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2 years ago

How could Brent use a rectangle to model the factors of x2 – 7x + 6?

2 answers:

Crank2 years ago

6 0

He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.

ivann1987 [24]2 years ago

6 0

Answer:

Step-by-step explanation:

Since Brent uses a rectangle that models the area = (x² - 7x + 6)

Now we will factorize this expression

x² - 7x + 6 = x² - 6x - x + 6

= x(x - 6) - 1(x - 6)

= (x - 1)(x - 6)

Therefore, (x -1) and (x - 6) will represent the sides of a rectangle so that multiplication of the sides will model the area of the rectangle.

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Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal

Nikolay [14]

Answer:

0.0359

Step-by-step explanation:

Data provided:

mean values of three independent times are 15, 30, and 20 minutes

the standard deviations are 2, 1, and 1.6 minutes

Now,

New Mean = 15 + 30 + 25 = 65

Variance = ( standard deviation )²

Variance = 2² + 1² + 1.6² = 7.56

therefore,

Standard deviation = √variance

Standard deviation = 2.75

Thus,

Z-value = $\frac{\textup{60 - 65}}{\textup{2.75}}$

Z-value = - 1.81

from the Z-table

the Probability of Z ≤ -1.81 = 0.0359

6 0

2 years ago

a sports statistician claim that the mean winning times for boston marathon women's open division champions is at least 2.68 hou

GenaCL600 [577]

Answer:

We conclude that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

Step-by-step explanation:

We are given that a sports statistician claim that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

The mean winning time of a sample of 30 randomly selected Boston marathon women's open division champions is 2.60 hours. assume the population standard deviation is 0.32 hours.

Let $\mu$ = mean winning times for Boston marathon women's open division champions.

So, Null Hypothesis, $H_0$ : $\mu\geq$ 2.68 hours {means that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours}

Alternate Hypothesis, $H_A$ : p < 2.68 hours {means that the mean winning times for Boston marathon women's open division champions is less than 2.68 hours}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean winning time = 2.60 hours

$\sigma$ = population standard deviation = 0.32 hours

n = sample of women's open division champions = 30

So, test statistics = $\frac{2.60-2.68}{\frac{0.32}{\sqrt{30} } }$

= -1.37

The value of z test statistics is -1.37.

Now, P-value of the test statistics is given by following formula;

P-value = P(Z < -1.37) = 1 - P(Z $\leq$ 1.37)

= 1 - 0.9147 = 0.0853

Since, P-value of the test statistics is more than the level of significance as 0.0853 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

6 0

2 years ago

Greatest common factor of 88 and 48

kupik [55]

GFC is 8. Use a tree of 88 and 48. 88= 2^3 x 11 or 2 x 2 x 2 x 11

48=2^4 x 3 or 2 x 2 x 2 x 2 x 3 see how many groups count as the number once and multiply and bam GFC. Hope I helped! (:

4 0

2 years ago

last night, julie's pet hamster zoe kept julie awake for at least an hour running on her exercise wheel and scratching at the co

borishaifa [10]

Answer: $x+y\geq 1$ , $x>\frac{1}{4}$ , $x\geq 2y$ and $y\geq 0$

Step-by-step explanation:

Here, x represents the number of hours Zoe spent running on her wheel and y represents the number of hours spent scratching her cage.

Julie was awoke for at least an hour running on her exercise wheel and scratching the of her cage.

⇒ $x+y\geq 1$

She ran on her wheel at least twice as long as she scratched at the corners of her cage.

⇒ $x\geq 2y$

Also, She spent more than 1/4 hour running on her wheel.

⇒ $x>\frac{1}{4}$

And, we know that number of hours can not be negative.

⇒ $y\geq 0$

Therefore, the complete system of inequality which shows the given situation is,

$x+y\geq 1$ , $x>\frac{1}{4}$ and $x\geq 2y$ , $y\geq 0$

Note: the feasible region ( covered by the given system) is shown in the below graph.

6 0

2 years ago

give me 3 pictures showing the application of the sum and the product of the roots of quadratic equations in real life . describ

Vlada [557]

We can apply Quadratic equations in real-world like; sports, bridges, projectile motion, shapes of bananas etc.

Following are three pictures of real world application of quadratics.

Example 1:- Here we can see a Cyclist follows a quadratic path to jump over the obstacles.

Example 2:- Here we see a man throwing a basketball towards the net following a slightly upward direction that goes through a quadratic path.

Example 3:- Here a football player kicks the ball in the sky and it goes through a quadratic path to cover some distance.

4 0

2 years ago

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