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kompoz [17]
3 years ago
8

Twelve years ago, Jane was five times as old as Anne. In three years' time, Anne will be half Jane's

Mathematics
1 answer:
Soloha48 [4]3 years ago
3 0

Answer:

Jane: 37 years old

Anne: 17

Step-by-step explanation:

Jane 12 years ago: 5x

Anne 12 years ago: x

In three years into the future:

Jane: 5x+15

Anne: x+15

CURRENT TIME:

Jane: 5x+12

Anne: x+12

Equation (using 3 years into the future ages): 5x+15=2(x+15)

5x+15=2x+30

(subtract 15 from both sides)

5x=2x+15

3x=15

x=5

Therefore, Jane is 37 years old and Anne is 17 years old.

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Which two equations would be most appropriately solved by using the zero product property?
anzhelika [568]
For the zero product property questions it's choices 2 and 3 since they're quadratics factored and set equal to zero.

for the quadratic formula questions it would be answer choices 2 and 3 also because they're unfactored trinomial quadratic expressions
6 0
3 years ago
Read 2 more answers
The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let µ denote the true average re
Zolol [24]

Answer:

a) df=n-1=16-1=15

The statistic calculated is given by t=3.3  

Since is a one-side upper test the p value would be:      

p_v =P(t_{15}>3.3)=0.0024  

So since the p value is lower than the significance level pv we reject the null hypothesis.

b) df=n-1=8-1=7

The statistic calculated is given by t=1.8  

Since is a one-side upper test the p value would be:      

p_v =P(t_{7}>1.8)=0.057  

So since the p value is higher than the significance level pv>\alpha we FAIL to reject the null hypothesis.

c) df=n-1=26-1=25

The statistic calculated is given by t=-0.6  

Since is a one-side upper test the p value would be:      

p_v =P(t_{25}>-0.6)=0.723  

So since the p value is higher than the significance level pv>\alpha we FAIL to reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation      

\bar X represent the sample mean

s represent the standard deviation for the sample

n sample size      

\mu_o =20 represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

t 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 determine if the true mean is higher than 20, the system of hypothesis would be:      

Null hypothesis:\mu \leq 20      

Alternative hypothesis:\mu > 20      

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:      

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)      

t-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".  

(a) n = 16, t = 3.3, a = 0.05, P-value =

First we need to calculate the degrees of freedom given by:  

df=n-1=16-1=15

The statistic calculated is given by t=3.3  

Since is a one-side upper test the p value would be:      

p_v =P(t_{15}>3.3)=0.0024  

So since the p value is lower than the significance level pv we reject the null hypothesis.

(b) n = 8, t = 1.8, a = 0.01, P-value =

First we need to calculate the degrees of freedom given by:  

df=n-1=8-1=7

The statistic calculated is given by t=1.8  

Since is a one-side upper test the p value would be:      

p_v =P(t_{7}>1.8)=0.057  

So since the p value is higher than the significance level pv>\alpha we FAIL to reject the null hypothesis.

(c) n = 26,t = -0.6, P-value =

 First we need to calculate the degrees of freedom given by:  

df=n-1=26-1=25

The statistic calculated is given by t=-0.6  

Since is a one-side upper test the p value would be:      

p_v =P(t_{25}>-0.6)=0.723  

So since the p value is higher than the significance level pv>\alpha we FAIL to reject the null hypothesis.

3 0
3 years ago
so There are 17 girls and 119 boys on a class field trip to the museum. The students need to be broken up into the largest possi
Step2247 [10]

1 student in each group with 126 groups in total

8 0
3 years ago
What 2 numbers can be added to make 16 as well as multiplied to make -36
Sladkaya [172]

Answer:

18 and -2

Step-by-step explanation:

Let x = 1st no.

y = 2nd no.

(1)    x + y = 16            (2)     xy = -36

           y = 16 - x                 x(16 - x) = -36

                                           16x - x^{2} = -36\\x^{2}  - 16x - 36 = 0\\

                                           (x - 18)(x + 2) = 0

                                               x = 18   or x = -2

          y = 16 - 18 = -2

         y = 16 -(- 2) = 16 + 2 - 18

The two numbers are 18 and -2

3 0
3 years ago
Which is a solution for 7 (x + 2) = 35?<br><br> A. -2<br> B. 7/33<br> C. 3 <br> D. 5<br> E. 26
enot [183]

7(x+2) = 35

Use the distributive property:

7x + 14 = 35

Subtract 14 from each side:

7x = 21

Divide both sides by 7:

x = 21 / 7

X = 3


The answer is C. 3

4 0
2 years ago
Read 2 more answers
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