Find a number whose product with 9 is the same as its sum with 56

The sum of the ages of Berma, her mother Rinna and her father Erwin is 80. Two years from now, Rinna’s age will be 13 less than

jekas [21]

Answer: Berma is 5 years old

Rinna is 38 years old

Erwin is 37 years old

Step-by-step explanation:

Let x represent Berma's age

Let y represent Rinna's age

Let z represent Erwin's age

Since the sum of their ages is 80,

x + y + z = 80 - - - - - - -1

Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that

y +2 = [ (z+2) + 2(x+2) ] - 13

y +2 = z + 2 + 2x + 4 - 13

2x - y + z = 13 + 2 - 4 -2

2x - y + z = 9 - - - - - - -2

Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that

15(x - 3) = (y - 3) - 5

15x - 45 = y - 3 - 5

15x - y = - 8 + 45

15x - y = 37 - - - - - - - -3

From equation 3, y = 15x - 37

Substituting y = 15x - 37 into equation 1 and equation 2, it becomes

x + 15x - 37 + z = 80

16x + z = 80 + 37 = 117 - - - - - - 4

2x - 15x + 37 + z = 9

-13x + 2 = -28 - - - - - - - - -5

subtracting equation 5 from equation 4,

29x = 145

x = 145/29 = 5

y = 15x - 37

y = 15×5 -37

y = 38

Substituting x= 5 and y = 38 into equation 1, it becomes

5 + 38 + z = 80

z = 80 - 43

z = 37

6 0

3 years ago

A rectangle with a length of 12 cm and a width of 6 cm has an area of 72 sq cm and a perimeter of 36 cm.

frozen [14]

So we should first start off by checking for the ones with the same area, which is 72sq cm

80×90=7200sq cm so A is incorrect

8×10=80sq cm so B is incorrect

3×24=72sq cm so, so far C is correct

4×14=56sq cm so D is incorrect

And because all are incorrect except C
Then C is the correct answer, just to be sure, we will check the perimeter

24+24=48
48+3=51
51+3= 54

So the perimeter is different, making C the correct answer

5 0

3 years ago

HELPP ILL GIVE BRAINLESS

kobusy [5.1K]

15x=1000 you get x=1000/15 which is approximately 67

7 0

3 years ago

The bacterial strain Acinetobacter has been tested for its adhesion properties. A sample of five measurements gave read- ings of

oksian1 [2.3K]

Answer:

Part a

We need to conduct a one tailed test

We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.5$

Alternative hypothesis: $\mu > 2.5$

Part b: Calculate the statistic

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

$z=\frac{3.372-2.5}{\frac{0.66}{\sqrt{5}}}=2.954$

Part c :P-value

Since is a one sided test the p value would be:

$p_v =P(z>2.954)=0.0016$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.

Step-by-step explanation:

a. Should the alternative hypothesis be one-sided or two-sided?

b. Test the hypothesis that the mean adhesion is 2.5 dyne-cm².

c. What is the P-value of the test statistic?

Data given and notation

Data: 2.69, 5.76, 2.67, 1.62 ,4.12

We can calculate the sample mean with this formula:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\bar X=3.372$ represent the sample mean

$\sigma=0.66$ represent the population standard deviation

$n=5$ sample size

$\mu_o =2.5$ represent the value that we want to test

$\alpha=0.01$ 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)

Part a: State the null and alternative hypotheses.

We need to conduct a one tailed test

We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.5$

Alternative hypothesis: $\mu > 2.5$

If we analyze the size for the sample is < 30 but 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".

Part b: Calculate the statistic

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

$z=\frac{3.372-2.5}{\frac{0.66}{\sqrt{5}}}=2.954$

Part c :P-value

Since is a one sided test the p value would be:

$p_v =P(z>2.954)=0.0016$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.

8 0

3 years ago

Find the zero of the following function. f(x)=x³-7x²+4x+12

chubhunter [2.5K]

Answer:

Step-by-step explanation:

Hello, we can notice that f(-1)=0 so (x+1) is a factor and we can write.

$f(x)=(x+1)(x^2-8x +12)\\\\=(x+1)(x-6)(x-2)$

The sum of the zeros is 8=6+2 and the product is 12=6*2

So the zeroes are 2, 6, -1

thanks

6 0

4 years ago