Alex has 512 cubes, with dimensions in feet (ft), like the one shown. He uses all the cubes to fill a box shaped like a larger rectangular prism. There are no gaps between the cubes.
A) First, find the volume of each cube:
V = s³
= (1/2)³
= 1/8 ft³
We have a total of 64 cubes, therefore the maximum volume will be:
Vmax = 64 · (1/8) = 8 ft³
B) The volume of a rectangular prism is given by:
V = w × l × h
Therefore any combination of w × l × h = Vmax = 8 will be fine.
Examples:
2 × 2 × 2
4 × 2 × 1
A 90% confidence interval for a proportion is found to be (0.37, 0.43). What is
the sample proportion?
A. 0.43
B. 0.39
C. 0.40
D. 0.41
Answer:
.4
Step-by-step explanation:
Sample proportion of 90% confidence interval for a proportion (0.37, 0.43) is 0.40 .
Thus option C is correct.
Given, A 90% confidence interval for a proportion is found to be (0.37, 0.43) .
Sample proportion - margin of error = 0.37
Sample proportion + margin of error = 0.43
Therefore, the sample proportion will.be the average of the values given above and this will be:
= (0.37 + 0.43)/2
= 0.80/2
= 0.40
Therefore option C is correct.
Know more about sample proportions,
https://brainly.com/question/32835750
#SPJ4
What is the identity of (sec^2theta-1)/sintheta = sintheta/(1-sin^2theta)
Please get this done and match the sides. Thank you!
Answer:
See Below.
Step-by-step explanation:
We want to prove the trigonometric identity:
[tex]\displaystyle \frac{\sec^2(\theta)-1}{\sin(\theta)}=\frac{\sin(\theta)}{1-\sin^2(\theta)}[/tex]
To start, let's simplify the right side. Recall the Pythagorean Identity:
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]
Therefore:
[tex]\cos^2(\theta)=1-\sin^2(\theta)[/tex]
Substitute:
[tex]\displaystyle \frac{\sin(\theta)}{1-\sin^2(\theta)}=\frac{\sin(\theta)}{\cos^2(\theta)}[/tex]
Split:
[tex]\displaystyle =\frac{\sin(\theta)}{\cos(\theta)}\left(\frac{1}{\cos(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]
Therefore, our equation becomes:
[tex]\displaystyle \frac{\sec^2(\theta)-1}{\sin(\theta)}=\tan(\theta)\sec(\theta)[/tex]
From the Pythagorean Identity, we can divide both sides by cos²(θ). This yields:
[tex]\displaystyle \tan^2(\theta)+1=\sec^2(\theta)[/tex]
So:
[tex]\tan^2(\theta)=\sec^2(\theta)-1[/tex]
Substitute:
[tex]\displaystyle \frac{\tan^2(\theta)}{\sin(\theta)}=\tan(\theta)\sec(\theta)[/tex]
Rewrite:
[tex]\displaystyle (\tan(\theta))^2\left(\frac{1}{\sin(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]
Recall that tan(θ) = sin(θ)/cos(θ). So:
[tex]\displaystyle \frac{\sin^2(\theta)}{\cos^2(\theta)}\left(\frac{1}{\sin(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]
Simplify:
[tex]\displaystyle \frac{\sin(\theta)}{\cos^2(\theta)}=\tan(\theta)\sec(\theta)[/tex]
Simplify:
[tex]\tan(\theta)\sec(\theta)=\tan(\theta)\sec(\theta)}[/tex]
Hence proven.
What is the volume of a rectangular prism with the dimensions
Para calcular el volumen de un prisma rectangular, multiplica sus 3 dimensiones: longitud x ancho x altura.
What number must be added to -9 to equal +4?
Answer:
[tex]13[/tex]
Step-by-step explanation:
let the unknown number be x
[tex]x + ( - 9) = 4 \\ x - 9 = 4 \\ x = 4 + 9 \\ x = 13[/tex]
hope this helps you.
Can I have the brainliest please?
Have a nice day!
What is
[tex] 30\sqrt{14} \: over \: 6\sqrt{2} [/tex]
Please help
Answer:
Step-by-step explanation:
30
Raincoats regularly priced at $24 were on sale for 33% off.
a. What is 33% of $24?
b. What is 33 % less than $24?
Yuki and Zana are on a swimming team. They often compete against each other in the 100 meter freestyle race. Yuki's times in this race are normally distributed with a mean of 808080 seconds and a standard deviation of 4.24.24, point, 2 seconds. Zana's times are also normally distributed with a mean of 858585 seconds and a standard deviation of 5.65.65, point, 6 seconds. We can assume that their times are independent.
Suppose we choose a random 100 meter freestyle race and calculate the difference between their times.
Find the probability that Yuki's time is faster than Zana's.
You may round your answer to two decimal places.
Answer:
0.2389 = 23.89% probability that Yuki's time is faster than Zana's.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, we get the probability that the value of the measure is greater than X.
