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____ [38]
3 years ago
8

Is​ f(x) continuous at x equals 4​? Why or why​ not? A. ​No, f(x) is not continuous at x equals 4 because ModifyingBelow lim Wit

h x right arrow 4 f (x )does not exist. B. ​Yes, f(x) is continuous at x equals 4 because f (4 )exists. C. ​No, f(x) is not continuous at x equals 4 because f (4 )is undefined. D. ​Yes, f(x) is continuous at x equals 4 because ModifyingBelow lim With x right arrow 4 f (x )equals f (4 ).
Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
3 0

<u>Corrected Question</u>

Is the function given by:

f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right ​

continuous at x=4​? Why or why​ not? Choose the correct answer below.

Answer:

(D) ​Yes, f(x) is continuous at x = 4 because Lim_{x \to 4}f(x)=f(4)

Step-by-step explanation:

Given the function:

f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right

A function to be continuous  at some value c in its domain if the following condition holds:

  • f(c) exists and is defined.
  • Lim_{x \to c}$ f(x) exists.
  • f(c)=Lim_{x \to c}$ f(x)

At x=4

  • f(4)=\dfrac{1}{4}*4+1=2
  • Lim_{x \to 4}f(x)=2

Therefore: Lim_{x \to 4}f(x)=f(4)=2

By the above, the function satisfies the condition for continuity.

The correct option is D.

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Answer:

Rational numbers are fractions composed of integers. An integer is a number with no fractional part. So 7/8 is a ratio of whole numbers, which makes it rational. Negative or positive does not matter.

Step-by-step explanation:

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3 years ago
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What is the product? 7⋅(−4)⋅(−6) −168 −3 17 168
Lunna [17]

Answer:

The Product of 7⋅(−4)⋅(−6) −168 −3 is<em> </em><u>-3</u>

8 0
2 years ago
Last Saturday, Camila practiced her dance routines for her upcoming competition. She spent some time practicing her tap routine,
Natalka [10]

Answer:

t = 28 minutes

Step-by-step explanation:

Last Saturday, Camila practiced her dance routines for her upcoming competition. She spent some time practicing her tap routine, and then she spent 17 minutes practicing her hip-hop routine. In all, she practiced for 45 minutes. Let t be the number of minutes that Camila practiced her tap routine. Write and solve an equation to find t.

45 minutes = Number of minutes for hip-hop routine + Number of minutes for tap dance

The equation is given as

45 = 17 + t

Solving for t

t = 45 - 17

t = 28 minutes

Shes spent 28 minutes tap dancing

4 0
2 years ago
James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The
Brrunno [24]

Answer:

The correct option is 4.

Step-by-step explanation:

Given information:

Bring lunch : 46 males, 254 females

Buy lunch   : 176 males, 264 females

Total number of peoples is

46+254+176+264=740

Total number of males is

46+176=222

The probability of male is

P(Male)=\frac{Males}{Total}=\frac{222}{740} =0.3

Since probability of males is 0.3, therefore options A and C are incorrect.

Total number of persons who buys lunch is

176+264=440

The probability of persons who buys lunch is

P(\text{Buys lunch})=\frac{\text{Buys lunch}}{Total}=\frac{440}{740} =\frac{22}{37}

We need to find the probability of P(male | buys lunch).

According to the conditional probability, we get

P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}

P(male | buys lunch)=\frac{P(\text{male }\cap \text{ buys lunch})}{P(\text{buys lunch})}

P(male | buys lunch)=\frac{\frac{176}{740}}{\frac{22}{37}}

P(male | buys lunch)=\frac{2}{5}=0.4

Therefore the correct option is 4.

8 0
3 years ago
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On a piece of paper, graph f(x) = 4 x (0.5)^x
tangare [24]

The complete question is

"On a piece of paper, graph f(x) = 4. (0.5)^x Then determine which answer choice matches the graph you drew."

The given function is an exponential function. The graph of option C is the correct answer.

<h3>What are exponential functions?</h3>

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

There usual form is specified below. They are written in several such equivalent forms.

For example, y^x

, where a is a constant is an exponential function.

The function is given as

f(x) = 4. (0.5)^x

AS we can see that the given function is an exponential function.

Thus, the graph of option C is the correct answer.

Learn more about exponential here:

brainly.com/question/2193820

#SPJ1

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