Drayton is an artist and will paint all six faces of the rectangular prism shown below. the numbers are 12.5, 10, and 8.5 What is the total surface area of this prism in square inches? 382.5 in.2 462.5 in.2 632.5 in.2 1,062.5 in.2

Answer:

Step-by-step explanation:

When the stick is placed along the diagonal  of the cuboid , shortest possible length will extend out above top of the crate .

Length of the diagonal

= [tex]\sqrt{36^2+36^2+60^2}[/tex]

= 78.69 cm

the length of the stick that extends out of the crate

= 90 - 78.69

= 11.31 cm

If θ be the angle made by stick with the base

cosθ = hypotenuse of base / diagonal of cuboid

=[tex]\frac{\sqrt{2}\times36 }{78.69}[/tex]

= [tex]\frac{50.90 }{78.69}[/tex]

θ = 50°

Answer: This is the answer to B) 47.9 degrees

Step-by-step explanation:

Pythagoras: a^2+b^2=c^2

36²+36²=C²

√2592=C

C=50.9cm

Used Trigonometry: SOH CAH TOA

Tan=Opposite/Adjacent

Tan=60/50.9

The angle stick makes when it meets the base:

Tan^-1(60/50.9)

=49.7˚

Answer:

Option B.

Step-by-step explanation:

The general equation of best fit line is

[tex]y=ax+b[/tex]

where, a is the slope of best fit line and b is y-intercept.

Using graphing calculator a=-4.54762 and b=43.7143. So equation of best fit line is

[tex]y=-4.54762x+43.7143[/tex]

Here,

[tex]Slope=-4.54762[/tex]

[tex]Slope\approx -4.5[/tex]

Note: In alternate method, you can use the below formula to find slope.

[tex]m=\dfrac{\overline{x}\cdot \overline{y}-\overline{xy}}{(\overline{x})^2-\overline{x^2}}[/tex]

Therefore, the correct option is B.

Answer:

B: -4.5

Step-by-step explanation:

edg2021

y ≈ -4.548x + 43.714 is the entire equation. So -4.548 or -4.5 is the slope.

Answer:

The correct option is;

2.81

Step-by-step explanation:

The critical value [tex]Z_{\alpha /2}[/tex], is found from the z score table as follows, where the the confidence level is 99.5

Therefore, we have α = 1 - 99.5/100 = 1 - 0.995 = 0.005

α/2 = 0.0025

The critical value is thus found from the z-score table value of 1 - 0.0025 = 0.9975

From the z-table, we can find the 0.9975 score on the row  with z = 2.8 where 0.9975 can be located under the 0.1 column giving the critical value as 2.81

Answer:

The answer is - 4x² + 8x - 8

Step-by-step explanation:

ƒ(x) = 3x – 1

g(x) = 4x2 – 5x + 7

(ƒ – g)(x) = 3x - 1 - ( 4x² - 5x + 7)

That's

3x - 1 - 4x² + 5x - 7

Group like terms

- 4x² + 3x + 5x - 1 - 7

The final answer is

- 4x² + 8x - 8

Hope this helps you.

Answer:

39.936 ( not rounded )

Step-by-step explanation:

Use Pythagorean theorem

a^2 + 6.4^2 = 9^2

height = 6.24 (rounded to nearest hundredth)

1/2 * base * height = area

1/2 * 12.8 * 6.24

= 39.936 ( not rounded )

Answer:

see explanation

Step-by-step explanation:

(a)

Given that y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition y = 8 when x = 10. then

8 = 10k ( divide both sides by 10 )

0.8 = k

y = 0.8k ← equation of proportion

(b)

when x = 25, then

y = 0.8 × 25 = 20

(c)

when y = 25, then

25 = 0.8x ( divide both sides by 0.8 )

x = 31.25

Answer:

I agree with your answer C!!

