Find the value of the variable.

Answer:

3

Step-by-step explanation:

To begin with notice that  

        [tex]\displaymode{ \tan(x) = \frac{30}{10 + 30\cot(y)} }[/tex]

From that equation you get that

10 tan(x)  +  30tan(x) cot(x) = 30

therefore

tan(x) + 3 tan(x) cot(x) = 3

Answer:

A) 95% confidence interval for the population mean PEF for children in biomass households = (3.214, 3.386)

95% confidence interval for the population mean PEF for children in LPG households

= (4.125, 4.375)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.

C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.375)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Step-by-step explanation:

A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.

Finding the critical value from the z-tables,

Significance level for 95% confidence interval

= (100% - 95%)/2 = 2.5% = 0.025

z (0.025) = 1.960 (from the z-tables)

For the children in the biomass households

Sample mean = 3.30

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.20

N = sample size = 755

σₓ = (1.20/√755) = 0.0436724715 = 0.04367

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 3.30 ± (1.960 × 0.04367)

CI = 3.30 ± 0.085598

95% CI = (3.214402, 3.385598)

95% Confidence interval = (3.214, 3.386)

For the children in the LPG households

Sample mean = 4.25

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.75

N = sample size = 750

σₓ = (1.75/√750) = 0.063900965 = 0.063901

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 4.25 ± (1.960 × 0.063901)

CI = 4.25 ± 0.125246

95% CI = (4.12475404, 4.37524596)

95% Confidence interval = (4.125, 4.375)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.

The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.

Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂

The null hypothesis is

H₀: μ ≥ 0 or μ₁ ≥ μ₂

The alternative hypothesis is

Hₐ: μ < 0 or μ₁ < μ₂

Test statistic for 2 sample mean data is given as

Test statistic = (μ₂ - μ₁)/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = 3.30

n₁ = 755

s₁ = 1.20

μ₂ = 4.25

n₂ = 750

s₂ = 1.75

σ = √[(1.20²/755) + (1.75²/750)] = 0.07740

z = (3.30 - 4.25) ÷ 0.07740 = -12.27

checking the tables for the p-value of this z-statistic

Significance level = 0.01

The hypothesis test uses a one-tailed condition because we're testing in only one direction.

p-value (for z = -12.27, at 0.01 significance level, with a one tailed condition) = < 0.000000001

The interpretation of p-values is that

When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.

Significance level = 0.01

p-value = 0.000000001

0.000000001 < 0.01

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.

C) For FEY for biomass households,

Sample mean = 2.3 L/s

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation = 0.5

N = sample size = 755

σₓ = (0.5/√755) = 0.0182

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 2.30 ± (1.960 × 0.0182)

CI = 2.30 ± 0.03567

95% CI = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.375)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Hope this Helps!!!

Answer:

657.96

Step-by-step explanation:

use formula A=P(1+r/n)^nt

A=500(1+.04/1)^1*7

A=500(1.04)^7

A=500(1.3159~)

A= 657.96~

Answer:

(CX3)+10

Step-by-step explanation:

Answer:

c×3+10= j

Step-by-step explanation:

Answer:

  no; 12

Step-by-step explanation:

A number divisible by 4 and 6 will be divisible by their least common multiple, 12. If it is an odd multiple of 12, it will not be divisible by 24.

Examples:

  12÷4 = 3; 12÷6 = 2; 12 is not divisible by 24

  24÷4 = 6; 24÷6 = 4; 24 is divisible by 24

  36÷4 = 9; 36÷6 = 6; 36 is not divisible by 24

Answer:

-2 < x < 35

Step-by-step explanation:

We have that the larger side has a larger opposite angle and the smaller sides and a smaller opposite angle.

The opposite angle of the 14 unit side is 37 °.

The opposite angle of the 13-unit side is (x + 2) °.

Since 13 <14, it would be:

x + 2 <37

we subtract 2 on both sides

x <35

The value of x must be less than 35.

Now, to form a triangle, the angle must be greater than 0.

x + 2> 0

we subtract 2 on both sides

x> -2

The value of x must be greater than - 2.

