How do i do this :(

Let f be continuous on [0, a] and differentiable on (0, a), Prove that if f(a)=0 then there is at least one value of x in (0, a)

asambeis [7]

Answer:

See picture attached

Step-by-step explanation:

6 0

3 years ago

Reuben learned in art class that a mosaic is made by arranging small pieces of colored material such as glass or tile to create

anastassius [24]

Pattern is the rule that guides the formation of a set.

The sequence of the first five mosaics is 5, 8, 11, 14, 17
The sequence is arithmetic
There are 32 tiles in the tenth mosaic.

From the given design, the number of tiles used is:

$T_1 = 5$

$T_2 = 8$

$T_3 = 11$

(a) The first five

Notice that the difference in the number of tiles of successive mosaic is 3.

This means that:

$T_4 = T_3 + 3 = 11 +3 = 14$

$T_5 = T_4 + 3 = 14 +3 = 17$

So, the sequence of the first five mosaics is 5, 8, 11, 14, 17

(b) The type of sequence

The sequence is arithmetic

This is so, because the difference in the number of tiles of successive mosaic is 3.

This difference is called the common difference

(c) The number of tiles in the tenth mosaic

The nth term of an arithmetic sequence is:

$T_n = T_1 + (n - 1) \times d$

In this case:

$T_1 = 5$

$d =3$

$n = 10$

So, we have:

$T_{10} = 5 + (10 - 1) \times 3$

$T_{10} = 5 + 9 \times 3$

$T_{10} = 5 + 27$

$T_{10} = 32$

There are 32 tiles in the tenth mosaic.

Read more about arithmetic sequence at:

brainly.com/question/18109692

5 0

3 years ago

Find the value of the test statistic z using . The claim is that the proportion of adults who smoked a cigarette in the past wee

kolezko [41]

Correct question is;

The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.35, and the sample statistics include n = 1168 subjects with 385 saying that they smoked a cigarette in the past week. Find the value of the test statistic

Answer:

Test statistic is z = -1.46

Step-by-step explanation:

Let's first of all define the hypotheses:

Null hypothesis:

H0: p = 0.35, i.e 35% in the sample of 1,168 adults have smoked cigarettes in the previous week.

Alternative hypothesis:

Ha: p < 0.35, i.e less than 35% in the sample of 1,168 adults have smoked cigarette in the previous week.

The sample size is, n = 1,168 while the number of adults who smoked in the previous week would be; x = 385

Therefore, the sample proportion of adults who smoked in the previous week would be calculated as;

p^ = x/n = 385/1168 ≈ 0.3296

Now, from Central Limit Theorem for large samples, The sampling distribution of the sample proportion p^, will have a mean of μ = p = 0.35

Formula for standard deviation is;

σ = √[p (1 – p)/n]

σ = √(0.35 × (1 – 0.35)/1168)

σ = √0.0001947774

σ = 0.014

Formula for test statistic is;

z = (p^ - p)/σ

z = (0.3296 - 0.35)/0.014

z = - 1.46

3 0

3 years ago

Describe how to solve problems for the area of a reduced or enlarged figure when the scale factor and dimensions of the original

Nataly [62]

Find the area of the original figure and multiply that by the square of the scale factor.

3 0

3 years ago

Read 2 more answers

Please help me; )!!!!!!!!!!!!!

Vaselesa [24]

To show how you decided, the simple way would be to draw a picture. Create 2 rectangles of the same length and divide them up according to the fraction. Then shade the number of pieces for the numerator and compare both fractions. Whichever is longer is the greater fraction.

5 0

3 years ago