1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
inna [77]
3 years ago
13

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

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

4 0
3 years ago
Other questions:
  • In fig. AB = AC, D is the midpoint of BC.<br><br> (i)Is  ADB ADC (ii) Is ∠B =∠C?
    11·1 answer
  • How many liters of 10% acid solution should be mixed with 30 liters of a 50% acid solution to get a mix that a 20% acid?
    10·1 answer
  • In this fraction, which number is the denominator?<br> 8<br> 16<br> O A. 16<br> OB. 8
    7·2 answers
  • Q(x)=-3x<br> r(x) = 4x-1<br> Find the following.<br> (r.q)(5) = <br> (r .q.)(5) =
    12·1 answer
  • The sun shines at a 30° angle to the ground. To the nearest inch, how long is the shadow cast by a 72-inch tall fence post?
    13·1 answer
  • Find the area of a triangle with a base of 4 meters and a height of 14 meters.
    9·2 answers
  • Please explain how to solve for x in the attached photo.
    8·1 answer
  • Please I need help with this​
    10·1 answer
  • Can u please help to warn: No links or I will report thank you, and have a blessed day!!
    7·1 answer
  • Find the equation of the line..<br><br> y= x+ <br><br> khan academy
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!