Therefore the answer would be:

-2 <x <35

Answer:

49.8 nautical miles

Step-by-step explanation:

Recall that speed = distance/time

Time = 2hours

Speed = 12knots and 16 knots respectively

D = speed×time

D1 = 12×2 = 24

D2 = 16×2 = 32

Using the 'cosine rule' we have:

a^2 = b^2+c^2-2bc cos Θ

Where a =?

b =24

c = 32

Θ = 125°

a² = 24² + 32² - 2(24)(32)cos125°

a^2 = 576+1024 - 1536cos125°

a² = 1600 - 1536(-0.57357)

a² = 1600+881.0134

a² = 2481.0134

Then, a² = 2481.013406

a =√2481.013406

Hence, a = 49.8 nautical miles

In this exercise we must use the knowledge about triangles to calculate the distance that a ship will travel, in this way we find that:

49.8 nautical miles

First, remember the formula for distance, which is:

[tex]Speed = distance/time[/tex]

And knowing that the data reported in the exercise are:

So putting the values ​​informed in the distance formula, we have:

[tex]D = speed*time\\D_1 = 12*2 = 24\\D_2 = 16*2 = 32[/tex]

Using the 'cosine rule' we have:

[tex]a^2 = b^2+c^2-2bc cos \theta[/tex]

Find the a, will have:

[tex]b =24 \ \ \ c = 32 \ \ \ \theta = 125\\a^2 = 24^2 + 32^2 - 2(24)(32)cos125\\a^2 = 576+1024 - 1536cos125\\a^2 = 1600 - 1536(-0.57357)\\a^2 = 1600+881.0134\\a^2 = 2481.0134\\a=49.8[/tex]

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Answer: [tex]2\sqrt{1+tant}+C[/tex]

Step-by-step explanation:

To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.

[tex]\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } } \[/tex]

Let's first use our identities to rewrite the function. Since [tex]\frac{1}{cosx} =secx[/tex], we can use this identity.

[tex]\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,[/tex]

[tex]u=\sqrt{1+tant}[/tex]

[tex]du=\frac{sec^2t}{2\sqrt{1+tant} } dt[/tex]

Now that we have u and du, we can plug them back in.

[tex]\int\limits {2} \, du[/tex]

[tex]\int\limits{2} \, du=2u[/tex]

Since we know u, we can plug that in.

[tex]2\sqrt{1+tant}[/tex]

This may seem like the correct answer, but we forgot to add the constant.

[tex]2\sqrt{1+tant}+C[/tex]

Answer: See bolded below

Step-by-step explanation:

With the given f(x) and g(x) given, we can directly plug them in to solve. The inverse is to replace the y with x and x with y, then solve for y.

A. f(g(-4))=143

g(-4)=3(-4)+1

g(-4)=-12+1

g(-4)=-11

With g(-4), we plug that into f(x) to find f(g(-4)).

f(-11)=(-11)²-2(-11)

f(-11)=121+22

f(-11)=143

------------------------------------------------------------------------------------

B. 9x²-1

(3x+1)²-2(3x+1)

(9x²+6x+1)-6x-2

9x²-1

------------------------------------------------------------------------------------

C. g⁻¹(x)=(x-1)/3

x=3y+1

x-1=3y

(x-1)/3=y

Answer:

48

Step-by-step explanation:

You are doubling 2 dimensions, so you just multiply the volume by 2 each time. Since you are doing it twice, you multiply the volume by 4. 12*4=48. You could also brute force it and just do 24*36*12/216(the volume of the 6 inch cube).

Given that, a box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.

We need to find that how many cubes it holds if the length and width of the base are doubled,

We know that,

Volume of a rectangular prism = length × width × height

Volume of the new rectangular prism, = 2length × 2width × height

= 4(length × width × height)

= 4(12·12·18)

= 4×2592

= 10,368

Volume of the cube = side³

= 6³ = 216

The number of cube that the new rectangular prism can hold = Volume of the rectangular prism / Volume of the cube

= 10,368 / 216

= 48

Hence, the new rectangular prism, can hold 48 cubes.

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Answer:

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

2¹³

13 x 13

Step-by-step explanation:

We simply find numbers that can multiply to 26 and write out the multiplication to get our answer.

Answer: option D on edge 2020

Step-by-step explanation:

if you reverse the formula for mean, then you just insert the numbers and you have your answer

Answer:

Step-by-step explanation:

Using the alternative hypothesis (µ < µ0),

To find the p-value with test statistic -1.25 and assuming a standard level of significance of 0.05, using a p value calculator, the p-value is 0.1057 which is great that 0.05. Thus, the results is not significant.

Using the p value calculation.

