If one meter is approximately 3.28 feet,how many meters are in 20 feet

(3) The difference between two numbers is 8. If the larger is

Alecsey [184]

Answer:

x= 62

y= 54

Step-by-step explanation:

Step one:

given data

let the numbers be x and y and the larger be x the smaller be y

The difference between two numbers is 8

x-y= 8-----------1

If the larger is subtracted from three times the smaller, the difference is 100

3y-x=100------------2

from eqn 1, x= 8+y

put this in eqn 2

3y-(8+y)=100

3y-8-y=100

collect liker terms

3y-y-8=100

2y=108

y= 54

put y= 54 in eqn 1

x-y=8

x-54= 8

x= 8+54

x=62

5 0

3 years ago

Find the slope and reduce of p=(3/4,1 1/4) q=(-1/2,-1)

sergij07 [2.7K]

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
p&({{ \frac{3}{4}}}\quad ,&{{ \frac{1}{4}}})\quad 
% (c,d)
q&({{ -\frac{1}{2}}}\quad ,&{{ -1}})
\end{array}$

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-1-\frac{1}{4}}{-\frac{1}{2}-\frac{3}{4}}\quad \cfrac{\leftarrow LCD=4}{\leftarrow LCD=4}
\\\\\\
\cfrac{\frac{-4-1}{4}}{\frac{-2\cdot 1-3}{4}}\implies \cfrac{\frac{-5}{4}}{\frac{-5}{4}}\implies \cfrac{-5}{4}\cdot \cfrac{4}{-5}\implies 1$

7 0

3 years ago

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

Cloud [144]

Answer:

$z=\frac{13-20}{4}=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu$

$p_v = P(Z$

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.2=20$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$

The z score is given by this formula:

$z=\frac{x-\mu}{\sigma}$

If we replace we got:

$z=\frac{13-20}{4}=-1.75$

Let's assume that we conduct the following test:

H0: $\mu \geq 20$

H1: $\mu$

We want to check is the score for the student is significantly less than the expected value using random guessing.

So on this case since we have the statistic we can calculate the p value on this way:

$p_v = P(Z$

5 0

3 years ago

All points having an x-coordinate of 1 whose distance from the point (-3,-6) is 5

vazorg [7]

Answer:

$They'll \: be \: on \: the \: circle:$

$(x+3)^2+(y+6)^2=25$

$x=1$

$(y+6)^2=9$

$y + 6 = 3$

$y = -3$

$(1,-3)$

$y + 6 = -3$

$y = -9$

$(1,-9)$

Step-by-step explanation:

$Thank \: you!!!!!!$

6 0

3 years ago

What is the value of y when line m is parallel to line n?

kvasek [131]

Angles B and D are supplementary angles, so if B's angle is 30 degrees, then D's angle at y would be 150, since they have to add to 180.
In short, angle y = 150

6 0

3 years ago

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