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
Tanya [424]
3 years ago
15

Suppose f is a continuous function on [-2, 2) such that

Mathematics
1 answer:
Leviafan [203]3 years ago
4 0

Answer:

2. a and b only.

Step-by-step explanation:

We can check all of the given conditions to see which is true and which false.

a. f(c)=0 for some c in (-2,2).

According to the intermediate value theorem this must be true, since the extreme values of the function are f(-2)=1 and f(2)=-1, so according to the theorem, there must be one x-value for which f(x)=0 (middle value between the extreme values) if the function is continuous.

b. the graph of f(-x)+x crosses the x-axis on (-2,2)

Let's test this condition, we will substitute x for the given values on the interval so we get:

f(-(-2))+(-2)

f(2)-2

-1-1=-3  lower limit

f(-2)+2

1+2=3 higher limit

according to these results, the graph must cross the x-axis at some point so the graph can move from f(x)=-3 to f(x)=3, so this must be true.

c. f(c)<1 for all c in (-2,2)

even though this might be true for some x-values of of the interval, there are some other points where this might not be the case. You can find one of those situations when finding f(-2)=1, which is a positive value of f(c), so this must be false.

The final answer is then 2. a and b only.

You might be interested in
greg's father can mow the lawn on his riding mower in 45 minutes. It takes Greg 1 hour 45 minutes to mow the lawn with a push mo
Andrei [34K]

Answer:

1 = t/45 + t/105

Step-by-step explanation:

Greg's father mow a lawn in 45 minutes that means that he mow in a rate of 1/45

Greg mow a lawn in 1 hour 45 minutes (105 minutes) that means that he mow in a rate of 1/105

If they mow a lawn in t minutes that means the rate is 1/t

Then, the rate in which they mow a lawn has to be equal to the sum of the rate individually as follows

1/t = 1/45 + 1/105

1 = t/45 + t/105

4 0
3 years ago
A university financial aid office polled a random sample of 670 male undergraduate students and 617 female undergraduate student
ahrayia [7]

Answer:

The 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer is (0.01, 0.1012).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Male undergraduates:

670, 388 were employed. So

p_M = \frac{388}{670} = 0.5791

s_M = \sqrt{\frac{0.5791*0.4209}{670}} = 0.0191

Female undergraduates:

Of 617, 323 were employed. So

p_F = \frac{323}{617} = 0.5235

s_F = \sqrt{\frac{0.5235*0.4765}{617}} = 0.0201

Distribution of the difference:

p = p_M - p_F = 0.5791 - 0.5235 = 0.0556

s = sqrt{s_M^2+s_F^2} = \sqrt{0.0201^2 + 0.0191^2} = 0.0277

Confidence interval:

The confidence interval is given by:

p \pm zs

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The lower bound of the interval is:

p - zs = 0.0556 - 1.645*0.0277 = 0.01

The upper bound of the interval is:

p + zs = 0.0556 + 1.645*0.0277 = 0.1012

The 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer is (0.01, 0.1012).

5 0
3 years ago
Please someone please hurry and help with this❣
ehidna [41]
She will have picked 3 gallons of strawberries in 2 hours. I hope this helped you!
7 0
3 years ago
Which expression simplifies to (-5 · 2² · 2⁰)⁻² ? Please show work.
lisov135 [29]
The answer is d. 2⁰ is 1 so you dont have to multiply that. (-5 x 4) ⁻² is -20⁻². -20⁻² = (1/-20)<span>² ; 1 x 1 = 1; -20 x -20 = 400. so it is 1/400 </span>
6 0
3 years ago
Question 2
notka56 [123]

Answer:

x is all real numbers

Step-by-step explanation:

you distribute the function.

1. 2x+2=2x+2

2. as we know that both of the functions are equal to each other x can be any real number, x can be to positve infinity or negative infinite

Hope this Helps

5 0
3 years ago
Read 2 more answers
Other questions:
  • A corner store sells two kinds of baked goods: cakes and pies. A cake costs $10 and a pie costs $7. In one
    5·1 answer
  • Writing to Explain: A circle is divided into 18 equal parts. How many degrees is the angle for each part??How many degrees is th
    8·1 answer
  • a recipe for sweet potato casserole calls for 3/4 cup of milk. Martina has 6 cups of milk. How many sweet potato casseroles can
    8·2 answers
  • Graph f(x) = 22 +1 and g(x) = -x +4 on the same graph
    9·1 answer
  • PLEASE help me with this equation ​
    15·2 answers
  • Solve the inequality.
    6·2 answers
  • What is the range of the function f(x) = 2 – 2 when the domain is {0, 2, 4}? O {-1, 2, 14} {3, 6, 8} {-2, 2, 6) All real numbers
    12·2 answers
  • What is the prime factorasation of 96
    9·2 answers
  • Lillian is going to invest in an account paying an interest rate of 5.7% compounded continuously. How much would Lillian need to
    7·1 answer
  • Question
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!