The length Of a rectangular air filter is 1 inches less than twice the width. Find the length and width of the filter if the area is 378 square inches

Answer:

The length of the mosquito in the picture is 117.6 mm.

Step-by-step explanation:

This question can be solved using a rule of three.

The real size of the mosquito is 16 mm, which is 100% = 1.

In the picture, the size is magnified 635%, so it is 100+635 = 735% = 7.35. So

16mm - 1

x mm - 7.35

x = 7.35*16 = 117.6

The length of the mosquito in the picture is 117.6 mm.

Final answer:

To find the magnified length of a mosquito in a picture, multiply its actual size (16 mm) by the magnification factor (6.35), resulting in a magnified length of 101.6 millimeters.

Explanation:

The question involves calculating the magnified length of a mosquito in a picture, given that the magnification is 635% of its actual size and the actual size is 16 millimeters. First, understand that 635% magnification means the mosquito's image is 6.35 times its actual size. To find the magnified length, multiply the actual length by the magnification factor.

Magnified length = Actual length × Magnification factor

= 16 mm × 6.35

= 101.6 mm

Therefore, the length of the mosquito in the picture is 101.6 millimeters.

Answer:

Yes, if I'm assuming that it was written as [tex]119*10^-3[/tex], then this is a basis for a scientific notation.

Answer:

The grammar has start symbol S, terminals are 1,3,5,7 an  9 ; and the variables are S, A, B, C and D

Step-by-step explanation:

CHECK THE ATTACHMENT FOR EXPLANATION

Answer:

She should guarantee a weight of 4.18 pounds.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 8.6, \sigma = 1.9[/tex]

What weight should she guarantee so that she will have to give her customer's money back only 1% of the time?

She should guarantee the 1st percentile of weights, which is X when Z has a pvalue of 0.01. So it is X when Z = -2.327.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.327 = \frac{X - 8.6}{1.9}[/tex]

[tex]X - 8.6 = -2.327*1.9[/tex]

[tex]X = 4.18[/tex]

She should guarantee a weight of 4.18 pounds.

The turkey farmer should guarantee that her 6-week poults will weigh at least  4.2 pounds to ensure that she will have to give money back only 1% of the time.

Given:

- Mean weight [tex](\( \mu \))[/tex] of poults: 8. 6 pounds

- Standard deviation [tex](\( \sigma \))[/tex] of poults: 1.9 pounds

1. Use the z-score corresponding to the 1st percentile of the normal distribution, which is approximately [tex]\( z_{0.01} \approx -2.3263 \)[/tex].

2. Calculate the guaranteed weight X:

  [tex]\[ X = \mu + z_{0.01} \cdot \sigma \] \[ X = 8.6 + (-2.3263) \cdot 1.9 \] \[ X \approx 4.2 \text{ pounds} \][/tex]

Therefore, the turkey farmer should guarantee that her 6-week poults will weigh at least 4.2 pounds to ensure that she will have to give her customers' money back only 1% of the time. This ensures that 99% of the poults will weigh at least 4.2 pounds.

Step-by-step explanation:

x/ 3 = 2 / 9

Cross multiply

9x = 6

x = 6 / 9

x = 2 / 3

Answer:

80 yards

Step-by-step explanation:

There are 3 feet in a yard, therefore you take 240 feet divided by 3 to get how many yards there are, and in your case it is 80 yards.

Answer:

[tex]a = \frac{w + 4 - 3b}{6} [/tex]

Step-by-step explanation:

[tex]w = 3(2a + b) - 4 \\ w + 4 = 6a + 3b \\ w + 4 - 3b = 6a \\ \frac{w + 4 - 3b}{6} = \frac{6a}{6} \\ a = \frac{w + 4 - 3b}{6} [/tex]

Thanks

hope this helps!!

I'd appreciate if you rate my answer and give a thanks.

Answer:

1 gallon does not belong

Step-by-step explanation:

4 pints = 2 quarts

2 quarts = 8 cups

8 cups does not equal 1 gallon, 16 cups does

The standard deviation of the sampling distribution of the sample​ mean is 4.587 and this can be determined by using the formula of the standard deviation of the sample mean.

Given :

The standard deviation of a random variable X is 20 and a random sample of size n equals 19.

The formula of the standard deviation of the sample mean can be used to determine the standard deviation of the sampling distribution of the sample​ mean.

The standard deviation of the sample mean is given by:

[tex]\sigma_m=\dfrac{\sigma}{\sqrt{n} }[/tex]   --- (1)

Now put the value of [tex]\sigma[/tex] that is 20 and the value n that is 19 in the equation (1).

[tex]\sigma_m = \dfrac{20}{\sqrt{19} }[/tex]

[tex]\sigma_m = \dfrac{20}{4.36}[/tex]

[tex]\sigma_m = 4.587[/tex]

So, the standard deviation of the sampling distribution of the sample​ mean is 4.587.

