What is 60% of 76???

Answer:

[tex]IG=28.9\ ft[/tex]

Step-by-step explanation:

we know that

In the right triangle GHI

[tex]cos(G)=\frac{IG}{GH}[/tex] ----> by CAH )adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(21^o)=\frac{IG}{31}[/tex]

solve for IG

[tex]IG=cos(21^o)(31)=28.9\ ft[/tex]

see the attached figure to better understand the problem

Answer:

24.6

Step-by-step explanation:

Answer: $1090.80

Step-by-step explanation:

Answer:

$1,090.80

Step-by-step explanation:

Bodily injury; 25/50=$220

Property; 100=$375

Collision deductibles;$250=$185

Comprehensive deductibles;$100=$129

220+375+185+129 = 909

909*1.2=1,090.8

Took the test

Answer: D

Step-by-step explanation: yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of

1/4.

The answer is D

Step-by-step explanation:

because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of

1

4

. The law of large numbers indicates that if an event of probability p is observed repeatedly during independent repetitions, the ratio of the observed frequency of that event to the total number of repetitions approaches p as the number of repetitions becomes arbitrarily large.

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Answer:

-0.125

Step-by-step explanation:

To find the decimal version of the fraction, divide using a calculator or long division.

-1 / 8 = -0.125

Best of Luck!

Answer:

Option A, V = π(7)^2h

Step-by-step explanation:

The formula for the volume of a cylinder:  V = πr^2h

Step 1:  Since the give us diameter we need to find radius

radius = diameter/2

radius = 14/2

radius = 7

Answer:  Option A, V = π(7)^2h

Answer:

A

Step-by-step explanation:

Volume of a cylinder = pi r2 h

Where pi = 3.14

Radius r = diameter/2

Diameter given is 14,

So radius = 24/2 = 7

Height h

Volume = pi(7)^2 h

A.12 grapes, 23 plums

Step-by-step explanation:

1. solve all the equations by multiplying each number by how much each item is worth

2. A: 290 =(12× 5)+(10×23)

B: 100 =(10×5)+(5×10)

C:125 =(5×5)+(10×10)

D:235 =(23×5)+(12×10)

The value of x that satisfies the equation 41 - x = 157 is x = -116.

To solve for x in the equation 41 - x = 157, we need to isolate x on one side of the equation.

Let's go step by step:

Step 1: Start with the given equation.

41 - x = 157

Step 2: Get rid of the constant term on the left side (41) by subtracting it from both sides of the equation.

(41 - x) - 41 = 157 - 41

Simplifying the left side:

41 - 41 - x = 157 - 41

0 - x = 116

Step 3: We have -x on the left side, and we want to solve for x, so we need to get rid of the negative sign in front of x.

To do that, we can multiply both sides of the equation by -1.

When we multiply a number by -1, the sign changes.

(-1) * (-x) = (-1) * 116

Simplifying the left side:

x = -116

Step 4: Now we have found the value of x, which is x = -116.

To verify our solution, we can substitute the value of x back into the original equation and see if it holds true:

41 - (-116) = 157

Simplifying:

41 + 116 = 157

157 = 157

Since both sides of the equation are equal after simplification, our solution x = -116 is correct.

Therefore, the value of x that satisfies the equation 41 - x = 157 is x = -116.

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Answer:

745.12

Step-by-step explanation:

30 x 30 = 900 which is the sign if it were a square

then you subtract the four corner pieces

900 - 4([tex]\frac{1}{2}[/tex](8.8 x 8.8))

900 - 2(77.44)

900 - 154.88

= 745.12

Let the two numbers be [tex]x,y[/tex].

We have

[tex]\begin{cases}x+y=-\frac{1}{3}\\x-y=18\end{cases}[/tex]

From the second equation, we derive [tex]x=18+y[/tex]

Plugging this value in the first equation, we have

[tex]18+y+y=-\dfrac{1}{3} \iff 2y=-\dfrac{1}{3}-18\iff 2y=-\dfrac{55}{3} \iff y=-\dfrac{55}{6}[/tex]

And we derive

[tex]x=18+y=18-\dfrac{55}{6}=\dfrac{53}{6}[/tex]

Answer:

The two numbers are: -9.17 and 8.83

Step-by-step explanation:

Let the two numbers represent 'x' and 'y'

Their sum is − 1/3 ==>          x + y = -1/3  .................(eqn 1)

Their difference is 18 ==>    x − y = 18  ....................(eqn 2)

from equation 2,

x = 18 + y

therefore, substitute for 'x' in (eqn 1) to get y

(18+y) + y = -1/3

18 + 2y = -1/3

2y = -1/3 − 18

2y = -[tex]18\frac{1}{3}[/tex]

2y = - 55/3

y = (-55/3) / 2

y = -55/3 x 1/2

y = -55/6 = -9.17

Substitute for 'y' in either equation

picking (eqn 2)

x − (-9.17) = 18

x + 9.17 = 18

x = 18 − 9.17

x = 8.83

Answer: 5.8 ft

Step-by-step explanation:

