HELP PLEASE!!
Find the length of side a?

7-2030 x g x 65 -=65 65 65 65

The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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Answer:

its 7,320 its the same

Step-by-step explanation:

The expanded form of 7,320 will be 7000 + 300 + 20.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the number 7,320

The expanded form of 7,320 contains thousand whole, hundred whole, and tens whole.

So,

The expanded form of 7320 = 7000 + 300 + 20.

Hence "7000 + 300 + 20 will be expanded form of the given number".

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Answer:143

Step-by-step explanation: When subtracting a negative number from a negative number(a minus sign followed by a negative turns the two signs into a positive sign) you are then adding a positive

The given recipe for 1 dozen biscuits is

• 2 cups of flour.

• 1 cup of shortening.

• 1 cup of milk.

Now, we have to multiply each number by 3 in order to triple the recipe. So, the recipe for 3 dozens is

• 6 cups of flour.

• 3 cups of shortening.

• 3 cups of milk.

ANSWER

3/2

EXPLANATION

The order of operations is:

0. Parenthesis

1. Exponents

2. Multiplication and division (left to right)

3. Addition and subtraction (left to right)

In this case, the operations are a division and a multiplication. Since they rank equally, we have to do them from left to right. First, divide 3 by 4 and then, multiply by 2,

Hence, the solution is 3/2.

Answer:

1.5

Step-by-step explanation:

3 divided by 4 = 0.75

0.75 x 2 = 1.5

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The volume of the spherical boulder is 7234.56 cubic feet.

What is the diameter?

A line connecting the center and the circumference at its opposite ends is called the diameter. Its length is double that of the circle's radius.

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\).

Given the diameter of the sphere is 24 feet.

therefore radius is equal to 12 feet.

The volume of the sphere is equal to

\(V=\frac{4}{3}\pi (12)^{3} \\V=\frac{4}{3} *3.14*1728\\V=7234.56\)

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Answer:

20.52 cm²

Step-by-step explanation:

\(\textsf{Area of a semicircle}=\sf \dfrac12\pi r^2 \quad \textsf{(where r is the radius)}\)

\(\textsf{Area of a triangle}=\sf \dfrac12bh \quad \textsf{(where b is the base and h is the height)}\)

Given:

\(\begin{aligned}\implies \textsf{Shaded area} & =\sf \dfrac12\pi r^2-\sf \dfrac12bh\\ & = \sf \dfrac12 \cdot 3.14 \cdot 6^2-\dfrac12 \cdot 12 \cdot 6\\ & = \sf 56.52-36\\ ^& = \sf 20.52\:\:cm^2\end{aligned}\)

Answer:

20.52cm^2

Step-by-step explanation:

from the picutre we can see that this is a semicircle with 2 right angle triangles inside it. to find the area we will solve for the semi circle then solve for the triangles and and subtract

circle area is \(\pi r^{2}\) leaving the semicircle to be \(\frac{\pi r^{2} }{2}\) for the semi circle

next we need the radius. since the diameter is given, we can solve for r by dividing it in two

12 ÷ 2 = 6

so the area of the semi circle is \(\frac{\pi 6^{2} }{2}\)

this gives 18\(\pi\)cm^2 if we simplify

next the triangles, since they are equal in size we can treat them as a square and stack them. this is because they have equal side lengths so when stacked they form a square:

base x height divided by 2 times 2 would be the normal process to find two equal triangles but you can see the division and multiplication cancel out

6x6= 36cm^2

finally subtracting the areas to find the shaded region and use 3.14 as pi

18\(\pi\)cm^2 - 36cm^2 = 20.52cm^2

The equivalent ratios are 8: 6 and 12:9.    

Two ratios are equivalent if they represent the same proportion or relative size. To find an equivalent ratio, we can multiply both terms of the ratio by the same non-zero number. This doesn't change the condition between the two terms.  

Here we have 4:3

To find equivalent ratios, we can multiply both terms by the same number.

Multiplying by 2

=> 4 × 2 : 3 × 2

=> 8 : 6

Multiplying by 3

=> 4 × 3 : 3 × 3

=> 12: 9

Therefore,

The equivalent ratios are 8: 6 and 12:9.    