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The standard deviation of the sampling distribution of the sample mean, also referred to as the standard error, for this scenario is approximately 4.58.

The standard deviation of a sampling distribution of the sample mean, also known as the standard error, can be calculated using the formula Standard Error = σ/√n, where σ is the population standard deviation and n is the sample size. In your case, the standard deviation (σ) of the random variable X is 20, and your sample size (n) is 19.

Plugging these values into the formula, we get Standard Error = 20/√19, which can be approximated as 4.58.

Therefore, the standard deviation of the sampling distribution of the sample mean for this scenario is approximately 4.58.

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Answer:

an exterior angle is the correct answer.....

Answer:

A

Step-by-step explanation:

Answer:

12,500 square millimeters

Step-by-step explanation:

Answer:

c(12,500)

Step-by-step explanation:

Answer:

1225000

Step-by-step explanation:

The hydrostatic force against one side of the submerged equilateral triangle can be obtained by integrating the product of the fluid pressure and the area of an infinitesimally small strip on the triangle from base to top, yielding a result of 49,000 Newton.

To express the hydrostatic force against one side of the equilateral triangular plate as an integral, we need to start with the equation for the pressure at any point in a fluid: P = ρgh. This is the product of the water density (ρ), gravitational acceleration (g), and height inside the fluid (h).

Next, we multiply this by the area of an infinitesimally small horizontal strip on our triangular plate, and then integrate to account for the entire side of the triangle, from the base to the top. In this problem, the area of the strip depends on the height, and for an equilateral triangle with a side length of 10m, it can be expressed as 10-2y.

Therefore, the hydrostatic force F becomes the integral ∫(0 to 10) ρg(10 - y)dy, where ρ is the weight density of water 1000 kg/m3, g stands for the acceleration due to gravity 9.8 m/s2, and y is the height varying from 0 to 10 m. Evaluating this integral, we get F = 49,000 Newton.

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Answer:

Step-by-step explanation:

Since x is a normally distributed random variable, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = the random variable

µ = mean

σ = standard deviation

From the information given,

µ = 16

σ = 2

a.​ P(x ≥ 17.5​) = 1 - (x < 17.5)

For x < 17.5

z = (17.5 - 16)/2 = 0.75

Looking at the normal distribution table, the probability corresponding to the z score is 0.77

P(x ≥ 17.5​) = 1 - 0.77 = 0.23

b.​ P(x ≤ 12​)

z = (12 - 16)/2 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

P(x ≤ 12​) = 0.023

c) P(16.78 ≤ x ≤ 20.46)

For x = 16.78,

z = (16.78 - 16)/2 = 0.39

Looking at the normal distribution table, the probability corresponding to the z score is 0.65

For x = 20.46,

z = (20.46 - 16)/2 = 2.23

Looking at the normal distribution table, the probability corresponding to the z score is 0.987

Therefore,

P(16.78 ≤ x ≤ 20.46) = 0.987 - 0.65 = 0.337

d) P(11.48 ≤ x ≤ 19.06)

For x = 11.48,

z = (11.48 - 16)/2 = - 2.26

Looking at the normal distribution table, the probability corresponding to the z score is 0.012

For x = 19.06,

z = (19.06 - 16)/2 = 1.53

Looking at the normal distribution table, the probability corresponding to the z score is 0.94

Therefore,

P(11.48 ≤ x ≤ 19.06) = 0.94 - 0.012 = 0.928

Answer:

option C is correct,the null hypothesis equals 1.8

Answer:

There are 154 children, 77 adults and 86 students in attendance

Step-by-step explanation:

Given

Seat capacity = 317

Total tickets = $2296

Charges is as follows;

Children = $5.00

Students = $7.00

Adults = $12.00

Required

Number of children, students and adults

Let A, C and S represent adults, children and students respectively.

So,

From sales of tickets, we have the following:

12A + 5C + 7S = 2296 --- Equation 1

From attendance, we have

A + C + S = 317 --- Equation 2

Given that, there are half as many adults as there are children.

So, A = ½C

Substitute ½C for A in equation 1 and 2

12A + 5C + 7S = 2296 becomes

12 * ½C + 5C + 7S = 2296

6C + 5C + 7S = 2296

11C + 7S = 2296 ---- Equation 3

A + C + S = 317

½C + C + S = 317

Multiply through by 2

2(½C + C + S) = 2 * 317

C +2C + 2S = 634

3C + 2S = 634 ----- Equation 4

We'll solve equations 3 and 4, simultaneously.

First, write out the two equations.

11C + 7S = 2296 ---- (3)

3C + 2S = 634 ------ (4)

Using elimination method to eliminate S.

Multiply (3) by 2 and multiply (4) by 7.

