I don't understand this tbh and I have been stuck on it foreverr​

I Don't Understand This Tbh And I Have Been Stuck On It Foreverr

Answers

Answer 1

The height of the balloon before it started its' descent is; 2660 ft

How to solve function tables?

We are given a function table with;

time after descent on x-axis in minutes

Height of descent on the y-axis in feet

Let us calculate the slope with the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

Picking two coordinates;

Slope = (1960 - 2380)/(5 - 2)

Slope = -420/3

Slope = -140 feet/minutes

Now, the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

when x = 11, y = 1120

Thus;

1120 = -140(11) + c

c = 1120 + (140 * 11)

c = 1120 + 1540

c = 2660 feet

We conclude that it is the height of the balloon before descent

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Related Questions

the sum of two numbers is 15. one number is 4 times the other. letimage andimage represent the two numbers. which system of equations correctly represents this problem?

Answers

The two numbers are 3 and 12 when 15 is the result of sum two numbers. One to two are compared in a 4:1 ratio.

Given that,

15 is the result of adding two numbers. One to two are compared in a 4:1 ratio.

We have to find which two numbers are they.

We know that,

Let take x and y to denote the two numbers

We get

x + y = 15   ----->equation(1)

x = 4y        ----->equation(2)

Substitute the 4y in equation(1)

(4y) + y = 15

5y = 15

Divide both sides by 5

y = 3.

Substitute y=3 in equation(2)

x=4(3)

x = 12

Therefore, The two numbers are 3 and 12 when 15 is the result of adding two numbers. One to two are compared in a 4:1 ratio.

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To lift a load of 100 n a distance of 1 m an effort of 25 n must be applied over an inclined plane of length 4 m. What must be done to lift the load 2 m, using the same effort?.

Answers

An inclined plane of length 8 m is used to lift the load 2 m, using the same effort.

A ramp that helps lift and lower heavy things is called an inclined plane. It is a flat surface that is positioned against a horizontal surface at an angle other than a right angle.

Work is defined as the use of force to move an object over a distance. It is derived as the product of displacement (d) and force (F). Work is given by W = F×d = 25 N×d.

When a body is lifted, we can express work as W = m×g×h where g is gravity and h is height. And the force is written as F = m×g where m is the mass of an object. Then, W = F×h

Calculating the work done to lift the load to 2 m, we get,

W = 100 N×2 m = 200 Nm.

Substitute this value in W = F×h, we get,

200 Nm = 25 N×d

Divide both sides by 25 N, and we get,

[tex]\begin{aligned}\frac{\mathrm{200\;Nm}}{\mathrm{25\;N}}&=\frac{\mathrm{25\;N\times d}}{\mathrm{25\;N}}\\d&=\mathrm{8\;m}\end{aligned}[/tex]

The value is 8 m. Therefore, the first statement is correct.

The complete question is -

To lift a load of 100 N a distance of 1 m an effort of 25 N must be applied over an inclined plane of length 4 m. What must be done to lift the load 2 m, using the same effort?

A. Use an inclined plane of length 8 m.

B. Use an inclined plane of length 2 m.

C. Use an inclined plane of length 10 m

D. Use an inclined plane of length 16 m.

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Carly is a catcher on the school softball team. By the end of the season she had played in 45 percent of the 40 games the team played. In how many games did Carly NOT play.

Answers

Number of games did Carly NOT play is 22.

How to calculate percentage?

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Given:

Total number of games = 40

It is given that  she had played in 45 percent of the 40 games the team played.

Number of games she played = 45% of 40

                                                 = [tex]\frac{45}{100}\times 40= 18[/tex]

Number of games she did not play = 40 - 18 = 22

Therefore, number of  games did Carly NOT play is 22.

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I also need this quickly :(

Answers

Answer:

Scale factor = 1/2

Step-by-step explanation:

Explanation:

    A scale factor is a number you multiply the dimensions of a shape by to get the image. Because figure B has half the length and width, we can conclude the scale factor is 1/2.

Mr. Patrick has 30 students in his class working on a project. Show at least 3 different ways he could equally group his students.

