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Musya8 [376]
3 years ago
6

In a certain game, a player can solve easy or hard puzzles. A player earns 30 points for solving an easy puzzle and 60 points fo

r solving a hard puzzle. Tina solved a total of 50 puzzles playing this game, earning 1,950 points in all. How many hard puzzles did Tina solve?
Mathematics
1 answer:
Karolina [17]3 years ago
3 0

This is a system of equations. We can solve it by recognizing the two linear equalities we've given to solve this equation.

First, let's start off by recognizing two variables: x and y. x will be our number of hard puzzles, and y will be our number of easy puzzles. We're given that the number of hard puzzles and easy puzzles sum to 50, so we can rewrite that as:

x+y=50

Next, we're given that the sum of the points gained from the hard puzzles (60x), and the number of points gained from the easy puzzles (30y), sum to 1950. We can rewrite that as:

60x+30y=1950

Now, we have our two linear equations, and we must solve for the hard puzzles, so x. Solving for the hard puzzles means eliminating the easy puzzles from our systems, so we can multiply our first equation by 30, and subtract it from the first equation. This is a technique called elimination.

30x+30y=1500 \\ 60x+30y=1950 \\ 30x=450 \implies x=15

Since x=15, Tina has solved 15 hard puzzles.

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27/6 can be written as 27 divided by 6 to make it easier for you to understand the answer would be 4.5 
4 0
3 years ago
Which of the following represents x =1/3y written in general form?
Serhud [2]

If you would like to write x = 1/3 * y in general form, you can do this using the following steps:

The general form of the equation is: ax + by + c = 0.

x = 1/3 * y

x - 1/3 * y = 0


The correct result would be x - 1/3 * y = 0.

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3 years ago
Given ​ f(x) = x^2 + 14x + 40 ​. Enter the quadratic function in vertex form in the box. f(x)=
finlep [7]
Recall that the vertex form of a quadratic function (or parabolic function) is equal to

f(x) = a(x - h)^{2} + k

Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.

One concept that we must remember when completing the square is that

(a + b)² = a² + 2ab + b²

So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.

So, going back to the function, we have

f(x) = (x^{2} + 14x + 40 + 0)
f(x) = (x^{2} + 14x + 40 + 49 - 49)
f(x) = (x^{2} + 14x + 49) + 40 - 49
f(x) = (x + 7)^{2} - 9

Thus, we have derived the vertex form of the function. 

Answer: f(x) = (x + 7)² - 9
6 0
3 years ago
Read 2 more answers
The annual rainfall in a certain region is approximately normally distributed with mean 41.4 inches and standard deviation 5.7 i
stich3 [128]

Complete question :

The annual rainfall in a certain region is approximately normally distributed with mean 41.4 inches and standard deviation 5.7 inches. Round answers to the nearest tenth of a percent. a) What percentage of years will have an annual rainfall of less than 43 inches? b) What percentage of years will have an annual rainfall of more than 39 inches? c) What percentage of years will have an annual rainfall of between 38 inches and 42 inches?

Answer:

0.61053

0.66314

0.26647

Step-by-step explanation:

Given that :

Mean (m) = 41.4 inches

Standard deviation (s) = 5.7 inches

a) What percentage of years will have an annual rainfall of less than 43 inches?

P(x < 43)

USing the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (43 - 41.4) / 5.7 = 0.2807017

p(Z < 0.2807) = 0.61053 ( Z probability calculator)

b) What percentage of years will have an annual rainfall of more than 39 inches? c)

P(x > 39)

USing the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (39 - 41.4) / 5.7 = −0.421052

p(Z > −0.421052) = 0.66314 ( Z probability calculator)

What percentage of years will have an annual rainfall of between 38 inches and 42 inches?

P(x < 38)

USing the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (38 - 41.4) / 5.7 = −0.596491

p(Z < −0.596491) = 0.27545 ( Z probability calculator)

P(x < 42)

USing the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (42 - 41.4) / 5.7 = 0.1052631

p(Z < 0.1052631) = 0.54192 ( Z probability calculator)

0.54192 - 0.27545 = 0.26647

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navik [9.2K]

Answer:

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Step-by-step explanation:

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