The unit cube is divided into identical rectangular prisms. What is the volume of one of the identical prisms?

Answer:

The angles are 13.7 degrees and 76.3 degrees

Step-by-step explanation:

Let the complementary angle be x

When two angles are complementary, they add up to 90 degrees

So if one is x , the other would be (x-62.6) as stated by the question

so, adding this two will give 90 degrees

We have this as;

x + x -62.6 = 90

2x = 90 + 62.6

2x = 152.6

x = 152.6/2

x = 76.3

The other angle will be;

76.3 -62.6 = 13.7

I'll help.

A student needs 15 minutes to solve an algebra problem. How many minutes does the student need to solve 5 problems?

it's easy, you only need to divide 15 by 5.

Like this :

15÷5= 3

• because 5×3 = 15 , so you just need to flip it over

so, the student need 3 minutes to solve 5 problems

Given:

Total number of marbles = 26

Number of blue marbles = 13

Number of red marbles = 10

Number of yellow marbles = 3

To find:

The probability of getting a blue marble then a red marble (without replacement).

Solution:

Total number of marbles = 26

Number of blue marbles = 13

Probability of getting a blue marble is first draw is:

[tex]P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}[/tex]

[tex]P(Blue)=\dfrac{13}{26}[/tex]

[tex]P(Blue)=\dfrac{1}{2}[/tex]

After drawing 1 marble, the remaining number of marbles in the bag is 25.

Probability of getting a red marble is second draw is:

[tex]P(Red)=\dfrac{\text{Number of red marbles}}{\text{Remaining number of marbles}}[/tex]

[tex]P(Red)=\dfrac{10}{25}[/tex]

[tex]P(Red)=\dfrac{2}{5}[/tex]

Now the probability of getting a blue marble then a red marble (without replacement) is:

[tex]P(\text{Blue then red})=P(Blue)\times P(Red)[/tex]

[tex]P(\text{Blue then red})=\dfrac{1}{2}\times \dfrac{2}{5}[/tex]

[tex]P(\text{Blue then red})=\dfrac{1}{5}[/tex]

Therefore, the probability of getting a blue marble then a red marble (without replacement) is [tex]\dfrac{1}{5}[/tex].

Answer:

50.27

Step-by-step explanation:

remember that the circumference of a circle is 2πr

so 3.15x8 and then multiply by two

Answer:

200.96 ft²

Step-by-step explanation:

Step 1: Define/formula

To find the area of a circle, multiply the radius by itself twice, then multiply the product by pi.

[tex]a=\pi r^2(3.14*radius*radius)[/tex]

Step 2: Solve

According to the word problem, the radius is 8.

From here, we plug the numbers into the formula.

[tex]\pi 8^2(3.14*8*8)=200.96ft^2.[/tex]

Step 3: Conclude

Therefore, the area of this circle is 200.96 ft.²

Answer:

y = -27.6

Step-by-step explanation:

To solve for y, you need to isolate the variable on one side of the equation. [tex]5(y+25)=-13[/tex] ⇒ [tex]y + 25 = -2.6[/tex] ⇒ [tex]y = -27.6[/tex].

Answer:

-27.6

Step-by-step explanation:

[tex]5(y + 25) = -13[/tex]

First, distribute the problem.

[tex]5y + 125 = -13[/tex]

Secondly, subtract 125 from -13 and 125.

[tex]125 - 125 = 0[/tex]

[tex]-13 - 125 = -138[/tex]

Now, we are left with 5y = -138.

Lastly, we divide -138 by 5.

[tex]-138 / 5 = -27.6[/tex]

Therefore, y is -27.6.

Here's an attachment to make this explanation clearer.

Answer:

352.

Step-by-step explanation:

The product will have 45 digits, the fisrt and last digit will be 4 and the middle 43 will be 8.

So the sum = 2*4 + 43*8

= 352.

Answer:

answer: 12

Step-by-step explanation:

You get 12 by doing base × height. So our base in this problem is 2.5 and our height is 4.8 so

2.5 × 4.8 = 12 Hope this helps!

Answer:

g. 92*

h. 88*

m. 89*

k. 91*

Step-by-step explanation:

To find h and m: All of the angles on a straight line added up equals 180*. So if there are two angles, the sum of them must equal 180* (angle A + angle B = 180*)

So in this case we have angle h + 92* = 180* using algebra, we subtract 92 from both sides and we get angle h = 88*

If you want to check, add 92 + 88 = 180.

