex]=+ \infty[/tex]

(d) As the function approaches 1 from the right [lim (x → 1⁺)]

We have;

[tex]\lim_{x\rightarrow 1^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(1.0001 - 1)\cdot (1.0001 - 4)} \right )[/tex]= [tex]\lim_{x\rightarrow 1^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(0.0001)\cdot (-2.999)} \right ) =- \infty[/tex]

Answer:

C: Jason’s camp counselor job pays a higher hourly rate than Mia’s lifeguard job.

Step-by-step explanation:

given:

y = 9x for Jason

For Mia

Tue  Thu  Sat

6       8      5

Tuesday : 52.50 for 6 hyours   => 8.75 / hour

Thursday :  70.00  for 8 hours  => 8.75 / hour

Saturday :   43.75 for 5 hours   => 8.75 / hour

Solution:

Therefore Mia makes 8.75 / hour

False : The two jobs pay the same hourly rate.

False : The comparison cannot be made with the information given.

True : Jason’s camp counselor job pays a higher hourly rate than Mia’s lifeguard job.

False : Jason’s camp counselor job pays a lower hourly rate than Mia’s lifeguard job.

Answer: C Jason’s camp counselor job pays a higher hourly rate than Mia’s lifeguard job.

Step-by-step explanation:

Answer:

b = 30

Step-by-step explanation:

-5=-1/6b

Multiply each side by -6 to isolate b

-5 * -6 = -6 * -1/6 b

30 = b