MATHEMATICS COLLEGE

Find the measures of the supplementary angles that satisfy each case.The measure of the first angle is 45° more than the measure of the second.
(I will make you braniliest if it is correct)

Answers

Answer 1
Answer:

Answer:

67.5°, 107.5°

Step-by-step explanation:

For supplementary angles, their sum equals 180°.

Let x be the first angle and y be the second angle, then

x + y = 180°.

It is given that x = y + 45°.

So x + y = 180°

substituting x into the equation, we have

y + 45° + y = 180°

simplifying, we have

2y + 45° = 180°

collecting like terms, we have

2y = 180° - 45°

2y = 135°

dividing through by 2, we have

y = 135°/2

y = 67.5°

Since y = 67.5°

then x = y + 45°

x = 67.5° + 45°

x = 107.5°
Answer 2
Answer:

Final answer:

The measures of the supplementary angles that satisfy the given conditions are 67.5° and 112.5°.

Explanation:

Let's say the measure of the second angle is x. Since the measure of the first angle is 45° more than the measure of the second, we can express the first angle as the measure of x + 45°.

By the definition of supplementary angles, we know that the sum of the measures of two supplementary angles is 180°. Therefore, we can create the following equation: x + (x + 45) = 180.

Solving this equation gives us:

  1. Add the expressions on the left side of the equation to get: 2x + 45 = 180.
  2. Subtract 45 from both sides of the equation to isolate the term containing x: 2x = 135.
  3. Divide both sides of the equation by 2 to solve for x: x = 67.5°.

So, "the second angle measures 67.5°, and the first angle, being x + 45°, measures 112.5°".

Learn more about Supplementary Angles here:

brainly.com/question/18164299

#SPJ12

Related Questions

Help help please I dont know how to do this
How much of the Fraction 3 over 8 is in the Fraction 1 over 4?
A line passes through the point (4,-6) and has the slope of -3/4. Which is the equation of the line? y=-3/4x-3 y=-3/4x-6 y=-3x-3/4 y=-6x-3/4
Chapter1Review & RefreshSimplify the expression.1. 18x - 6x + 2x2. 4b – 7 – 15b + 33. 15(6-g)4. –24 + 2(y – 9)Please help me with these 4 problems!!:))
Pls answer the question important

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____.

Answers

Answer:

Step-by-step explanation:

Given that an ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations.

Hence total observations are 30*4 =120

No of groups = 3

Hence numerator df = 3-1 =2

Now total degrees of freedom = 120-1 =119

So denominator degrees of freedom = 119-2 = 117

Thus F statistic will have numerator as 2 degrees of freedom and denominator as 117 degrees of freedom.

Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two designs. Tests on customer checkout times conducted at two stores where the two new systems have been installed result in the following summary of the data.System System B
n1=120 n2=100
x1=4.1 minutes x2=3.4 minutes
σ1=2.2minutes σ2= 1.5 minutes

Test at the 0.05 level of significance to determinewhether the population mean checkout times of the two newsystems differ. Which system is preferred?

Answers

Answer:

We conclude that the population means checkout times of the two new systems differ.

Step-by-step explanation:

We are given the result in the following summary of the data;

System          System B

n1=120             n2=100

x1=4.1 min       x2=3.4 min

σ1=2.2 min     σ2= 1.5 min

Let \mu_1 = population mean checkout time of the first new system

\mu_2 = population mean checkout time of the second new system

So, Null Hypothesis, H_0 : \mu_1=\mu_2      {means that the population mean checkout times of the two new systems are equal}

Alternate Hypothesis,H_A : \mu_1\neq \mu_2      {means that the population mean checkout times of the two new systems differ}

The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;

                          T.S.  =  \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{(\sigma_1^(2) )/(n_1) + (\sigma_2^(2) )/(n_2)} }  ~ N(0,1)

where, \bar X_1 = sample mean checkout time of the first new systems = 4.1 min

\bar X_2 = sample mean checkout time of the second new systems = 3.4 min

\sigma_1 = population standard deviation of the first new systems = 2.2 min

\sigma_2 = population standard deviation of the second new systems = 1.5 min

n_1 = sample of the first new systems = 120

n_2 = sample of the second new systems = 100

So, the test statistics =  \frac{(4.1-3.4)-(0)}{\sqrt{(2.2^(2) )/(120) + (1.5^(2) )/(100)} }  

                                    =  2.792

The value of z-test statistics is 2.792.

Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean checkout times of the two new systems differ.

Calcular: log 4 2 = (escribir el resultado como decimal)

Answers

Answer:

1/2 or 0.5

Step-by-step explanation:

Suppose that the expected number of accidents per week at an industrial plant is 5. Suppose also that the number of workers injured in each accident are independent random variables with a common mean of 2.5. If the number of workers injured in each accident is independent of the number of accidents that occur, what is the expected number of workers injured in a week?

Answers

Answer:

12.5

Step-by-step explanation:

If the number of workers injured in each accident is independent of the number of accidents that occur, then the expected number of workers injured in a week equals the expected number of accidents per week times the expected number of workers injured in each accident.

But the expected number of workers injured in each accident is precisely the average or mean, so

Expected number of workers injured in a week = 5*2.5 = 12.5.

Or in other words, in 10 weeks there will probably be 125 workers injured.

Final answer:

The expected number of workers injured in a week at the industrial plant is 12.5, calculated by multiplying the expected number of accidents per week (5) by the expected number of workers injured per accident (2.5).

Explanation:

The expected number of accidents at an industrial plant per week is given as 5 and the mean number of workers injured per accident is given as 2.5. As the number of workers injured per accident is stated to be independent from the number of accidents that occur, we can merely multiply the two expected values to find the overall expected value of workers injured in a week.

So, Expected number of workers injured per week = Expected number of accidents per week * Expected number of workers injured per accident = 5 * 2.5 = 12.5.

This implies that, on average, we can expect 12.5 workers to be injured at the industrial plant per week.

Learn more about Expectation of Random Variables here:

brainly.com/question/39199683

#SPJ3

(c) Simplify fully
exexexf
————
exex fxf

Answers

Answer:

i know its a bit late but the answer below

Step-by-step explanation:

e/f
Could u be more specific

A basketball player is 6ft 8in tall. A model of the basketball player is 5 inches tall. What is the scale factor

Answers

Answer:

1 ft. = 16 in.

Step-by-step explanation:

6 ft. 8 in. is 80 in.

then you would divide 80 by 5 to get 16.

not sure what scale factor you were looking for, so i did ft. to in.

not 100% sure though

best of luck!
Other Questions
Consider the following hypothesis test:H 0: = 17H a: 17A sample of 40 provided a sample mean of 14.12. The population standard deviation is 4.a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus "-" sign.)b. What is the p-value (to 4 decimals)?c. Using = .05, can it be concluded that the population mean is not equal to 17? SelectYesNoItem 3Answer the next three questions using the critical value approach.d. Using = .05, what are the critical values for the test statistic (to 2 decimals)? ±e. State the rejection rule: Reject H 0 if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the lower critical value and is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 6 the upper critical value.f. Can it be concluded that the population mean is not equal to 17?
1. Solve the equation: p + 15 = 51a. p = 65b. p = 46C. p = 66d. p = 36
Which number is an irrational number?StartFraction negative 22 Over 9 EndFractionNegative StartRoot 3 EndRoot2.56StartRoot 15 EndRoot
A computer shop sold 400 computers last month. And 523 computers were sold this month. What is the percentage increase?