Also angle m + 91* = 180*. Same thing as above, subtract 91 from both sides and we get angle m = 89*

If you want to check, add 91 + 89 = 180.

When you have two straight lines intersecting (crossing), the opposing angles at that crossing are going to be equal. So in this case angle g is opposite from the anbgle that we know is 92*, so angle g is also 92*. Same thing for angle k, we know the angle opposite angle k is 91*, so we know that angle k is also 91*.

Answer:

3

Step-by-step explanation:

[tex]4^{(x+2)} = 48 \\ \\ {4}^{x} . {4}^{2} = 16.3 \\ \\ {4}^{x} . \cancel {16} = \cancel {16} .3 \\ \\ {4}^{x} = 3[/tex]

Answer:

80

Step-by-step explanation:

110-180=70

30+70=100

100-180=80

Answer:

I think the answer is 80

Step-by-step explanation:

[tex]\text{State Income Tax Rate: }6.65\%, \\\text{Deduction: }\$7,702.03[/tex]

Answer:

State income tax: [tex]6.65\%[/tex]

Step-by-step explanation:

Based on the interface, it seems like you have chosen lawyer as a career with the given salary of $115,820.

The chart given for state income tax is broken into two categories:

$21,400-$80,650 => 6.45%

$80,651-$215,400 => 6.65%

Since the chosen career's salary is $115,820, the career falls into the second range of 6.65% state income tax.

The deduction is simply the amount of money taxed. For a 6.65% state income tax, the deduction can be found from:

[tex]115,820\cdot 0.0665=\boxed{\$7,702.03}[/tex]

Answer:

x = 51.5

Step-by-step explanation:

Answer:

the answer is 0

hope it helps have a nice dayyy

The right box plot that summarizes the data should look like the one constructed below in the diagram attached.

We are given the data set 25, 28, 29, 29, 30, 34, 35, 35, 37, and 38, which are already in order and we need to derive the min, max, median, Q1, and Q3 from the given data set. We need all of these values to construct a box plot to summarize the data.

Now, we will find the minimum value which is 25. The maximum value in the data set is 38. The median is the middle value of the data set and it will lie between the 5th and the 6th data points. The average of both values would give us our median data point = (30 + 34) ÷ 2 = 32

Our Q1 would be the middle data point of the bottom half of the data set which is 29. Q3 would be the middle data point of the top half of the data set = 35. As we have derived these values, we can now construct a box plot to summarize the given data.

Therefore, the right box plot that summarizes the data should look like the one constructed below in the diagram attached.

To learn more about box plots;

https://brainly.com/question/14277132

#SPJ1

Answer:

b = 5

Step-by-step explanation:

This triangle is a 30 - 60 - 90 special right triangle

As you can see in the image provided below the longer leg is equal to the short leg times √3

This means that the short leg is equal to the long leg divided by √3

Thus, b = [tex]\frac{5\sqrt{3} }{\sqrt{3} }[/tex] which is equivalent to 5

Answer:

m<RPQ = 22°

Step-by-step explanation:

Given:

m<SRQ = 90°

PS = PQ

m<SQR = 46°

Required:

m<RPQ

Solution:

m<SQR + m<SRQ + m<RSQ = 180°

Substitute

46° + 90° + m<RSQ = 180°

m<RSQ = 180° - 136°

m<RSQ = 44°

Find m<PSQ:

m<PSQ = 180° - m<RSQ (Angles on a straight line

m<PSQ = 180° - 44° (Substitution)

m<PSQ = 136°

Find m<RPQ:

∆QSP is an isosceles triangle with two equal base angles. Therefore:

m<RPQ = ½(180° - 136°)

m<RPQ = 22°

the answer is F

or x=3

Hope this helped!

