A cylinder shaped storage tank has a radius of (x+5) metres and a height of x metres. Determine the dimensions (round to two decimal places) of the tank if the volume is about 192 cubic metres.

Answer:

5, 10, 15, 20, 25 table.

Step-by-step explanation:

So the top table, for sure has a much more consistent, and or constant variable. That just means that the numbers are continuously being put into the table at the right amount, speed, etc. As it is increasing, your y is constant, and x remains in the appropraite way!

5, 10, 15, 20, 25..

It is very good.

Hope that helped.!

Answer:

First

Step-by-step explanation:

● tan 30° = opposite/adjacent

Let x be the missing hight

● tan 30° = x/15

Multiply both sides by 15

● tan 30° *15 = (x/15)*15

● tan 30°*15 = x

● x = 8.66 wich is approximatively 5×√(3)

Answer:  D) CPCTC

Step-by-step explanation:

step 6 proves the triangles are congruent.

step 7 states that if the triangles are congruent, then parts of the triangle are congruent.

Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Answer:

3x³ - 15x² + 18x

Step-by-step explanation:

Given

3x(x² - 5x + 6) ← distribute the parenthesis by 3x

= 3x³ - 15x² + 18x ← in standard form

Answer: the graph farthest to the right is almost correct. If you substitute values for x in the function f(x)= -3√x , the output does not match the curve on the graphs shown.

If you have a choice that includes only a curve to the right of the y- axis, that would be better.

Step-by-step explanation: Square roots of Negative x-values will result in imaginary numbers. Otherwise the graph with the curve passing through coordinates (1,-3) (4,-6) and (9,-9) is a good choice.

(And ask your teacher about the square root of negative numbers on this graph.)

Answer:

0.375

Hope this helps....

Have a nice day!!!!

Answer:

3/8

Step-by-step explanation:

Hey there!

[tex]\frac{3}{8} = \frac{3*8+3}{8} = \frac{24 + 3}{8} = \frac{27}{8}[/tex]

[tex]\frac{27}{8} = \frac{27 / 9}{8} = \frac{3}{8}[/tex]

= 3/8

Hope this helps :)

Answer:

x = 4 or x = - [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Given

(2x - 8)(7x + 5) = 0

Equate each factor to zero and solve for x

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4

7x + 5 = 0 ⇒ 7x = - 5 ⇒ x = - [tex]\frac{5}{7}[/tex]

Answer:

0.00375

Step-by-step explanation:

The money factor for a lease is used to determine how much is charged monthly on a lease payment. If the money factor is low, the lease payment is low making it a good transaction but if the money factor is high, the lease payment is also high and this is not desirable. The money factor is given by:

Money factor = Interest rate / 2400

Given an interest rate of 9%, the money factor is calculated as:

Money factor = Interest rate / 2400 = 9% / 2400 = 0.00375

Answer:

Take a line segment AB = 2 units (consider 1 unit = 2 cm) on x-axis.

Draw a perpendicular on B and construct a line BC = 1 unit length.

Join AC which will be √5 (Pythagoras theorem). Take A as center, and AC as radius draw an which cuts the x-axis at point E.

The line segment AC represents √5 unit

Answer:

x = 2

Step-by-step explanation:

5x = 10

x = 2

Answer:

x = 2

Step-by-step explanation:

5x-10=0

Add 10 to each side

5x-10+10=0+10

5x = 10

Divide by 5

5x/5 = 10/5

x = 2

Answer:

a) Because the confidence interval  does not include  0​ it appears that there

is  a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

b)There is​ 95% confidence that the interval from  −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2

c)   1.62 < μ1−μ2< 1.76

Step-by-step explanation:

a) What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men?

Given:

95% confidence interval for the difference between the two population​ means:

−1.76g/dL< μ1−μ2 < −1.62g/dL

population 1 =  measures from women

population 2 =  measures from men

Solution:

a)

The given confidence interval has upper and lower bound of 1-62 and -1.76. This confidence interval does not contain 0. This shows that the population means difference is not likely to be 0. Thus the confidence interval implies that the mean hemoglobin level in women and the mean hemoglobin level in​ men is not equal and that the  women are likely to have less hemoglobin than men. This depicts that there is significant difference between mean hemoglobin level in women and the mean hemoglobin level in​ men.

b)  

There is​ 95% confidence that the interval −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2.

c)

If we interchange men and women then

                                          1.62 g/dL<μ1−μ2<1.76 g/dL.

