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2 years ago

Which is the value of x in the equation? 4(x-3) = 40

Mathematics

2 answers:

mario62 [17]2 years ago

8 0

Answer:14

Step-by-step explanation:

liraira [26]2 years ago

3 0

Answer:

x = 13

Step-by-step explanation:

4(x-3)=40

4x - 12 = 40

4x = 40 + 12

4x = 52

x = 13

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A quality analyst of a tennis racquet manufacturing plant investigates if the length of a junior's tennis racquet conforms to th

Burka [1]

Answer:

Confidence interval : $21.506$ to $24.493$

Step-by-step explanation:

A quality analyst selects twenty racquets and obtains the following lengths:

21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

So, sample size = n =20

Now we are supposed to find Construct a 99.9% confidence interval for the mean length of all the junior's tennis racquets manufactured at this plant.

Since n < 30

So we will use t-distribution

Confidence level = 99.9%

Significance level = α = 0.001

Now calculate the sample mean

X=21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

Sample mean = $\bar{x}=\frac{\sum x}{n}$

Sample mean = $\bar{x}=\frac{21+25+23+22+24+21+25+21+23+ 26+ 21+24+22+ 24+23+21+ 21+ 26+23+ 24}{20}$

Sample mean = $\bar{x}=23$

Sample standard deviation = $\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$

Sample standard deviation = $\sqrt{\frac{(21-23)^2+(25-23)^2+(23-23)^2+(22-23)^2+(24-23)^2+(21-23)^2+(25-23)^2+(21-23)^2+(23-23)^2+(26-23)^2+(21-23)^2+(24-23)^2+(22-23)^2+(24-23)^2+(23-23)^2+(21-23)^2+(21-23)^2+(26-23)^2+(23-23)^2+(24-23)^2}{20-1}}$

Sample standard deviation= s = $1.72$

Degree of freedom = n-1 = 20-1 -19

Critical value of t using the t-distribution table $t_{\frac{\alpha}{2}$ = 3.883

Formula of confidence interval : $\bar{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}$

Substitute the values in the formula

Confidence interval : $23 \pm 1.73 \times \frac{1.72}{\sqrt{20}}$

Confidence interval : $23 -3.883 \times \frac{1.72}{\sqrt{20}}$ to $23 + 3.883 \times \frac{1.72}{\sqrt{20}}$

Confidence interval : $21.506$ to $24.493$

Hence Confidence interval : $21.506$ to $24.493$

3 0

3 years ago

Read 2 more answers

Why is every prime number greater than 2 an odd number?

Arlecino [84]

Because if it was even, then it would be divisble by 2 which makes it not prime

4 0

3 years ago

Read 2 more answers

Write a numerical expression for the phrase and simplify the expression. The sum of -6 and -10 increased by 11.

BlackZzzverrR [31]

Answer:

-116

Step-by-step explanation:

5 0

3 years ago

Find the lengths of the sides of the triangle PQR. P(4, 3, 4), Q(2, 1, 3), R(2, 7, 0) a. |PQ| = b. |QR| = c. |RP| =

Nat2105 [25]

Given :

Three points , P(4, 3, 4), Q(2, 1, 3), R(2, 7, 0) .

To Find :

The length of sides .

Given :

We know , length of two points P(x,y ,z) and Q(a,b,c) is given by :

$L=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}$

Length of PQ :

$PQ=\sqrt{(4-2)^2+(3-1)^2+(4-3)^2}\\\\PQ=\sqrt{4+4+1}=\sqrt{9}\\\\PQ=3$

Length of QR :

$QR=\sqrt{(2-2)^2+(1-7)^2+(3-0)^2}\\\\QR=\sqrt{0+6^2+3^2}\\\\QR=\sqrt{36+9}\\\\QR=\sqrt{45}\\\\QR=3\sqrt{5}$ :

Length of RP :

$RP=\sqrt{(2-4)^2+(7-3)^2+(0-4)^2}\\\\RP=\sqrt{2^2+4^2+4^2}\\\\RP=\sqrt{4+16+16}\\\\RP=\sqrt{36}\\\\RP=6$

Hence , this is the required solution .

4 0

3 years ago

How to find when,<br>y=-1/3x - 3<br>

Montano1993 [528]

The -3 would be where your line crosses the y-axis, so you would plot your point at -3. your slope will always be counted as rise/run, basically meaning you would count along the y-axis a certain amount of times, in this case -1, and along the x-axis a certain amount of times, here would be three. your next plot point would be (3,-4) and so on. hope this helped!

7 0

2 years ago