Step-by-step explanation:

Answer:

5√17=

20.6

Step-by-step explanation:

[tex]adj \: = 5 \\ opp \: = 20 \\ hyp \: = \: \\ pythagoras \: theorem \: \: = \\ {hyp}^{2} = {opp}^{2} + {adj}^{2} [/tex]

[tex] {hyp \:}^{2} = {20}^{2} + {5}^{2} \\ {hyp }^{2} = 400 + 25 \\ {hyp}^{2} = 425 \\ \sqrt{ {hyp}^{2} } = \sqrt{425} [/tex]

[tex]hypotenuse \: = 5 \sqrt{17} [/tex]

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the tree is 20.6257 feet.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The digram for the given condition is given below. Now, in ΔABC, the tangent value for ∠A can be written as,

tan(38°) = BC/AB

tan(38°) = 5 feet / AB

AB = 6.3997 feet

Now, in ΔABC and ΔADE for ∠A the value of the tangent can be written as,

tan(38°) = BC/AB = ED/AD

5/6.3997 = ED/(20 + 6.3997)

ED = 20.6257 feet

Hence, the height of the tree is 20.6257 feet.

Learn more about Tangent (Tanθ):

https://brainly.com/question/10623976

#SPJ2

Answer:

a, No

Step-by-step explanation:

We can just substitute the numbers (x, y) into the inequality to see if the inequality is valid.

y=40

5(4) + 8 = 28

"<" means the number on the left is smaller than the number on the right.

40 is not smaller than 28, so in this inequality,

(4, 40) is not valid in y<5x+8

Answer:

She deposited £10,000 in the 5% yield account and deposited £20,000 in the 8% yield account

Step-by-step explanation:

Let the amount she put in each account be £x and £y respectively

Total amount deposited is ;

x + y = 30,000 ••••••(i)

Now, let’s look at the earnings:

in the £x , amount earned would be;

5/100 * x = 5x/100

For the £y, amount earned would be;

8/100 * y = 8y/100

Adding both gives the total which is £2,1000

5x/100 + 8y/100 = 2,100

Multiply through by 100

5x + 8y = 210,000 ••••••••(ii)

From the first equation, we know that

x = 30,000 -y

Let’s put this into the second

5(30,000-y) + 8y = 210,000

150,000-5y + 8y = 210,000

3y = 210,000 -150,0000

3y = 60,000

y = 60,000/3

y = £20,000

So mathematically;

x = 30,000-y

x = 30,000 -20,000

x = £10,000

Answer:

0.4 ; 0.8

Step-by-step explanation:

Given that :

y varies jointly as x and z and inversely as the square of w

y ∝ xz ∝ 1/w^2

y = kxz/w^2 - - - - (1)

Given that y =3 when x=3, z=10, w=2

Inputting the values into (1)

3 = (k*3*10) / 2^2

3 = 30 × k / 4

k × 30 = 3 × 4

k × 30 = 12

k = 12/30

k = 0.4

B.) Given that ;

y=4 when x=4 z=20 w=4

Input values into (1)

y = kxz/w^2

4 = ( k * 4 * 20) / 4^2

4 = (k * 80) / 16

k * 80 = 16 * 4

k * 80 = 64

k = 64 / 80

k = 0.8

Answer:

False

Step-by-step explanation:

Took the test and got it wrong

Answer:

$60.42

Step-by-step explanation:

0.06 x $57 = $3.42

$57 + $3.42 = $60.42

Hope this helped! :)

Answer:

Its -3,2,7

Step-by-step explanation:

Simply put, you plug in all values greater than -2. Which is what thst function tells you.

Answer:

Sushil got 15 sweets

Step-by-step explanation:

we can use law of indices property as shown below

a:b:c = ax:bx:cx

that if we multiply each term of ratio by same number , the ratio does not change

____________________________

given

Malachy, Sushil and Fiona share some sweets in the ratio 1:3:1.

let

Malachy gets 1x sweets

sushil gets 3x sweets

Fiona gets 1x sweets

but given that

Malachy got 5 sweets

thus

1x = 5

x = 5

Sushil got 3x sweets = 3*5 = 15 sweets.

Sushil got 15 sweets.

Answer:

58°C

Step-by-step explanation:

Heat absorbed by hot water + heat absorbed by cold water = 0

m₁C₁ΔT₁ + m₂C₂ΔT₂ = 0

(300 g) (4.184 J/g/K) (T − 90°C) + (200 g) (4.184 J/g/K) (T − 10°C) = 0

(300 g) (T − 90°C) + (200 g) (T − 10°C) = 0

(300 g) (T − 90°C) = -(200 g) (T − 10°C)

3 (T − 90°C) = -2 (T − 10°C)

3T − 270°C = -2T + 20°C

5T = 290°C

T = 58°C

Answer:

9x9

Step-by-step explanation:

Divide 108/12

108/12=9

you have a 9x9 photo

hope this helps!