There is a significant difference between the mean level of hemoglobin in women and in men.

The confidence interval of the mean is given as:

[tex]-1.76 g/dL < \mu_1-\mu_2 < -1.62 g/dL[/tex]

The above confidence interval shows that the confidence interval is exclusive of 0.

This means that 0 is not part of the confidence interval

Since the confidence interval is exclusive of 0, then there is a significant difference between the mean level of hemoglobin in women and in men.

Read more about confidence intervals at:

https://brainly.com/question/17097944

Answer:

12 gallons

Step-by-step explanation:

Given the following :

Total amount of gas used by aircraft = 51 gallons

Flight departure time = 9:30 a.m

Arrival time of flight = 1:45p.m

Number of hours traveled by flight:

Arrival time - Departure time

1:45pm - 9:30a.m = 4hrs 15 minutes = [(60*4)+15] minutes = 240 + 15 = 255 minutes

Amount of gallons used per hour :

255 minutes = 51 gallons

I minutes = x

255x = 51 gallons

x = 51 / 255

x = 0.2 gallons

0.2 gallons per minute

1 hour = 60 minutes

Number of gallons per hour = (0.2 * 60) = 12 gallons

Answer:

5/18

Step-by-step explanation:

There are 36 possible outcomes

There are 6 with a 2 as the first roll

There are 4 with a sum of 9

P( sum is 9 or that the first number is a 2)

                        =  sum is 9 or that the first number is a 2/total

                           ( 6+4) / 36

                          =10/36

                           =5/18

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

Explanation:

The information about angle 2 is unnecessary info that your teacher likely put in there as a distraction. All we need is angle 8, which is 124 degrees. Angle 7 adds to this to form a 180 degree straight angle.

(angle 7) + (angle 8) = 180

(angle 7) + 124 = 180

angle 7 = 180 - 124

angle 7 = 56 degrees

Answer:

The measure of angle 7 is 56°.

Step-by-step explanation:

here, angle 8 = 124°

now, angle 8+ angle 7=180° (as the sum of linear pair is 180°)

or, 124°+angle 7=180°

or, angle 7=180°-124°

Therefore, tge measure of angle 7 is 56°.

Hope it helps.

Answer:

60.75

Step-by-step explanation:

sinA    sinB

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

a           b

sin(79)/9 = sinB/8

inverse sin B = 0.87

B = 60.75

Answer:

  2.86 seconds

Step-by-step explanation:

A graphing calculator shows the ball hits the ground at t = 2.86 seconds.

_____

You can use the quadratic formula with a=-16, b=45, c=2:

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-45\pm\sqrt{45^2-4(-16)(2)}}{2(-16)}=\dfrac{45\pm\sqrt{2153}}{32}\approx\{-0.0438,2.8563\}[/tex]

The ball is in the air for about 2.86 seconds.

Answer: Pam's total salary is $41666.666

Step-by-step explanation:

Assume her total earning or salary per year = y

Personal expenses spent yearly = $7500

Personal expenses yearly ($7500) = 18% of y

100%y =

18% of y = 7500

(18/100)y = $7500

100% y = Total salary

0.18y = $7500 - - - - - - - (1)

1y = Total salary

(Total salary * 0.18y) = (7500 * y)

Total salary = 7500y / 0.18y

Total salary = 7500/0.18

Total salary = $41666.666

Answer:

Real interest rate = -1%

Step-by-step explanation:

Real interest rate=Nominal interest rate - inflation rate

From the above,

Nominal interest rate=1%

Inflation rate=2%

Real interest rate=Nominal interest rate - inflation rate

=1% - 2%

= -1%

Real interest rate = -1%

Real interest rate shows you what it really costs borrowers to pay back their loans.

if the real interest rate is greater than zero, the amount you pay back is worth more in real terms than the money you borrowed.

if the real interest rate is below zero as in the above case, the amount you will pay back is less worth in real terms than the money you borrowed.

