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Liula [17]
3 years ago
13

A civics teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the othe

r was true, but the students did not know this. The probability that a student selected at random believed the true headline was 90\%90%90, percent and the probability that the student believed the false headline was 82\%82%82, percent. She found that 75\%75%75, percent of the students believed both headlines.
Mathematics
1 answer:
dusya [7]3 years ago
8 0

Answer:

The events are not mutually exclusive.

Step-by-step explanation:

To determine that in the sample, are the events "believed the false headline" and "believed the true headline" mutually exclusive.

For two events, let say E₁ and E₂ are said to be mutually exclusive if they cannot both occur simultaneously. In set-theoretical notation, we can say that the two sets  E₁ and E₂ are disjoint. i.e.  E₁ ∩  E₂ = ∅ and the probability of them occurring at the same time is zero. i.e. Pr(  E₁ ∩  E₂ ) = 0

So, we can say;

Let P(true) = E₁  

P(false) = E₂

Thus; statistically:

Pr(  E₁ ∩  E₂ ) = Pr(E₁) + Pr(E₂) - P( E₁  ∪ E₂ )

So;

the probability of students that believed the true headline P(E₁) = 0.90

the probability of students that believed the false headline P(E₁) = 0.82

the probability of students that believed both P( E₁  ∪ E₂ ) = 0.75

∴

Pr(  E₁ ∩  E₂ ) = 0.90 + 0.82 - 0.75

Pr(  E₁ ∩  E₂ ) = 0.97

Thus, the events are not mutually exclusive.

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Find the quadratic function y=​f(x) whose graph has a vertex ​(−3​,4​) and passes through the point ​(−7​,0). Write the function
olganol [36]

Answer:

Step-by-step explanation:

This is a parabola since a quadratic is a parabola.  The standard form for a parabola is y = ax² + bx + c

but before we do that, we will use the vertex form, since it will make our work easier at the beginning.  

First and foremost, when we plot the vertex and the given point, the vertex is higher up than is the point; that means that this parabola opens upside down, and its vertex form will be

y=-|a|(x - h)² + k

The absolute value is out in front of the a, so we know that the value of a is positive, but the quadratic itself is negative (upside down) and we will find that math takes care of that negative that needs to be out front.  So we need to solve for a by filling in the x, y, h, and k values from the point and the vertex:  x = -7, y = 0, h = -3, k = 4

0 = a(-7 - (-3))² + 4 and

0 = a(-7 + 3)² + 4 and

0 = a(-4)² + 4 and

0 = a(16) + 4 and

0 = 16a + 4 and

-4 = 16a so

a=-\frac{1}{4}

Now that we know a, we can plug it back into the vertex form and then put it into standard form from there.

y=-\frac{1}{4}(x+3)^2+4

Now we will FOIL out what's inside the parenthesis to get

y=-\frac{1}{4}(x^2+6x+9)+4

Simplify by distributing the -1/4 into the parenthesis:

y=-\frac{1}{4}x^2-\frac{3}{2}x-\frac{9}{4}+4

Combine like terms to get

y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{7}{4}

And there you go!

5 0
3 years ago
Round each amount to the nearest hundred to find the estimate of 9635 - 4891
vovikov84 [41]

Answer:

the answer is 4,744

Step-by-step explanation:

just subtract

7 0
3 years ago
Can someone double check my work for this problem? I got 38°??
scoundrel [369]
We need to use Law of sine.

sin A/a = sin C/c
sin A/|CB| = sin C/|AB|

sin A/14 = sin(118⁰)/ 20
sin A = (14*sin(118⁰))/ 20

A=arcsin((14*sin(118⁰))/ 20) ≈ 38⁰
4 0
3 years ago
Explain why an account balance less than -40 dollars represents a dept greater than 40 dollars
nevsk [136]
You need to pay $40 to make your balance 0 and then another $40 to make it $40.
In all you will have to pay $80
8 0
3 years ago
A development economist is studying income growth in a rural area of a developing country. The last census of the population of
kykrilka [37]

Answer:

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can say that the population mean is not singificantly higher than 425.  

Step-by-step explanation:

Data given and notation  

\bar X=433.75 represent the mean height for the sample  

\sigma=\sqrt{2500}=50 represent the population standard deviation for the sample  

n=100 sample size  

\mu_o =425 represent the value that we want to test

\alpha=0.01 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean height actually is higher than the mean height for men in 1960, the system of hypothesis would be:  

Null hypothesis:\mu \leq 425  

Alternative hypothesis:\mu > 425  

Since we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

z=\frac{433.75-425}{\frac{50}{\sqrt{100}}}=1.75    

P-value

Since is a one right tail test the p value would be:  

p_v =P(z>1.75)=1-P(z  

Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can say that the population mean is not singificantly higher than 425.  

3 0
3 years ago
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