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The number of questions in the test is 30

Step-by-step explanation:

Let's call the total number of questions in the test N.

We know that Laura answered 27 questions, and these 27 questions represent the 90% of the test.

Therefore, we can say that 27 is the 90% of N.

Re-writing the percentage as a fraction,

[tex]90\% = 0.90[/tex]

This means that:

[tex]0.90 N = 27[/tex]

And now we can solve for N to find the number of questions in the test:

[tex]N=\frac{27}{0.90}=30[/tex]

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Answer:

see attached picture.

Answer:

35/9

Step-by-step explanation:

2 1/3=7/3

1 5/9=14/9

------------------

7/3+14/9=21/9+14/9=35/9

Answer: 2 1/3 + 1 5/9 = 3 8/9

Step-by-step explanation: You make the fractions the same so 3/9 is equal to 1/3 so you multiply both numbers in fraction #1 (1/3) by 3 & just add, not the denominators though

Incomplete Question the complete Qs is

Which of the following is a correct equation for the line passing through the point (-2,1) and having slope m = 1/2?  

a: y=1/2x+2

b: y=-2x+1/2

c: x-2y=-4

d: y-1=1/2(x+2)

Answer:

The Correct option is c. x-2y=-4

Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

[tex]x-2y=-4[/tex]

Step-by-step explanation:

Given:

[tex]Slope = m =\dfrac{1}{2}[/tex]

point A(x₁, y₁)=(-2,1)  

To Find:  

Equation of Line  =?  

Solution:  

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,  

i.e equation in point - slope form

[tex](y-y_{1})=m(x-x_{1})[/tex]

Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2 , 1) we get

[tex](y-1)=\dfrac{1}{2}(x-(-2))\\\\2y-2=x+2\\x-2y=-2-2=-4\\x-2y=-4[/tex] As required

Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

[tex]x-2y=-4[/tex]

The profit on each book is $ 5.25

Solution:

Given that, the drama club at school sells $ 15.00  coupon books

Their profit is 35% of the  total sales

Therefore,

Cost of a coupon book = $ 15

Profit = 35% of the  total sales

We have to find the profit on each book

If a book is sold for $ 15 and then profit will be 35 % of 15

Let us find 35 % of 15

[tex]Profit\ on\ each\ book = 35 \% \times 15\\\\Profit\ on\ each\ book = \frac{35}{100} \times 15\\\\Profit\ on\ each\ book = 0.35 \times 15\\\\Profit\ on\ each\ book = 5.25[/tex]

Thus profit on each book is $ 5.25

Answer:

x = 41

Step-by-step explanation:

To solve this problem, we want to find the value of 'x' by isolating it (separating 'x' from all other numbers).

First, simplify the expression by using the distributive property, where you multiply the number outside the brackets with each term inside the brackets.

Then isolate 'x' by doing reverse operations (on both sides) for every number that is on the same side as 'x'. Reverse operations are opposites (addition and subtraction, multiplication and division) and "cancel out" a number, which "moves" it to the other side.

7(x - 5) = 252        Use the distributive property

7x - 35 = 252        Result of 7 times x and 7 times -5

7x - 35 + 35 = 252 + 35        Add 35 to both sides

7x = 252 + 35        -35+35 on the left side cancelled out. Simplify right side

7x = 287        Continue to isolate 'x'

7x/7 = 287/7        Divide both sides by 7

x = 287/7        Left side cancelled out to be 'x'. Simplify the right side

x = 41        Answer

Check your answer:

Substitute 'x' for 41 in the original equation. Then, make sure that the equation is still balanced. Keep in mind BEDMAS order (brackets, exponents, division, multiplication, addition, subtraction).

7(x - 5) = 252

7(41 - 5) = 252        Simplify inside the brackets first

7(36) = 252        Multiply

252 = 252        Same answer

LS = RS

Since left side (LS) equals (=) right side (RS), the equation is still balanced and we got the correct value for 'x'.

We have two lines intersected by a transversal. There is a relationship between <6 and <2. They are corresponding angles and are congruent. So if the m<6 = 75° then the m<2 = 75°.

answer: m<2 = 75°

Answer:

Step-by-step explanation:

-x (4x^2 - 6x + 1).....distribute the -x through the parenthesis

- 4x^3 + 6x^2 - x <===

Answer:

b

Step-by-step explanation:

The length of hypotenuse is 39.

Step-by-step explanation:

Given,

Vertical side = a = 15

Horizontal side = b = 36

Hypotenuse = c

Using pythagorean theorem

[tex]a^2+b^2=c^2\\(15)^2+(36)^2=c^2\\225+1296=c^2\\1521=c^2\\c^2=1521[/tex]

Taking square root on both sides

[tex]\sqrt{c^2}=\sqrt{1521}\\c=39[/tex]

The length of hypotenuse is 39.

Keywords: square root, addition

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Answer:

Step-by-step explanation:

x-5=1

+5   +5

x=6

x-5=-1

 +5  +5

x=4

Answer: x= 6, 4

Neither Ibuki nor Melodie factored 12x² correctly based on the expressions given. However, if Melodie's (2x)(6x) was meant for 12x², then her factorization would be correct.

The students are attempting to factor the expression 12x². Factoring is the process of finding two or more expressions that multiply together to get the original expression. Ibuki's factorization of 12x² as (4x)(3x⁴) contains an error since 3x⁴ would imply raising x to the fourth power, which is not present in the original expression. Melodie's factorization of 12x² as (2x)(6x) is also incorrect since when you multiply 2x and 6x, you get 12x², not 12x⁷ as her expression suggests. The correct factorization of 12x² is (2x)(6x) since 2x multiplied by 6x equals 12x².

