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3 years ago

Rewrite with only sin x and cos x.

1 answer:

8 0

The answer is a. cos2x - sin2x - sin x. Use the rule: cos2x = (cos^2)x - (sin^2)x. So, substitute cos2x in the expression: cos2x - sinx = ((cos^2)x - (sin^2)x) - sinx = (cos^2)x - (sin^2)x - sinx. Therefore, choice a. is correct choice.

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Bart wants to deposit his piggy bank savings into a savings account. If he deposits $325. 76, how many whole years will it take,

vladimir1956 [14]

Answer:

Step-by-step explanation:

Compounding interest :

Future value of money = Present value * (1+ r)^N

r - interest rate

n - number of period

In our example, Present value = 325.76, FV = 400, r = 2%, and we need to find N

by solving that we can find it that N is equal to 10.3675

Simple interest :

400 - 325.76 = 74.26$ we need to increase

325.76*2% = 6.5152$ each year

74.26 / 6.5152 = 11.3949

as a whole year = 12years

6 0

2 years ago

A survey of 700 adults from a certain region asked, "What do you buy from your mobile device?" The results indicated that 59%

Kryger [21]

Answer:

a) the test statistic z = 1.891

the null hypothesis accepted at 95% level of significance

b) the critical values of 95% level of significance is zα =1.96

c) 95% of confidence intervals are (0.523 ,0.596)

Step-by-step explanation:

A survey of 700 adults from a certain region

Given sample sizes $n_{1} = 400 and n_{2} = 300$

Proportion of mean $p_{1} = \frac{236}{400} = 0.59 and p_{2} = \frac{156}{300} = 0.52$

Null hypothesis H0 : assume that there is no significant difference between males and women reported they buy clothing from their mobile device

p1 = p2

Alternative hypothesis H1:- p1 ≠ p2

a) The test statistic is

$Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} )} } }$

where $p = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1}+n_{2}}= \frac{400X0.59+300X0.52}{700}$

on calculation we get p = 0.56

now q =1-p = 1-0.56=0.44

$Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} )} } }\\ =\frac{0.56-0.52}{\sqrt{0.56X0.44}(\frac{1}{400}+\frac{1}{300} }$

after calculation we get z = 1.891

b) The critical value at 95% confidence interval zα = 1.96 (from z-table)

The calculated z- value < the tabulated value

therefore the null hypothesis accepted

conclusion:-

assume that there is no significant difference between males and women reported they buy clothing from their mobile device

p1 = p2

c) 95% confidence intervals

The confidence intervals are P± 1.96(√PQ/n)

we know that = $p = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1}+n_{2}}= \frac{400X0.59+300X0.52}{700}$

after calculation we get P = 0.56 and Q =1-P =0.44

Confidence intervals are ( P- 1.96(√PQ/n), P+ 1.96(√PQ/n))

now substitute values , we get

( 0.56- 1.96(√0.56X0.44/700), 0.56+ 1.96(0.56X0.44/700))

on simplification we get (0.523 ,0.596)

Therefore the population proportion (0.56) lies in between the 95% of confidence intervals (0.523 ,0.596)

3 0

3 years ago

How long does it take the ball to hit the ground when dropped from 50ft.?

bixtya [17]

I hope it's about 1.8 sec

4 0

3 years ago

Jason and Jenny are out on a lunch date. Jason gives Jenny a bouquet that has 4 roses, 3 carnations, and 4 orchids. They decide

Law Incorporation [45]

The probability that Jenny gets to choose lunch is 64% 0.64 (rounded) or 0.636.

Work:

Number of roses and carnations divided by the total number of flowers

7/11 = 0.636 = 0.64 (rounded)

once again same answer

4 0

3 years ago

ASAP IM BEING TIME PLEASE!!

andre [41]

x° = 14°, y° = 14°; Use vertical and supplementary angles.

Step-by-step explanation:

The image of the answer is attached below.

In the given image two lines are parallel with transversal.

(9x + 12)° and ∠1 are vertically opposite angles.

Vertically opposite angles are equal.

∠1 = (9x + 12)°

Consecutive interior angles are supplementary.

(9x + 12)° + 3x° = 180°

⇒ 12x° = 168°

⇒ x° = 14°

Sum of the adjacent angles in a line are supplementary.

3x° + (4y – 10)° = 180°

⇒ 3(14)° + 4y° – 10° = 180°

⇒ 4y° = 148°

⇒ y° = 14°

Hence, x° = 14°, y° = 14°; Use vertical and supplementary angles.

6 0

3 years ago