suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes. if we choose 5 members of the colony, what is the probability that at least one of them lives more than 87 minutes?

The function lim x-->a [sin(x) + a₀ + a₁x + ...+ aₙxⁿ ] has lim x-->a [sin(a) + a₀ + a₁a + ...+ aₙaⁿ] as the limit of the function as x approaches a.

Generally, To evaluate the limit of a function as x approaches a certain value, we need to substitute the value of x with the limit value and see what the function evaluates to.

In this case, we have:

lim x-->a [sin(x) + a₀ + a₁x + ...+ aₙxⁿ]

Substituting x with a, we get:

lim x-->a [sin(a) + a₀ + a₁a + ...+ aₙaⁿ]

This is the limit of the function as x approaches a.

Note that the terms a₀, a₁x, etc. are constants and will not affect the limit of the function. Therefore, the limit of the function as x approaches a is simply sin(a).

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Answer:

SSA

Step-by-step explanation:

If you have 2 triangles that have 2 congruent sides, and a congruent non-included angle, there is 2 possible values for the third side, so SSA does not work

The full expansion of the expression (2x - 1) (x + 5) is 2x² + 9x - 5

From the question, we have the following parameters that can be used in our computation:

(2x - 1) (x + 5)

Combine the factors of the expression using the product sign

So, we have

(2x - 1) (x + 5) = (2x - 1)*  (x + 5)

Evaluate the products

This gives

(2x - 1) (x + 5) = 2x² - x + 10x - 5

Evaluate the like terms in the expression

(2x - 1) (x + 5) = 2x² + 9x - 5

Hence, the expanded expression is 2x² + 9x - 5

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Therefore, the volume of the given cone is V=33.51 [tex]ft^{3}[/tex]

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume and length definitions are connected.

Here,

Cone has a radius of 4ft

A height of 2ft.

Thus,

The formula for volume of cone is used

V=π[tex]r^{2} \frac{h}{3}[/tex]

V=3.14*[tex]4^{2}[/tex]*2/3

V=50.24*2/3

V=100.48/3

V=33.51 [tex]ft^{3}[/tex]

Therefore, the volume of the given cone is V=33.51 [tex]ft^{3}[/tex]

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Answer: x=16

Step-by-step explanation:

The two angles in the picture is equal to each other.

So the 6x + 4 = 100 degree

6x = 96

x= 16

Yes, the data in this sample indicate that these individuals have average total cholesterol levels that are desirable.

Average:

In math average refers mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

Here we have the data of the national health and nutrition examination survey contains data on 2,263 US. adults. one of the variables is total cholesterol. total cholesterol levels less than 200 milligrams per deciliter (mg/dl) are considered desirable for adults. a reading between 200 and 239 mg/dl is considered borderline high and a reading of 240 mg/dl and above is considered high.

And we need to find that does the data in this sample indicate that these individuals have average total cholesterol levels that are desirable.

While we looking into the given question,

Total number pf participants = 2,263

Desirable level of cholesterol = less than 200 milligram

Border line level of cholesterol = Between 200 and 239 mg

Higher level of cholesterol = 240 mg

So, based on the given details, we know that at least 25% of people must have the desirable.

Therefore, the given level is a desirable one.

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Answer: 8.6 miles

Step-by-step explanation:

Takes 21 divided by 3 = 1 mile in 7 minute

Then take 60 divided by 7 = 8.57

ground to nearest tenth = 8.6 miles

Answer:

Grey dice.                  White dice

Step-by-step explanation:

Flip them around, this one really got me lol

Answer:

The answer is acually 54.3

Step-by-st

The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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Answer:

because the absolute value of -5 is positive 5

The Theoretical yield of solid precipitate is 1.42g/mol

Now, consider solid precipitate as cacl2

let us take the mass of cacl2 and calculate the moles of cacl2.