I will offer more points​ soon

Answers

Answer:

10 groups of 3, 3 groups of 10 and 5 groups of 6

Step-by-step explanation:

you are bored at a lunch meeting and decide to place a raisin in your glass of water. the raisin swells to twice its original size. relative to the water, the raisin must have been:

Answers

If the raisin swells to twice its original size, relative to the water, the raisin must have been hypertonic solution.

A response that is hypertonic refers to one that has a larger osmotic strain than another arrangement. In the end, a hypertonic arrangement is one in which the concentration of solute particles outside of a layer is greater than that inside.An arrangement that has a higher solute fixation than another arrangement is said to be hypertonic.The inside of a red platelet compared with the solute concentration of fresh water serve as illustrations of a hypertonic arrangement.When two arrangements come into contact, the solute or dissolvable moves until the arrangements reach harmony and are isotonic with one another.

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Suppose IQ scores were obtained for randomly selected sets of . The pairs of measurements yield , , r , P-value 0.000, and , where x represents the IQ score of the . Find the best predicted value of given that the has an IQ of ?

Use a significance level of 0.05. 20 siblings 20 x=99.42 y=97.2 =0.867 = = −21.33+1.19x y older child y older child 97 Click the icon to view the critical values of the Pearson correlation coefficient r.1 The best predicted value of is . y (Round to two decimal places as needed.) Critical Values of the Pearson Correlation Coefficient r n 0.05 α = 0.01 α = NOTE: To test H0 : 0 against H1: 0, reject H0 if the absolute value of r is greater than the critical value in the table. rho= rho≠4 0.950 0.990 5 0.878 0.959 6 0.811 0.917

Answers

The best predicted value given that a person has an IQ of 91 is 94.03.

Here, we are given that-

sample size n = 20

sample mean for the independent value x = 100.39

sample mean for the dependent value y = 103.6

coefficient of correlation r = 0.925

The general expression for representing a linear model is given by-

y = β₀ + β₁x

where β₀ is the intercept and β₁ is the slope

For the above given case, the linear model will be given as-

y = -3.34 + 1.07x

where -3.34 is the intercept and 1.07 the slope.

To find the best predicted value when X = 91, we substitute the value of x as 91 in the equation as follows-

y = -3.34 + 1.07(91)

y = 94.03

Thus, the best predicted value given that a person has an IQ of 91 is 94.03.

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Evaluate the expression for the given value of the variable. 32 + 1/9t. T = - 1/2

Answers

Answer: 32 1/18

Step-by-step explanation: So first, I did 1/9 (-1/2) and I got 1/18. Yes although it was negative, when multiplying, it will become positive, then 1 x 1 is 1, and 9 x 2 is 18. Then, when adding it to 32, you get 32 1/18. I hoped this helped!

One weekend, there were 77 pizzas ordered for the sophomore dorm. That weekend 12 customers ordered their pizza with just pepperoni, 19 customers ordered their pizza with just sausage, 20 ordered theirs with just onions, 13 ordered theirs with pepperoni and sausage, 12 ordered theirs with sausage and onions, 11 ordered theirs with pepperoni and onions, and 7 ordered theirs with all three items. How many customers ordered their pizza with pepperoni or sausage (or both)?

Answers

41 customers ordered their pizza with pepperoni or sausage (or both).

What is customer?

Customer is an individual or organization who buys goods or services from another. Customers are essential to businesses, as they are the ones that provide the revenue needed to keep the business running. Customers are the lifeblood of any business and are the ones who determine its success or failure. Customers can be internal, such as employees, or external, such as retailers or other businesses. Companies must strive to understand their customer’s needs, wants and preferences in order to keep them satisfied and coming back for more. Companies must also be aware of customer trends, preferences and behaviour to stay competitive. Companies can use customer feedback to improve their products and services, as well as their customer service. Finally, companies must ensure that their customers receive good value for their money, as well as excellent customer service.

This is calculated by adding the number of customers who ordered their pizza with just pepperoni (12) and the number of customers who ordered their pizza with just sausage (19) and the number of customers who ordered their pizza with pepperoni and sausage (13).
12 + 19 + 13 = 41.

