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bekas [8.4K]
3 years ago
12

Someone plz solve and check thanks

Mathematics
1 answer:
maksim [4K]3 years ago
8 0

Remember to follow the order of operation, PEMDAS. PEMDAS stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

5. 9(7x - 4) = 27

First, distribute 9 to all terms within the parenthesis:

9(7x - 4) = 27

(9 * 7x) - (9 * 4) = 27

63x - 36 = 27

Next, isolate the variable, x. Do the opposite of PEMDAS.

First, add 36 to both sides:

63x - 36 (+36) = 27 (+36)

63x = 27 + 36

63x = 63

Isolate the variable, x. Divide 63 from both sides:

(63x)/63 = (63)/63

x = 63/63 = 1

x = 1

~

6. 5(3x + 8) = 175

First, distribute 5 to all terms within the parenthesis:

5(3x + 8) = (5 * 3x) + (5 * 8) = 15x + 40

15x + 40 = 175

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 40 from both sides:

15x + 40 (-40) = 175 (-40)

15x = 175 - 40

15x = 135

Next, divide 15 from both sides of the equation:

(15x)/15 = (135)/15

x = 135/15 = 9

x = 9

~

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Answer: The confidence interval would be (120.6, 159.4).

Step-by-step explanation:

Since we have given that

n = 200

mean = \bar{x}=140\ mm

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So, 95% confidence interval would be

\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=140\pm 1.96\times \dfrac{140}{\sqrt{200}}\\\\=140\pm 19.40\\\\=(140-19.4,140+19.4)\\\\=(120.6,159.4)

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Answer:

The values of a and b are:

  • a = 2
  • b = 2

Step-by-step explanation:

We know that the slope-intercept form of the line equation

y = ax+b

where

  • a is the slope
  • b is the y-intercept

From the diagram of the line graph, we can fetch the two points

  • (0, 2)
  • (-1, 0)

Determining the slope between (0, 2) and (-1, 0)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(-1,\:0\right)

a=\frac{0-2}{-1-0}

a=2

Thus, the value of a = 2

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 2

Thus, the y-intercept b = 2

now substituting a = 2 and b = 2 in the slope-intercept form of the line equation

y = ax+b

y = 2x + 2         ∵ a = 2 , b = 2

Thus, the line of equation is:

y = 2x+2

now comparing with y = ax+b

Here:

a = 2

b = 2

Therefore, the values of a and b are:

  • a = 2
  • b = 2
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