1. Check the left tailed z table as the test statistic is negative,

2. Then find the probabilitythat z is greater than your test statistic (look up your test statistic on the z-table- the value under 1.2 and 0.05 which is 0.8944

3. Then, find its corresponding probability, and subtract it from 1 to get your p-value- 1-0.8944 = 0.1056.

Answer:

P ≈ 317.08 m

Step-by-step explanation:

Circumference: C = πd

Step 1: Find circumference of both domes

C = π(50)

Since it's a dome, we divide by 2

50π/2 = 25π

Since we have 2 domes, we simply multiply by 2 again

25π(2) = 50π

Step 2: Find perimeter of track

50π + 80(2)

P = 50π + 160

P = 317.08 m

Answer:

It's written as

[tex]89.7 \times {10}^{9} [/tex]

Or

[tex]8.97 \times {10}^{10} [/tex]

Hope this helps you

Answer:

8.97 * 10 ^10

Step-by-step explanation:

We want one nonzero digit to the left of the decimal

8.97

We moved the decimal 10 places to the left

The exponent is positive 10 since we moved 10 places to the left

8.97 * 10 ^10

Answer:

Step-by-step explanation:

[tex]7^{0}=1[/tex]

[tex](7^{13})^{3}*7^{0}=7^{13*3}*1\\\\=7^{39}[/tex]

Answer:

P = 1/2

Step-by-step explanation:

If the tourist spends more than 275$, they must not arrive in Chicago by bus.

( 150 + 60 < 275, 150 + 40 < 275)

The total options the tourist can make:

3 x 2 = 6

(1st leg: 3 possible options, 2nd leg: 2 possible options)

The number of options the tourist can make after excluding bus option:

2 x 2 = 4

(1st leg: 2 remaining possible options, 2nd leg: 2 possible options)

The number of options the tourist can make after excluding the bus option and spend more than 275$:

4 - 1 = 3

(excluding the case of selecting train and cab, because 225 + 40 < 275)

=> The probability that the tourist will spend more than 275$ on these 2 legs of the trip:

P = 3/6 = 1/2

Probability helps us to know the chances of an event occurring. The probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that Tourists have three choices for how to travel from New York to Chicago. They can take an aeroplane for $350, a bus for $150, or a train for $225. Also, when they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. Therefore, the cost of different routes is,

As it can be seen that there are 3 cases where a tourist will spend more than $275, while the total number of cases is 6. Therefore, the probability that a tourist will spend more than $275 on these 2 legs of the trip is,

Probability = 3/6 = 1/2 =0.5z

Hence, the probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.

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Answer:

The area of the sheet is approximately 50.59 m² or 50.6 m²

Step-by-step explanation:

The area of a rectangle is given by the following expression:

[tex]area = width*height[/tex]

Since breadth is the same as the width of the sheet, we can calculate its area as shown below:

[tex]area = 9.96*5.08 = 50.59[/tex]

The area of the sheet is approximately 50.59 m² or 50.6 m²

Answer:

10

Step-by-step explanation:

for this you need to sub the value of -3 for x

Q(-3)=(-3)^2-(-3)-2

=9+3-2

=10

Answer:

Q= x - X/x - 2/x

Step-by-step explanation:

hope this helps !

Answer:

0.1/4-3/20=1/40-6/40=-1/8 200% of this is -1/4

Step-by-step explanation:

This shows that  200 percent of (0.020(5/4) + 3 ((1/5) - (1/4))) is -2.75

Given the expression as shown in the question:

[tex]200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{1}{5}- \frac{1}{4} )][/tex]

Expand the expression in the square bracket using the distribution law as shown:

[tex]=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{4-5}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{-1}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )-(\frac{3}{20} )]\\=200\% \ of \ [0.020(1.25 )-\frac{3}{20}]\\=\frac{200}{100} \times [0.025-0.15]\\=2 \times [-0.125]\\=-2.75[/tex]

Hence the correct answer to the expression is -2.75.

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Answer:

the correct answer is 2x

Answer:

D. 2x

Step-by-step explanation:

20x² : 1, 2, 4, 5, 10, 20, x

14x : 1, 2, 7, 14, x

The greatest common factor of the polynomial is 2x.

2x(10x² - 7)

Answer:

The null and alternative hypothesis can be written as:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

This claim will be reflected in the alternnative hypothesis, that will state that the population proportion 1 (18 to 34) is significantly smaller than the population proportion 2 (35 to 49).

On the contrary, the null hypothesis will state that the population proportion 1 is ot significantly smaller than the population proportion 2.

Then, the null and alternative hypothesis can be written as:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

The significance level is assumed to be 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.63.

[tex]p_1=X_1/n_1=126/200=0.63[/tex]

The sample 2, of size n2=175 has a proportion of p2=0.68.

