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FrozenT [24]
3 years ago
6

A survey was conducted with x students. 30% of those surveyed said that they have traveled out of the country. Of the students w

ho have never been out of the country, 40 students want to eventually travel to another country. Write an algebraic expression that represents the students who never want to travel to another country.
Mathematics
1 answer:
mart [117]3 years ago
3 0
T=x
t=30%x
n=70%x
w=40%n
=40%(70%x)
w=28%x
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Use the method of elimination to solve the pair of simultaneous equation 3a=2b+1,3b=5a-3​
BARSIC [14]

Answer:

       a = 3

        b = 4

Step-by-step explanation:

Simultaneous equation

              3a = 2b + 1

         3a - 2b = 1  ------------------(I)

               3b  = 5a - 3

       -5a + 3b = -3 --------------(II)

Multiply equation (I) by 3  & equation (II) by  2 and then add. So, now 'b' will be eliminated and we can find the value of 'a'.

(I)*3       9a - 6b = 3

(II)*2    <u>-10a + 6b = -6</u>  {Now add}

            -a            = -3

                       a = -3/(-1)

        \sf \boxed{a  = 3}

Plugin a = 3 in equation (I)

              3*3 - 2b = 1

                  9 - 2b = 1

                     -2b  = 1 - 9   {Subtracting 9 from both sides}

                      -2b = - 8        

                         b = (-8)/(-2)         {Dividing both sides by (-2_}

          \sf \boxed{b = 4}                      

7 0
2 years ago
Read 2 more answers
Leah multiplied the number 2 by itself 4 times (2x2x2x2). Deshon multiplied the number 4 by itself 2 times (4x4). Which product
Bas_tet [7]

Answer:

The answer is 2x2x2x2.

Step-by-step explanation:

2x2=4, 4x2=8, 8x2=16

4 0
2 years ago
Read 2 more answers
A recent survey found that 86% of employees plan to devote at least some work time to follow games during the NCAA Men's Basketb
trasher [3.6K]

Answer:

4.18% probability that less than 80% of this sample will devote work time to follow games

Step-by-step explanation:

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question, we have that:

p = 0.86, n = 100

So

\mu = 0.86, s = \sqrt{\frac{0.86*0.14}{100}} = 0.0347

What is the probability that less than 80% of this sample will devote work time to follow games?

This is the pvalue of Z when X = 0.8. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.8 - 0.86}{0.0347}

Z = -1.73

Z = -1.73 has a pvalue of 0.0418

4.18% probability that less than 80% of this sample will devote work time to follow games

7 0
3 years ago
What is 1(4x+7y)+2(5y-9x)​
patriot [66]
1(4x+7y)+2(5y-9x)
=4x+7y+10y-18x
=-14x+17y

The solution is -14x+17y.
3 0
3 years ago
14. Solve: (a) 2y - 1/2 = -1/3 (b) 6 + 5 (a - 1) = 30
Strike441 [17]

A)2y - 1/2 = -1/3

2y=-1/3+1/2

FIND THE LCM TO MAKE THE FRACTIONS LIKE FRACTIONS

LCM OF 3 AND 2 IS 6

-1/3*2=-2/6

1/2*3=3/6

-2/6+3/6=1/6

2y=1/6

y=1/6 ÷ 2

TAKING THE RECIPROCAL,

RECIPROCAL OF 2 IS 1/2

y=1/6*1/2

y=1/12

B) 6 + 5 (a - 1) = 30

6+(5)*(a)+(5)*(−1)=30(Distribute)

6+5a+−5=30

(5a)+(6+−5)=30(Combine Like Terms)

5a+1=30

5a=30-1

5a=29

a=29/5

15.sum of three consecutive integers=48

let the numbers be x ,x+1,x+2

x+x+1+x+2==48

3x+3=48

3x=48-3

3x=45

x=45/3

x=15

x+1=15+1=16

x+2=15+2=17

the numbers are 15,16,17

​​  

7 0
3 years ago
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