2 (11C + 7S = 2296 )

22C + 14S = 4592 ---- Equation 5

7 (3C + 2S = 634 )

21C + 14S = 4438 ------ Equation 6

Subtract (6) from (5)

22C + 14S = 4592

21C + 14S = 4438

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

22C - 21C + 14S - 14S = 4592 - 4438

C = 154

Recall that A = ½C

So, A = ½ * 154

A = 77

Recall equation 2

A + C + S = 317

Make S the subject of formula

S = 317 - A - C

Substituton 77 for A and 154 for C

So,

S = 317 - 77 - 154

S = 86

Hence, there are 154 children, 77 adults and 86 students in attendance

The mathematical statement translates to an inequality 20 ≤ 4C - 8, and solving this results in C ≥ 7.

The question provides a mathematical statement which can be translated into an equation. The statement 'The number 20 is no less the difference of 4 times the number C and 8' translates into the equation 20 ≤ 4C - 8. In this equation, 4 times a number C minus 8 can result in a value that is at least 20. To find the value for C, you would need to isolate C. This is done by first adding 8 to both sides to get 28 ≤ 4C, then dividing by 4 to get C ≥ 7. C, therefore, could be any value that is 7 or greater.

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Answer:

(A)The sample comes from a population of tires with 60,000 miles where 5% of tires are worn out.

Step-by-step explanation:

The tire manufacturer has a 60,000 mile warranty for tread life. To verify the authenticity of its claim, it picks a sample of 250 tires (out of the population of tires) that have been used for 60,000 miles.  

Given the hypothesis:

[tex]H_0[/tex]: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.  

[tex]H_a[/tex]: The proportion of tires that are worn out after 60,000 miles is less than 0.05.

It is assumed that 5% of the tires in the sample are worn out and the hypothesis is formulated to prove or disprove this assumption.

Answer:

[tex]95-2.76\frac{6.6}{\sqrt{30}}=91.674[/tex]    

[tex]95+2.76\frac{6.6}{\sqrt{30}}=98.326[/tex]    

We can say at 99% confidence that the true mean is between (91.674;98.326)    

Step-by-step explanation:

Data given

[tex]\bar X=95[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=6.6 represent the sample standard deviation

n=30 represent the sample size  

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

We need to find the critical value [tex]t_{\alpha/2}[/tex] and we need to find first the degrees of freedom, given by:

[tex]df=n-1=30-1=29[/tex]

Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,29)".And we see that [tex]t_{\alpha/2}=2.76[/tex]

And replacing we got:

[tex]95-2.76\frac{6.6}{\sqrt{30}}=91.674[/tex]    

[tex]95+2.76\frac{6.6}{\sqrt{30}}=98.326[/tex]    

We can say at 99% confidence that the true mean is between (91.674;98.326)    

Answer:

A. 5 * 1/7

Step-by-step explanation:

When solving division, you can also multiply by the reciprocal of the second number to get the same answer.

Answer

Step-by-step explanation:

H*W*L

280=7*W*(6+W)

280=42W+7W^2

40=6w+w^2

W^2+6W-40=0

(W-4)(W+10)=0

W=4

We can only use positive results

L=6+W

L=4+6=10

Given that, the height of the cardboard box=10 inches and volume = 540 cubic inches.

Let the width of the cardboard box be x, then the length will be 3x.

The formula to find the volume of a rectangular prism is Volume=Length×Width×Height.

Now, 540=10×x×3x

⇒x²=18

⇒x=3√2 inches.

Therefore, the width of a cardboard box is 3√2 inches.

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Answer:

16*pi=50.24

Step-by-step explanation:

Answer:

16* pi = 50.24

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cost of Truck = $60,000

Expected  use = 100,000 miles

Residual value = $10,000

Depreciation per mile = ( Cost of Truck- Residual value)/ Estimated use

= ( 60,000-10,000)/100,000

= 50,000/100,000

= $0.5

Miles driven in first year = 16,000

Depreciation expense for first year = Miles driven in first year x Depreciation per mile

= 16,000 x 0.5

= $8,000

The depreciation expense in the first year using activity-based depreciation is $ 8,000.

An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline.

Depreciation, or a decline in asset value, can be brought on by a variety of other variables, such as bad market conditions, etc.

