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2 years ago

If sin(2x + 7) = cos(4x - 7)º, what is the value of x?

Mathematics

1 answer:

ella [17]2 years ago

6 0

Answer:

x = 15°

Step-by-step explanation:

We are given;

sin(2x + 7) = cos(4x - 7)

We are required to solve for the value of x

We need to know that for complementary angles;

Sin θ = Cos (90-θ) where, θ and 90-θ are complementary angles.

Complementary angles are angles that add to 90°
Therefore;

(2x +7) + (4x - 7) = 90

6x = 90

x = 15°

Therefore, the value of x is 15°

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it takes max 1.8 hours to walk home from work at a rate of 3.5km/h. how long would it take max to cover the same distance walkin

NikAS [45]

Time taken by Max to cover the same distance walking at 4.2 km/h is 1.5 hours

<h3>Solution:</h3>

Given it takes Max 1.8 hours to walk home from work at a rate of 3.5km/h

We have to find time taken by Max to cover the same distance walking at 4.2 km/h

The relation between speed and time is given as:

$speed = \frac{distance}{time}$

CASE 1:

It takes Max 1.8 hours to walk home from work at a rate of 3.5km/h

Let us first find the distance covered

Time taken = 1.8 hours and speed = 3.5 km/hr

$3.5 = \frac{distance}{1.8}\\\\distance = 3.5 \times 1.8 = 6.3$

Hence distance covered is 6.3 km

Now we have to find the time taken to cover same 6.3 km walking at 4.2 km\hr

$4.2 = \frac{6.3}{time taken}\\\\time taken = \frac{6.3}{4.2} = 1.5$

So time taken by Max to cover the same distance walking at 4.2 km/h is 1.5 hours

3 0

1 year ago

A sample of 1714 cultures from individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiot

Damm [24]

Answer:

a) $p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

b) $\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

c) We are confident (95%) that the true proportion of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic is between 54.5% to 59.1%.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

Description in words of the parameter p

$p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

$\hat p$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

n=1714 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part b

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

$\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

Part c

The confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.568 - 1.96 \sqrt{\frac{0.568(1-0.568)}{1714}}=0.545$

$0.568 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1714}}=0.591$

And the 95% confidence interval would be given (0.545;0.591).

We are confident that about 54.5% to 59.1% of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic.

5 0

2 years ago

(b) A department store has 7,000 charge accounts. The comptroller takes a random sample of 36 of

galben [10]

Answer:

a.0.8664

b. 0.23753

c. 0.15866

Step-by-step explanation:

The comptroller takes a random sample of 36 of the account balances and calculates the standard deviation to be N42.00. If the actual mean (1) of the account balances is N175.00, what is the probability that the sample mean would be between

a. N164.50 and N185.50?

b. greater than N180.00?

c. less than N168.00?

We solve the above question using z score formula

z = (x-μ)/σ/√n where

x is the raw score,

μ is the population mean = N175

σ is the population standard deviation = N42

n is random number of sample = 36

a. Between N164.50 and N185.50?

For x = N 164.50

z = 164.50 - 175/42 /√36

z = -1.5

Probability value from Z-Table:

P(x = 164.50) = 0.066807

For x = N185.50

z = 185.50 - 175/42 /√36

z =1.5

Probability value from Z-Table:

P(x=185.50) = 0.93319

Hence:

P(x = 185.50) - P(x =164.50)

= 0.93319 - 0.066807

= 0.866383

Approximately = 0.8664

b. greater than N180.00?

x > N 180

Hence:

z = 180 - 175/42 /√36

z = 5/42/6

z = 5/7

= 0.71429

Probability value from Z-Table:

P(x<180) = 0.76247

P(x>180) = 1 - P(x<180) = 0.23753

c. less than N168.00?

x < N168.

z = 168 - 175/42 /√36

z = -7/42/6

z = -7/7

z = -1

Probability value from Z-Table:

P(x<168) = 0.15866

4 0

2 years ago

In right triangle ABC, angle A and angle B are complementary angles. The value of cos A is 9/41. What is the value of sin B?

Margaret [11]

SinB = 9/41

I explained my reasoning down below

5 0

2 years ago

Marisol wants to determine how many students plan to attend the girls varsity basketball game . Find her mistake and correct it

Contact [7]

Boys bvarsity is wrong and so is Bastet

7 0

2 years ago

If sin(2x + 7) = cos(4x - 7)º, what is the value of x?​

If sin(2x + 7) = cos(4x - 7)º, what is the value of x?