Share £180 in the ratio<br> 1:9

Select all of the answers below that are equivalent to T = {Tinkey-Winky, Laa-Laa,

stepan [7]

Answer:

{thermometer, fridge, rusty nail, deoderant}
{credit card, face wash, tweezers, shovel}
{clothes, glass, car, greeting card}

Step-by-step explanation:

The options that will be equivalent to T will have to be the options that have the same Cardinality as T. Cardinality refers to the number of elements in a set and in the set T, there are 4 elements being Tinkey-Winky, Laa-Laa, Dipsy, Po so the Cardinality is 4.

The equivalent sets would therefore be sets with a cardinality of 4 as well and those are;

{thermometer, fridge, rusty nail, deoderant}
{credit card, face wash, tweezers, shovel}
{clothes, glass, car, greeting card}

3 0

2 years ago

3.30 Survey response rate. Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a pa

Artist 52 [7]

Answer:

0% probability that at least 1,500 will agree to respond

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 15000, p = 0.09$

So

$\mu = E(X) = np = 15000*0.09 = 1350$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15000*0.09*0.91} = 35.05$

What is the probability that at least 1,500 will agree to respond

This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1499 - 1350}{35.05}$

$Z = 4.25$

$Z = 4.25$ has a pvalue of 1.

1 - 1 = 0

0% probability that at least 1,500 will agree to respond

6 0

2 years ago

You deposit $2,900 into a bank account with a simple interest rate of 10% how do you find your account balance after 5 years

MAVERICK [17]

Formula: A = P(1 + rt)<span>
P= 2,900
R= 10%
T= 5 years

Answer: $4,350.00</span>

6 0

2 years ago

A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every ba

Ahat [919]

Answer:

$z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68$

Step-by-step explanation:

Information provided

n=100 represent the random sample taken

X=21 represent the number of bags overfilled

$\hat p=\frac{21}{100}=0.21$ estimated proportion of overfilled bags

$p_o=0.15$ is the value that we want to test

z would represent the statistic

Hypothesis

We need to conduct a hypothesis in order to test if the true proportion of overfilled bags is higher than 0.15.:

Null hypothesis: $p =0.7$

Alternative hypothesis: $p > 0.15$

The statistic for this case is:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

And replacing the info given we got:

$z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68$

5 0

2 years ago

Which sequence of transformations produces R'S'T' from RST? On a coordinate plane, triangle R S T has points (0, 0), (negative 2

arsen [322]

Answer:

Step-by-step explanation:

Given is a triangle RST and another triangle R'S'T' tranformed from RST

Vertices of RST are (0, 0), (negative 2, 3), (negative 3, 1).

Vertices of R'S'T' are (2, 0), (0, negative 3), (negative 1, negative 1).

Comparing the corresponding vertices we find that x coordinate increased by 2 while y coordinate got the different sign.

This indicates that there is both reflection and transformation horizontally to the right by 2 units

So first shifted right by 2 units so that vertices became

(2,0) (0,3) (-1,1)

Now reflected on the line y=0 i.e. x axis

New vertices are

(2,0) (0,-3) (-1,-1)

8 0

2 years ago

Share £180 in the ratio 1:9