Mass of CaCl2 =2.0 g

By, default the molar mass of CaCl2 =110.98 g/mol

To calculate the Moles we have a formula:

Moles=Given mass*1 mol/Molar mass of a precipitate.-----(1)

substitute the values in equation (1)

Moles of CaCl2 =2.0 g * 1 mol/110.98g

                           = 0.018 mol

Take another solid precipitate:

Mass of K2Co3=2.0 g

The molar mass of K2Co3 =138.205 g/mol

Now calculating the moles of K2Co3

substitute the values in equation(1)

Moles of K2Co3 =2.0 g * 1 mol/ 138.205g

                             =0.0145 moles

According to balanced equation 1mole of CaCl2 reacts with 1 mole of K2CO

Thus, 0.018 moles of CaCl2 will react with 0.018 moles of K2CO3

And,0.0145 moles of K2CO3 will produce 0.0145 moles of CaCO3

Molar mass of CaCO3 =100.0869 g/mol

Theoretical yield of CaCO3 =moles of CaCO3 *molar mass of CaCO3

                                                =0.0145 moles * 100.0869 g/mol

                                                 =1.45g/mol

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The inequality to describe the number of subscriptions Andre must sell to reach his goal is  3s + 25 ≥ C.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Assuming the cost of soccer cleats to be 'C' and the number of subscriptions to be 's'.

∴ The inequality that represents this situation is 3s + 25 ≥ C to real his goal.

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1. Distribute

2. Subtract 1/2z on both sides

3. Subtract 9 on each side

4. x=-3

5. CHECK

Answer:

y+3 = -7/3(x-3)

y = -7/3x + 4

Answer:

246.5

Step-by-step explanation:

86275÷35

= 246.5

approximately 247

On solving the provided question we can say that  the equation of the line will be  y+11 = 0.

The slope of a line is how steeply it slopes from left to right. The slope of a line is determined by dividing its rise (vertical change) by its slope, which is its horizontal change. Regardless of whatever two locations on the line you pick, the slope of the line is always constant (it never changes).

To find the coordinates of two points on the line, choose two. Find the difference between these two locations' y-coordinates (gradients). Find the difference between these two places' x coordinates (runs). Divide the change in the y coordinate by the difference in the x coordinate (slope/history or slope).

Here,

slope, m= 0 as these are parallel line.

so the equation of the line will be

y-y1 = m(x-x1)

y+11 = 0

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The area of the curved surface of the dryer is 11.775m

The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centers of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centers.

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a certain height from the center. Real-world examples of cylinders are toilet paper rolls and cold beverage cans.

We know, the formula for curved surface of cylinder is 2pirh

putting the desired value in the equation we get

11.775m

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For the given data analysis  , The correct function is : RIGHT(B3,5), which is the correct syntax.

Here it is related to data cleaning which is the process of removing or fixing data that are incorrect or formatted incorrectly, corrupted, duplicate, or even incomplete data within a dataset that exists. When we mix  multiple data sources, it depicts that  there can be opportunities for the data to be mislabeled or duplicated, since we are guiven  that the customer names and addresses, so the correct syntax will be  =RIGHT(B3,5), where the RIGHT  Function  that returns set  number of characters of  a text string from the  right side

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At [00:16:00] timestamping (every 2 minutes) start in the audio segment of 15-20 minutes

Timestamping is frequently used to highlight a certain section of an audio file and indicate its significance.

In general, timestamps are utilised for the transcription process, in which the audio is used as a reference to convert it to a written form, if there is speech in an audio file other than music. Usually, this occurs in the press and media.

The timestamping software has the following formats: [HH:MM:SS]

HH stands for hours, MM for minutes, and SS for seconds.

For Audio segment of 15-20 minutes ,  [00:16:00] is timestamping every 2 minutes.

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Answer: Congruent

Step-by-step explanation:

F distribution is used with the global test of the regression model to reject the null hypothesis.

The hypothesis test will be conducted using a novel distribution. After the English statistician Sir Ronald Fisher, it is known as the F distribution. A ratio, the F statistic is (a fraction). One set of degrees of freedom is for the denominator, and the other set is for the numerator.

According to the null hypothesis, all group population means are equal. Because it is assumed that the populations are normal and that they have similar variances, the equal means hypothesis indicates that the populations have the same normal distribution. All groups are samples from populations with the same normal distribution, according to the null hypothesis. According to the alternative theory, at least two of the sample groups are drawn from populations with various normal distributions.

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.13 can be expressed in the form of percentage as 13%.