Answer:   e

Step-by-step explanation: 12/16          6/8    3/4

Answer:

B and E.

Step-by-step Explanation:

B: 6/8

    6*2=12

    8*2=16

    12/16

E: 3/4

    3*4=12

    4*4=16

    12/16

Hope this helps!!!!!

Answer:

1 and 3; 1 and 4; 2 and 3; 2 and 4

Step-by-step explanation:

Adjacent angles are those with a common side and common vertex (corner point). Of your choices, the ones provided above are the ones that meet the needs of adjacent angles.

Answer:

a) green: 0.3

yellow: 0.1

b) 12

Step-by-step explanation:

Unfortunately, I cant write on the table. But, I CAN help you with this question.

Since all probabilities have to add up to one, we can for an equation like this

(where y is yellow)

0.35+0.25+3y+y=1

This simplified is

0.6+4y=1

4y=0.4

So, we now know that green is 0.3, and yellow is 0.1.

For b, we set 0.35x to 14. Dividing gives us:

14/0.35=1400/35=40.

Multiply 0.3 by 40, and you get 12.

Hope this helped!

Answer:

6

Step-by-step explanation:

6 is the answer

? =6

Answer:

6

Step-by-step explanation:

1. 17 * 10 = 170

2. 17 * 4 = 68

3. 170 - 68 = 102

4. 102 / 17 = 6

Answer:

A and B

Step-by-step explanation:

It's definitely not equilateral or isosceles because none of the side lengths are equal. Therefore, it is scalene. Since all of the angles are acute, it's not obtuse or right, therefore it is acute.

Answer: R = {0kg, 59.5kg}

Step-by-step explanation:

When we have a function f(x) = y.

The set of the possible values of x is called the domain of the function, and the set of the possible values of y is called the range of the function,

In this case, we have that:

the plant recycled 4.9kg the first hour, and 7.8 kg per hour after.

So this function can be written as piecewise function, with one part for the first hour, and another part for the time after the first hour.

F(x) = 4.9kg*x if 0h < x ≤ 1h

F(x) = 4.9kg + 7.8kg/h*(x -1) if x ≥ 1h

We use (x - 1) for the second part because if  x = 1 h, we must have the same result in both parts of the function.

Where x is the number of hours.

And we know that the domain is (0hours, 8 hours)

Then the minimum value of y will be:

F(0h) = 4.9kg*0h = 0kg.

And the maximum value in the range will be:

F(8h) = 4.9kg + 7.8kg*7  = 59.5kg

Then the range is:

R = {0kg, 59.5kg}

Answer:

9 weeks ,1kg is equal to 1000grams so 109kg minus 9kg is equal to 100kg

Answer:

A

Step-by-step explanation:

Solving the equation ignoring the greater than equal to sign, you get x is greater than or equal to 54. Greater than implies that the arrow should point to the right and the arrow should start at 54, so the answer is A.

Answer:

A

Step-by-step explanation:

2/3 x ≥ 36

Multiply each side by 3/2

3/2 *2/3 x ≥ 36*3/2

x ≥ 54

Closed circle at 54, line going to the right

Answer:

x<-8

Step-by-step explanation:

x+6<-2

subract 6 from both sides

x+6-6<-2-6

x<-8

Answer:

B = {(5, 3), (−2, −9), (−3, 8), (9, 3)}

Step-by-step explanation:

A function has no repeating inputs (x-values). One input is assigned to exactly one output.

In set 'A', the input of two is repeated.

A = {(2, 7), (1, −5), (7, 2), (2, −9)}

In set 'B', there are no repeating inputs.

Set 'B' is a function.

Brainilest Appreciated.

Answer: 55

Step-by-step explanation:

There are two sides that are equal (5 and 5). That means that this is an isoceles triangle. The unmarked angle and the x angle are equal to each other because isoceles triangles have also have two equal angles. Because every triangle has 180 degrees, that means that all three angles added up should equal 180.

Since the unmarked and x angle are equal you can write the equation out as 180=70+2x. Subtract 70 from both sides to get the variable and nonvariable on different sides.

110=2x. Divide both sides by 2(in order to isolate the variable). X is 55

Hope this helped you:)

Answer:

Step-by-step explanation:

the x-intercepts of the graph are the zeros of the quadratic function