Grade 8 Module 4 Mid Module Assessment

1.)Match each equation with the appropriate solution type.

x(5-2)=4x-x

whats that type of solution ????
​

The original price of the camera is x = $ 324

Given data ,

Let the original price of the camera be x.

Iskandar sells the camera to Teck Meng at a profit of 15%, so he sells it for 1.15x.

Teck Meng then sells the camera to Ryan at a loss of 10%, which means he sells it for 0.9(414) = 372.60.

Since Teck Meng bought the camera for 1.15x and sold it for 372.60, we can set up the equation:

1.15x = 372.60

Divide by 1.15 on both sides , we get

x = 324

Hence , the original price of the camera was $ 324

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40 pounds of salami are purchased by a deli for its renowned grinder sandwiches. An illustration of an intermediate good is salami.

Given fill-in-the-blank;

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of___ goods.

The answer for this case is Intermediate.

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of Intermediate goods.

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Answer:

J. V = 12h cubic units

Step-by-step explanation:

Volume if a square pyramid = ⅓*a²*h

Where,

h = height = ?

a = edge = 6 in.

Plug in the values

Volume = ⅓*6²*h

V = ⅓*36*h

V = 12*h

V = 12h cubic units

Answer: D

break it into two shapes:

square: side length^2      7^2

49

triangle: side length x side length divided by two     (7 x 12) / 2

                                                                                        84 / 2

                                                                                       42

add them together:

49 + 42= 91

The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³)  is equal to w = -1.

As given in the question,

Given equation is equal to :

7 ( w + 7 )³ = 7(6³)

Divide both the side of the equation by 7 we get,

⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7

⇒( w + 7 )³ = (6³)  

Take cube root both the side of the equation we get,

⇒∛( w + 7 )³ = ∛(6³)  

⇒ w + 7 = 6

Now subtract 7 from both the side of the equation we get,

⇒w + 7 - 7 = 6 - 7

⇒ w = -1

Therefore, the value of the variable 'w' for the given equation is equal to w = -1.

The complete question is:

Solve this equation:

7 ( w + 7 )³ = 7(6³)

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The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).

In determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.

Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.

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Given:-

Nick would like to buy his dream house for $270,000. He finances the whole purchase price of $270,000.

To find the monthly payment if he secures a home mortgage loan at 3% APR for 30 years.

The first step is to calculate an APR payment amount. This is done by adding your closing costs to your loan amount, and then calculating a new monthly payment at your loan's interest rate. In this case, if you borrowed ($270,000.00 + $6,200.00) at 3% for 30 years, your APR monthly payment would be $1,164.47. Notice that this is different than your actual payment of $1,138.33.

The second step is to calculate what interest rate produces a monthly payment equal to the APR payment amount. In this case, we calculate the interest rate that would require a $1,164.47 monthly payment on a loan of 30 years in the amount of $270,000.00. The result is 3.178% which is the APR for your loan.

So we get the details as,

Using the z-distribution, as we have the standard deviation for the population, to test the hypothesis, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

At the null hypothesis, it is tested if the mean time is of 28 minutes, that is:

\(H_0: \mu = 28\)

At the alternative hypothesis, it is tested if the mean time is greater than 28 minutes, that is:

\(H_1: \mu > 28\).

The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

The parameters are:

In this problem, the values of the parameters are given by:

\(\overline{x} = 32, \mu = 28, \sigma = 5, n = 10\)

Hence:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{32 - 28}{\frac{5}{\sqrt{10}}}\)

\(z = 2.53\)

Considering that we have a right-tailed test, as we are testing if the mean is greater than a value, with a standard significance level of 0.05, the critical value is of \(z^\ast = 1.645\).

Since the test statistic is greater than the critical value, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

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Given that,

Total ladybugs = 10

Total butterflies = 5

More ladybugs than butterflies are = ladybugs - butterflies

=> 10 - 5

=> 5

Therefore, there will be 5 more ladybugs than butterflies.

Answer:

C. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

hope i helped

Answer:

Look down

Step-by-step explanation:

Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.

let's put h(x) in vertex form, and then let's see if we can get f(x) from there.

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{vertex}{\stackrel{h}{0}~~,~~\stackrel{k}{-3}}\qquad h(x)=a(x-0)^2-3 \\\\[-0.35em] ~\dotfill\)

\(h(x+2)=a[(x+2)-0]^2-3\implies h(x+2)=\underline{a(x+2)^2-3} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \underline{h(x+2)}-5\implies [a(x+2)^2-3]~~ - ~~5\implies &\boxed{a(x+2)^2-8=f(x)} \\\\ &a[x-\stackrel{h}{(-2)}]^2\stackrel{k}{-8}=f(x)\\\\ &\stackrel{vertex}{-2~~,~~-8} \end{array}\)

There are total 15 students per teacher and 8 students per tutor. For 100 students, total 13 tutors are required.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the given data provided in the question,

4 teachers  = 60 students

For 1 teacher = 60/4 = 15 students

Similarly,

6 tutors = 48 students

For 1 tutor = 48/6 = 8 students.

For total 100 students, total number of tutors = 100/8

= 12.5 or 13 tutors are required.

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Answer:

See step by step.

Step-by-step explanation:

lets define the events:
A: cuban festival        C: tropical Garden
B: street art show      D: african festival

a) theoretically the probability is

\(P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\\)
This is 25% (for each one, equally)

b) The experimental probability is given by:

\(P(A)= \frac{32}{150} =0.2133\)

\(P(B)= \frac{38}{150} =0.2533\)

\(P(C)= \frac{35}{150} =0.2333\)
\(P(D)= \frac{45}{150} =0.3000\)

c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.  

