Kiran was running around the track. The graph shows the time, t, he took to run various distances, d. The table shows his time in seconds after every three meters.

How long did it take Kiran to run 6 meters?

a. The probability that a person has the virus given that they have tested positive is approximately 4.3%.

b. The probability that a person does not have the virus given that they test negative is approximately 99.0%.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

a) We need to find the probability that a person has the virus given that they have tested positive, i.e., P(A|B). We can use Bayes' theorem to calculate this probability:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus, and P(B) is the probability of testing positive.

From the problem statement, we know that:

To calculate P(B), we can use the law of total probability:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

= 0.9 * 0.005 + 0.1 * (1 - 0.005)

= 0.1045

Therefore, we can compute P(A|B) as:

P(A|B) = P(B|A) * P(A) / P(B)

= 0.9 * 0.005 / 0.1045

≈ 4.3%

So, the probability that a person has the virus given that they have tested positive is approximately 4.3%.

b) We need to find the probability that a person does not have the virus given that they test negative, i.e., P(A'|B'). We can again use Bayes' theorem:

P(A'|B') = P(B'|A') * P(A') / P(B')

where P(B'|A') is the probability of testing negative given that the person does not have the virus, P(A') is the prior probability of a person not having the virus, and P(B') is the probability of testing negative.

From the problem statement, we know that:

To calculate P(B'), we can again use the law of total probability:

P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')

= 0.1 * 0.005 + 0.9 * 0.995

≈ 0.895

Therefore, we can compute P(A'|B') as:

P(A'|B') = P(B'|A') * P(A') / P(B')

= 0.9 * 0.995 / 0.895

≈ 99.0%

So, the probability that a person does not have the virus given that they test negative is approximately 99.0%.

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The surface area of the rectangular prism is 502 mm²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The surface area of the prism = 2(8 mm * 13 mm) + 2(8 mm * 7 mm) + 2(7 mm * 13 mm) = 502 mm²

The surface area is 502 mm²

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Answer:

22 1/2

Step-by-step explanation:

try it

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

15 miles

Step-by-step explanation:

Speed of John biking = 10 miles per hour

Time taken by John to travel the route = 1.5 hours

We know that

distance = speed * time

now that we know time and speed for John

we can distance by using the above formula

distance = 10  miles per hour* 1.5  hour = 15 Miles

Thus, the route was 15 miles long.

Answer:

15 miles

Step-by-step explanation:

The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

The image basically means ALL numbers greater than -10.

When looking at number lines like these: you should pay attention to 2 things.

1. which way the arrow is pointing

2. whether the circle on the point (in this case, -10) is open or not.

1. which way the arrow is pointing

it can be right or left. in this case, it is pointing to the right. you can tell because the part on the right is shaded/bolded with an arrow.

what does it mean?

lets look at the one shown. the given point is -10. the arrow is pointing right. this means the graph wants numbers that are above -10. but another question remains-- is the -10 included? to know if it is included, look at 2.

2. whether the circle on the point (in this case, -10) is open or not.

how do you know if it is open or not?

to tell if a point is open, you need to check if the point is colored or not. look at the image attached (i made it! :D ) to know which one is which. in this question, it is an open circle (not colored).  

what does it mean?

a closed circle means including the number (the one the point is at) and an open circle does not include the number. in answers the question in 1. (is the -10 included?). in this question, it shows an open circle, so it does not include the -10.

therefore, the number line shows numbers that are greater than -10.

important: numbers greater than -10, not greater and equal to (-10 doesnt count !!! )

because the arrow is pointing to the right and the circle is open, we know that the number line means all numbers greater than -10

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

done !! this took me a lot of time so i hope it helps ^_^ have a great day you are appreciated, stay strong we love you.

-- bella-chan ~~

Answer: S wanted points I

Step-by-step explanation:

The number of grams of cocoa is 50.9 grams

This is the mass of an object

Since we have that a chocolate bar contains 53% cocoa and the weight of the chocolate bar is 96 grams.

Let

So, we have that

x = pW

Given that

Substituting the values of the variables into the equation, we have that

x = pW

x = 0.53 × 96 grams

x = 50.88

x ≅ 50.9 grams

So, the number of grams of cocoa is 50.9 grams

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Answer:

Step-by-step explanation:

Answer:

7 units is the distance

Answer:

Option B

Step-by-step explanation:

704 cubic centimeters

The student would spend $18 on books and lab manuals.

An expenditure refers to the spending of money on something or the money that is spent on something.

