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3 years ago

40. What is the value of x? (7x – 8)° (6x +11°) Drawing not to scale

Mathematics

2 answers:

fenix001 [56]3 years ago

5 0

Answer:

The value of x is 19.

Step-by-step explanation:

We know that both of these expressions are equal because of vertically opposite angles. Let's solve.

=> 7x - 8 = 6x + 11
=> 7x - 6x = 19
=> x = 19

Hence, the value of x is 19.

Hoped this helped.

$BrainiacUser1357$

Leni [432]3 years ago

5 0

Answer:

x= 19

Step-by-step explanation:

Recall the Vertical Angles Theorem which states that when two lines intersect, vertical angles are congruent. In this case, 7x-8 and 6x +11 are vertical angles, so they are congruent. We can conclude that an equation can be made to find the value of x where:

$7x-8=6x+11$

Solve out the equation to find the value of x.

$7x-8+8=6x+11+8$

$7x=6x+19$

$7x-6x=6x+19-6x$

$x=19$

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Marianna [84]

2+4z-18
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the same can be done for the second one 2+k-8

make it 2+k-8=0

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3 years ago

Find the range of the function for given domain f(x)=2x-7; (-2,-1,0,1,2)

Gelneren [198K]

Answer:

{-11, -9, -7, -5, -3}

Step-by-step explanation:

Put each domain value into the function to find the corresponding range value. The range is the list of all of those values.

range = f(domain)

= 2{-2, -1, 0, 1, 2} -7 = {-4, -2, 0, 2, 4} -7

= {-11, -9, -7, -5, -3} . . . . . the range for the given domain

_____

If you have a lot of function values to find, a spreadsheet or calculator can be helpful.

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3 years ago

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3 years ago

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books check

Verdich [7]

Answer:

$n=(\frac{1.960(150)}{90})^2 =10.67 \approx 11$

So the answer for this case would be n=11 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =150$ represent the population standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The confidence interval for this case is given by: (740, 920)

We can find the estimate for the mean and we got:

$\bar X = \frac{740+920}{2} = 830$

and the margin of error is given by :

$ME = \frac{920-740}{2}= 90$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =90 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(150)}{90})^2 =10.67 \approx 11$

So the answer for this case would be n=11 rounded up to the nearest integer

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3 years ago