Martha Martha and Steven are in the same math class. The box plot shows the number of minutes that Martha and Steven spent studying for their final exam each day for a week. Steven 0 5 10 Study Time 15 20 Number of Hours 25 30 35 Which statement is best supported by the information in the box plots? 2 of 9 A 07:34​

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 32}}{\left( \cfrac{15}{100} \right)32}\implies 4.8\hspace{5em}\underset{ \textit{meal \& tip} }{\stackrel{ 32~~ + ~~4.8 }{\text{\LARGE 36.8}}}[/tex]

The conditional probability that a randomly selected contestant played an acoustic guitar is 2/5.

What is conditional probability?

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.

Here, we have

Given: Riley was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Riley recorded which type of guitar each contestant played.

Let A be the event of a contestant playing acoustic guitar.

Let B be the event of a contestant wearing leather pants

The conditional probability of a contestant playing acoustic guitar given he wears leather pants, P(A|B) is-

P(A|B) = P(A∩B)|P(B)

Where,

P(A∩B) =  is the probability of simultaneous occurrence of events A and B.

P(A∩B) = 6

P(B) = no. of contestants wearing leather pants

P(B) = 15

P(A|B) = 6/15 = 2/5

Hence, the conditional probability that a randomly selected contestant played an acoustic guitar is 2/5.

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Answer:

Step-by-step explanation:

35 is the answer because where it says frequency you have to add it all together.

Step-by-step explanation:

blue box is x^2

orange box is 5x

yellow box is 3x

green box is 15

The straight sections each have a length of 100. So, the total distance around the inner lane of the track is 200 + 40pi units

The area of one of the blue half circles can be found using the formula:

Area = pi x radius squared.

The diameter of the circle is given as 40, so the radius is half of that, which is 20.

Therefore, the area of one blue half circle is:
Area = pi x [tex]\frac{20^{2} }{2}[/tex]

Area = 200pi square units
To cover the entire circle, we need both blue half circles. So the total area needed to be covered with grass is:
Total area = 2 x 200pi = 400pi square units
The distance around one of the semicircles at either end of the soccer field can be found using the formula: Circumference = pi x diameter.

Since the diameter is given as 40.

The circumference is:
Circumference = pi x [tex]\frac{40}{2}[/tex]

Circumference = 20pi units

To find the distance around the inner lane of the track, we need to add the lengths of the straight distances (which are 100 each) to the circumference of the two blue half circles.

The circumference of one blue half circle is 20pi, so the total distance around the inner lane of the track is:
Distance = 2 x 100 + 2 x 20pi

Distance = 200 + 40pi units

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The value of x in right angle whose hypotenuse is given 74 m  one angle is 90° and other angle given is 30° to the nearest tenth is approximately 37 meters.

The branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles is known as Trigonometry. It involves studying the properties of trigonometric functions, which are mathematical functions that relate the angles of a triangle to the ratios of its sides.

In this triangle, the height is opposite the 30° angle and the hypotenuse is the longest side of the triangle. We can use the trigonometric function sine to relate the height and the hypotenuse:

sin(30°) = x / 74

To solve for x, we can multiply both sides by 74 and simplify:

x = 74 sin(30°)

x ≈ 37 (to the nearest tenth)

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Step-by-step explanation:

The first two are not equations, there is no ' = ' sign. Tey are expressions.

C) -3 + (5-4) = ) (-3+5) -4

     -3 +1   = 2 -4

         -2    = -2       True

D)  -5 -4 = -5 +( -4)

        -9    =   -9      True

I will assume the + sign is supposed to =   ( same key)

A)   -3 (5-4)  = -3(5) - 4

       -3  = -19     FALSE

B)  -5 + (-4) =  -4 + (-5)

        -9       =   -9    True

Answer:

Step-by-step explanation:

To add numbers in base 5, we need to follow the same process as adding numbers in base 10. We will start by aligning the digits based on their place value and then add them up, carrying any remainders as necessary.

4023 base 5

3102 base 5

11325 base 5

Therefore, the sum of 4023 base 5 and 3102 in base 5 is 11325 base 5.

Answer:

approximately 3.84 degrees.

Step-by-step explanation:

The angle of depression is the angle between a horizontal line and the line of sight when looking downwards. We can use trigonometry to calculate this angle.

Let's draw a diagram to represent the situation:

A

/|

/ |

18.5/ | 280

/ |

/θ |

/_____|

B

Here, point A represents the top of the sledding run, point B represents the bottom of the run, and θ is the angle of depression we want to find.

