In a scavenger hunt, Team A collected 4 items more than twice the number of items collected by Team B. Let b represent the number of items collected by Team B. What is an expression that can be used to find the number of items collected by Team A

Answer:

Step-by-step explanation:

is A

Answer:

[tex]-22.8[/tex]

Step-by-step explanation:

[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]

Answer:

7 cents

Step-by-step explanation:

0.072222 rounded to the nearest cent is 0.07

Answer:

[tex]\frac{5\sqrt{2} }{2}[/tex]

Step-by-step explanation:

The square cut in half makes the right side a right triangle.

The equation for these types of questions is short side * square root of 2 = long side

So that means that x * [tex]\sqrt{2}[/tex] = 10

So then divide by square root of 2 on both sides to cancel it out

x = 10/[tex]\sqrt{2}[/tex]

Then to simplify it multiply the top and bottom by square root of 2, since you can't have an irrational number in the denominator

That makes it [tex]\frac{10\sqrt{2} }{2}[/tex]

Divide 10/2 to make [tex]\frac{5\sqrt{2} }{2}[/tex]

The temperature change for Monday is -30 degrees Fahrenheit,

The completed table is: Monday: -30, Tuesday: +7, Wednesday: +12, Thursday: +2, Friday: -6, to make the total change from Monday to Saturday equal to -15 degrees Fahrenheit.

To complete the table, we need to find the temperature change for Monday that makes the total change from Monday to Saturday equal to -15 degrees Fahrenheit.

Let x be the temperature change for Monday. Then, we can set up the equation:

x + 7 + 12 + 2 - 6 = -15

Simplifying and solving for x, we get:

x = -30

Therefore,

The temperature change for Monday is -30 degrees Fahrenheit, and the completed table is:

Monday: -30

Tuesday: +7

Wednesday: +12

Thursday: +2

Friday: -6

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The lower bound for the number of minutes it takes for all the people to leave is 67 minutes.

What is lower bound?

Lower bound refers to the smallest possible value in a range or interval of values. In the context of measurements or estimates, it represents the minimum value that a quantity or measurement is expected to be, based on the precision or accuracy of the measuring instrument or method.

To calculate the lower bound for the number of minutes it takes for all the people to leave, we need to use the following formula:

Lower bound = (total number of people - 0.5) / departure rate (in people per minute)

Using the given information, we have:

Total number of people = 29800 (correct to the nearest 100)

Departure rate = 400 (correct to the nearest 50)

To ensure we have a conservative estimate, we will round down the total number of people to 29750 and round up the departure rate to 450.

Therefore, the lower bound for the number of minutes it takes for all the people to leave is:

Lower bound = (29750 - 0.5) / 450

= 66.1 (rounded up to the nearest minute)

So the lower bound for the number of minutes it takes for all the people to leave is 67 minutes.

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Here both triangles are congruent by SAS.

What is congruent by SAS?

Side-Angle-Side congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

In the given triangles it's given that,

in both triangles the two sides are similar along with an angle.

So Here both triangles are congruent by SAS.

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It would take Tracy and Dave approximately 4.8 hours to complete the task together. So, the correct option is C.

To solve this problem, we can use the formula:

time = work / rate

where work is the amount of work to be done (in this case, collecting signal strength data from each house), and rate is the rate at which the work is being done.

Let's start by finding Tracy's and Dave's individual rates:

Tracy's rate: 1 job / 8 hours = 0.125 jobs per hour

Dave's rate: 1 job / 12 hours = 0.0833 jobs per hour

Now, let's find their combined rate when they work together:

Combined rate = Tracy's rate + Dave's rate

Combined rate = 0.125 + 0.0833

Combined rate = 0.2083 jobs per hour

Finally, we can use the formula time = work / rate to find how long it would take them to complete the task together:

time = 1 job / 0.2083 jobs per hour

time ≈ 4.8 hours

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Answer:

x=-60

Step-by-step explanation:

Answer:

-60

Step-by-step explanation:

1/3 x = -20  Multiply both sides by 3

3(1/3) x = 3(-20)

x = -60

Check

1/3(-60) = -20

-20 = -20

The number of chips sold is 10

The number of candy bars sold is 23

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

The price of each candy bar = $1.50.

The price of each bag of chips = $1.25.

Number of chips = x

Number of candy bar = x + 13

Yesterday Melanie made $33.25.

So,

x + x + 13 = 33.25

Solve for x.

x + x + 13 = 33.25

2x + 13 = 33.25

2x = 33.25 - 13

2x = 20.25

x = 10.125

x = 10

Now,

Number of chips = 10

Number of candy bar = 10 + 13 = 23

Thus,

Number of chips sold = 10

Number of candy bar sold = 23

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Answer:

50) i. C 800cm^2

50)ii. B 120cm

Step-by-step explanation:

Use the picture in its given 2-d to mark the unknown measures. Such as, the gray rectangle on top has a bottom that is also 20 and the left side is 15.

The small horizontal jutting out on the left mid-way down is 5cm same as the 5cm just below.