Calculation of Depreciation for  first year

Purchase Cost  of Truck = $60,000

Estimated lifetime  use = 100,000 miles

Salvage value = $10,000

Depreciation per mile = ( Cost of Truck- Residual value)/ Estimated use

= ( 60,000-10,000)/100,000

= 50,000/100,000

= $0.5

Miles driven in first year = 16,000

Depreciation for 1st year = Miles drove in first year x Depreciation per mile

= 16,000 x 0.5

= $8,000

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Answer:

In the screenshot you have the right answer, it is indeed 1000 times greater

Step-by-step explanation:

Answer:

area of sector = 40.192 unit²

Step-by-step explanation:

Area of a sector = ∅/360 × πr²

where

∅ = angle in degree

r = radius

Area of sector  when ∅ = radian

area of a sector = 1/2r²∅

where

∅ = radian

r = radius

area of sector = 1/2 × 4² × 8/5 × π

area of sector = 1/2 × 16 × 8/5 × π

area of sector = 128/10 × π

area of sector = 12.8 × π

area of sector = 12.8 × 3.14

area of sector = 40.192 unit²

Answer:

12m^3

Step-by-step explanation:

Basically, you are looking for the volume of the Oil. In order to do that you simply need to use the rectangular prism volume formula: lwh

lwh=V

(5)(2)(1.2)=V

10(1.2)=V

12=V

Answer: a) [tex]E(x)=\dfrac{-5945}{(30x+11)(5x+200)}[/tex], b) 0.7975, demand is inelastic, c) increase.

Step-by-step explanation:

Since we have given that

[tex]D(x)=\dfrac{5x+200}{30+11}[/tex]

So, derivative w.r.t x would be

[tex]D'(x)=\dfrac{5(30x+11)-30(5x+200)}{(30x+11)^2}\\\\D'(x)=\dfrac{150x+55-150x-6000}{(30x+11)^2}\\\\D'(x)=\dfrac{5945}{(30x+11)^2}[/tex]

As we know that

[tex]E(x)=\dfrac{-xD'(x)}{D(x)}\\\\\\E(x)=\dfrac{\dfrac{-(-)5945x}{(30x+11)^2}}{\dfrac{5x+200}{30x+11}}\\\\\\E(x)=\dfrac{5945x}{(30x+11)(5x+200)}[/tex]

(b) Find the elasticity when x = 2.

So, we put x = 2, we get that

[tex]E(2)=\dfrac{5945\times 2}{(30(2)+11)((5(2)+200))}\\\\E(2)=\dfrac{11890}{(60+11)(10+200)}\\\\E(2)=\dfrac{11890}{71\times 210}\\\\E(2)=\dfrac{11890}{14910}\\\\E(2)=0.7975[/tex]

Since, 0.7975 < 1, so the demand is inelastic.

(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?

The total revenue will also increase with increase in price.

As total revenue = [tex]price\times quantity[/tex]

Hence, a) [tex]E(x)=\dfrac{-5945}{(30x+11)(5x+200)}[/tex], b) 0.7975, demand is inelastic, c) increase.

This problem involves the calculation of the elasticity of a demand function using the derivative of the function. The elasticity is then used to analyze the effect on the total revenue when the price changes. The elasticity at a specific point is calculated and used for further analysis.

For part (a), to find the elasticity of the demand function, we need to use the formula for the price elasticity of demand, which is E = (dQ/dX) * (X/Q). Here, dQ/dX is the derivative of the demand function concerning X. This needs to be calculated first. The value of E provides us with the measure of elasticity.

For part (b), when x = 2 we substitute this value into the formula for E to get the elasticity at x = 2.

For part (c), based on the concept of elasticity, if E > 1, the demand is said to be elastic and a price decrease will result in an increase in total revenue, and vice versa. If E < 1, the demand is said to be inelastic and a price decrease will result in a decrease in total revenue, and vice versa. So, after calculating E at x = 2, we can use it to determine the effect on total revenue.

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Answer:

B=16

Step-by-step explanation:

If 75% is 12, 100% would be 16. B = 16!

Answer:16

Step-by-step explanation:

12/3=4 4=25%of b 4+12=16

Answer:

The mean of the sampling distribution = $1350

Step-by-step explanation:

Given -

Population mean [tex]\boldsymbol{(\nu)}[/tex] = $1350

Standard deviation = $150

Sample size ( n ) = 25

The mean of the sampling distribution = population mean

[tex]\boldsymbol{(\nu)_{M}} = \boldsymbol{(\nu)}[/tex]

The mean of the sampling distribution = $1350

Answer:

17

Step-by-step explanation:

32+2=34

34/2= 17

Half of the sum of 32 and twice a number 'x' expressed as '2ans' would be calculated by adding 32 and 2x and then dividing by 2, resulting in the expression 16 + x.

The question asks to find half of the sum of 32 and an unspecified number (mentioned as '2ans'). Assuming '2ans' means twice the number 'ans', which can be represented as 2x, where 'x' is the particular value of 'ans'. First, calculate the sum of 32 and 2x, and then divide that sum by two to find half of it.

The steps to solve this are:

Calculate the sum: 32 + 2x.

To find half of the sum, divide by 2: (32 + 2x) / 2.

Simplify the expression: 16 + x.

Therefore, half of the sum of 32 and twice a number 'x' (2x) is 16 + x.

Answer: 0.25

Step-by-step explanation:

I did the quiz

Answer:

0.25

Step-by-step explanation:

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