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An art teacher has 2,532 crayons. He plans to give 12 crayons to each student who takes his class. How many students take his art class?

Answers

Answer:

The art class is attended by 211 students, each one with 12 crayons.

Step-by-step explanation:

Total crayons = 2532

If the teacher gives 12 crayons, then:

Total students = 2532/12 = 211

211 students

Because 2532 divided by 12 crayons for every student equals 211.

Find the midpoint of the line segment with the given endpoint. (9,-7),(-9,5)

PLEASE HELPPP

Answers

Answer:

[tex](0,-1)[/tex]

Step-by-step explanation:

[tex]\left(\frac{-9+9}{2}, \frac{5-7}{2} \right)=(0, -1)[/tex]

How do i solve this?

Answers

Answer:

7, 14,21 28

4,8,12,16

Step-by-step explanation:

Answer:

8, 21, 16

Step-by-step explanation:

The ratio from sugar to cups is 7:4, which is 1.75.

Divide and multiply to solve.

14 / 1.75 = 8

12 * 1.75 = 21

28 / 1.75 = 16

Teen cigarette use is down the us centers for disease control conducts the national youth tobacco survey each year. The preliminary results3 of 2019 show that e-cigarette use is up among us teens while cigarette use is down. We examined e-cigarette use in exercise 3. 137 and here we estimate cigarette use. In the sample of 1582 teens, 92 reported smoking a cigarette in the last 30 days. Give notation and define the parameter we are estimating. Give notation and value of the sample statistic. Find the standard error for this estimate. What is z* for a 99% confidence interval? what is the 99% confidence interval? what is the best estimate for the parameter we are estimating? what is the margin of error?

Answers

Answer of the following questions as per the given sample and confidence interval are:

The sample statistic value for the give samples is 0.058.The standard error for the given estimate is equal to 0.0068.The z score for 99% confidence interval is 2.576.The best estimate is the sample mean.Margin of error is equal to 0.0176.

As given in the question,

Number of teens smoking cigarette = 92

Sample size 'n' = 1582

Sample statistic = 92 / 1582

                          = 0.058

Standard error = √ p ( 1 - p ) / n

                          = √ 0.058 ( 1 - 0.058 ) / 1582

                          = √0.0000345

                          = 0.0058

                          = 0.006

z-score for 99% confidence interval = 2.576

margin of error = z ×√ p ( 1 - p )/n

                         = 2.576 √ 0.058 ( 1 - 0.058 ) / 1582

                         = 2.576 × 0.006

                         = 0.0155

                         = ±0.016

lower bound = 2.576 - 0.016

                     = 2.56

Upper bound = 2.576   + 0.016

                      = 2.592

Therefore, for the given samples and confidence interval answer of the following questions are:

The sample statistic value for the give samples is 0.058.The standard error for the given estimate is equal to 0.0068.The z score for 99% confidence interval is 2.576.The best estimate is the sample mean.Margin of error is equal to 0.0176.

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Which type of rigid transformation is the equivalent of two reflections across intersecting lines?

Answers

according to the question,

given data in the question,

the type of rigid transformation is the equivalent of two across intersecting lines

Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.

The intersection of the two reflection lines is the center of rotation.

An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.

The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation

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The type of transformation that is equivalent to 2 reflections across intersecting lines is rotation

Which transformation is equivalent to a double reflection over parallel lines?

A slide or a shift is a translation. By executing two composite reflections along parallel lines, translations may be produced. Translations maintain orientation and are isometric.

Which type of isometry is the equivalent of two reflections in parallel lines?

An isometry is made up of two other isometries. The translation is equal to the combination of two reflections over two parallel lines.

according to the question,

the type of rigid transformation is the equivalent of two across intersecting lines

Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.

The intersection of the two reflection lines is the center of rotation.

An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.

The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation

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suppose that x is uniformly distributed on the interval from 0 to 1. consider a random sample of size 4 from x. what is the joint probability density function of the sample?

