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olchik [2.2K]
3 years ago
8

A student said that the surface area of the figure below was 57.4 square centimeters. Is the student correct? Explain.

Mathematics
1 answer:
FrozenT [24]3 years ago
3 0

Answer:

  no

Step-by-step explanation:

The surface area is the sum of the areas of the faces.

There are 4 faces that are 5 cm wide. Their respective heights (from front, over the top) are ...

  1 cm, 2.5 cm, 2 cm, 2.3 cm

for a total height of 7.8 cm. Thus, those 4 faces have a total area of ...

  (5 cm)(7.8 cm) = 39.0 cm^2

__

The two trapezoidal faces each have bases of length 1 and 2 cm, and a "height" of 2.3 cm. Together, their areas are ...

  A = 2×(1/2)(b1 +b2)h = (b1 +b2)h

  A = (1 cm +2 cm)(2.3 cm) = 6.9 cm^2

__

The surface area of the entire trapezoidal prism is then ...

  total area = base area + lateral area = 6.9 cm^2 +39 cm^2

  total area = 45.9 cm^2

The student's answer of 57.4 cm^2 is not correct. (We don't know where that calculation came from.)

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Find f(-5) f(x) -4x + 3
Fiesta28 [93]

Answer:

if f(x)= -4x+3

f(-5)= 23

Step-by-step explanation:

first you substitute x for -5

f(-5)= -4(-5)+3

then you multiply

-4(-5)

f(-5)=20+3

you get the positive 20 because negative times negative equals positive

then you just add the rest (20+3) which will give you your answer

f(-5)= 23

8 0
2 years ago
A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random
Yuliya22 [10]

Answer:

b) independent samples t-test

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: \mu_1 = \mu_2  

Alternative hypothesis: \mu_1 \neq \mu_2  

Or equivalently:  

Null hypothesis: \mu_1 - \mu_2 = 0  

Alternative hypothesis: \mu_1 -\mu_2\neq 0  

Our notation on this case :  

n_1 =5 represent the sample size for group 1  

n_2 =5 represent the sample size for group 2  

We can calculate the mean and deviation for eaach group with the following formulas:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X_1 =5.92 represent the sample mean for the group 1  

\bar X_2 =5.74 represent the sample mean for the group 2  

s_1=1.88 represent the sample standard deviation for group 1  

s_2=1.81 represent the sample standard deviation for group 2  

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:  

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}  

And now we can calculate the statistic:  

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

The degrees of freedom are given by:  

df=5+5-2=8

And now we can calculate the p value using the altenative hypothesis:  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

7 0
3 years ago
What is the volume of a rectangular prism with length 7 cm, width 2 cm, height 5 cm?
gayaneshka [121]

Answer:

7x2x5= 70

Hope This Helps! :)

4 0
2 years ago
PLEASE HELP!!! 20 POINTS!!!!
stealth61 [152]
To evaluate the expression all you have to do is substitute the value for the variable.

3 + y + 6, y = 5
3 + 5 + 6
8 + 6
14.

The solution is 14.
8 0
3 years ago
Read 2 more answers
Please answer<br> fasttt
-BARSIC- [3]

Answer:

7.5 lb/cu ft

Step-by-step explanation:

75 lb / 10 cu ft = 7.5 lb/cu ft

4 0
2 years ago
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