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3 years ago

Find 3 consecutive odd integers whose sum is 225, explain please

2 answers:

4 0

73,75,77

do it like this
(x-2)+x+(x+2)=225
add it all up
3x=225
x=75

so, 75-2=73
and 75+2=77 so, 73,75,77 is the answer

Gre4nikov [31]3 years ago

3 0

Three consecutive integers whose sum is 225 are 74, 75, and 76.

Three consecutive odd integers add up to 225. This means the middle of the three numbers is one third of 225.

225/3=75

The middle number is 75. The other two numbers are 74 and 76.

Three consecutive integers whose sum is 225 are 74, 75, and 76.

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The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32

myrzilka [38]

Answer:

a) $(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

b) $t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

Step-by-step explanation:

Data given and notation

$\bar X_{A}=14.68$ represent the mean for Pirates

$\bar X_{B}=18.77$ represent the mean for Splash Mountain

$s_{A}=11.87$ represent the sample standard deviation for the sample Pirates

$s_{B}=16.79$ represent the sample standard deviation for the sample Slpash Mountain

$n_{A}=32$ sample size selected for Pirates

$n_{B}=30$ sample size selected for Splash Mountain

$\alpha=0.02$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

Part a

The confidence interval would be given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 32+30-2 = 60$

Since we want 98% of confidence the significance level is $\alpha =1-0.98 =0.02$ and $\alpha/2 =0.01$ , we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

$t_{\alpha/2}= 2.39$

And replacing we got for the confidence interval:

$(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis: $\mu_{A} = \mu_{B}$

Alternative hypothesis: $\mu_{A} \neq \mu_{B}$

the statistic is given by:

$t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

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

$t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

6 0

3 years ago

a local parts shop buys a machine that costs $500,000. its value depreciates exponentially each year by 10%. what is the machine

jeka94

Hello!

Answer:

$295.295

Explanation:

Of the statement, we have that the price of the machine decreased 10% every year exponentially, so in the first year it real value drops to 90% of the costs. For 5 years, It can be expressed and simplified by the following equation:

We can't use that the percent drop as a percent itself, so we are going to divide 90% by 100%, and it will give us an entire number.

$\frac{90}{100}=0,9 \\ \\ Value=Costs.(0.9)^{years}$

By substituting we have:

$Value=500000.(0.9)^{5}$

Value: $295.245

Have a nice day!

8 0

3 years ago

Write the equation of the line that passes through (3, 4) and (2, –1) in slope-intercept form.

Inessa [10]

The equation of the line is
y = 5x-11

7 0

3 years ago

What is the solution to the equation 13.7y = 6.2y + 30?

il63 [147K]

Here, we are required to determine the solution to the equation: 13.7y = 6.2y + 30?

The solution to the equation is y = 7.5

The solution is thus,

13.7y = 6.2y + 30
13.7y - 6.2y = 30
7.5y = 30

Therefore, y = 30/7.5 = 4

Therefore, y = 4 is the solution to the equation.

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8 0

3 years ago

Draw two different perimeters of a rectangle with an area of 14 units. Name their dimensions.

Alenkasestr [34]

1:
Length: 7
Width:2
Perimeter: 18

2:
Length: 5
Width: 2.8
Perimeter: 15.6

8 0

3 years ago