Answers

The joint probability density function of the sample is 1

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

Every Xi has distribution as shown below:

f(xi) = 1, 0<xi<1

When all Xis are independent, then the following is true.

f(x1,x2,x3,x4) = f(x1) f(x2) f(x3) f(x4)

                     = 1,  for all xi between 0 and 1

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how many times can 64 go into 51

Answers

There are 2times 64 in 151. The answer you divide 151 by 64 which would get you 2.359375. The remainder is 23

Answer:

none

Step-by-step explanation:

64 is a bigger number so unless I am wrong it should not be able to go into 51.

an anova procedure is used for data that was obtained from five sample groups each comprised of six observations. the degrees of freedom for the critical value of f are

Answers

The degrees of freedom for the critical value F are (k-1,n-k).

Assume there are 4 sample groups, i.e.

k=4.

Also suppose that each of the four groups contains five observations.

So,

n=4*5

n=20

critical value F has degrees of freedom

(k-1,n-k)

( 4-1:20-4)

(3: 16).

Therefore , the degrees of freedom for the critical value of F is (3.16).

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Which values are solutions to K-3 >-2? Select two options.
4
Ok=-10
Ok=-7
Ok=-5
Ok=-1
Ok = 0
D

Answers

Answer:

The values that are solutions to K-3 >-2 are -7 and -5. To solve this inequality, we need to isolate the K term on one side of the inequality. We can do this by subtracting 3 from both sides of the inequality, like this:

K - 3 > -2

K - 3 - 3 > -2 - 3

K > -5

Therefore, the solutions to the inequality K-3 >-2 are all values of K that are greater than -5. This means that the values -7 and -5 are solutions to the inequality, but the other values listed are not.

Step-by-step explanation:

The formula F(C) =
9
5
C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius.

You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function’s

Answers

An equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit can be determine and it will be:  [tex]C = \frac{F - 32}{95}[/tex].

What is temperature?

The degree to which an object is hot or cold is measured by its temperature.

Formula to calculate temperature in degrees Fahrenheit:

F = 95C+32   --- (1)

The given equation (1) can be used to determine the equation to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit.

To determine equation for degrees Celsius following steps can be used:

Subtract 32 from both sides of the above equation,

F - 32 = 95C + 32 - 32

F - 32 = 95C

95C = F - 32

Divide both sides by 95

C = (F - 32)/ 95

Hence, by using some arithmetic operations, equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit can be determine and it will be:  [tex]C = \frac{F - 32}{95}[/tex].

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Answer:

inverse

Step-by-step explanation:

ed 2023

someone help me with this plss

Answers

The values of u and v of the given triangles using HL Congruency postulate are;

u = 8 and v = 7

How to prove congruent angles?

There are different congruency postulates for triangles namely;

SSS which means Side - Side - Side Congruency

SAS which is Side Angle Side Congruency Postulate. The angle is the included angle.

ASA which is Angle Side Angle Congruency Postulate. The side is the included side.

AAS Congruency Postulate. This is Angle Angle Side and the side is the non-included side. The angle is the included angle.

HL Congruency postulate which is Hypotenuse Leg theorem.

Now, we are given two triangles with 2 given sides each and the non - included angle. Thus, this is the Hypotenuse Leg congruency theorem.

Therefore for both triangles to be congruent;

5u = u + 32

4u = 32

u = 8

Similarly;

v + 7 = 2v

2v - v = 7

v = 7

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pls !!!!!!!!! do ti. 24 3/5 +4^3x(8 1/5 -2) ??????????

Answers

Answer: 2107/5

Explanation: Simplify the Equation

With Converting 24 3/5 to a improper fraction

Calculate the Power of 4^3

Then convert 8 1/5 to a improper fraction

Subtract 41/5 and 2 to get 31/5

Then Multiple the product 64 • 31/5 to get 1984/5

After add the fractions up
123/5 + 1984/5
=
2107/5

The solution is, the simplified value is 2107/5 = 421.4.

What is  simplification?

