Gwen, Tristan, and Keith like to work out at the gym. They each have an app on their phone that estimates the calories they burn. By the time Tristan and Keith started exercising, Gwen had already burned 100 calories. Gwen burns 10 calories every minute, Tristan burns 125 every 10 minutes, and Keith burns 300 calories every 30 minutes. Let x represent the number of minutes since Tristan and Keith started exercising and y represent the number of app-estimated calories burned. Part A

The answer is A) 3 / 20 on USA Test Prep!

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Answer with explanation:

The Given Quadratic Polynomial which can be Broken into integer factors:

 [tex]\rightarrow 6 x^2 + 37 x - 60\\\\ \text{Splitting the Middle term}}\\\\ \rightarrow 6 x^2 + 37 x - 60\\\\\rightarrow 6 x^2 + 45 x-8 x - 60\\\\ \rightarrow 3x \times (2 x+15)-4 (2 x +15)\\\\\rightarrow (3 x -4)(2 x+15)[/tex]

Factors of the above Expression are:

     = (3 x -4)(2 x+15)  

Answer:

The correct answer is 151.

Step-by-step explanation:

Given,

In triangle ABC,

BC = a = 9 unit,

AB = c = 5 unit,

m∠B = 120°,

We have to find : b² or AC²,

By the cosine law,

[tex]b^2=a^2+c^2-2ac cosB[/tex]

[tex]=9^2+5^2-2\times 9\times 5\times cos 120^{\circ}[/tex]

[tex]=81+25-90\times -0.5[/tex]

[tex]=81+25+45[/tex]

[tex]=151[/tex]

Hence, the value of [tex]b^2[/tex] is 151.

Answer:

Option D) [tex]b^2 = 151[/tex]  

Step-by-step explanation:

We are given the following information in the question:

[tex]\triangle ABC\\\text{Side } a = 9\text{ units}\\\text{Side } c = 5\text{ units}\\\angle ABC = 120^{\circ}[/tex]

We have to find [tex]b^2[/tex]

The law of cosines state that if a, b and c are the sides of triangle and b is the side opposite to angle B, then,

[tex]b^2 = a^2 + c^2 - 2ac~\cos(B)[/tex]

Putting the values, we have,

[tex]b^2 = (9)^2 + (5)^2 - 2(9)(5)~\cos(120)\\\\b^2 = 81 + 25 - 90(-0.5)\\\\b^2 = 151[/tex]

Option D) [tex]b^2 = 151[/tex]

A binomial experiment has a fixed number of trials, all are independent and conducted under identical conditions. Only two results—success or failure—are possible with each trial, each having the same probability, fitting a binomial probability distribution.

For a random experiment to be binomial, it must meet certain conditions. Firstly, there should be a fixed number of trials, denoted as 'n'. The results of these trials don't influence each other, meaning that the trials are independent. This signifies that the outcome of a trial, for example, the first one, does not affect the outcomes of the subsequent trials. Moreover, all these trials should be conducted under identical conditions.

In a binomial experiment, there are only two possible results, often referred to as 'success' and 'failure'. Each trial has the same probability of success, denoted as 'p'. The outcomes of a binomial experiment fit a binomial probability distribution. The random variable 'X' stands for the number of successful trials. The mean 'µ' is given by 'np', and the standard deviation 'o' by √npq. The probability of exactly 'x' successes in 'n' trials is P(X = x).

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The unknown number A, when rounded to the nearest thousand and hundred, is determined to be within the range from 20500 to 20549. A can be any number within this range.

In mathematics, when you're given that a number A, when rounded to the nearest thousand, ends up being 21000 or that when rounded to the nearest hundred, it ends up being 20500, you can infer that the unknown number A lies somewhere between two specific values. Since A rounds to 21000 when we round to the nearest thousand, this implies that A is between 20500 and 21499.

However, we also know that, when rounded to the nearest hundred, A is 20500. This implies that A is between 20450 and 20549. Comparing these two ranges, the unknown number A must lie within the common range, which is from 20500 to 20549. Therefore, the number A can be any number within this range.