Total Expenditure = Lab fee + Materials fee + Tuition + Books and lab manuals + Tools

Total Expenditure = 8% + 10% + 38% + 18% + 26%

Total Expenditure = 100%

We will calculate the amount spent on books and lab manuals. The amount spent on books and lab manuals is:

= (Books and lab manuals percentage / Total Expenditure percentage) * $100

= (18% / 100%) * $100

= 0.18 * $100

= $18.

Missing details:

On pie chart  for School Expenditures; Lab fee = 8% Materials fee =10% Tuition = 38% Books and lab manuals = 18% Tools = 26%

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

angle DOC

Step-by-step explanation:

An complementary angle is when you add 2 angles to equal 90 degrees, or a right angle

Answer:

Angle DOC

Complementary angle to Angle EOD means which angle will sum up with it to measure 90°

From the figure we can say,

Angle DOC +Angle EOD = 90°

Answer:

ayannah is correct

Step-by-step explanation:

Ayannah is correct becauseyou can divide both 19 and 133 by 19 which gives you 1/7. 1/7 isn't divisible by anything else so that's the simplest form.

Answer:

Ayanna is correct because 19/133= 1/7

Step-by-step explanation:

Simplest form means reducing fractions to its lowest term.

Answer:

19 boys

Step-by-step explanation:

38 kids on the bus

1/2 are girls, that means 1/2 are boys

1/2 * 38 = 19

There are 19 girls and 19 boys

Answer:

gradient=4      y intersept: B(0;-2)   Point (1;12) doesn't lie on y=3x+8

(-2,10) lies on the line  y=14+2x

Step-by-step explanation:

2y=8x+1 => divide both sides by 2=> y=4x+1/2  => gradient = 4

4y+8x= -8 => 4y= -8-8x => y=-2-2x   . -2 - I indicated this number with the bold ( this ratio is the y coordinate of y- intersept. x coordinate=0

So the y-intersept is (0;-2)

We have a point (1;12)   1 is x coordinate of the point and 12 is y coordinate.

Put 1 and 12 instead x and y in the given formula. If we get the correct expression => the point lies on the line, if the expression is false=> doesn't lie on the line.

Now lets check !

12=3*1+8

12=  11  - false => the point  (1;12) doesn't lie on y=3x+8

Similarly proceed:  10=14+2*(2)

10=14-4

10=10 - right ! Point (-2;10)  lies on y=14+2x

Each dose of amoxicillin, when dispensed at a concentration of 50 mg/mL, would be 1.5 mL.

To calculate the volume of each dose of amoxicillin in milliliters (mL), we need to know the concentration of the medication and the prescribed dosage.

Given:

Amoxicillin concentration: 50 mg/mL

Prescribed dosage: 75 mg t.i.d. (three times a day) for 10 days

To determine the volume of each dose, we can use the formula:

Volume (mL) = Dosage (mg) / Concentration (mg/mL)

First, let's calculate the dosage for one dose:

Dosage per dose = 75 mg

Now we can calculate the volume of each dose using the concentration of amoxicillin:

Volume (mL) = 75 mg / 50 mg/mL

Volume (mL) = 1.5 mL

Amoxicillin would therefore be administered in 1.5 mL doses at a dosage of 50 mg/mL.

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Answer:

2-cup carton of frozen yogurt for $0.80

Step-by-step explanation:

We know

2-cup carton of frozen yogurt for $0.80

1 cup = 0.25 quart

2 cups = 0.50 quart

0.80 / 0.50 = $1.60 per quart

2-quart carton of frozen yogurt of $5.52

5.52 / 2 = $2.76 per quart

So, 2-cup carton of frozen yogurt for $0.80 is better buy.

Answer:

Step-by-step explanation:

To determine which option is a better buy, we need to compare the price per unit (in this case, the price per cup) of the two options.

For the 2-cup carton of frozen yogurt that costs $0.80, the price per cup can be calculated as:

$0.80 / 2 cups = $0.40 per cup

For the 2-quart carton of frozen yogurt that costs $5.52, we first need to convert quarts to cups. There are 4 cups in a quart, so a 2-quart carton contains:

2 quarts x 4 cups per quart = 8 cups

The price per cup can then be calculated as:

$5.52 / 8 cups = $0.69 per cup

Therefore, the 2-cup carton of frozen yogurt for $0.80 is a better buy, as the price per cup is lower at $0.40, compared to $0.69 per cup for the 2-quart carton.