In summary, neither student has factored the expression correctly. However, if we take Melodie's answer as a typo and she meant (2x)(6x) for 12x², then her factored form would be correct.

Final answer:

To create the equation representing the situation, calculate the total meal cost by multiplying each friend's share by four and then add four times the tip to equal the final bill of $61. The equation is 4 times $12.75 + 4  imes t = $61.

Explanation:

To solve the problem using an equation, we need to consider the cost of each meal and the tip each friend left. Four friends each paid $12.75 for their meal, which gives us the cost of the meals alone: 4 times $12.75 = $51. The tip, t, needs to be added four times (once for each friend) to the total cost of the meals to reach the final bill of $61.

Therefore, the equation to represent the situation would be: 4 times $12.75 + 4 times t = $61.

Once we have the equation, we can solve for the tip, t, to find out how much each friend left for the tip.

Answer:

14x-13y

Step-by-step explanation:

Answer:

1 hour and 30 maybe my math might be wrong

Step-by-step explanation:

Answer:

1. Using the Pythagorean theorem.

2. Using the ratio 1 : 1 : √2.

Step-by-step explanation:

There are two options to find the value of x:

1. Using the Pythagorean theorem:

Hypotenuse = 5√2 inches and legs are equal in a 90 - 45 - 45 triangle like this.

Hypotenuse² = Leg² + Leg²

(5√2)² = 2Leg²

50 = 2Leg²

50/2 = Leg²

Leg² = 25

√Leg² = √25

Leg = 5 inches ⇒ x = 5

2. Using the ratio 1 : 1 : √2, this way:

1 : 1 : √2

x : x : 5√2

x = 5√2/√2

x = 5 and let's recall that in a 90 - 45 - 45 triangle legs are equal, therefore. ratio is:

5 : 5 : 5√2

Answer:

4 is the square root of 16 :)

Step-by-step explanation:

Answer:

I think the answer you're looking for is four?

The value of z in the equation [tex]1\frac{4}{11}[/tex] of z is 45 is 33.

Solution:

Given: [tex]1\frac{4}{11}[/tex] of z = 45

To find: The value of z

On solving the given equation,

[tex]1\frac{4}{11}\times z=45[/tex]

[tex]\Rightarrow\frac{1\times11+4}{11}\times z=45[/tex]

[tex]\Rightarrow\frac{15}{11}z=45[/tex]

On grouping the like terms in one side we get,

[tex]\Rightarrow z=45\times\frac{11}{15}[/tex]

On solving the values we get,

[tex]\Rightarrow z=3\times11\rightarrow33[/tex]

The required value of z is 33.

Steps to convert a mixed fraction into an improper fraction:

Step 1: Multiply the whole number part by the fraction's denominator.

Step 2: Add that to the numerator.

Step 3: Then write the result on top of the denominator.

Answer:

20 %.

Step-by-step explanation:

(40/200) * 100

= (2/ 10) * 100

= 2 * 10

= 20.

Final answer:

To express 40 as a percentage of 200, you set up a proportion and solve for x, finding that 40 is 20% of 200.

Explanation:

To express 40 as a percentage of 200, we can set up a proportion where 40 is to 200 as x is to 100 (since percentages are out of 100). This gives us the proportion 40/200 = x/100. Solving for x, we multiply both sides by 100 to isolate x on one side of the equation. This gives us x = (40 × 100) / 200.

Next, we perform the multiplication and division: x = 4000 / 200. Simplifying that, we get x = 20. Therefore, 40 is 20% of 200.

Answer:

0.13 tax

Step-by-step explanation:

0.044*3=0.132

Answer:

8000

Step-by-step explanation:

So n equals 0.00 and then in the parentheses 1.1 you would multiply those two numbers X 1300. and then you would ×that answer by 8000 and you get 8000 .

Answer:

Step-by-step explanation:

The mean means the average of the numbers.

The mean will be [tex]\frac{25000\times5 + 27000\times3 + 34000}{5 + 3 + 1} = \frac{240000}{9} = 26666.666666666[/tex].

The differences of the earnings from the mean are 1666.67, 26997.33, 33997.33.

Squaring the numbers we get, 2777788.89, 728855827.13, 1155818447.12.

We need to find the mean of the above numbers to get the standard deviation.

Thus, the standard deviation is [tex]\frac{2777788.89\times5 + 728855827.13\times3 + 1155818447.12}{9} = 372919430.33[/tex].

The number is 5.

Step-by-step explanation:

Let,

x represent the unknown number.

According to given statement;

add five to twice a number the results is fifteen

2x + 5 = 15

Subtracting 5 from both sides

[tex]2x+5-5=15-5\\2x=10[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{10}{2}\\x=5[/tex]

The number is 5.

Keywords: variable, addition

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Answer:

-15

Step-by-step explanation:

The pattern is adding 3 and adding a negative sign

Answer:3

Step-by-step explanation:

Answer:

x=24

Step-by-step explanation:

Here, you need to make proportion and find x.

12:16=18:x

We multiply 12 by x and 16 by 18:

12x=288

Divide by 12 both sides :

x=24

For this case we must simplify the following expression:

[tex]x ^ 2-3xy-5xy-7y ^ 2 + 4x ^ 2 + 8y ^ 2[/tex]

We must add similar terms taking into account that:

[tex](x ^ 2 + 4x ^ 2) + (- 3xy-5xy) + (- 7y ^ 2 + 8y ^ 2) =\\5x ^ 2-8xy + y ^ 2[/tex]

Thus, the simplified expression is:

[tex]5x ^ 2-8xy + y ^ 2[/tex]

Answer:

[tex]5x ^ 2-8xy + y ^ 2[/tex]

To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles.

Step-by-step explanation: To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles.

Answer:

62.5 gallons

Step-by-step explanation:

Divide by 8