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Answer:  Fourth and Fifth options are correct.

Step-by-step explanation:

Since we have given two points i.e. A, E, and J

We can see from the graph that

A, E, J are non coplanar and non collinear.

Coplanar means that all the points lie in the same plane.

Collinear means that all the points lie in the same line.

But A, E, and J are neither  in the same plane nor in the same line.

Hence, Fourth and Fifth options are correct.

To find the diameter of the circular hot tub, divide the circumference by π.

To find the diameter of the circular hot tub, we need to use the formula for the circumference of a circle. The formula is C = πd, where C represents the circumference and d represents the diameter.

In this case, the circumference is given as 56.5 yards. So we can plug that value into the formula and solve for d: 56.5 = πd.

To isolate the variable d, we divide both sides of the equation by π. This gives us: d = 56.5/π.

Using a calculator, we can find the approximate value of d to be 18 yards.

The diameter of the hot tub is approximately 18 yards, calculated using the formula [tex]\(D = \frac{56.5}{\pi}\)[/tex] from the given circumference.

The circumference of a circle is given by the formula [tex]\(C = \pi \times D\)[/tex], where C is the circumference and D is the diameter. In this case, the circumference of the hot tub is given as 56.5 yards. So, the formula can be rearranged to solve for the diameter:

[tex]\[ C = \pi \times D \][/tex]

[tex]\[ 56.5 = \pi \times D \][/tex]

To find D, divide both sides of the equation by [tex]\(\pi\)[/tex]:

[tex]\[ D = \frac{56.5}{\pi} \][/tex]

Using the value of  [tex]\(\pi \approx 3.14159\)[/tex], the diameter D is approximately:

[tex]\[ D \approx \frac{56.5}{3.14159} \approx 18 \][/tex]

Therefore, the diameter of the hot tub is approximately 18 yards.

For the inequality y ≥ x, the boundary line should be solid, the slope should be 1, the y-intercept should be 0, and shading should be above the line. Therefore, the error could be an incorrect slope, an incorrect y-intercept, or shading below the line.

Without seeing the graph it is difficult to determine exactly what is wrong, but based on the question and the options given, we can review the conditions of the inequality y ≥ x. For this inequality:

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The line of linear function h(x) = –6 + x is not going to enter in the second quadrant so option second will be correct.

The link between lines and points is described by a graph, which is a diagrammatic representation of a network.

A graph is made up of some points and the distance between two. It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.

Given equation is h(x) = –6 + x

at x = 0 , h(x) = -6 so ( 0 , -6 ) is first point.

at x =1 , h(x) = -5 so ( 1 , -5 ) is second point.

If we draw a line by the two-point which I have attached then you can see it not going to the second quarter.

For more details about the graph

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Final answer:

The probability that fewer than 32 out of 60 victims did not know their murderer can be found using the binomial probability formula, summing the probabilities where x ranges from 0 to 31 with a success rate of 42% for each trial.

Explanation:

To find the probability that fewer than 32 out of 60 murder victims did not know their murderer, given that 58% of victims did know their murderer, we can use the binomial probability formula. Considering that 42% (=100%-58%) of the victims did not know their murderer, we want the cumulative probability of x=0 to x=31 successes (victims not knowing the murderer) out of n=60 trials (total murder cases).

 This can be calculated using a statistical program or a binomial probability table, as manually computing this would be time-consuming and complex. However, the specific steps would involve summing up the probabilities of all scenarios where the number of victims not knowing their murderer ranged from 0 to 31, factoring in the binomial coefficient, the probability of a single victim not knowing the murderer (42%), and its complement for each case.

The unit rate at which Belmond cuts bricks is 28 bricks per hour, which is calculated by dividing the total number of bricks (84) by the total hours worked (3).

