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3 years ago

Which number line represents the solutions to 1-2x1 = 4?

Mathematics

1 answer:

kaheart [24]3 years ago

8 0

Answer:

Third option: $x = -2$ and $x = 2$

Step-by-step explanation:

Given:

$|-2x|=4$

For a modulus function, if $|f(x)|=a$ , then,

$f(x)=\pm a$

Here, $f(x)=-2x$ , $a=4$

∴ $-2x=\pm 4\\ -2x=-4\textrm{ or } -2x=4\\ x=\frac{-4}{-2}\textrm{ or }x=\frac{4}{-2}\\ x= 2\textrm{ or }x=-2$

Therefore, the third option is the correct answer as the graph has $x$ values as -2 and 2

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What is KN + IK?<br> !it’s not 1!

sergiy2304 [10]

The answer is 6, K-N is 4, and I-K is 2, and as we all know, 4+2=6

6 0

3 years ago

Melanie's room measures 10 ft by 12 ft. Her rug covers 90 ft². Explain how to determine the percent of floor covered by the rug.

Inessa [10]

$\huge \bf༆ Answer ༄$

Here's the solution ~

Area of floor is ;

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:10 \times 12$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:120 \: ft {}^{2}$

Area covered by rug is ;

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:90 \: ft {}^{2}$

So, the percentage of floor covered by rug is ~

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \dfrac{90}{120} \times 100$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \dfrac{3}{4} \times 100$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:3 \times 25$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:75 \%$

5 0

3 years ago

Read 2 more answers

Bob's carpet cleaning company uses the equation y=22x+30 to calculate cost, y, to clean x numbers of rooms. Andy's carpet cleani

olga_2 [115]

Bob charges $140
Andy charges $135
Andy is cheaper

6 0

4 years ago

A random sample of size n1= 25, taken from a normal population with a standard deviation σ1= 5, has a mean X1= 80. A second rand

sesenic [268]

Answer:

The 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

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".

$\bar X_1 =80$ represent the sample mean 1

$\bar X_2 =75$ represent the sample mean 2

n1=25 represent the sample 1 size

n2=36 represent the sample 2 size

$\sigma_1 =5$ sample standard deviation for sample 1

$\sigma_2 =3$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =80-75=5$

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.88$