What is 4 times 5/12

Evaluate the expression if xequalsminus1 and yequals7. <br><br> 5x over x-y

erica [24]

The answer is 5 over 8.

3 0

2 years ago

Three percent of the caterpillars metamorphosed into butterflies. If Ramona could count 120 butterflies, how many caterpillars h

Harman [31]

The answer to your problem would be 400 because to find the answer you need to multiply 120 by .3 to get the answer because 3 % means per 100 and that is why you make it .3 hope i help.

3 0

2 years ago

The equation of function h is h... PLEASE HELP MATH

Flura [38]

Answer:

Part A: the value of h(4) - m(16) is -4

Part B: The y-intercepts are 4 units apart

Part C: m(x) can not exceed h(x) for any value of x

Step-by-step explanation:

Let us use the table to find the function m(x)

There is a constant difference between each two consecutive values of x and also in y, then the table represents a linear function

The form of the linear function is m(x) = a x + b, where

a is the slope of the function
b is the y-intercept

The slope = Δm(x)/Δx

∵ At x = 8, m(x) = 2

∵ At x = 10, m(x) = 3

∴ The slope = $\frac{3-2}{10-8}=\frac{1}{2}$

∴ a = $\frac{1}{2}$

- Substitute it in the form of the function

∴ m(x) = $\frac{1}{2}$ x + b

- To find b substitute x and m(x) in the function by (8 , 2)

∵ 2 = $\frac{1}{2}$ (8) + b

∴ 2 = 4 + b

- Subtract 4 from both sides

∴ -2 = b

∴ m(x) = $\frac{1}{2}$ x - 2

Now let us answer the questions

Part A:

∵ h(x) = $\frac{1}{2}$ (x - 2)²

∴ h(4) = $\frac{1}{2}$ (4 - 2)²

∴ h(4) = $\frac{1}{2}$ (2)²

∴ h(4) = $\frac{1}{2}$ (4)

∴ h(4) = 2

∵ m(x) = $\frac{1}{2}$ x - 2

∴ m(16) = $\frac{1}{2}$ (16) - 2

∴ m(16) = 8 - 2

∴ m(16) = 6

- Find now h(4) - m(16)

∵ h(4) - m(16) = 2 - 6

∴ h(4) - m(16) = -4

Part B:

The y-intercept is the value of h(x) at x = 0

∵ h(x) = $\frac{1}{2}$ (x - 2)²

∵ x = 0

∴ h(0) = $\frac{1}{2}$ (0 - 2)²

∴ h(0) = $\frac{1}{2}$ (-2)² =

∴ h(0) = 2

∴ The y-intercept of h(x) is 2

∵ m(x) = $\frac{1}{2}$ x - 2

∵ x = 0

∴ m(0) = $\frac{1}{2}$ (0) - 2 = 0 - 2

∴ m(0) = -2

∴ The y-intercept of m(x) is -2

- Find the distance between y = 2 and y = -2

∴ The difference between the y-intercepts of the graphs = 2 - (-2)

∴ The difference between the y-intercepts of the graphs = 4

∴ The y-intercepts are 4 units apart

Part C:

The minimum/maximum point of a quadratic function f(x) = a(x - h) + k is point (h , k)

Compare this form with the form of h(x)

∵ h = 2 and k = 0

∴ The minimum point of the graph of h(x) is (2 , 0)

∵ k is the minimum value of f(x)

∴ 0 is the minimum value of h(x)

∴ The domain of h(x) is all real numbers

∴ The range of h(x) is h(x) ≥ 2

∵ m(8) = 2

∵ m(14) = 5

∵ h(8) = $\frac{1}{2}$ (8 - 2)² = 18

∵ h(14) = $\frac{1}{2}$ (14 - 2)² = 72

∴ h(x) is always > m(x)

∴ m(x) can not exceed h(x) for any value of x

<em>Look to the attached graph for more understand</em>

The blue graph represents h(x)

The green graph represents m(x)

The blue graph is above the green graph for all values of x, then there is no value of x make m(x) exceeds h(x)

7 0

3 years ago

Unit rates 25 letters in 4 days

jeka94

25/4= 6.25

In one day, there are 6.25 letters.

Hope this helps!

5 0

3 years ago

第 5 个问题 a multiple choice exam has 10 questions. each question has 3 possible answers, of which one is correct. a student knows

tatuchka [14]

The chances that the student was merely guessing is 1/3.

Bayes Theorem determines the conditional probability of an event A given that event B has already occurred.

denoted by

$P(A/B)=\frac{P(A)*P(B/A)}{P(B)}$

let A be the event that the student knows the answer .

B be the event that the student does not knows the answer .

and

E be the event he gets answer correct .

According to the given question

$P(A)=\frac{4}{10} \\\\ P(B)=1-\frac{4}{10} =\frac{6}{10}$

Probability that the answer is correct ,given that he knows the answer is

$P(E/A)=1$

Probability that the answer is correct ,given that he guesses it is

$P(E/B)=\frac{1}{3}$ [as the MCQ has 3 options and only one is correct]

We need to find the probability that he guesses the answer given that it is correct.

Required probability $P(B/E)=\frac{P(B)*P(E/B)}{P(A)*P(E/A)+P(B)*P(E/B)}$

Substituting the values we get

$P(B/E)=\frac{\frac{6}{10} *\frac{1}{3} }{\frac{4}{10} *1+\frac{6}{10} *\frac{1}{3} }$

$=\frac{6}{30}*\frac{30}{18} \\ \\ =\frac{6}{18} \\ \\ =\frac{1}{3}$

Therefore , the chances that the student was merely guessing is 1/3.

Learn more about Probability here brainly.com/question/13140147

#SPJ4

8 0

8 months ago