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3 years ago

Please help me with Q 7 c

Mathematics

2 answers:

frez [133]3 years ago

8 0

Answer:

11.25 km h^-2

Step-by-step explanation:

Acceleration = increase in velocity / time

= 90 - 0 / 8

= 11.25 km h^-2.

DIA [1.3K]3 years ago

4 0

$v_{i} = 0 \: (from \: rest) \\ v_{f} = 90 \: km \: per \: hr \\ t_{i} = 0 \\ t_{f} = 8 \: hr \\ a = \frac{(v_{f} - v_{i})}{(t_{f} - t_{i})} \\ a = \frac{90}{8} \\ a = \frac{45}{4} km/ {hr}^{2}$

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the initial vertical velocity of a rocket shot straight up is 42 meters per second. How long does it take for the rocket to retu

Snowcat [4.5K]

It takes 4.3 seconds for the rocket to return to earth.

The equation is:
$0=-9.8t^2+v_0t+h_0$
where -9.8m/sec² is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height. We will go from the assumption that the rocket is launched from the ground, so h₀=0, and we are told that the initial velocity, v₀, is 42. This gives us:

$0=-9.8t^2+42t$

We will use the quadratic formula to solve this. The quadratic formula is:
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Plugging in our information we have:
$t=\frac{-42\pm \sqrt{42^2-4(-9.8)(0)}}{2(-9.8)}
\\
\\=\frac{-42\pm \sqrt{1764-0}}{-19.6}
\\
\\=\frac{-42\pm \sqrt{1764}}{-19.6}
\\
\\=\frac{-42\pm 42}{-19.6}=\frac{-42-42}{-19.6} \text{ or } \frac{-42+42}{-19.6}
\\
\\=\frac{-84}{-19.6}\text{ or }\frac{0}{-19.6}
\\
\\=4.3\text{ or }0$

x=0 is when the rocket is launched; x=4.3 is when the rocket lands.

8 0

3 years ago

Paulo can run a marathon in four hours and 20 minutes. If he's able to cut of 18% of his time, how long will it take him to run

Inga [223]

Cut out 18%
100=all,
all-cut out=remaining
100-18=82

4hrs 20mins=240+20mins=260mins
82% of 260 is 0.82*20=213.2=3 hours and 33.2 minutes

he can runi s 3 hours and 33.2 minutes

7 0

3 years ago

If IQ scores are normally distributed with a mean of 100 and a standard deviation of 5, what is the probability that a person se

notsponge [240]

Answer:

2.28% probability that a person selected at random will have an IQ of 110 or higher

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 100, \sigma = 5$

What is the probability that a person selected at random will have an IQ of 110 or higher?

This is 1 subtracted by the pvalue of Z when X = 110. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{110 - 100}{5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.0228

2.28% probability that a person selected at random will have an IQ of 110 or higher

5 0

3 years ago

In a study, researchers wanted to measure the effect of alcohol in the development of the hippocampal region in adolescents. The

lbvjy [14]

Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Sample size, n = 30

Tcritical value = 2.045

Null hypothesis :

H0: μ = 9.08

Alternative hypothesis :

H1: μ≠ 9.08

Sample mean, m = 8.25

Samole standard deviation, s = 1.67

Test statistic : (m - μ) ÷ s/sqrt(n)

Test statistic : (8.25 - 9.08) ÷ 1.67/sqrt(30)

Test statistic : - 0.83 ÷ 0.3048988

Test statistic : - 2.722

Tstatistic = - 2.722

Decision region :

Reject Null ; if

Tstatistic < Tcritical

Tcritical : - 2.045

-2.722 < - 2.045 ; We reject the Null

Using the α - level (confidence interval) 0.05

The Pvalue for the data from Tstatistic calculator:

df = n - 1 =. 30 - 1 = 29

Pvalue = 0.0108

Reject H0 if :

Pvalue < α

0.0108 < 0.05 ; Hence, we reject the Null

4 0

2 years ago

50 PTS ANSWER ALL <3333333

11Alexandr11 [23.1K]

QUESTION 33

The length of the legs of the right triangle are given as,

6 centimeters and 8 centimeters.

The length of the hypotenuse can be found using the Pythagoras Theorem.

${h}^{2} = {6}^{2} + {8}^{2}$

${h}^{2} = 36+ 64$

${h}^{2} = 100$

$h = \sqrt{100}$

$h = 10cm$

Answer: C

QUESTION 34

The triangle has a hypotenuse of length, 55 inches and a leg of 33 inches.

The length of the other leg can be found using the Pythagoras Theorem,

${l}^{2} + {33}^{2} = {55}^{2}$

${l}^{2} = {55}^{2} - {33}^{2}$

${l}^{2} = 1936$

$l = \sqrt{1936}$

$l = 44cm$

Answer:B

QUESTION 35.

We want to find the distance between,

(2,-1) and (-1,3).

Recall the distance formula,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the values to get,

$d=\sqrt{( - 1-2)^2+(3- - 1)^2}$

$d=\sqrt{( - 3)^2+(4)^2}$

$d=\sqrt{9+16}$

$d=\sqrt{25}$

$d = 5$

Answer: 5 units.

QUESTION 36

We want to find the distance between,

(2,2) and (-3,-3).

We use the distance formula again,

$d=\sqrt{( - 3-2)^2+( - 3- 2)^2}$

$d=\sqrt{( - 5)^2+( - 5)^2}$

$d=\sqrt{25+25}$

$d=\sqrt{50}$

$d=5\sqrt{2}$

Answer: D

8 0

3 years ago

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