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

24 3/5 +4^3x(8 1/5 -2)

we have to

Simplify the Equation

With Converting 24 3/5 to a improper fraction

Calculate the Power of 4^3

Then convert 8 1/5 to a improper fraction

Subtract 41/5 and 2 to get 31/5

Then Multiple the product,

64 • 31/5 to get 1984/5

After add the fractions up

123/5 + 1984/5

=2107/5

=421.4

Hence, The solution is, the simplified value is 2107/5 = 421.4.

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can anyone help me I don't know how to do this

Answers

Step-by-step explanation:

its me ryan , 15 from michigan . Its just that i needed friends . If you want to be my good friend , please do comment below and we can be real good friends. ?

11. suppose the spot rate over a 3-year period is 2.658%, the forward rate for the first year is f0;1 54:5%, and the forward rate for the second year is f1;2 51:5%. what is the forward rate for the third year?

Answers

The forward rate for the third year 3.06%

The forward rate is the interest rate applied to future financial transactions. The forward rate is calculated from the spot rate, adjusted for maintenance costs to determine future interest rates that equalize the strategy to extend short-term investments and the total return on long-term investments.

This term can also refer to interest rates charged on future financial obligations, such as interest rates on loan payments.

(n1 – n2) reservation rate calculation number. A few years later n2 no. The number of years of Forward rate = [(1 + S1)n1 / (1 + S2)n2]1/(n1-n2) – 1.

According the question:

S3 = [(1 + S₁) × (1 + F(1,2))²]¹/³ ⁻¹

= [(1 + 2.658%) × (1 + 2.340%)²]¹/³ ⁻¹

= [1.02658 × 11.1556]¹/³ ⁻¹

= (12.18)¹/³ ⁻¹

= 3.06

Therefore, calculation of spot rate for three years will be, 3.06%

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the soccer filed has a width of 6.its length is double the size of the width what is the total area of the soccer field

Answers

Answer:72 lol

Step-by-step explanation: do the math 6 x 2 = 12

6 x 12 = 72

five people check identical suitcases before boarding an airplane. at the baggage claim, each person takes one of the five suitcases at random. what is the probability that every person ends up with the wrong suitcase?

Answers

5% probability is there that every person ends up with the wrong suitcase.

Given,

Number of people checked in  = 5

Number of suitcases = 5

We have to find the probability that when each person taken a suitcase randomly and it ends up with the wrong suitcase;

Here,

5 people can take 5 suitcases in 5 different ways.

So,

Probability = possible outcomes / original outcome

Probability = 5 x 5 / 5

Probability = 25/5 = 5

That is,

The probability that every person ends up with the wrong suitcase is 5%

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Draw a line of fit using (5,35) and (10,30)

Answers

The equation of a line in two-dimensional space is typically given in the form y is mx + b.

What is equation of a line ?The equation of line in two-dimensional space is typically given in the form y = mx + b, where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis. For example, the equation y = 3x + 2 describes a line with slope 3 and y-intercept (0, 2).Alternatively, the equation of a line can also be given in the slope-intercept form, which is the same as the standard form except that the slope and y-intercept are written explicitly. For example, the equation of the line y = 3x + 2 can also be written as slope = 3, y-intercept = 2.The equation of a line can also be given in the point-slope form, which is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. For example, the equation of a line with slope 2 passing through the point (3, 4) would be y - 4 = 2(x - 3).There is also the general form of the equation of a line, which is given by the equation Ax + By + C = 0, where A and B are the coefficients of the x and y terms and C is the constant term. For example, the equation 2x - 3y + 4 = 0 is in the general form.

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(2) a test for extrasensory powers (esp) involves asking a person to tell which of 5 shapes (a circle, star, triangle, diamond, or heart) appears on a hidden computer screen. on each trial, the computer is equally likely to select any of the 5 shapes. suppose researchers are testing a person who does not have esp and so is just guessing on each trial. what is the probability that the person guesses the first 4 first shapes incorrectly but gets the fifth correct?

Answers

The probability that the person guesses the first 4 first shapes incorrectly but gets the fifth correct is an [tex](\frac{4}{5})^{4}\frac{1}{5}[/tex].

what is probability?