We can use the Pithagorean Theorem in this problem, in order to find the length of the rope:

[tex]h^{2}=a^{2}+b^{2}[/tex]

Where:

[tex]h[/tex] is the length of the rope (the hypotenuse of the right triangle formed by the height of the tent, the rope and the ground)

[tex]a=5 ft[/tex] is the height of the tent (one of the legs of the right triangle)

[tex]b=3 ft[/tex] is the other leg of the right triangle

Solving the equation with the given data:

[tex]h^{2}=5^{2}+3^{2}[/tex]

Finding [tex]h[/tex]:

[tex]h=\sqrt{(5 ft)^{2}+(3 ft)^{2}}[/tex]

[tex]h=\sqrt{25 ft+9 ft}[/tex]

[tex]h=5.83 ft \approx 5.8 ft[/tex] This is the total length of nylon rope

Question 1: Option B: [tex]\frac{10}{14}=\frac{5}{7}[/tex]

Question 2: Option C: [tex]\frac{12}{18}=\frac{4}{6}[/tex]

Solution:

Question 1:

Given ratio is [tex]\frac{10}{14}[/tex].

To find the equivalent ratio of [tex]\frac{10}{14}[/tex].

10 and 14 have the common factor 2.

So divide both numerator and denominator by the common factor 2.

[tex]$\frac{10}{14}=\frac{10\div2}{14\div 2}[/tex]

    [tex]$=\frac{5}{7}[/tex]

[tex]$\frac{10}{14}=\frac{5}{7}[/tex]

Hence option B is the correct answer.

Question 2:

Given ratio is [tex]\frac{10}{14}[/tex].

To find the equivalent ratio of [tex]\frac{12}{18}[/tex].

12 and 18 have the common factor 3.

So divide both numerator and denominator by the common factor 3.

[tex]$\frac{12}{18}=\frac{12\div3}{18\div 3}[/tex]

    [tex]$=\frac{4}{6}[/tex]

[tex]$\frac{12}{18}=\frac{4}{6}[/tex]

Hence option C is the correct answer.

Answer:

Step-by-step explanation:

We need to analyze the surface

Look at the L shape, it has a mirror image at the back, which is symmetrical to the front side

Then,

area of rectangle = length × breadth

The L shape can be divided into two plane shape

1. A rectangle of length 10in and breadth 6in,

Then, A=l×b=10×6 = 60in²

2. To a square of side a=4in

Then, A=s²=4²=16in²

Then, the total area of one side of the L shape is

A=60+16=76in²

Also, the total area of the two L shape is =2×76

A=152in²

Then, let look at the back side of the solid and the front side, they are also symmetrical.

It forms a rectangle of length 10in and breadth 6in

Then, A= l×b=10×6=60in²

Area of the two sides is =60×2

A=120in²

The total are of the front and back side is 120in²

A=120in²

Let take a look at the top and bottom, they are also symmetrical and has a dimension of length 10in and breadth 6in

Then, A=l×b=10×6=60in²

So, total area =2×60 =120in²

The total area of the shape is the total area of top+ total are of the sides + total area of the L shape

Total area=152+120+120=392in²

A(total)=392in²

Then, the total area of the solid shape is 392in²

The first option is correct

Answer:

24 stations

Step-by-step explanation:

we know that

six stations represent 25% of the stations offered

so

using a proportion

Find out how many stations represent a percentage of 100%

[tex]\frac{6}{25\%}=\frac{x}{100\%}\\\\x=6(100)/25\\\\x=24\ stations[/tex]

Answer:

40

Step-by-step explanation:

add 21 + 20

hope this helps :)

Final answer:

To find the width of a rectangle when the length is 2 units more than the width and the area is known to be 48 units, you can use algebraic equations to determine the width. In this case, the width of the rectangle is 6 units.

Explanation:

To find the width of the rectangle:

Let x be the width of the rectangle.

Since the length is 2 units more than the width, the length is x + 2.

Given that the area is 48 units, use the formula for the area of a rectangle: width x length = area. Therefore, x(x + 2) = 48.

Solve for x by setting up the equation: x^2 + 2x - 48 = 0.

Factor the quadratic equation: (x + 8)(x - 6) = 0.

Since the width cannot be negative, the width of the rectangle is 6 units.

The width of the rectangle is 6 units.

According to the question, the length is 2 units more than the width, so we can express the length as ( w + 2 ) units.

The area of a rectangle is given by the product of its length and width. Therefore, we can set up the following equation to represent the area of the rectangle:

[tex]\[ \text{Area} = \text{length} \times \text{width} \] \[ 48 = (w + 2) \times w \][/tex]

Expanding the right side of the equation, we get:

[tex]\[ 48 = w^2 + 2w \][/tex]

To find the value of w, we need to solve the quadratic equation. Let's rearrange the equation to set it equal to zero:

[tex]\[ w^2 + 2w - 48 = 0 \][/tex]

Now, we can factor this quadratic equation:

[tex]\[ (w + 8)(w - 6) = 0 \][/tex]

Setting each factor equal to zero gives us two possible solutions for w:

[tex]\[ w + 8 = 0 \quad \text{or} \quad w - 6 = 0 \][/tex]

Solving for w, we get:

[tex]\[ w = -8 \quad \text{or} \quad w = 6 \][/tex]

Since the width of a rectangle cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is:

[tex]\[ w = 6 \text{ units} \][/tex]

Answer:

26 gallons of juice

Step-by-step explanation:

156/12 = 13

13x2=26

Answer: 26 gallons

Step-by-step explanation:

2 gallons for every 12 people so you want to do 156 divided by 12 which would be 13. That shows that there are 13 times more people than there were before. You would then multiply 2 by 13 which would give you 26 gallons of juice.

