MATHEMATICS HIGH SCHOOL

Simplify.
10 – 5.3 • (–4 + –6)
a. 63
b. 47
c. –43
d. –47

Answers

Answer 1
Answer: 10-5.3*(-4+-6)
10-5.3*(-10)
10-(-53)=63

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What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0?

Answers

Answer:  The required equation of the line is 4x+y=6.

Step-by-step explanation:  We are given to find the equation of the line that passes through (1, 2) and is parallel to the line whose equation is as follows:

4x+y-1=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)

The slope-intercept form of the given line (i) is

4x+y-1=0\n\n\Rightarrow 4x+y=1\n\n\Rightarrow y=-4x+1,

where, slope of the line is, m = - 4.

Since parallel lines have equal slopes, so the slope of the new line that passes through the point (1, 2) is

m = - 4.

Therefore, the equation of the line will be

y-2=m(x-1)\n\n\Rightarrow y-2=-4(x-1)\n\n\Rightarrow y-2=-4x+4\n\n\Rightarrow 4x+y=6.

Thus, the required equation of the line is 4x+y=6.
y=-4x+6
or if you need it in the original format
4x+y-6=0

Natalie tried to evaluate the expression \left( 4^{-3} \cdot 2^{-3} \right)^{0}(4 −3 ⋅2 −3 ) 0 left parenthesis, 4, start superscript, minus, 3, end superscript, dot, 2, start superscript, minus, 3, end superscript, right parenthesis, start superscript, 0, end superscript. \begin{aligned} &\phantom{=}\left( 4^{-3} \cdot 2^{-3} \right)^{0} \\\\ &=\left( 8^{-3}\right)^{0} &\text{Step } 1 \\\\ &= 8^{0} &\text{Step } 2 \\\\ &=0&\text{Step } 3 \end{aligned} ​ =(4 −3 ⋅2 −3 ) 0 =(8 −3 ) 0 =8 0 =0 ​ Step 1 Step 2 Step 3 ​ Did Natalie make a mistake? If so, in which step?

Answers

Given:

The expression is

\left( 4^(-3) \cdot 2^(-3) \right)^(0)

To find:

The Natalie's mistake.

Solution:

We have,

\left( 4^(-3) \cdot 2^(-3) \right)^(0)

Using properties of exponents, we get

=\left( (4* 2)^(-3) \right)^(0)       [\because a^mb^m=(ab)^m]

=\left( (8)^(-3) \right)^(0)

=\left( 8 \right)^(0)               [\because (a^m)^n=a^(mn)]

=1                 [\because a^0=1,\text{ where, a is any non zero number}]

Therefore, Natalie make a mistake in Step 3. She write 8^0=0 instead of 8^0=1.

Answer:

d

Step-by-step explanation:

Given the values in the probability distribution table, determine the standard deviation. A. 3.2
B. 13.9
C. 3.9
D. 2.0

Answers

Answer:

D. 2.0 is the right answer

Step-by-step explanation:

Note: All decimals were converted to fractions.

The standard deviation of the given distribution is:

σ=1.965

Answer:

1.96

Step-by-step explanation:

Solution:-

- We will use the table given to determine the standard deviation of random variable x. From descriptive statistics we have the following formula for standard deviation (s.d) :

                s.d (x) = sqrt ( Var(x) )

- The formula for Variance ( Var (x) ) is also taken from descriptive statistics as follows:

                Var(X) = E ( X^2) + [ E(X) ] ^2

- Where,

                E ( X^2) = 0^2*0.15 + 1^2*0.07 + 2^2*0.19 + 3^2*0.09 + 4^2*0.16 + 5^2*0.23 +6^2*0.11 \n\nE ( X^2) = 13.91 \n\n

               

                E(X) = 0*0.15\:+\:1*0.07\:+\:2*0.19\:+\:3\cdot \:0.09\:+\:4\cdot \:0.16\:+\:5\cdot \:0.23\:+6\cdot \:0.11\n\nE(X) = 3.17\n\n(E(X))^2 = 10.0489

- So the variance is:

                Var ( X ) = 13.91 - 10.0489 = 3.8611

                s.d (x) = √3.8611 = 1.96

A shop is giving 20% discount in a sale. A shirt in the shop normally costs $60. How much does it cost in the sale?

Answers

20 percent of 60 is 1260 dollars minus 12 is?That's your answer.
Since the shop is giving 20% discount, that means the paid amount would actually
be (100 -20) % = 80 %

So for a $60 shirt,  amount =  80% of 60

= (80/100) x 60 
= (8/10) x 60
= 48.

Cost in sale = $48.
Cheers.

Simplify 3j - {2k - [5h - (3j + k)]

Answers

Simplification:

3j-[2k-[5h-(3j+k)]]

= 3j-[2k-(5h-3j-k)]

= 3j-(2k-5h+3j+k)

= 3j-2k+5h-3j-k

= 3j-3j-2k-k+5h

= 0-3k+5h

= -3k+5h

= 5h-3k

Answer: the correct answer is 5h-3k

Albert used 3/8 of a half gallon of paint.  What fraction of a gallon of paint did he use?

Answers