We can see that AB is the hypotenuse of a right triangle, and the vertical drop of 18.5 yards is the opposite side. We can use the tangent function to relate the opposite side to the adjacent side, which is the horizontal distance of the run:

tan θ = opposite/adjacent

tan θ = 18.5/280

Now we can use a calculator to find the value of the tangent:

θ = tan^(-1) (18.5/280)

θ ≈ 3.84 degrees

Therefore, the angle of depression of the run is approximately 3.84 degrees.

[tex]A-x=\cfrac{xr}{t}\implies At-xt=xr\implies At=xt+xr \\\\\\ At=x(t+r)\implies \cfrac{At}{t+r}=x[/tex]

make x the subject means write all terms in terms of x

look at attachment.

The probability that the student was NOT a female that got a “A” is given as follows:

p = 10/19.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability that the student was NOT a female that got a “A” is obtained as follows:

p = 20/38

p = 10/19.

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Using the prοbability cοncept, it is fοund that there is a 0.0887 = 8.87% prοbability all three marbles are the same cοlοr.

A prοbability is the number οf desired οutcοmes divided by the number οf tοtal οutcοmes.

The οrder in which the marbles are chοsen is nοt impοrtant, and they are alsο chοsen withοut replacement, which means that the cοmbinatiοn fοrmula is used tο find the number οf οutcοmes.

Tο find the prοbability that all three marbles selected are the same cοlοr, we need tο cοnsider three cases: selecting three red marbles, selecting three white marbles, οr selecting three blue marbles.

Let's first calculate the tοtal number οf ways tο select three marbles frοm the urn. This can be dοne using the cοmbinatiοn fοrmula:

C(19, 3) = 19! / (3! * 16!) = 969

Sο there are 969 pοssible ways tο select three marbles frοm the urn.

Nοw let's calculate the number οf ways tο select three marbles οf the same cοlοr:

Sο the tοtal number οf ways tο select three marbles οf the same cοlοr is:

20 + 10 + 56 = 86

Therefοre, the prοbability οf selecting three marbles οf the same cοlοr is:

86 / 969 = 0.0887 (rοunded tο fοur decimal places)

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Answer: 28/5

Step-by-step explanation:

each toy had a mass of 4/5 kilograms .there are 7 toys.so the total mass is

7 times 4/5=28/5 kilograms

hope it helps

Answer:

Bathtub currently has 45 gallons of water.

It drains 7 gallons every three minutes.

How much gallons will it have after 5 minutes.

First, find how much it drains in one minute and multiply it by 5.

7 gallons per 3 minutes.

So 7/3 = 2.3333 or roughly 2 gallons per minute.

How many gallons will it have after 5 minutes of draining.

2*5 = 10 litres will have been drained.

So, 45 - 10 = 35 gallons of water would remain after 5 minutes of draining.

Answer:

the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent.  option (C) √(2x² + x) is equivalent to the original expression √(2x) * √(x+3) when x > 0.

Step-by-step explanation:

To simplify the expression √(2x) * √(x+3), we can use the property of radicals that says:

√(a) * √(b) = √(a * b)

So, we have:

√(2x) * √(x+3) = √(2x * (x+3))

Multiplying out the terms inside the radical, we get:

√(2x * (x+3)) = √(2x² + 6x)

Therefore, the expression √(2x) * √(x+3) is equivalent to the radical expression √(2x² + 6x) when x > 0.

So, the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent:

√(2x² + 6x) = √(2x² + x + 5x) = √(x * (2x + 5)) = √x * √(2x + 5)

Cameron would pay $11 for 5.5 pounds of cherries at the same rate.

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

We can start by finding the cost of cherries per pound:

2 3/5 pounds = (2 × 5 + 3) / 5 = 13/5 pounds

Cost of 13/5 pounds of cherries = $5.25

Cost of 1 pound of cherries = $5.25 ÷ (13/5) = $2

Now we can find the cost of 5.5 pounds of cherries:

Cost of 5.5 pounds of cherries = $2 × 5.5 = $11

Therefore, Cameron would pay $11 for 5.5 pounds of cherries at the same rate.

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Step-by-step explanation:

For RIGHT triangles such as this one:

sin (60) = opposite LEG/ hypotenuse =  sqrt(3) / 2  / CB       solve for CB

tan (60°) =  opposite LEG / adjacent LEG = sqrt(3)/2  / AC    solve for AC

Therefore , the solution of the given problem of percentage comes out to be  the account's yearly percentage yield (APY) is 2.24%.