Answer:

I believe it would be true

Answer:

-12

Step-by-step explanation:

we know that

(fºg)(x)=f(g(x))

To find out the composite function f(g(x)) substitute the variable x in the function f(x) by the function g(x)

we have

[tex]f(x)=-3x-9[/tex]

[tex]g(x)=x+7[/tex]

so

[tex]f(g(x))=-3(x+7)-9[/tex]

For x=-6

substitute

[tex]f(g(-6))=-3(-6+7)-9[/tex]

[tex]f(g(-6))=-3(1)-9[/tex]

[tex]f(g(-6))=-12[/tex]

The app uses 2^28 bytes.

Step-by-step explanation:

⇒ 4^4 × 2^20 = (2²)^4 × 2^20 = 2^8 × 2^20

                       = 2^8+20

                       = 2^28 bytes (using the law of exponents a^m × a^n = a^m+n)

Answer:

The right answer is, -420

Step-by-step explanation:

Because we use common factor:

60 (x - 15)

We multiply for each term:

60 (x) - 60 (15)

60 (8) - 60 (15)

We solve:

480 - 900 = -420

Answer:

Eli has to run for 2.25 minutes at this pace to win the bet.

Step-by-step explanation:

At his last track meet, Eli ran the 400-meter dash in 54 seconds.

So, the speed of Eli's run is [tex]\frac{400}{54} \times 60 = 444.44[/tex] meters per minute.

Now, if Eli is determined to run a whole kilometer with the same speed, then it will take Eli to run 1 kilometer within [tex]\frac{1000}{444.44} = 2.25[/tex] minutes.

Hence, Eli has to run for 2.25 minutes at this pace to win the bet. (Answer)

Answer

3

Step-by-step explanation:

the formulas say it

Answer:

55m

Step-by-step explanation:

a²+b²=c²

19 x 19 = 361

52 x 52 = 2704

2704 + 361= 3065

the square root of 3065 is 55.4 so round that to 55.

Answer:

B) associative

Step-by-step explanation:

The associative property of multiplication says you can choose which pair of numbers to multiply first, so when every operation is multiplication, you can move parentheses without changing the answer.

The given equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. This is the property which states that the order in which numbers are multiplied or added does not affect the result.

The equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. In mathematics, the Commutative Property refers to the fact that the order in which numbers are multiplied does not change the result of the multiplication. This is why we can rearrange the factors 4, 7, and 3 in any order and still get the same product.

For instance, we can express the commutative property of multiplication as a×b = b×a. So, in your example, the equation 4×7×3 = 7×4×3, is an application of this principle as you are simply rearranging the order of numbers being multiplied.

Please remember that this rule applies only to addition and multiplication, not subtraction or division.

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The volume of the lid is approximately 113.8 cubic inches.

The volume of the lid can be found by multiplying the area of the triangular base by the height of the lid. The area of a triangle can be found by using the formula: Area = (base x height) / 2. In this case, the base is 6 1/2 inches and the height is 3 1/2 inches. Plugging these values into the formula, we get: Area = (6.5 x 3.5) / 2 = 11.375 square inches. Now, to find the volume of the lid, we multiply the area by the height: Volume = 11.375 x 10 = 113.75 cubic inches. Rounding to the nearest tenth, the volume of the lid is 113.8 cubic inches.

The volume of the lid is 113.8 cubic inches.

To determine the volume of the lid of the jewelry box, we need to use the formula for the volume of a triangular prism, which is V = (1/2 * base * height of triangular base) * height of the prism.

First, calculate the area of the triangular base:

Next, multiply the area of the triangular base by the height of the prism:

Therefore, the volume of the lid to the nearest tenth is 113.8 cubic inches.

Answer:

y = 6x − 11

Step-by-step explanation:

x = t + (1/t), y = t² + (1/t²)

If we square x:

x² = t² + 2 + (1/t²)

x² = y + 2

When x = 3, y = 7.

Taking derivative with respect to time:

2x = dy/dx

dy/dx = 6

So the equation of the tangent line is:

y − 7 = 6 (x − 3)

y − 7 = 6x − 18

y = 6x − 11

Answer:

1,607  volume

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Rewrite the equation into the form of y=mx+c

m is the gradient of the line.

2x-3y=6

3y= 2x-6 (bring y terms to one side, the rest to the other)

y= 2/3x -2 (÷3 throughout)

Thus the gradient is 2/3.