To find the unit rate of bricks cut per hour by Belmond, we simply divide the total number of bricks by the total time in hours. Belmond cuts 84 bricks in 3 hours, so the unit rate is:

Unit rate = Total bricks \/ Total time in hours
Unit rate = 84 bricks \/ 3 hours = 28 bricks per hour

This means that Belmond cuts 28 bricks every hour. When you need to find a unit rate, it is a matter of dividing the total quantity by the time it takes to accomplish that quantity, thus yielding the rate per single time unit (in this case, per hour).

dive distance traveled by time

 90 feet / 15 seconds = 6

 since the diver is below the surface they are changing position at -6 feet per second

We know that there is no universal acceptance meaning of a percentile. When someone told you that you are in the 80th percentile, the meaning of that is you have achieved the lowest score that is greater than 80 percent of the score. It is calculated by using the formula     R = P/100 x (N + 1)

Final answer:

The 80th percentile represents the score below which 80% of the scores fall.

Explanation:

The 80th percentile represents the score below which 80% of the scores fall. It is calculated by finding the value at which 80% of the data is below and 20% is above. For example, if you scored in the 80th percentile on a 60-point assignment, it means that 80% of students scored equal to or below 49 points and 20% scored above.

Answer:

Option A - 4

Step-by-step explanation:

Given : Inequality [tex]30 - x^2 < 3x + 7[/tex]

To find : Choose the value of x that makes the open sentence true  ?

Solution :

We substitute the value of x from options to check which is true,

A) x=4

[tex]30 - 4^2 < 3(4) + 7[/tex]

[tex]30-16 < 12+ 7[/tex]

[tex]14< 19[/tex]

It is true.

B) x=3

[tex]30 - 3^2 < 3(3) + 7[/tex]

[tex]30-9< 9+ 7[/tex]

[tex]21< 16[/tex]

It is false.

C) x=2

[tex]30 - 2^2 < 3(2) + 7[/tex]

[tex]30-4<6+ 7[/tex]

[tex]26< 13[/tex]

It is false.

D) x=1

[tex]30 - 1^2 < 3(1) + 7[/tex]

[tex]30-1<3+ 7[/tex]

[tex]29< 10[/tex]

It is false.

Therefore, Option A is correct.

Answer: 0.8%

Step-by-step explanation:

Given : In a batch of 960 calculators, 8 were found to be defective.

i.e. Total calculators =960

Number of defective calculator = 8

We know that the probability of any event is given by :-

[tex]\dfrac{\text{No. of favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{8}{960}=0.00833333333333[/tex]

In percent, [tex]0.00833333333333\times100=0.833333333333\%\\\\\approx0.8\%\ \ \ [\text{Rounding to the nearest tenth.}][/tex]

Hence, the probability that a calculator chosen at random will be defective=0.8%

Answer:

[tex]s(t)=(9 cost,9 sint , 32805 cos^4 t) , t\in (0,2\pi)[/tex]

Step-by-step explanation:

We are given that two surfaces

[tex]x^2+y^2=81[/tex]

and [tex]z=5x^4[/tex]

We have to find the parametrize the intersection of the given surfaces using cost and sin t with positive coefficient.

We know that intersection curve S(t) is given by

S(t)=(x(t),y(t),z(t)),[tex]t\in(0,2\pi)[/tex]

[tex]x^2+y^2=(9)^2[/tex]

Compare with the equation of circle [tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h,k) is center of circle and r is the radius of the circle.

The center and radius of given circle is (0,0) and 9.

[tex]x=9cost,y=9 sint[/tex]

because cost  takes along x - axis and sin t takes along y- axis.

When we substitute these values then we get

[tex]81cos^2t+81sin^2t=81(cos^2t+sin^2t)=81 [/tex] ([tex]sin^2t+cos^2t)=1[/tex])

Hence, [tex]x=9 cost, y= 9sint [/tex]

Substitute the value of x in second equation of surface

[tex]z=5(9cost)^4=32805 cos^4t[/tex]

Hence, the intersection curve s(t) is given by

[tex]s(t)=(9 cost,9 sint , 32805 cos^4 t) , t\in (0,2\pi)[/tex]