When you mentally "unfold" the shape to its full rectangular shape and size, all the lengths are marked.

Use:

Area=length×width

and,

Perimeter

=L + w + L + w

There are lots of perimeter formulas, for perimeter, you just add up all the sides all the way around the shape.

see image.

Answer:

7.09

Step-by-step explanation:

s = r∅ = 7.09

s = (7 cm)(1.0123) = 7.086

58 deg x π/180 = 1.0123 radians

Answer:

CB ≈ 7.09 cm

Step-by-step explanation:

the length of arc CB is calculated as

AB = circumference of circle × fraction of circle

    = 2πr × [tex]\frac{58}{360}[/tex] ( r is the radius )

   = 2π × 7 × [tex]\frac{29}{180}[/tex]

  = [tex]\frac{14\pi (29)}{180}[/tex]

  ≈ 7.09 cm ( to 2 decimal places )

The probability that the next component brought in for repair is a compact disc player given that it is already known to be an audio component is 0.83 or 83%.

Probability is a fundamental concept in mathematics, statistics, and various fields of science. It is used to measure the likelihood of an event occurring

In the given scenario, we are told that a certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player. We are also given that P(A) = 0.6 and P(B) = 0.5.

The probability of B given A, denoted by P(B|A), represents the probability that event B will occur given that event A has already occurred. In other words, it tells us how likely it is that the next component brought in for repair is a compact disc player given that it is already known to be an audio component.

To calculate P(B|A), we use the formula for conditional probability:

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

Here, P(A and B) denotes the probability that both events A and B occur. We know that event B is contained in event A, so it follows that P(A and B) = P(B). Therefore:

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

Substituting the given values, we have:

P(B|A) = 0.5 / 0.6

P(B|A) = 5/6 or 0.83 (rounded to two decimal places)

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Complete Question:

A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A).  Suppose that P(A) = .6and P(B) = .5. What is P(B|A) ?

Answer:

C.

Step-by-step explanation:

Multiply then divide

The probability that a randomly chosen person has diabetes is 34.2 million / (0.105 * total population).

The probability that a randomly chosen person has diabetes is equal to the number of people who have diabetes divided by the total population:

probability = number of people with diabetes / total population

Substituting the given values:

probability = 34.2 million / (10.5% of the total population)

To calculate this, we need to convert the percentage to a decimal by dividing by 100:

probability = 34.2 million / (0.105 * total population)

Assuming the total population remains constant between 2018 and now, and that the percentage of people with diabetes has also remained constant, we can use this probability to estimate the current number of people with diabetes in the United States.

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The required ordered pair represents the center of the new circle after the transformation is (-x,y). Option A is correct.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them.

Here,
If a circle is reflected across the y-axis, its center, which was originally located at (x, y), will move to a new location that is the same distance from the y-axis but on the opposite side. Since the y-coordinate does not change during a reflection across the y-axis, the y-coordinate of the new center will remain the same as the original, which is y.

However, the x-coordinate will be negated, since the reflection across the y-axis involves flipping points to the opposite side of the y-axis. Therefore, the center of the new circle will have the coordinates (-x, y).

So the answer is A) (-x, y).

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The vertex of the function g(x) is (1,-5).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=-3(x-1)²+2 and g(x)=-3(x-1)²-5.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:

(1,-5)

Focus:

(1,-61/12)

Axis of Symmetry:

x=1

Directrix:

y= -59/12

Therefore, the vertex of g(x) is (1,-5).

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The probability that at least one is a boy, given that at least one is a girl is 0.823

To solve this problem, we can use conditional probability.

Let A be the event that at least one student is a boy, and let B be the event that at least one student is a girl.

We want to find the probability of A given B, denoted as P(A|B).

Let total student is,

Total girls (10) + Total boys (12) = 22

First calculating the probability of event B, which is probability that all three students are boys. This can be calculated as:

P(B) = 1 - (10/22)^3 = 1 - 0.214 = 0.906

The probability of event A intersecting B is then calculated, which is the probability that at least one student is a boy and at least one student is a girl. We can use the complement of this event, which is the likelihood that all three students are male or female:

P(A intersect B) = 1 - P(all girls) - P(all boys)

= 1 - (10/22)^3 - (12/22)^3

= 1 - 0.077 - 0.245

= 0.743

Finally, we use the formula for conditional probability to calculate P(A|B):

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

= 0.743 / 0.906

= 0.822

Therefore, the probability that at least one student is a boy, given that at least one is a girl, is 0.862.

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Statistics is a rigorous field that provides a set of tools and techniques for understanding and making decisions based on data. Correct option is C.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. Statistics is used in a wide range of fields, from business and finance to social sciences, engineering, and healthcare.

One of the key goals of statistics is to summarize and make sense of complex data, and this is often done through the use of visualization techniques such as histograms, scatterplots, and box plots.

Statistics also involves techniques such as data mining, which involves the use of algorithms and computational methods to analyze large data sets, and linear regression, which is a technique for modeling the relationship between two variables.