Answer:

Bags = 22

Hat = 14

22 x 2 = 44

14 x 4 = 56

So the first part is true

3 x 22 = 66

7 x 14 = 98

So the second part is true

14 is the answer

It's trial and error

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

12 ÷ 1 1/5

Change to an improper fraction

12 ÷ ( 5*1+1)/5

12 ÷ 6/5

Copy dot flip

12 * 5/6

12/6 * 5

2*5

10

Answer:

10

Step-by-step explanation:

12 ÷ 1 1/5

Change into an improper fraction.

12 ÷ 6/5

Reciprocal and it becomes multiplication.

12 × 5/6

60/6

= 10

Answer:

P(AB) = 837/9100

Step-by-step explanation:

The given parameters are;

The number of marbles in the bag = 100 marbles

The number of red marbles = 27

The number of green marbles = 42

The number of blue marbles = 100 - 27 - 42 =  31

The probability, A of drawing a blue marble = 31/100

The probability,B of drawing a red marble after a blue marble has been taken without replacement = 27/91

The probability P(AB) = 31/100× 27/91 = 837/9100

The probability that Eric randomly draws two marbles without replacing the first one where the first one is a blue marble and the second marble is a red marble is 837/9100.

Answer:

[tex]h=13\,\sqrt{3}[/tex]

[tex]x=52[/tex]

Step-by-step explanation:

Using the triangle formed in the far left, we can use the Pythagorean theorem to solve for h:

[tex]h^2+a^2=y^2\\h^2+39^2=(26\,\sqrt{3} )^2\\h^2=26^2\,(3)-39^2\\h^2=507\\h=\sqrt{507}\\h=13\,\sqrt{3}[/tex]

Now, using the right angle triangle on the right we solve for x:

[tex](x-a)^2+h^2=z^2\\(x-39)^2+507=26^2\\(x-39)^2=676-507\\(x-39)^2=169\\x-39=+/-13\\x=26\,\,\,or\,\,\,x=52[/tex]

since x has to be larger than "a" (39), we use the second answer:

[tex]x=52[/tex]

The correct answer is D. [tex]72 \pi[/tex] [tex]units^{2}[/tex]

Explanation:

The surface area refers to the sum of the area of all sides in a 3D shape such as a cube or cylinder. Additionally, the formula used to calculate the surface area varies with the shape. In the case of cylinders, the general formula is [tex]A = 2\pi r h + 2\pi r^{2}[/tex]. Moreover in this, the r represents the radius (measure from the center of a circle to any side), while the h represents height. Below, all the process is shown:

[tex]A = 2\pi r h + 2\pi r^{2}[/tex]

[tex]A = 2\pi (8 x 3) + 2\pi 8^{2}[/tex]

[tex]A = 2\pi 24 + 2\pi 64[/tex]

[tex]A = 48\pi + 128\pi[/tex]

[tex]A = 176\pi[/tex]

In this point, you have the answer without solving [tex]\pi[/tex] (3.1416). This makes option A the correct answer.

Answer:

m∠B = 60°

b = 26 units

c = 30 units

Step-by-step explanation:

In a right triangle ACB,

By applying Sine rule,

[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{SinC}{c}[/tex]

m∠A = 30°, m∠C = 90°

m∠A + m∠B + m∠C = 180°

30° + m∠B + 90° = 180°

m∠B = 180° - 120°

m∠B = 60°

Therefore, [tex]\frac{\text{Sin30}}{15}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]

[tex]\frac{1}{30}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]

[tex]\frac{1}{30} =\frac{1}{c}=\frac{\frac{\sqrt{3}}{2}}{b}[/tex]

[tex]\frac{1}{30}=\frac{1}{c}=\frac{\sqrt{3}}{2b}[/tex]

[tex]\frac{1}{30} =\frac{1}{c}[/tex] ⇒ c = 30 units

[tex]\frac{1}{30}=\frac{\sqrt{3}}{2b}[/tex]

b = 15√3

b = 25.98

b ≈ 26 units

Answer:

[tex] slope (m) = -\frac{3}{2} [/tex]

Step-by-step explanation:

We can find the slope (m) by using coordinate pairs of any 2 points located along the slope of the line that we have on the graph.