The exchange rate between Japanese Yen and Nepali Rupees in this case is given by Rs 0.92 per Yen.

The exchange rate between Japanese Yen and Nepali Rupees is

1 JPY = 0.7184 NPR

Therefore, the exchange rate is  6,852 JPY = 6,320 NPR

Therefore, the exchange rate between Japanese Yen and Nepali Rupees is 0.7184 NPR per 1 JPY.

The exchange rate between Japanese Yen and Nepali Rupees is given by the following formula:

Exchange Rate = (Total Amount in Nepali Rupees/Total Number of Japanese Yen)

Exchange Rate = (Rs 6320/6852 Yens) = Rs 0.92 per Yen.

Therefore, the exchange rate between Japanese Yen and Nepali Rupees in this case is given by Rs 0.92 per Yen.

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Answer:

The answer is d

Step-by-step explanation:

Answer:

C) 0degress<=x<=60 and 300<=x<=360

Step-by-step explanation:

Right on edge

Answer:

$50

Step-by-step explanation:

Answer:

I know that someone else already answered and got brainliest but I just thought to give some steps to solving because you never know who needs it ;)

The answer is 50 as the person who answered above me said.

Step-by-step explanation:

Now, to get to solving.

I hope this will be helpful to somebody and feel free to comment, ask questions, give feedback, and correct my steps if they are not correct!

Have a great day! :)

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer: 49 and 55

Step-by-step explanation:

The two unknown numbers are 64 and 40.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x be the larger number and y be the smaller number.

The sum of two numbers is 104.

So, x+y=104 --------(i)

The difference of two numbers is 24.

x-y=24 --------(ii)

From equation (ii), x=24+y

Substitute x=24+y in equation(i), we get

24+y+y=104

2y=80

y=40

Substitute y=40 in equation (i), we get

x=64

Therefore, the two numbers are 64 and 40.

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An equation that could be the equation of this parabola include the following: C. x = 1/12(y²).

In Mathematics, the standard equation of the directrix lines for any parabola that opens to the right is represented by this mathematical expression:

x = a(y - k)² + h.

Where:

By critically observing the graph which models the equation of this parabola, we can logically deduce that the vertex is at point (0, 0) and as such, we have the following:

h = 0

k = 0

a = positive.

x = a(y - k)² + h.

x = a(y - 0)² + 0.

x = ay²

Therefore, a possible equation is x = 1/12(y²).

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Answer:   \(\;\;\frac{1}{6} , \;\; 0.16667,\;\; \text{or about}\;\;17\%\)

Step-by-step explanation:

   A regular dice has 6 sides, and only one of those sides side has a six.

        We write probability as;

   \(\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} = \frac{\text{number of times six is on the dice}}{\text{number of numberss on the dice}} =\frac{1}{6}\)

Hi, there!

 _______

\(\boxed{\boxed{\sf{Probability=\dfrac{Favorable \ Outcomes}{Total \ Outcomes}}}}\)

Here,

» Favourable Outcome(s) -> getting a 6 on a die (1 outcome),  because only one side of a die has a six on it

» Total Outcomes -> 6 (you can only get 1, 2, 3, 4, 5, 6 if you roll one die)

So,

\(\sf{Probability_{(6)}=\dfrac{1}{6}}\)

Hope the answer - and explanation - made sense to you,

happy studying!!

                                                                                                        \(\tiny\textit{frozen \ melody}\)

The calculated volume of the cylinder is 424.3 cubic cm

From the question, we have the following parameters that can be used in our computation:

Base diameter = 6 cm

Height = 15 cm

Using the above as a guide, we have the following:

r = 6/2 = 3

h = 15

So, we have

V = πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 22/7 * 3² * 15

Evaluate

V = 424.3

Hence, the volume is 424.3 cubic cm

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Answer:

69.53 or 70(depending on rounding)

Step-by-step explanation:

The squares area is (9*2)^2 which is 324.

The circles area is 9^2 pi or 254.47 approx.

Subtract and you get 69.53 or 70

Answer:-(-1,026/3

Step-by-step explanation:

According to the data, Alondra would have to save $275 each month if she wants to have $7,000 after two years.

To calculate the savings that Alondra must make to have $7,000 after 2 years we must carry out the following procedure:

First, we must subtract $400 from her initial contribution to your savings.

$7,000 - $400 = $6,600

Then we must divide $6,600 into the number of months that are 2 years (24 months).

$6,600 / 24 = $275

Based on the above, if she saves $275 of her salary each month, she will have $7,000 after 2 years. This is possible because her monthly payment is $358.41

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(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

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15 is divisible by 75 true or false

Answer:

True

The difference between the low temperature and the high temperature on Tuesday is -1.1°C.

From the information given, the temperature Monday evening was 16.4 c the temperature dropped an average of 1 1/4 degrees each hour for the next 14 hours until it reached its lowest temperature for the day on Tuesday.

Therefore, the temperature on Tuesday will be:

= 1 1/4(14)

= 17.5

The difference in the temperature will then be:

= 16.4°C - 17.5°C

= -1.1°C.

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The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that the selling price of strawberries each pound = $2.50,

The selling price of grapes each pound = $2

The total earning = $160

Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,

x = y + 12 and 2.50x + 2y= 160

Solve the equation by substitution method;

x = 32 and  y = 20

Therefore, the number of pounds of strawberries sold is 32

the number of pounds of grapes sold is 20.

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