[tex]p_2=X_2/n_2=119/175=0.68[/tex]

The difference between proportions is (p1-p2)=-0.05.

[tex]p_d=p_1-p_2=0.63-0.68=-0.05[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{126+119}{200+175}=\dfrac{245}{375}=0.653[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.653*0.347}{200}+\dfrac{0.653*0.347}{175}}\\\\\\s_{p1-p2}=\sqrt{0.001132+0.001294}=\sqrt{0.002427}=0.049[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.05-0}{0.049}=\dfrac{-0.05}{0.049}=-1.01[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=P(z<-1.01)=0.1554[/tex]

As the P-value (0.1554) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

Answer:

620 comic books

2480 / 4 is 620.

620 x 3 is 1860.

1860 + 620 is 2480.

Done!

Answer:

y=6x-13

Step-by-step explanation:

Since we are given a point and a slope, we can use the slope intercept formula.

[tex]y-y_{1} = m(x-x_{1} )[/tex]

where (x1, y1) is a point and m is the slope.

We know that the slope is 6 and the point is (3,5). Therefore,

x1= 3

y1= 5

m=6

Substitute these into the formula.

[tex]y-5 = 6(x-3 )[/tex]

Distribute the 6. Multiply each term inside the parentheses by the number outside the parentheses.

[tex]y-5= (6*x) + (6*-3)[/tex]

[tex]y-5=6x-18[/tex]

We want to find the slope-intercept form, or y=mx+b. Therefore, we must get y by itself.

5 is being subtracted from y. The inverse of subtraction is addition. Add 5 to both sides.

[tex]y-5+5=6x-18+5[/tex]

[tex]y= 6x-18+5[/tex]

[tex]y= 6x -13[/tex]

Answer:

Step-by-step explanation:

y + 8 = 0(x - 0)

y + 8 = 0

y = -8

Answer:

one side is [tex]\sqrt{10}[/tex] and other 3[tex]\sqrt{10}[/tex]

in decimal one side = 3.16

other side =  9.48

Step-by-step explanation:

In right angle

if two sides containing right angle is a and b and h is hypotenuse then

by Pythagoras theorem

a^2 + b^2 = h^2

__________________________________

let one side be x

given

One of the triangle’s legs is 3  times the length of the other leg

then other leg = 3x

given h = 10 cm

applying Pythagoras theorem

[tex]a^2 + b^2 = h^2\\x^2 + (3x)^2 = 10^2\\x^2 + 9x^2 = 100\\10x^2 = 100\\x^2 = 100/10 = 10\\x = \sqrt{10}[/tex]

Thus, one side is [tex]\sqrt{10}[/tex] and other 3[tex]\sqrt{10}[/tex]

[tex]\sqrt{10} = 3.16\\[/tex]

thus, in decimal one side = 3.16

other side = 3.16*3 = 9.48

Answer:

(x + 2) ^2 (x - 2) ^ 2 so A is the answer.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

P(Chase) > P(Ava)

700 > 587

Therefore, Ava's claim is wrong!

On day 14, Chase's bacteria population will be greater than Ava's bacteria population.

Step-by-step explanation:

Please refer to the attached image.

Ava's bacteria population is modeled by the following equation.

[tex]$ b(t) = 200(1+0.08)^t $[/tex]

Where t is time in days and b(t) is the population of the bacteria after t days.

The graph represents the population of Chase's bacteria.

Ava claims that on day 14, she will have more bacteria than Chase.

Let us compare the population of both bacteria.

Chase bacteria population when t = 14 days:

From the graph, the population is approximately 700 at t = 14 days

P(Chase) ≈ 700

Ava bacteria population when t = 14 days:

at t = 14 days

[tex]b(t) = 200(1+0.08)^t \\\\ b(14) = 200(1.08)^{14} \\\\ b(14) = 200 (2.93719)\\\\ b(14) = 587.44[/tex]

So, the population is approximately 587 at t = 14 days

P(Ava) ≈ 587

P(Chase) > P(Ava)

700 > 587

Therefore, Ava's claim is wrong!

On day 14, Chase's bacteria population will be greater than Ava's bacteria population.

Answer:

D

Step-by-step explanation:

Trust

Answer:

12x/2 or 52/2

Step-by-step explanation:

Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.

Answer:

Option B

Step-by-step explanation:

The null hypothesis for a chi-square goodness of fit test states that the data are consistent with a specified distribution.

While the alternative hypothesis states that the data are not consistent with a specified distribution.

In this case study, the test is for a nose distribution. Thus the null hypothesis would be that the population has a normal distribution.