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Complete Question

What is the equivalent ratio for 4: 3

Answer:

-2<=y<=-7

Step-by-step explanation:

Answer:

when someone is pretending to be you and like using your credit card or other form of like identity

Step-by-step explanation:

The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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Data:

• ( 16, 2188 )

• ( 48, 2364 )

• Linear function

Procedure:

0. Building up the linear equation: finding the slope (,m,)

2. Finding the intersection with y-axis ( b ): choosing the first point given to replace the values in the linear function.

3. Obtaining the linear function of the given problem:

4. Finding the weight of the airplane when it is carrying 64 gallons of fuel.

Answer: 2452 pounds

The number of hours where the fees for both studios would be the same is 5 hours.

From the information illustrated Midwest charges a $10 signup fee and $32 per hour for rental fees. This will be 10 + 32h.

Big & Bad charges only $20 each hour plus a $70 registration fee. This will be 70 + 20h.

Let h = number of hours

The equation will be:

10 + 32h = 70 + 20h

Collect like terms

32h - 20h = 70 - 10

12h = 60

Divide

h = 60/12

h = 5

The number of hours is 5.

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Answer:

5/2 or 2.5

Step-by-step explanation:

Divide both sides by 2.

Answer: 49/120kg

Step-by-step explanation:

7/8•7/15 = 49/120

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

9514 1404 393

Answer:

  (-4√494)/13i +(6√494)/13k ≈ -6.8388i +0j +10.2585k

Step-by-step explanation:

To answer this question, you need to know two things:

  1) the direction of vector v

  2) the magnitude of vector u

__

direction of v

A direction is specified by a "unit vector", one with the proper ratio of components, and a magnitude of 1. It is found from a given vector by dividing that vector by its magnitude.

The unit vector in the v direction is ...

  v/|v| = (-2i +3k)/(√((-2)² +3²) = (-2i +3k)/√13

__

magnitude of u

The magnitude of vector u is ...

  |u| = √(5² +(-2)² +3²) = √38

__

Then the desired vector is ...

  (2|u|)(v/|v|) = 2√38(-2i+3k)/√13 = (-4√494)/13i +(6√494)/13k

_____

Additional comment

We have chosen to "rationalize the denominator" by writing √(38/13) as (√494)/13.

The linear function that models the situation is given as follows:

d = 0.85t.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The constant ratio for this problem is given as follows:

k = 0.83, as each division of d by t has a result of 0.83.

Hence the equation is given as follows:

d = 0.83t.

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Answer:  The answer is:  " x = 2.833333333333...." .

___________________________

             or:  write as:  " 2 \(\frac{5}{6}\) " .  

___________________________

Step-by-step explanation:

___________________________

Set up a ratio:

Note:  Segment FH =  (x + 35)

         Segment JL = 20 ;

         Segment FH ~ Segment JL ;

___________________________

Note:  Segment GH = (x - 4) ;

         Segment  KL  =  5 ;

         Segment GH ~ Segment KL .

___________________________

So, ( x + 3.5) : 20 :: (x-4) : 5 ;

Write this ratio in fraction format:

___________________________

→  \(\frac{(x+3.5) }{20 } = \frac{(x-4) }{5}\)  ;

Now; "cross-factor multiply" :

→  \(\frac{a}{b} = \frac{c}{d }\)  ;  → \(ad = bc\) ; { \({ a\neq0 ; b\neq0 ; c\neq0 ; d\neq0\) .}.

___________________________

So:

  5(x + 3.5)  =  20(x - 4) ;  

___________________________

→ To simplify, start by divide each side of the equation by "5" ;

___________________________

  →   {5(x + 3.5) } / 5  =  { 20(x - 4)  } / 5 ;

to get:

      →  (x + 3.5)  =  4(x - 4) ;

___________________________

Now, on the right-hand side of the equation;

  let us expand the expression;

___________________________

We have the expression:  " 4(x - 4) " ;

 To expand:

Note the "distributive property of multiplication:

     →   a(b + c)  = ab + ac ;

Likewise:

     →   4(x - 4)  = 4x  - 16 ;

___________________________

Now, we can rewrite our equation:

___________________________

     →   " x + 3.5  =  4x - 15 "  ;

Now, we can subtract "x" from each side of the question;

     & add "15" to each side of the equation; as folllows:

___________________________

     →     x + 3.5  =  4x - 15 ;

          - x + 15   =  - x  +15

___________________________

to get:        8.5  =  3x ;  

                   ↔  3x  = 8.5 ;

Now, divide each side of the equation by "3" ;

       to isolate "x" on one side of the equation;

       & to solve for "x" ;  as follows:

                     →  3x / 3 = 8.5 / 3 ;

             to get:   x  = 8.5 /3  

                              = 2.83333333333 ;  

                         or; write as:  " 2 \(\frac{5}{6}\) ."