The abbreviation "a%" is used to indicate a value or number in statistics that is expressed as a percentage of 100. Versions with "pct," "pct," or "pc" as the initials are also rare. However, the most popular method to do this is to use the percentage symbol ("%"). Additionally, both hints nor a constant ratio of every element to the overall amount exist. Since numbers commonly add up to 100, they are essentially integers.

Here,

The following equation can be used to determine the worth of an account after t years, compounded quarterly:

=>  A = P * (1 + r/4)⁴ⁿ

When we enter the numbers, we obtain:

=>  A = 240 * (1 + 0.022/4⁴ⁿ

By condensing the solution, we obtain:

=>  A = 240 * 1.0055⁴ⁿ

Consequently, the following is the function displaying the account's worth after t years:

=>  f(t) = 240 * 1.0055⁴ⁿ

We can use the following formula to determine the yearly percentage yield (APY):

=> APY = (1 + r/n)ⁿ - 1

where r equals the 2.2% yearly interest rate.

n is the quantity of times interest is added annually. (4, since interest is compounded quarterly)

When we enter the numbers, we obtain:

=> APY = (1 + 0.022/4)⁴ - 1

APY = 0.02237 or 2.24% (rounded to the nearest hundredth of a percent)

As a result, the account's yearly percentage yield (APY) is 2.24%.

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Rounding to the nearest whole number, the number of bacteria still present in the culture after 7 hours is approximately 3481.

How many whole numbers are there?

All natural numbers are added together to form whole numbers. both a fraction and neither a decimal. Integer 0 through 11: 2, 3, 5, 6, 7, 8, 9, & 10. 0 is a counting number or the opposite.

To determine the number of bacteria inside the culture at t hours, use the formula Pt = Po 2(t/d), in which Po is simply the initial population and d is the doubling time.

The values of Po are 870, d, and t are respectively 3 and 7. When we use the formula with these numbers, we get:

[tex]Pt = 870 * 2^{(7/3)}[/tex]

Pt ≈ 3480.5

Hence, the number of bacteria still present in the culture after 7 hours is approximately 3481.

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Answer:

c) The Diameter is Half of the radius

Step-by-step explanation:

A) A diameter ALWAYS passes through the center of the circle, so EVERY diameter WILL pass through the Center of the circle, making this statement valid.

b) A center of a circle will ALWAYS lie in the interior of the circle. it is an Axiom

c) False, the RADIUS is half of the Diameter of a circle.

d) The Longest Chord IS the Diameter, which passes through the circle, so this statement is valid.

So the false option is (C)

Answer:

The answer is -5. To do this you first draw your number line and label it from +7 to -10. You then count from from seven till the 11th number which in this case it's -5

The fractions equivalent to 2/5 are 4/10, 6/15, 8/20. The correct option is B.

When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.

Hence, the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

The fractions equivalent to 2/5 are 4/10, 6/15, 8/20,.

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Which of the lists below includes all of the above expressions that are equivalent to 2/5?

I, 2/6

II,  4/10

III, 6/15

IV. 10/20

V. 4 / 12

VI 8/20

A. I, III, V, VI

B. III, VI

C. II, III, VI

D. II, III, IV, VI

Answer:

To simplify the expression p/ab+2q/ac, we need to find a common denominator for the two fractions in the denominator. The common denominator is abc.

Thus,

p/ab + 2q/ac

= p*c/abc + 2q*b/abc (multiplying the first fraction by c/c and the second fraction by b/b)

= pc/abc + 2qb/abc

= (pc + 2qb) / abc

Therefore, the simplified expression is (pc + 2qb) / abc.

The probability that the subject tested negative or did not use marijuana is approximately 0.57.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is a way of quantifying the uncertainty or randomness associated with an event or an experiment.

In the given question,

To solve this problem, we can construct a table that summarizes the given information:

We are given the following information:

There are 143 subjects with positive test results, of which 20 are false positives.

There are 153 subjects with negative test results, of which 4 are false negatives.

Using this information, we can fill in the table as follows:

The numbers in parentheses are the counts of subjects in each category.

To find the probability that the subject tested negative or did not use marijuana, we need to add the probabilities of the two mutually exclusive events:

Tested negative and did not use marijuana (True Negative): P(True Negative) = 149/296

Tested positive but did not use marijuana (False Positive): P(False Positive) = 20/296

Therefore, the probability that the subject tested negative or did not use marijuana is:

P(Tested Negative or Did not use marijuana) = P(True Negative) + P(False Positive)

= 149/296 + 20/296

= 169/296

≈ 0.57

So, the probability that the subject tested negative or did not use marijuana is approximately 0.57.

