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Delvig [45]
3 years ago
13

3/4 x 3 2/5 - 5/5(find the value of each of the following) ​

Mathematics
1 answer:
Triss [41]3 years ago
7 0

The value of the given expression is \frac{-13}{20}.

Solution:

Given expression is \frac{3}{4} \times3\frac{2}{5}-\frac{5}{5}.

Let us first convert mixed fraction into improper fraction.

3\frac{2}{5}=\frac{(3\times5)+2}{5}=\frac{17}{5}

Substitute this in the given expression.

\frac{3}{4} \times3\frac{2}{5}-\frac{5}{5}=\frac{3}{4} \times\frac{7}{15}-\frac{5}{5}

                  =\frac{21}{60}-\frac{5}{5}

To simplify the above expression, 21 and 60 are cancelled by 3.

                 =\frac{7}{20}-\frac{1}{1}

Do cross multiplication to make the denominator same.

                 =\frac{7}{20}-\frac{20}{20}

                 =\frac{7-20}{20}

                 =\frac{-13}{20}

The value of the given expression is \frac{-13}{20}.

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Consider angle θ in Quadrant II, where sinθ = 4/5 . What is the value of cosθ?
Kay [80]

Answer:

3/5

Step-by-step explanation:

sin theta=opposite/hypotenuse

4/5=opposite/hypotenuse

therefore opposite=4 and hypotenuse=5

for adjacent

using pythagoras theorem

a^2+b^2=c^2

opposite^2 + adjacent^2 =hypotenuse^2

4^2 + adjacent^2 =5^2

16 + adjacent^2 =25

adjacent^2 =25-16

adjacent =\sqrt{9

adjacent=3

cos theta=adjacent/hypotenuse

=3/5

therefore the value of cos theta is 3/5

8 0
3 years ago
A martial artist is practicing breaking 5 boards. He is able to break a board with probability 0.8. (a) What is the probability
konstantin123 [22]

Answer:

(a) = 0.32 or 8/25

(b) = 0.48 or 12/25

(c) = 4 Boards

Step-by-step explanation:

(a):

0.8 x 2/5

8/10 x 4/10

(8 x 4) / (10 x 10)

(32) / (100)

0.32 or 8/25

(b):

0.8 x 3/5

8/10 x 6/10

(8 x 6) / (10 x 10)

(48) / (100)

0.48 or 12/25

(c):

0.8 x 5

8/10 x 50/10

(8 x 50) / (10 x 10)

(400) / (100)

4 Boards

4 0
3 years ago
Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 70 bacteria are present to begin
Sauron [17]

Answer:

1 day: 4480

2 days: 8960

3 days: 13440

f^{-1}(x) = \sqrt{\frac{x -4}{4}} ---- function inverse

Step-by-step explanation:

Given

f(x) = 70 \cdot 64x

Solving (a): The amount present after 1 day.

Here, x =1

So:

f(1) = 70 \cdot 64*1= 4480

Solving (b): The amount present after 2 days.

Here, x =2

So:

f(2) = 70 \cdot 64*2= 8960

Solving (c): The amount present after 3 days.

Here, x = 3

So:

f(3) = 70 \cdot 64*2= 13440

Solving (d): The inverse function of:

f(x)= 4x^2 + 4

Replace f(x) with y

y= 4x^2 + 4

Swap x and y

x= 4y^2 + 4

Rewrite as:

4y^2 = x -4

Divide by 4

y^2 = \frac{x -4}{4}

Take square roots

y = \sqrt{\frac{x -4}{4}}

Replace y with function inverse

f^{-1}(x) = \sqrt{\frac{x -4}{4}}

6 0
3 years ago
What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and
Ipatiy [6.2K]

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.24

For the alternative hypothesis,

p ≠ 0.24

This is a two tailed test

Considering the population proportion, probability of success, p = 0.24

q = probability of failure = 1 - p

q = 1 - 0.24 = 0.76

Considering the sample,

Sample proportion, P = r/n

Where

r = 12

n = 52

P = 12/52 = 0.23

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.23 - 0.24)/√(0.24 × 0.76)/52 = - 0.17

Recall, population proportion, P = 0.24

The difference between sample proportion and population proportion(p - P) is 0.24 - 0.23 = 0.01

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.24 - 0.01 = 0.23

the p for the right tail is 0.24 + 0.01 = 0.25

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail 0.43

We would double this area to include the area in the right tail of z = 0.17 Thus

p = 0.43 × 2 = 0.86

The level of significance is 5%

Since alpha, 0.05 < than the p value, 0.86, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, this information does not imply that the color preference of all college students is different (either way) from that of the general population.

7 0
3 years ago
Question: If two lines intersect, then the opposite angles formed at this intersect are congruent.
leonid [27]

Answer:

B

Step-by-step explanation:

False

7 0
3 years ago
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