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When two or more fractions are provided, the least common denominator is defined as the smallest common multiple of all the common multiples of the denominators.

Let's assume we have to add the fractions: (2/9)+(3/4)

We need to determine a common integer that is a multiple of both denominators, which are 9 and 4.

This common multiple will aid in the solution of the problem. As a result, the least frequent multiple for 9 and 4 is 36. As a result, the expression can be written as follows:

(2/9)+(3/4) = (2/9 × 4/4) + (3/4 × 9/9) = (8/36) + (27/36) = 35/36

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The total number of strawberries needed for making all the smoothies can be represented by the expression -

y = 15x

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Amy who is making all three smoothies for each of her x number friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6.

Number of friends [n] = x

Each of the three friends will get smoothies made from recipe 1, recipe 2 and recipe 3.

Then -

Number of strawberries needed for smoothie made from recipe 1 for x friends = n[1] = 4x

Similarly, for smoothies made from recipe 2 and 3 will need -

n[2] = 5x and n[3] = 6x number of strawberries.

Assume that total number of strawberries needed for making all the smoothies are y. Then, we can write -

y = 4x + 5x + 6x

y = 15x

Therefore, the total number of strawberries needed for making all the smoothies can be represented by the expression -

y = 15x

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[tex]21+a=90 \implies a=69^{\circ} [/tex]

This is because the angles are complementary.

Solution

Number 6

for this case we can see that we have two common angles and one equal side. By the way we have also a common side and then since we have right triangles the correct postulate would be:

SSS

Number 9

Solution:

Given;

The z-score is calculated using;

Thus;

(b) The z-score of 99.7 probability is between -3 and 3. Thus;

ANSWER: Approximately 99.7% of men have cranial capacities between 560 cc and 1760 cc

The table of values of the relationship between time and earnings is a linear relation

From the question, we have the following parameters:

Number of hours = 2 hours

Total earnings in this time = $35

Also from the question, we understand that:

She makes a constant hourly wage

A constant hourly wage implies that the table of values has a linear relationship

In this case, the linear relationship is represented as

A(t) = constant hourly wage * t

Where

A(t) represents the earnings

t represents the number of hours

So, we have

constant hourly wage * 2 = 35

Divide both sides of the equation by 2

So, we have

constant hourly wage = 17.5

Substitute constant hourly wage = 17.5 in A(t) = constant hourly wage * t

A(t) = 17.5 * t

Evaluate

A(t) = 17.5t

Using the values of t as:

t = 0, 2, 4, 6

We have the following table of values

Number of hours (t) || Amount earned

0                                              0

2                                              35

4                                              70

6                                              105

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The amount of times that 14 goes into 78 is; 5 times

We want to find how many 14 goes into 78.

Now, it is pertinent to note that this expression is used in our common daily lives for basic things of life. For example, if i want to know how many 10 dollars can go into 100 dollars, i will just divide 100 by 10.

Similarly another example is if i want to know how many 5 liters container of fuel would go into a 60 liters tank, i will just divide 60 by 5 to get the number.

In a similar vein, we can solve this question by dividing 78 by 14 to get;

78/14 = 5 ⁸/₁₄

This means 14 can only go in 5 full times as we will not count the fraction.

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Answer:

3

because 3 divided by one is 3 so then you would have to divide with nine which we know is 3

Step-by-step explanation:

Have a great day!

With the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.

So, h(t) = 24:

Then, calculate as follows:

Therefore, with the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.

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Answer:

75

Step-by-step explanation:

Answer:

75. ..... ............................

Answer: 31.25%

Step-by-step explanation:

Draw a Ven diagram in a rectangle with 2 circles one for F and the other for C. The intersection overlap will have the 10 who play both outside the circles but within the rectangle the 7 who do neither so then fill the rest of F with 4 to give a total of 14 and 11 for the C to total 21. When you add all the numbers you’ll get a class total of 32. Then the % who play both F and C is = (10/32)*100 = 31.25%

SOLUTION:

Case: Pythagoras Triple

Method:

The Pythagorean triple:

(8, 15, 17) can be formed with factor integers

8----> 4

15---->3.

Final answer:

x=4, y= 3

Step-by-step explanation:

1 m = 4 cm

therefore,

A = 2.5 m = 2.5×1 m = 2.5×4 cm = 10 cm

B = 2.75 m = 2.75×1 m = 2.75×4 cm = 11 cm

D = 3.75 m = 3.75×1 m = 3.75×4 cm = 15 cm

The plane containing point B and parallel to the plane CDH is plane ABF.

As, from the diagram we can see that there are two plane passing from point B; plane ABF and ABC.

But plane ABC is intersecting the given plane CDH, while plane ABF is not.

Thus, plane ABF is parallel to the plane CDH.