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The period, phase shift, and cosine function of the graph are;

The period = π

The phase shift = π/8

The cosine function is; y = 2·cos(2·(x - π/8)) - 1

The period of the graph is the distance between two consecutive peaks of the wave.

The maximum value of the graph is 1 at x = π/8 and x = 9·π/8, and the minimum value of the function is; -3 at 5·π/8.

The vertical displacement can be obtained from half the sum of the max and min point as follows;

Vertical displacement = (1 + (-3))/2 = -1

The vertical displacement = -1

The amplitude = Half the distance between the max and min point of the graph

Amplitude, a = (1 - (-3))/2 = 2

The amplitude, a = 2

The period of the graph = 9·π/8 - π/8 = 8·π/8 = π

The period = 2·π/b

Therefore; 2·π/b = π

b = 2·π/π = 2

b = 2

The phase shift = π/8

The cosine function is therefore;

y = 2·cos(2·(x - π/8) - 1

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Therefore, the perimeter P of the nonagon is 19.5 units.

Perimeter refers to the total length of the boundary or the outer edge of a closed figure or shape. It is the sum of the lengths of all the sides or edges that enclose the shape.

Here,

Since O is the center of the regular nonagon, all the sides of the nonagon are equal in length. Let the length of one side of the nonagon be s. Then, the perimeter P of the nonagon is given by:

P = 9s

To find s, we can use the fact that the sum of the interior angles of a nonagon is given by (9-2)×180° = 1260°. Since the nonagon is regular, each angle is equal to 1260°/9 = 140°.

Consider the triangle OAB, where A and B are two adjacent vertices of the nonagon. Since O is the center of the nonagon, angle AOB is equal to 360°/9 = 40°. Also, angle OAB and angle OBA are equal to half of (180° - 140°) = 20°.

Therefore, angle AOB is isosceles, and we can use the cosine rule to find s:

cos(20°) = (s/2) / s

cos(20°) = 1/2

s = 2 / cos(20°)

Using a calculator, we get s ≈ 2.165. Therefore, the perimeter P of the nonagon is:

P = 9s

≈ 19.5 (rounded to the nearest tenth)

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The Space Shuttle Discovery traveled 22.3 million miles more distance than the Space Shuttle Atlantis.

What is distance ?

To find how many more miles the Space Shuttle Discovery traveled than the Space Shuttle Atlantis, we can subtract the distance traveled by Atlantis from the distance traveled by Discovery:

148.2 million miles - 125.9 million miles = 22.3 million miles

Therefore, the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.

What is Space Shuttle ?

The Space Shuttle was a reusable spacecraft designed and operated by NASA (the National Aeronautics and Space Administration) to carry astronauts and cargo into space. It was in service from 1981 until 2011, when the final mission was completed.

The Space Shuttle consisted of several components, including the orbiter, which was the main spacecraft, and the two solid rocket boosters and external fuel tank that provided the initial propulsion during liftoff. The orbiter was designed to carry up to seven crew members and could be used to deploy satellites, conduct scientific experiments, and perform other tasks in space.

The Space Shuttle was unique in that it could land like an airplane, allowing it to be reused multiple times. After completing a mission, the orbiter would re-enter Earth's atmosphere and glide to a landing on a runway.

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Complete question is: The space shuttle discovery traveled 148.2 million miles during its mission. The space shuttle Atlantis traveled 125.9 million miles. the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.

Town B will have a larger population than Town A in the year 2019.

To solve this problem, we can use a year-by-year approach to see when the population of town B surpasses that of town A.

Let's start with year 0 (2015):

Town A population: 9,000

Town B population: 8,000

In year 1 (2016):

Town A population: 9,500 (9,000 + 500)

Town B population: 8,720 (8,000 x 1.09)

In year 2 (2017):

Town A population: 10,000 (9,500 + 500)

Town B population: 9,504.8 (8,720 x 1.09)

In year 3 (2018):

Town A population: 10,500 (10,000 + 500)

Town B population: 10,360.232 (9,508.8 x 1.09)

In year 4 (2019):

Town A population: 11,000 (10,500 + 500)

Town B population: 11,292.653 (10,394.912 x 1.09)

From this calculation, we can see that in the year 2019, the population of Town B will be larger than that of Town A. Therefore, the answer is:

Town B will have a larger population than Town A in the year 2019.

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Answer:

Step-by-step explanation:

P(international | on time)< P(delayed | domestic) <P(on time and domestic)

correct in plato

Answer:

Step-by-step explanation:

50+40+15+40+85

=230