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3 years ago

The sum of two numbers is 49. The sum of the smaller and 2 times the larger is 83. Find the two numbers.

2 answers:

8 0

Let the smaller no be x and the larger no be y.So according to given conditions,
x+y=49--------(1)
x+2y=83-------(2)
subtracting eq2 from eq1, we get
y=34.put in eq.1, we get x=15, so the two numbers are 15 and 34.

levacccp [35]3 years ago

3 0

Let the small number be x and the big number be y
x+y=49
x+2y=83
by solving simultaneously,
x=15 and y=34

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3 years ago

Solve the system of equations using substitution and Elimination

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<h2>Greetings!</h2>

Answer:

y = $\frac{-18}{7}$ and x = $\frac{50}{7}$

Step-by-step explanation:

To solve simultaneous equations, you need to have the number in front of both x's or y's the same. (signs doesn't matter)

To get -x to -10x we simply need to multiply the first equation by 10:

-x * 10 = -10x

-9y * 10 = -90y

16 * 10 = 160

-10x - 90y = 160

Now we can add the two equations:

-10x + 10x = 0

-90y + 20y = -70y

160 + 20 = 180

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70y = -180

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y = $\frac{-18}{7}$

Now plug $\frac{-18}{7}$ into the second equation:

10x + 20( $\frac{-18}{7}$ ) = 20

10x - $\frac{360}{7}$ = 20

Move the $\frac{360}{7}$ over to the other side, making it a positive:

10x = 20 + $\frac{360}{7}$

10x = $\frac{500}{7}$

Divide both sides by 10:

x = $\frac{50}{7}$

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3 years ago

A recent poll of 120 randomly selected adults who frequent the local farmer's market found that 54 have purchased reusable clot

Olenka [21]

Answer:

95% Confidence interval: (0.361,0.539)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 120

Number of farmers who reusable cloth bags, x = 54

$\hat{p} = \dfrac{x}{n} = \dfrac{54}{120} = 0.45$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96$

Putting the values, we get:

$0.45\pm 1.96(\sqrt{\dfrac{0.45(1-0.45)}{120}}) = 0.45\pm 0.089\\\\=(0.361,0.539)$

is the required 95% confidence interval for the proportion of adults who have purchased reusable cloth bags.

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4 years ago