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2 years ago

Find the distance between (1,2) and (-3,5)

Mathematics

2 answers:

m_a_m_a [10]2 years ago

8 0

Answer:

Step-by-step explanation:

√((5-2)^2 + (-3-1)^2) = √(9+16) = 5

Amanda [17]2 years ago

7 0

Answer:

5 units

Step-by-step explanation:

To Find :-

Distance

Solution :-

Using Distance Formula ,

> d = √[ ( 1 +3)²+ ( 2-5)² ]

> d = √[ 4² + 3² ]

> d = √ [ 16 + 9 ]

> d = √25

> d = 5

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How do you compute fractions

Elan Coil [88]

Step 1: Make sure the bottom numbers (the denominators) are the same.
Step 2: Add the top numbers (the numerators), put the answer over the denominator.
Step 3: Simplify the fraction (if needed)

6 0

3 years ago

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in t

andreyandreev [35.5K]

Answer:

The test statistic is c. 2.00

The p-value is a. 0.0456

At the 5% level, you b. reject the null hypothesis

Step-by-step explanation:

We want to test to determine whether or not the mean waiting time of all customers is significantly different than 3 minutes.

This means that the mean and the alternate hypothesis are:

Null: $H_{0} = 3$

Alternate: $H_{a} = 3$

The test-statistic is given by:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

Sample of 100 customers.

This means that $n = 100$

3 tested at the null hypothesis

This means that $\mu = 3$

The average length of time it took the customers in the sample to check out was 3.1 minutes.

This means that $X = 3.1$

The population standard deviation is known at 0.5 minutes.

This means that $\sigma = 0.5$

Value of the test-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}}$

$z = 2$

The test statistic is z = 2.

The p-value is

Mean different than 3, so the pvalue is 2 multiplied by 1 subtracted by the pvalue of Z when z = 2.

z = 2 has a pvalue of 0.9772

2*(1 - 0.9772) = 2*0.0228 = 0.0456

At the 5% level

0.0456 < 0.05, which means that the null hypothesis is rejected.

7 0

3 years ago

Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, we can notice that 1 is a trivial solution as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago

Solve the inequality. –6 < 2x – 4 < 4

Darya [45]

Answer:

–1 < x < 4

Step-by-step explanation:

Let's solve your inequality step-by-step.

−6<2x−4<4

−6+4<2x−4+4<4+4(Add 4 to all parts)

−2<2x<8

(−2 /2) < (2x /2 )< (8 /2)

(Divide all parts by 2)

−1<x<4

6 0

3 years ago

Please please please help me with this. I can't remember how to work this problem out. If someone could explain to me how to do

RideAnS [48]

If the two triangles are congruent it means that their side lengths are equal, so we can assume that x = 3x - 8 and so 2x = 8 and x = 4. Hope that helps :)

6 0

3 years ago