In addition to its practical applications, statistics is also important for understanding the world around us. It can be used to test hypotheses, evaluate the reliability of data, and make predictions about future events. Overall, statistics plays a vital role in modern society by helping us make sense of the vast amounts of data that we encounter every day.

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Complete question is:

Statistics is a rigorous branch of mathematics that deals with

group of answer choices

A. data mining

B. visualization

C. understanding data

D. linear regression

E. all of the above

Answer: To calculate the amount of US dollars you can buy for R12,500 at an exchange rate of 1 US$ = R8.76, you can use the following formula:

US$ = R12,500 / R8.76

Plugging in the values, we get:

US$ = R12,500 / R8.76 = 1,421.51

So, with R12,500, you can buy 1,421.51 US dollars at an exchange rate of 1 US$ = R8.76.

Step-by-step explanation:

The given functions f(x) = 3x + 6 and g(x) = (x+5)/3 are not inverses of each other, as their compositions of functions are not equal.

When we want to check if two functions are inverses of each other, we need to verify if composing the functions in both orders results in the input variable. In other words, we need to check if (f ∘ g)(x) = x and (g ∘ f)(x) = x, where f and g are the two functions.

For this problem, we have two functions:

f(x) = 3x + 6

g(x) = (x + 5)/3

Let's start by computing (f ∘ g)(x):

(f ∘ g)(x) = f(g(x)) = f((x + 5)/3) = 3((x + 5)/3) + 6

We can simplify this by canceling the 3's:

(f ∘ g)(x) = x + 5 + 6 = x + 11

Now let's compute (g ∘ f)(x):

(g ∘ f)(x) = g(f(x)) = g(3x + 6) = ((3x + 6) + 5)/3

Again, we can simplify this by canceling the 3's:

(g ∘ f)(x) = (3x + 11)/3

We can see that neither (f ∘ g)(x) nor (g ∘ f)(x) is equal to x, so we can conclude that the functions f(x) = 3x + 6 and g(x) = (x + 5)/3 are not inverses of each other.

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Answer:

change the 2w value

Step-by-step explanation:

first, check the equation:

14w + 21 = 14w + 20

when subtracting the 14w from both sides you can see that

21 is NOT EQUAL to 20, making the answer NS.

now, reread the question... create a new equation with ONE solution.

to fix this, we need to change the amount of W's, NOT the amount of constant.

let's try out another number in place of 2w

7 ( 3w + 3 ) = 14w + 20

21 w + 21 = 14w + 20

7 w = -1

w = -1/7

so now it is clear. to change the outcome of the equation, try out another value instead of 2w. Maybe try 3w, 3.5w, or maybe even 1w, or 1.5w .

Answer:

change the 2w

Step-by-step explanation:

=> 7 ( 3w + 3 ) = 14w + 20

=> 21 w + 21 = 14w + 20

=> 7 w = -1

=> w = -1/7

So everything is now evident. Change the value of 2w to anything else to alter the equation's result. Try 3w, 3.5w, or even 1w or 1.5w if you can.

Hope it have been helpful.

Answer: I think B. 7 only

Step-by-step explanation: I hope this helps and I hope everyone is having a good day/Friday&weekend^^

If a red ball is drawn from two urns containing colored balls , then the probability that it came from the first urn is  0.625 or 62.5%   .

Let A = the event that the first urn is chosen, and

B is = the event that a red ball is drawn.

We have to find P(A|B), which means , the probability that the first urn was chosen given that a red ball was drawn.

So , By Bayes' theorem:

we have , P(A|B) = P(B|A) × P(A) / P(B)  ;

Since each urn has an equal probability of being chosen, we have P(A) = P(B) = 1/2 ; and

the probability of drawing a red ball is the same regardless of which urn was chosen.

We need to find P(B|A), the probability of drawing a red ball from the first urn is 50/100 = 0.5   ;

To find P(B), the overall probability of drawing a red ball, we can use the law of total probability:

that is ; P(B) = P(B|A) × P(A) + P(B|A') × P(A')  ;

where A' = event that the second urn was chosen.

Now , we find P(B|A'), which is the probability of drawing a red ball from the second urn is = 30/100 = 0.3    ;

We know that P(A') = 1/2 = 0.5 , because there are only 2 urns.

So , we have : P(A|B) = P(B|A)×P(A) / P(B)  ;

= (0.5×0.5) / (0.5×0.5 + 0.3×0.5)

= 5/8

= 0.625

Therefore, the probability that the red ball came from the first urn is 0.625 or 62.5%   .

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Answer: I assume you are trying to find how many jars the beekeeper has produced per week.

The answer is: 53

Step-by-step explanation:

We know that he produced 636 jars of honey over 12 weeks.

Therefore, to find out the number of jars he made each week, we divide the amount by the time.

So 636/12

Answer 53.

The possible rational roots of the equation 3x³ + 9x - 6 = 0 are given as follows:

± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.

To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.

The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.

The parameters for this function are given as follows:

The factors are given as follows:

Hence the possible roots are given as follows:

± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.

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[tex]40(x )+6( 1.5x) = 612.5[/tex]

So C.

B:

49x=612.5

x=12.5$