All categories

3 years ago

Find the values of x and y if 5 ˣ⁻³ x 3²ʸ⁻⁸ =225

Mathematics

1 answer:

-BARSIC- [3]3 years ago

5 0

Answer:

x = 5, y = 5

Step-by-step explanation:

${5}^{x - 3} \times {3}^{2y - 8} = 225 \\ {5}^{x - 3} \times {3}^{2y - 8} = 25 \times 9 \\ {5}^{x - 3} \times {3}^{2y - 8} = {5}^{2} \times {3}^{2} \\ equating \: like \: power \: terms \: from \: both \:\\ sides \\ {5}^{x - 3} = {5}^{2} \\ x - 3 = 2 (Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal) \\ x = 3 + 2 \\ \huge \red{ \boxed{ x = 5}} \\ \\ {3}^{2y - 8} = {3}^{2} \\ 2y - 8 = 2(Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal) \\ 2y = 2 + 8 \\ 2y = 10 \\ y = \frac{10}{2} \\ \huge \purple{ \boxed{y = 5}}$

You might be interested in

PLS HALP I’L GIVE 30 POINTS

11111nata11111 [884]

The answer is 40 and 41

3 0

3 years ago

Read 2 more answers

A researcher at a large company has collected data on both the beginning salary and the current salary of 48 randomly selected e

Stolb23 [73]

Answer:

dgrfgfgrfsdfsg

Step-by-step explanation:

aeswrfehghfdgsgbgdfhtgrtfdgf

3 0

3 years ago

Iris has never had a pet before, but today she took in a stray cat named Luna. For Iris, kitty litter is most likely what type o

erik [133]

the answer is Minor New Purchase Decision. <span>It refers to a decision, in which the purchase of something totally new for the consumer is involved, but the purchase is not important in terms of need and / or money</span>

5 0

3 years ago

What is the maximum number of possible extreme values for the function, F(x)=x^3-7x-6

Olin [163]

2 is the max number because it's one less than the degree

5 0

3 years ago

Read 2 more answers

To compare two programs for training industrial workers to perform a skilled job, 20 workers are included in an experiment. Of t

nikklg [1K]

Answer:

$t=\frac{19.1-23.3}{\sqrt{\frac{4.818^2}{10}+\frac{5.559^2}{10}}}}=-1.805$

$p_v =P(t_{(18)}$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude the the true mean for method 1 is lower than the mean for the method 2 at 5% of significance

Step-by-step explanation:

Data given and notation

We can calculate the sample mean and deviation with these formulas:

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

$s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X_{1}=19.1$ represent the mean for the sample mean for 1

$\bar X_{2}=23.3$ represent the mean for the sample mean for 2

$s_{1}=4.818$ represent the sample standard deviation for the sample 1

$s_{2}=5.559$ represent the sample standard deviation for the sample 2

$n_{1}=10$ sample size selected 1

$n_{2}=10$ sample size selected 2

$\alpha$ 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 check if the average time taken when training under method 1 is less than the average time for Method 2, the system of hypothesis would be:

Null hypothesis: $\mu_{1} \geq \mu_{2}$

Alternative hypothesis: $\mu_{1} < \mu_{2}$

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

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

$t=\frac{19.1-23.3}{\sqrt{\frac{4.818^2}{10}+\frac{5.559^2}{10}}}}=-1.805$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n_{1}+n_{2}-2=10+10-2=18$

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

$p_v =P(t_{(18)}$

Conclusion

4 0

3 years ago