Answer:

8×ED=3×15

ED=45/8

the radius is the half of the diameter

so its 45/16

Answer:

[tex] \frac{ae}{be} = \frac{ce}{de} = \frac{bc - be}{ad - ae} \\ \\ = > \frac{8}{3} = \frac{15 - 3}{ad - 8} \\ \\ < = > \frac{8}{3} = \frac{12}{ad - 8} \\ \\ = > ad - 8 = \frac{12 \times 3}{8} = 4.5 \\ \\ < = > ad = 4.5 + 8 = 12.5 \\ \\ = > r = 12.5 \div 2 = 6.25[/tex]

Answer:

20 cups of applesauce

Step-by-step explanation:

8 ounces = 0.5 pounds

Pounds of apples : cups of applesauce

0.5 pounds : 1 cup = 10 pounds : x cups

0.5/1 = 10/x

0.5*x = 1*10

0.5x = 10

x = 10/0.5

x = 20 cups of applesauce

10 pounds of apples will make 20 cups of applesauce

Answer:

60%

Step-by-step explanation:

Im almost positive this is right if not sorry have a blessed day :)

Answer:

76

Step-by-step explanation:

n a competitive exam of 40 questions, +3 is awarded for a correct answer and -1 for every wrong answer. Find the total score if a student had 11 wrong answers in his attempt of all questions.

Answers gotten wrong = 11

answers gotten right = 40 - 11 = 29

total score = (point for correct answer x number of correct answer) +  (point for wrong answer x number of wrong answer)

(+3 x 29) + (-1 x 11) = 76

Answer:

[tex] \displaystyle GH = 2 \sqrt{30} [/tex]

[tex] \displaystyle FH = 2 \sqrt{10} [/tex]

[tex] \displaystyle m \angle G = {30}^{ \circ} [/tex]

Step-by-step explanation:

we are given a right angle triangle

it's a 30-60-90 triangle of which FH is the shortest side

remember that,in case of 30-60-90 triangle the the longest side is twice as much as the shortest side thus

our equation is

[tex] \displaystyle 2FH=4\sqrt{10}[/tex]

divide both sides by 2

[tex] \displaystyle\frac{2FH}{2}= \frac{ 4 \sqrt{10} }{2}[/tex]

[tex] \displaystyle FH =2 \sqrt{10}[/tex]

in order to figure out GH we can use Trigonometry because the given triangle is a right angle triangle

as we want to figure out GH we'll use sin function

remember that,

[tex] \displaystyle \sin( \theta) = \frac{opp}{hypo} [/tex]

let our opp, hypo and [tex]\theta[/tex] be GH, 4√10 and 60° respectively

thus substitute:

[tex] \displaystyle \sin( {60}^{ \circ} ) = \frac{GH}{4 \sqrt{10} } [/tex]

recall unit circle:

[tex] \displaystyle \frac{ \sqrt{3} }{2} = \frac{GH}{4 \sqrt{10} } [/tex]

cross multiplication:

[tex] \displaystyle 2 GH = 4 \sqrt{10} \times \sqrt{3} [/tex]

simplify multiplication:

[tex] \displaystyle 2 GH = 4 \sqrt{30} [/tex]

divide both sides by 2:

[tex] \displaystyle GH = 2 \sqrt{30} [/tex]

Recall that, the sum of the interior angles of a triangle is 180°

therefore,

[tex] \displaystyle m \angle G + {60}^{ \circ} + {90}^{ \circ} = {180}^{ \circ} [/tex]

simplify addition:

[tex] \displaystyle m \angle G + {150}^{ \circ} = {180}^{ \circ} [/tex]

cancel 150° from both sides

[tex] \displaystyle m \angle G = {30}^{ \circ} [/tex]

Answer:

26.563, 1.977

Step-by-step explanation:

I will be honest I'm not 100% sure but i believe that the total distance all together is 26.563. I simply added all the distances.

Jada ran 1.977 miles further than Noah.

I'm so sorry if im wrong hope this helps though <3

Answer:

Option 3

Step-by-step explanation:

We need to simpify the given expression. The given expression to us is ,

Given Expression :-

[tex]\sf\implies \dfrac{ cos^2\theta -1}{4 \ sin^2\theta }[/tex]

Using Identity :-

[tex]\sf\implies \red{ sin^2\theta + cos^2\theta = 1}[/tex]

So that :-

[tex]\sf\implies - sin^2\theta = cos^2\theta -1[/tex]

We have :-

[tex]\sf\implies \dfrac{ cos^2\theta -1}{4 \ sin^2\theta } \\\\\sf\implies\dfrac{ - sin^2\theta}{4sin^2\theta}=\boxed{\sf -\dfrac{1}{4}} [/tex]

Hence the required answer is -1/4.