The likelihood that something will happen is called the probability. the total number of conceivable outcomes. Because there is only one way to receive a head and there are a total of two possible outcomes, the probability of flipping a coin and getting heads is 1 in 2. (a head or tail).

given,

You can find out if someone has extrasensory perception (ESP) by asking them to identify which of the following shapes—a circle, star, triangle, diamond, or heart—appear on a hidden computer screen.

The probability is determined by dividing the number of favorable outcomes by the total number of possible outcomes.

p= P(win) = # of favorable outcomes  /   # of possible outcomes

The distribution is geometric since the variable indicates how many trials must pass before a success.

The distribution is geometric since the variable indicates how many trials must pass before a success.

P( X = k ) = [tex]q^{k-1}p[/tex]

=  [tex](1-p)^{k-1} p[/tex]

Review at k=5

P(X=5) = [tex](1-\frac{1}{5})^{5-1}\frac{1}{5}[/tex]

=[tex](\frac{4}{5})^{4}\frac{1}{5}[/tex]

probability that the person guesses the first 4 first shapes incorrectly but gets the fifth correct is an [tex](\frac{4}{5})^{4}\frac{1}{5}[/tex]

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approximately 40 % of the population have type o blood . if 4 people are randomly selected to be donors . find the probability that at least one is type o.

Answers

The probability that at least one is type O is 0.8704.

What is a binomial distribution probability?

A value's likelihood of taking one of two independent values is summarised by the statistical distribution known as the binomial distribution.

Given,  40 % of the population has type O blood and 4 people are randomly selected to be donors

Then, binomial distribution can be given by

X ~ = Binomial(n = 4, p = 0.4)

P(at least one type O)

P[X ≥ 1]

= 1- P[X < 1]

= 1- P[X = 0]

= [tex]1 -C(4,0) * (0.4)^{0} * (1 - 0.4)^{4-0}[/tex]

=1-0.1296

=0.8704

Hence, the probability that at least one is type O is 0.8704.

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In triangle def, if m∠d = (2x)°, m∠e = (2x − 4)°, and m∠f = (x 9)°, what is the value of x? 35 37 44 71

Answers

Option A is correct, the required simplified value of the x is given as 35.

In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°.

for the triangle sum of the interior angles is equal to 180°.

∠D + ∠E + ∠F = 180

2x + 2x - 4 + x + 9 = 180

5x + 5 = 180

5x = 175

x = 35

Thus, the required simplified value of the x is given as 35.

The sum of the measures of the interior angles of a triangle in Euclidean space is continually 180 stages. This reality is equal to Euclid's parallel postulate. This permits the determination of the degree of the 1/3 perspective of any triangle, given the measure of angles. An exterior perspective of a triangle is an attitude that is a linear pair (and subsequently supplementary) to an indoor angle.  

The degree of an exterior perspective of a triangle is the same as the sum of the measures of the 2 indoor angles that aren't adjoining to it; this is the outside perspective theorem. The sum of the measures of the 3 exterior angles (one for every vertex) of any triangle is 360 degrees.

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g an inverted conical tank has a height of 18 feet and a diameter of 6 feet. water is flowing into the cone at a rate of 24 cubic feet per second. at what rate is the height of the water in the tank increasing when there is 10 feet of water in the tank.

Answers

The rate at which the height of the tank is increasing when there is 10 feet of water in the tank is 2.75 ft/sec .

In the question ,

it is given that ,

the height of the conical tank is =18 feet ,

the radius of the tank is = 6/2 = 3 feet .

the rate at which the water is flowing is = 24 cubic feet per second .

that is dv/dt = 24 .

the ratio of height and radius is

h/r = 18/3

h/r = 6

r = h/6

we know that the Volume of Conical tank is = (πr²h)/3

On substituting r = h/6 and differentiating with respect to time "t" ,

we get ,

dv/dt = (π/108)×3×h²×dh/dt

substituting the value of h = 10 and dv/dt = 24 ,

we get ,

24 =  (π/108)×3×10²×dh/dt

dh/dt = (24 * 36)/100π

= 2.7501

≈ 2.75 ft/sec .

Therefore , the rate of change of the height of the tank is 2.75 ft/sec .

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