\(\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \underline{\ln(2)+\ln(8)}-\ln(4)\implies \underline{\ln(2\cdot 8)}-\ln(4)\implies \ln(16)-\ln(4) \\\\\\ \ln\left(\cfrac{16}{4} \right)\implies \ln(4)\)

Given:

A circle with a center at C.

Required:

We need to find the names of the given parts.

Explanation:

Recall that radius is a line segment extending from the center of a circle to the circumference.

Line segment AC extends from the center C of a circle to the circumference.

Recall that the arc of a circle is defined as the part of the circumference of a circle.

AE is the part of the circumference of a circle.

Recall that a straight line segment joins and is included between two points on a circle.

D and E are two points on a circle.

A straight line DE line segment joins and is included between two points D and E on a circle.

Recall that meeting a curve or surface in a single point if a sufficiently small interval is considered a straight line tangent to a curve.

AB is tangent.

Recall that an inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.

Recall that a central angle is an angle formed by two radii with the vertex at the center of the circle.

Recall that an angle formed by an intersecting tangent and chord has its vertex "on" the circle.

Final answer:

To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.

We are given the following measures:

\(\sf\:m\angle AB = 56 \\\)

\(\sf\:m\angle BC = 59 \\\)

\(\sf\:m\angle CD = 63 \\\)

\(\sf\:m\angle DE = 63 \\\)

\(\sf\:m\angle EF = 31 \\\)

To find the measure of the geometry-big circle, we add up these measures:

\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)

Substituting the given values:

\(\sf\:56 + 59 + 63 + 63 + 31 \\\)

Simplifying the expression:

\(\sf\:272 \\\)

Therefore, the measure of the geometry-big circle is 272.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

The answer to your question is A. Yes, because the total will be $3.27

0.35(2)+0.99(2)+0.59≤4.

Then you multiply: .35(2)=.70. .99(2)=1.98.

Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 :)

Step-by-step explanation:

I hope this helps and have a good day!

Answer:

Step-by-step explanation:

1)

total area = rectangle area + 2 triangle area

                =  length * width = 2 ( \(\frac{1}{2}\) * base * height )

                =  7.5 * 6 + 2 (  \(\frac{1}{2}\) * 3 * 4 )

                = 57 ft²

2)

separate it into two rectangles:

length * width + length * width

  6  *   2  +  9 * 4

      48 cm²

3)

parallelogram area =  base * height

                                = 20 * 25

                                 = 500 in²

Scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 9, 3 comma 6, 4 comma 8, 5 comma 5, 6 comma 7, 7 comma 5, 8 comma 7, 9 comma 4, and 10 comma 2, and a line drawn through about 3 comma 6 and 5 comma 6.

We must examine the scatter plot and look for a pattern or trend in the data to determine which of the graphs shows a line that fits the data.

The scatter plot with the given data is shown below:

code:

       |

    10 |         ●

       |

     9 |        ●

       |

     8 |      ●

       |

     7 |    ●     ●

       |

     6 |  ●        ●

       |

     5 |        ●     ●

       |

     4 |           ●

       |

--------|----------------> x

       |

       |

       |

       |

       |

       |

The scatter plot shows that the data has a general upward trend, but it is not a perfectly straight line. We can, however, draw a line that roughly fits the data.

Looking at the options, the first option, with a line drawn between 3,6 and 5,6, appears to be the best fit for the data. The line runs through the centre of the points, capturing the overall trend of the data.

As a result, the answer is:

Scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 9, 3 comma 6, 4 comma 8, 5 comma 5, 6 comma 7, 7 comma 5, 8 comma 7, 9 comma 4, and 10 comma 2, and a line drawn through about 3 comma 6 and 5 comma 6.

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Answer: $5400

Step-by-step explanation:

x =  amount raised so far

13500 - x = amt. still needed

x/3 = (13500 - x)/2

2x = 3(13500 - x)

2x = 40500 - 3x

5x = 40500

x = 40500/5 = 8100 (amt. raised so far)

13500 - 8100 = 5400 (amt. still needed)

Answer:

A

Step-by-step explanation:

That is because the open circle means greater/less than and the closed circle means greater/less than or equal to.

Answer: No

To check if (-5,6) is a solution to the equation y=-7, we need to substitute -5 for x and 6 for y in the equation.

If the equation is true, then the ordered pair is a solution to the equation.

If we put (-5,6) into y=-7, we get 6=-7, which is not true.

So, (-5,6) is not a solution to the equation y=-7.