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2 years ago

What is the measure of angle LKJ?

Mathematics

1 answer:

Dmitry_Shevchenko [17]2 years ago

8 0

Where is the angle? How can I solve this without the problem?

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The graph below represents which system of inequalities?

ziro4ka [17]

Answer:

The system of inequalities is

$y\leq x+3$

$y\leq -2x+3$

Step-by-step explanation:

step 1

Find the equation of the solid line that goes through the points negative 3, 0, negative 4, negative 1

Let

A(-3,0),B(-4,-1)

Find the slope

m=(-1-0)/(-4+3)

m=-1/-1=1

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

m=1

point A(-3,0)

substitute

y-0=(1)(x+3)

y=x+3

The solution is the shaded area below the solid line

therefore

The equation of the first inequality is equal to

$y\leq x+3$

step 2

Find the equation of the solid line that goes through the points 1, 1, 2, negative 1

Let

C(1,1),D(2,-1)

Find the slope

m=(-1-1)/(2-1)

m=-2/1=-2

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

m=-2

point C(1,1)

substitute

y-1=(-2)(x-1)

y=-2x+2+1

y=-2x+3

The solution is the shaded area below the solid line

therefore

The equation of the first inequality is equal to

$y\leq -2x+3$

therefore

The system of inequalities is

$y\leq x+3$

$y\leq -2x+3$

3 0

3 years ago

Lydia bought a shirt at 20% off its retail price is $40. She paid 5% tax on the price after the discount. How much did Lydia pay

Naya [18.7K]

Answer:

Step-by-step explanation:

multiply .20 with 40

which gets you 8

subtract 8 from 40

which is 32

multiply .05 with 32

which is 1.6

subtract 1.6 from 32 which gets you $30.40

4 0

2 years ago

Find the measure of the angle x to the nearest hundredth.

vfiekz [6]

Answer:

Are you in k12? Bc I failed this :(

Step-by-step explanation:

8 0

3 years ago

PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)

Anvisha [2.4K]

1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
$\left\begin{array}{c}x+y=80 . . . (1)\\70x+80y=76(80) . . . (2)\end{array}\right \\ \\ \Rightarrow \left\begin{array}{c}80x+80y=6400 . . . (3)\\70x+80y=6080 . . . (4)\end{array}\right \\ \\ \Rightarrow10x=320 \\ \\ \Rightarrow x=32 \\ \\ \Rightarrow y=80-32=48$
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.

2.) Volume of alcohol in the original mixture
$\frac{35}{100} \times 40=14$ quarts

Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
$\frac{48}{100} \times (40+x)=14+x \\ \\ \Rightarrow19.2+0.48x=14+x \\ \\ \Rightarrow0.52x=5.2 \\ \\ \Rightarrow x=10$

Therefore, 10 quarts of pure alcohol should be added

3.) Original proportion of white paint in the mixture
$=\frac{5}{5+11}=\frac{5}{16}$

Let x be the number of gallons of white paint to be added, then
$\frac{5+x}{16+x}=\frac{2}{3} \\ \\ \Rightarrow3(5+x)=2(16+x) \\ \\ \Rightarrow15+3x=32+2x \\ \\ \Rightarrow x=32-15=17$
Therefore, 17 gallons of white paint should be added.

4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
$x - 2 + x + x + 2 = 25 \\ \\ \Rightarrow3x=25\Rightarrow x=8.33$
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.

4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
$x - 2 + x + x + 2 = 45 \\ \\ \Rightarrow3x=45\Rightarrow x=15$
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.

5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
$\frac{1}{t} = \frac{1}{9} + \frac{1}{12} - \frac{1}{15} = \frac{20+15-12}{180} = \frac{23}{180} \\ \\ \Rightarrow t= \frac{180}{23} =7.83$
Therefore, it will take 7.83 hours to get the tank filled up.

3 0

3 years ago

A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$