___________________________

Hope this is helpful to you!  Best wishes!

___________________________

The dimensions of the rectangle are:

Length = 10 m

Width = 6.5 m

Recall that the area of aa rectangle is given as, length × width.

Given the following:

Area of the rectangle = 65 m²

Let the width of the rectangle be represented as w.

Length of the rectangle = 2w - 3 m

Therefore:

(2w - 3)(w) = 65

Expand:]

2w² - 3w = 65

2w² - 3w - 65 = 0

Factorize:

w = 6.5 or w = -5

The width cannot be negative, therefore, the width = 6.5 m.

Length of the rectangle = 2w - 3 = 2(6.5) - 3 = 10 m

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Answer:

7x + 6 = 55; x=7

Step-by-step explanation:

"six more than" -> +6

"product of seven and a number" -> 7x

7x + 6 = 55

7x = 55 - 6

7x = 49

x=7

Answer:

6+7x=55, x=7

Step-by-step explanation:

7x=55-6

7x=49

x=7

Answer:

35

Step-by-step explanation:

the answer is 35 because a straight line is 170° and 135+35 is 170

Answer:

\(\huge\boxed{B.\ \dfrac{12}{35}}\)

Step-by-step explanation:

Look at the picture.

We know:

\(\sin\theta=\dfrac{a}{c}\\\\\tan\theta=\dfrac{a}{b}\)

We have

\(\sin\theta=\dfrac{12}{37}\Rightarrow a=12,\ c=37\)

Use the Pythagorean theorem.

\(a^2+b^2=c^2\\\\12^2+b^2=37^2\\\\144+b^2=1369\qquad|\text{subtract 144 from both sides}\\\\b^2=1225\to b=\sqrt{1225}\\\\b=35\)

Calculate tangent:

\(\tan\theta=\dfrac{12}{35}\)

The loan amount at 9% interest is $48,000.

The loan amount at 12% interest is $17,000

The first step is to form a system of equations that can be used to determine the required values:

0.09a + 0.12b = $6,360 equation 1

a + b = $65,000 equation 2

Where:

a = amount of the loan at 9% interest

b = amount of the loan at 12% interest

Multiply equation 2 by 0.09

0.09a + 0.09b = 5850 equation 3

Subtract equation 3 from equation 2

0.03b = 510

Divide both sides of the equation by 0.03

b = 510 / 0.03

b = $17,000

Subtract 17,000 from 65,000

a = 65,000 - 17,000

a = $48,000

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ANSWER :

The answer is :

0.8369

EXPLANATION :

From the problem, we have :

Using the normal distribution table which indicates an area under the curve to the left of the given negative z.

and the other one is the positive z.

So if we subtract the areas under the two curves. we will get the area between the two z's.

That will be :

That will be :

Look for the value of z = 1.0, and that is 0.8413

The other value is at z = -2.62 :

and that is 0.0044

Get the difference between the two.

Answer:

\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)

The measure of angle A is 63°, the measure of side b is 22.34 feet and the measure of side a is 37.57 feet.

From the given triangle ABC,

∠A+∠B+∠C=180° (Angle sum property of a triangle)

∠A+32°+85°=180°

∠A+117°=180°

∠A=180°-117°

∠A=63°

We know that, the formula for sine rule is sinA/a=sinB/b=sinC/c

Here, sin63°/a = sin32°/b = sin85°/42

sin63°/a = sin32°/b = 0.9961/42

sin32°/b = 0.9961/42 and sin63°/a = 0.9961/42

0.5299/b = 0.9961/42

0.9961b=22.2558

b=22.2558/0.9961

b=22.34 feet

sin63°/a = 0.9961/42

0.8910/a = 0.9961/42

0.9961a=37.422

a=37.422/0.9961

a=37.57 feet

Therefore, the measure of angle A is 63°, the measure of side b is 22.34 feet and the measure of side a is 37.57 feet.

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