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yKpoI14uk [10]
2 years ago
9

A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s^2. How much time does it take to travel

95.1 m?
Mathematics
1 answer:
leva [86]2 years ago
4 0

The school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².

<h3>What is a quadratic equation?</h3>

Any equation of the form \rm ax^2+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}

We have:

A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².

From the second equation of motion:

\rm s = u + \dfrac{1}{2}at^2

We have given:

s = 95.1 m

u = 26.8 m/s

a = 4.73 m/s²

\rm 95.1 = 26.8 + \dfrac{1}{2}(4.73)t^2

The above equation is a quadratic equation:

After simplification:

\rm \dfrac{4.73}{2}t^2=68.3

\rm t^2=28.879

t = 5.373 seconds ≈ 5.34 seconds

Thus, the school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².

Learn more about quadratic equations here:

brainly.com/question/2263981

#SPJ1

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Answer: E. Convenience

Step-by-step explanation:

  • A convenience sampling is a method of sampling whose structure is based on accessibility to the researcher .

Given : An internet site asks its members to call in their opinion regarding their web searching habits.

Here the internet site is working according to its accessibility .

Hence, this is a type of convenience sampling .

8 0
3 years ago
Which functions are symmetric with respect to the origin?
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Answer:

The correct option is;

y = arcsinx and y = arctanx

Step-by-step explanation:

The given options are;

1) y = arcsinx and y = arccosx

Here, we have at the origin, where x = 0,  arccosx ≈ 1.57 while arcsinx = 0

Therefore arccosx does not intersect arcsinx at the origin for it to be symmetrical to arcsinx or the origin

2)  y = arccosxy and y = arctanx

Here arctanx = 0 when x = 0 and arcos x = 1.57 when x = 0 therefore, they are not symmetrical

3) y = arctanx and y = arccotx

Similarly, At x = 0, arccotx = 1.57 therefore, they are not symmetrical

4) y = arcsinx and y = arctanx

Both functions arcsinx and arctanx pass through the origin and their shapes are similar but inverted as they go from negative to positive.

3 0
3 years ago
Kelly blends coffee. She mixes brand A costing $6 per kilogram with brand B costing $8 per kilogram. How many kilograms of each
sukhopar [10]

Step-by-step explanation:

Let

x

be the kg of coffee of brand A in the mix and

y

be the kg of coffee of brand B in the mix.

The total kg must be

50

.

x

+

y

=

50

The cost per kg of the mix must br

$

7.20

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6

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+

8

y

, so the total cost per kg of the mix will be

6

x

+

8

y

50

.

6

x

+

8

y

50

=

7.20

Now that we have our two equations, we can solve.

6

x

+

8

y

=

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⋅

50

6

x

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y

=

360

From the first equation, we can multiply both sides by

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6

x

+

6

y

=

300

Subtracting, we get:

2

y

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y

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6 0
3 years ago
Popular magazines rank colleges and universities on their ""academic quality"" in serving undergraduate students. Describe two c
Reika [66]

Answer:

Quantitative: i) The number of students in the school vis - a - vis the number of classes in the school. In order words, simply number of students per class

ii) The rate of graduation of students.

Categorical:i) Courses being taken by students

ii) Region of country of students.

Step-by-step explanation:

To answer this question effectively, it's important for us to know that a quantitative variable usually has numerical values, and also have units of measure as well while categorical variables simply places each student into a specific category.

Now, the two quantitative variables we will consider are;

i) The number of students in the school vis - a - vis the number of classes in the school. In order words, number of students per class

ii) The rate of graduation of students.

Also, the two categorical variables we will consider are;

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5 0
3 years ago
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the
a_sh-v [17]

Answer:

Probability that the sample proportion will be less than 0.03 is 0.10204.

Step-by-step explanation:

We are given that a courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.04.

Also, 469 are sampled.

<em>Let </em>\hat p<em> = sample proportion</em>

The z-score probability distribution for sample proportion is given by;

              Z = \frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion

           p = true proportion = 0.04

           n = sample size = 469

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample proportion will be less than 0.03 is given by = P( \hat p < 0.03)

       P( \hat p < 0.03) = P( \frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < \frac{0.03-0.04}{\sqrt{\frac{0.03(1-0.03)}{469} } } ) = P(Z < -1.27) = 1 - P(Z \leq 1.27)

                                                                      = 1 - 0.89796 = 0.10204

Now, in the z table the P(Z \leq x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.27 in the z table which has an area of 0.89796.

Therefore, probability that the sample proportion will be less than 0.03 is 0.10204.

5 0
3 years ago
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