This, let's use the coordinate pairs at:

x = -4, y = 2 (-4, 2) => (x2, y2)

x = 0, y = -4 (0, -4) => (x1, y1)

[tex] slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex] slope (m) = \frac{2 -(-4)}{-4 - 0} [/tex]

[tex] slope (m) = \frac{2 + 4}{-4 - 0} [/tex]

[tex] slope (m) = \frac{6}{-4} [/tex]

[tex] slope (m) = \frac{3}{-2} [/tex]

[tex] slope (m) = -\frac{3}{2} [/tex]

Answer:

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

Step-by-step explanation:

The interior angle of a regular heptagon = = 900/7° = 128.57°

Therefore, angle DAB = 128.57°

The interior angle of the square = 90°

Therefore, angle DAC = 90°

Therefore, we have

angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))

Angle BAC = 360° - angle DAB - angle DAC =  360° - 900/7° - 90° = 990/7°

Angle BAC = 141.43°

Expressing 141.43° as a common fraction gives;

[tex]141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}[/tex]

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

 The degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex]

Given, A square and a regular heptagon are coplanar as shown in below figure attached.

We have find the exterior angle of BAC.

We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,

[tex]\frac{180(n-2)}{n}[/tex]  where n is the number of sides.  

Since the heptagon has 7 no. of sides.

So regular heptagon's interior angle measures,

[tex]\frac{180(7-2)}{7}=128\frac{4}{7}[/tex]

Hence [tex]\angle A[/tex] will be[tex]128\frac{4}{7}[/tex] degrees.

We know that a square's interior angle is 90 degrees and a heptagon's interior angle is  128.57 degrees. We will subtract those from 360 degrees to find angle BAC.

[tex]\angle BAC = 360 - (\angle A + 90)\\[/tex]

[tex]\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ[/tex]

Hence the degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex].

For more details on Exterior angle follow the link:

https://brainly.com/question/2125016            

Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

Step-by-step explanation:

Notice that the cone and the pyramid have the same volume. This is important.

This follows the Cavalieri's principle that, for the case of 3 dimensions, as the present case, it states, roughly, that if we have two bodies like the cone and the pyramid, and if we have parallel planes crossing each section, and we always have the same area, these two bodies have the same volume.

In this case, both, cone and pyramid have the same volume, then (reciprocally):

B. The horizontal cross-sections of the prisms at the same height have the same area.

Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

Step-by-step explanation:

ap333x

Answer:

74°

Step-by-step explanation:

A rhombus is a quadrilateral (has four sides). For a rhombus: opposite sides are equal, opposite angles are equal, all the sides are equal, the diagonals bisect each other, adjacent angles are supplementary, diagonals bisect the angles.

From the diagram below since adjacent angles of a rhombus are supplementary therefore:

32° + 2∠1 (diagonals bisect the angles) = 180

2∠1 = 180 - 32

2∠1 = 148

∠1 = 148 / 2

∠1 = 74°

Answer:

(x - y)(x + y)(x - 2y)(x + 2y)

Step-by-step explanation:

Given

[tex]x^{4}[/tex] - 5x²y² + 4[tex]y^{4}[/tex]

Consider the factors of the coefficient of the [tex]y^{4}[/tex] term (+ 4) which sum to give the coefficient of the x²y² term (+ 5)

The factors are - 1 and - 4 , thus

[tex]x^{4}[/tex] - 5x²y² + 4[tex]y^{4}[/tex]

= (x² - y²)(x² - 4y²)

Both of these factors are differences of squares which factor in general as

a² - b² = (a - b)(a + b) , so

x² - y² = (x - y)(x + y)

x² - 4y²

= x² - (2y)² = (x - 2y)(x + 2y)

Hence

[tex]x^{4}[/tex] - 5x²y² + 4[tex]y^{4}[/tex]

= (x - y)(x + y)(x - 2y)(x + 2y) ← in factor form

Answer: a

Step-by-step explanation:

substitute the coordinate values for x and y

y<3x+3, (1,-5)

-5<3(1)+3

-5<3+3

-5<6

the coordinate (1,-5) works, so a is the answer