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ki77a [65]
3 years ago
14

Can somebody help me?

Mathematics
1 answer:
kari74 [83]3 years ago
7 0

Answer:

6

Step-by-step explanation:

Arc length = radius * central angle

s = rθ

A circle is 2π radians, so 1/3 of that is 2/3 π.

Given that s = 12 and θ = 2/3 π:

12 = r (2/3 π)

r = 18/π

r ≈ 6

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The average yield of the standard variety off soybeans per acre on a farm in a region is 48.8 bushels per acre, with a standard
I am Lyosha [343]

Answer:

z=\frac{53.4-48.8}{\frac{12}{\sqrt{36}}}=2.3  

p_v =P(Z>2.3)=1-P(Z  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 48.8 at 1% of signficance.  

Step-by-step explanation:

1) Data given and notation  

\bar X=53.4 represent the sample mean

\sigma=12 represent the population standard deviation assumed

n=36 sample size  

\mu_o =48.8 represent the value that we want to test  

\alpha=0.01 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

2) State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is higher than 48.8, the system of hypothesis would be:  

Null hypothesis:\mu \leq 48  

Alternative hypothesis:\mu > 48  

Since we assume that know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

3) Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{53.4-48.8}{\frac{12}{\sqrt{36}}}=2.3  

4)P-value  

Since is a right tailed test the p value would be:  

p_v =P(Z>2.3)=1-P(Z  

5) Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 48.8 at 1% of signficance.  

3 0
3 years ago
Yesterday, 4/7 of the 210 students in a contest gave their speeches. How many students gave their speeches?
Elenna [48]

Answer:

120.

Step-by-step explanation:

210 * 4/7

=  30 * 4

= 120.

6 0
3 years ago
The amount of money Samantha earns from selling sculptures at a craft show can be determined by the equation e = $35s, where e r
riadik2000 [5.3K]
The constant would be 35 because a variable added onto it would make it a 
3 0
3 years ago
The oven tray is 600mm by 500mm. A cake tin is 25cm in diameter. How many cake tins can jenny fit on the oven tray at one time?
vlada-n [284]
Area of Circle= \pi 
r^{2}
                      = \frac{22}{7} x ( \frac{25cm}{2}) ^{2}
                      = 490.87cm^{2}

Area of Oven tray= 60cm x 50cm
                            = 3000cm^{2}

: . # tin that can hold on bake tray= 3000cm^{2} / <span>490.87cm^{2}                                 = 6.11
Thus making it logically 6..... </span>
8 0
3 years ago
A car rental agency has 150 cars. The owner finds that at a price of $48 per day, he can rent all the cars. For each $2 increase
hram777 [196]
Given that for each <span>$2 increase in price, the demand is less and 4 fewer cars are rented.

Let x be the number of $2 increases in price, then the revenue from renting cars is given by
(48 + 2x) \times (150 - 4x)=7,200+108x-8x^2.

Also, given that f</span><span>or each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by
5(150-4x)=750-20x

Profit is given by revenue - cost.
Thus, the profit from renting cars is given by
</span><span>(7,200+108x-8x^2)-(750-20x)=6,450+128x-8x^2

For maximum profit, the differentiation of the profit function equals zero.
i.e.
</span><span>\frac{d}{dx} (6,450+128x-8x^2)=0 \\  \\ 128-16x=0 \\  \\ x= \frac{128}{16} =8

The price of renting a car is given by 48 + 2x = 48 + 2(8) = 48 + 16 = 64.

Therefore, the </span><span>rental charge will maximize profit is $64.</span>
3 0
3 years ago
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