In order to convert numbers in decimal into percentage we only need to multiply the given number with 100 and after multiplying the number with hundred it can be written in percentage form. Like in the question given number is 0.13 and we need to express this in form of percentage. So in order to express this number in percentage we just multiply it with 100 which will be equal to 13% i.e

0.13 x 100 = 13%

By multiplying a decimal value by 100 and adding the percentage (%) sign, you can turn a decimal value into a percentage. A decimal multiplied moves the decimal point two places to the right.

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The required interest earned in the 6 months is $320 and the balance after a year is $8,652.8.

Given that,
John deposits $ 8,000 in a certificate of deposit that pays .8% interest, compounded semi-annually.

Investment is defined as when an individual is spend money on something that returns him or her higher money than the money they or invest.

Here,

Interest earned in the 6 months,
= 8000 [0.08/2]
= $320
Balance after a year,
Amount = principal [1 + rate/n]ⁿ
= 8000[1 + 0.08/2]²
= $8652.8

Thus, the required interest earned in the 6 months is $320 and the balance after a year is $8,652.8.

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Answer:

P(A) =0.5 obviously since it didn't say like P(AC) or P(AD)

Answer:

To find the cost of a ruler and the cost of a pencil, we can set up a system of equations using the given information. Let R be the cost of a ruler and P be the cost of a pencil.We know that 3R + 2P = 3.10 and 2R + 5P = 3.90Subtracting the first equation from the second, we get:5P - 3P = 3.90 - 3.10

2P = 0.80Dividing both sides by 2, we get:P = 0.40Substituting this value back into one of the original equations, we get:3R + 2(0.40) = 3.10

3R = 2.70

R = 0.90Therefore, the cost of a ruler is £0.90 and the cost of a pencil is £0.40.

Step-by-step explanation:

-57 decrease

In this equation.

The value of the function at x=0 is 17.78(4.86)^0 = 17.78(1) = 17.78.

ii. The ratio of output values ​​corresponding to an increment of 1 in input values ​​is (4.86)^1 = 4.86.

iii. A percent change of 1 unit is (4.86 - 1) × 100% = 286% increase.

For the function h(x) = 94.71(0.57)^x:

Thus, the value of the function at x=0 is 94.71(0.57)^0 = 94.71(1) = 94.71.

ii. The ratio of the output value corresponding to an increment of 1 in the input value is (0.57)^2 = 0.57.

iii. Percentage change of 1 unit is (0.57 - 1) × 100% = -57 reduction

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Sarah needs 7 and three-fourths of pounds of clay to make 31 small vases. By using the proportion of pounds of clay to the number of small vases, the required value is calculated.

Proportions are equations in which two ratios are made equal to each other. By using these we can relate a part to a whole. The formula for the proportions is written as

a : b = c : d or a/b = c/d or ad = bc

Here the variables a and d are said to be the extreme terms and the variables b and c are the mean terms.

Mostly used proportions are inverse proportion, direct proportion, compound proportion, etc.

Given that,

Sarah uses 3 and 1/2 pounds of clay to make 14 small vases.

And x pounds of clay to make 31 small vases.

So, applying the proportions formula for finding the x value as

[tex]3\frac{1}{2}:x=14:31[/tex]

Then, we can write them as

bc = ad ⇒ 14x = 7/2 × 31

⇒ 14x = 217/2

⇒ x = 217/28

⇒ x = 7.75 = [tex]7\frac{3}{4}[/tex]

Therefore, Sarah needs 7 and three-fourths pounds of clay to make 31 small vases. So, option C is correct.

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Step-by-step explanation:

so, for (4, 8) × 1/4, what is 4×1/4 ? and what is 8×1/4 ?

(1, 2)

similar for (4, -8) it is (1, -2).

similar for (-8, 0) it is (-2, 0).

similar for (8, 0) it is (2, 0).

that's it. that's really all there is to it. you multiply all the coordinates by the scale factor.

The numbers which are greater than 1 are 2 ÷ 1/3 and 3/4 ÷ 2/3 so options (B) and (D) are correct.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, the fraction is the division of the two numbers but the division is not wholly complete.

As per the given fractions,

2 ÷ 1/3 = 2 x 3/1 = 6 > 1

3/4 ÷ 2/3 = 3/4 x 3/2 = 9/8 > 1

Hence "The numbers which are greater than 1 are 2 ÷ 1/3 and 3/4 ÷ 2/3".

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The complete question below,