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The solution to 1/4(n - 6) = 1/4n - 3/2 is infinite many solutions

The equation is given as

1/4(n - 6) = 1/4n - 3/2

Multiply through the fraction equation by 4

So, we have the following equation

4 x 1/4(n - 6) = 4 x 1/4n - 4 x 3/2

Evaluate the products in the equation

So, we have the following equation

n - 6 = n - 6

Evaluate the like terms

0 = 0

The equation cannot be solved further

If the solution to an equation is 0 = 0, then the equation has infinite many solutions

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Answer: infinite many answers

Step-by-step explanation:

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-1\\ k=9 \end{cases}\implies y=a(~~x(-1)~~)^2 +9\implies y=a(x+1)^2 + 9 \\\\\\ \textit{we also know that} \begin{cases} x=-2\\ y=-8 \end{cases}\implies -8=a(-2+1)^2 + 9 \\\\\\ -17=a(-1)^2\implies -17=a\hspace{9em}\boxed{y=-17(x+1)^2 + 9}[/tex]

Answer: $4.20

Step-by-step explanation:

The sale price is $12 * .35 = 4.2

Answer:

the first answer option : all lengths and angles stay the same.

Step-by-step explanation:

imagine you have a piece of plastic or glass of a triangular shape on your table.

now, lower your hand on the table, so that your thumb touches the table and one of your other fingers touches the triangle on the top.

and now twist your hand that your thumb stays at the same point, and your finger holding the triangle starts making a circular motion.

that finger is dragging the triangle along.

what happens to the triangle ? it keeps its original shape, and changes only its location and orientation.

that is what a rotation is.

Based on the dimensions of the right triangle, the equation to be used to find the missing lengths is hypotenuse² = Known leg² + Unknown leg².

To find the missing length of a right-angled triangle, you should use Pythagoras theorem.

This theorem allows you to find the dimensions of missing leg as:

hypotenuse² = Known leg² + Unknown leg²

When you solve for the missing length, the length is:

9² = 6² + Unknown leg²

81 = 36 + Unknown leg²

Unknown leg² = 81 - 36

Unknown leg = √(81 - 36)

Unknown leg = 6.7

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The probability that the student will be prepared for exactly 4​ questions is; 0.3427

Hypergeometric distribution is defined as a discrete probability distribution that expresses the probability of k successes in n draws, done without replacement, from a finite population of size N that contains exactly K objects with that feature. In this disdtribution, each draw is either a success or a failure.

The probability mass function of Hypergeometric distribution is given by the formula;

P(K = k) = KCk * N-KCn-k ]/NCn

Now, the probability that the student will be prepared for exactly 4​ questions will be;

P(K = 4) where;

N = 16

K = 9

n = 8

Solving P(K = 4) = 9C4* 16-9C8-4 ]/16C8 = 0.3427

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Solution

A

Using pythagorean theorem

The final answer

The height of window A is

Answer:
domain: [-1,4]
range: [-2,4]
the graph is not a function, this is proven by using the vertical line test.

hope this helps :)

In a case whereby Tammy has 4 more then five times the amount of dimes than nickels in her pocket and have total of $1.50 in her pocket the equation that could be used to determine the number of nickels(x) she has in her pocket is (0.05)(X+3) = 1.50.

The  number of nickels(x) that can be found her pocket be determined by  adding the the number of times the amount of dimes is than nickels, which can be expressed as :

let x will be number of dimes

let x+4 will be number of nickels

Therefore the number of nickels(x)  that is required will be (0.10)X + (0.05)(X+3) = 1.50

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Answer:

Step-by-step explanation:

The value of 8 in 8.260 is 8 units.

Based on the relationship between the number of phone calls that Amy received for the three evenings, the number of phone calls received on each evening was:

The first evening saw Amy receiving 7 more calls than the second evening while the third evening saw Amy receiving 3 times as many calls as the second evening.

Assuming the second evening is x, the relationship can be represented by the equation:

First evening calls + Second evening calls + Third evening calls = Total number of calls

(7 + x) + x + 3x = 112

Solving for the number of phone calls on the second evening gives:

(7 + x) + x + 3x = 112

7 +  x + x + 3x = 112

7 + 5x = 112

5x = 112 - 7

x = 105 /5

= 21 calls

Number of calls on first evening:

= 21 + 7

= 28 calls

Number of calls on third evening:

= 21 x 3

= 63 calls

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The result of the function f(3) is 3.

Given:

f(x) = -x² + 8x - 12

x = 3

Putting the value of x in the given function to obtain the outcome of the function,

f(3) = -(3)² + 8 × 3 - 12

     = -9 + 24 - 12

     = 24 - 21

     = 3

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Answer:

D. infinite

Step-by-step explanation:

2(x+4) -1 = 2x + 7

To solve for x

Distribute

2x+8 -1 = 2x+7

Combine like terms

2x +7 = 2x + 7

Subtract 2x from each side

2x+7-2x = 2x+7-2x

7 = 7

This is always true, so there are infinite solutions

Given: The velocity function of a moving particle as

To Determine: The time at which the acceleration equals to zero

Solution

Note that at time t=0, the particle is at origin, so

Determine the acceleration function

The acceleration of a particle is the rate of change of velocity or the derivative of the velocity function. Therefore,

When the acceleration is equal to zero, then we have

Let us plot the graph of the acceleration function

The time for given interval for which the acceleration is zero are

ence, thre first time the acceleration is zero is π/2 or 1.571