Subtraction of normal variables:
When normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Yuki's times in this race are normally distributed with a mean 80 seconds and standard deviation of 4.2 seconds. Zana's times are also normally distributed with a mean of 85 seconds and a standard deviation of 5.6 seconds.
Yuki's is faster than Zana if the subtraction of Yuki by Zana is larger than 0.
The mean is:
[tex]\mu = 80 - 85 = -5[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{4.2^2 + 5.6^2} = 7[/tex]
Find the probability that Yuki's time is faster than Zana's.
This is P(X > 0), which is 1 subtracted by the pvalue of Z when X = 0.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-5)}{7}[/tex]
[tex]Z = 0.71[/tex]
[tex]Z = 0.71[/tex] has a pvalue of 0.7611
1 - 0.7611 = 0.2389
0.2389 = 23.89% probability that Yuki's time is faster than Zana's.
A large school district claims that 80% of the children are from low-income families. 150 children from the district are chosen to participate in a community project. Of the 150 only 70% are from low-income families. The children were supposed to be randomly selected. Do you think they really were
Incomplete question. However, I answered from a general research perspective.
Explanation:
Note, the term sample used in statistical research refers to subjects or persons carefully selected (using a particular sampling method/type ) to represent the target population.
A randomly selected sample could be done as either:
Simple Random Sampling Stratified Random Sampling Cluster Random Sampling.Systematic Random Sampling.Using any of the above sampling methods could result in 70% of the population being from low-income families as this is a matter of chance. Hence, we can agree with the research results.
Using the z-distribution, it is found that since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the children were not randomly selected.
At the null hypothesis, we test if they were really randomly selected, that is, the proportion is of 80%:
[tex]H_0: p = 0.8[/tex]
At the alternative hypothesis, we test if they were not randomly selected, that is, the proportion is of less than 80%.
[tex]H_1: p < 0.8[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are:
[tex]p = 0.8, n = 150, \overline{p} = 0.7[/tex]
Then, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.7 - 0.8}{\sqrt{\frac{0.8(0.2)}{150}}}[/tex]
[tex]z = -3.06[/tex]
The critical value for a left-tailed test, as we are testing if the proportion is less than a value, with a significance level of 0.05, is of [tex]z^{\ast} = -1.645[/tex].
Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the children were not randomly selected.
A similar problem is given at https://brainly.com/question/24166849
Please solve!!!
3x^2 + 6x + 1
What is the value of x?
Enter your answer in the box.
x =
$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
The figure shows 2 right triangles, triangle A B C with right angle B and triangle B D C with right angle D. The measure of angle B A C is 45 degrees. The measure of angle D B C is 60 degrees. The length of side C A is 6 square root 2. The length of side B D is x.
Answer:
That did not make sense
Answer:
x = 3
Step-by-step explanation:
Verified correct with test results.
Just had to delete the jibberish to find the actual question for this problem:
The figure shows 2 right triangles, triangle A B C with right angle B and triangle B D C with right angle D. The measure of angle B A C is 45 degrees. The measure of angle D B C is 60 degrees. The length of side C A is 6 square root 2. The length of side B D is x. What is the value of x?
Please I need these 2 pages to be answered I’ll give you 100 pts just please do these pages please no links or bad answers
Answer:
Step-by-step explanation:
i don't know sorry
Question 1 of 10
Which function results after applying the sequence of transformations to
Rx) = x5?
• compress vertically by
• shift left 2 units
• shift down 1 unit
O A. g(x) = }(x-2)5.1
O B. g(x) = + (x + 2,5-1
O C. g(x) = (3x+2)5-1
O D. g(x) = ž (x-1)5-2
HELP PLEASE ❗️❗️❗️❗️
Answer:
A (g(x) = }(x-2)5.1).
Step-by-step explanation:
The function which results after the sequence of transformations given is B. g(x) = 1/2 (x + 2)⁵ - 1.
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given function is,
f(x) = x⁵
When a function is compressed vertically, then new function formed will be of the form, k f(x), where k is the factor that is compressed.
After compress vertically by 1/2,
f(x) changes to 1/2 f(x) = 1/2 x⁵
After the horizontal translation of 2 units to the left,
1/2 f(x) changes to 1/2 f(x + 2) = 1/2 (x + 2)⁵.
After vertical translation of 1 unit to the down,
1/2 f(x + 2) changes to 1/2 f(x + 2) - 1 = 1/2 (x + 2)⁵ - 1
Hence the correct option is B . g(x) = 1/2 (x + 2)⁵ - 1.
Learn more about Transformations of Functions here :
https://brainly.com/question/13810353
#SPJ7
Triangles JKL and PQR are congruent, where I corresponds to P, and K corresponds to Q.
The measure of angle J is 20°, the measure of angle K is 15°, and the measure of angle L is 145º.
What is the measure of angle P?
15°
20°
35°
145°
PLEASE HELPPPP
Answer:
20°
Step-by-step explanation:
Congruent Triangles:
If two triangles are congruent, their angles have the same measure.
Angle P corresponds to Angle J
Angle J measures 20º, so angle P will also measure 20º
To find the AREA of any shape, you must calculate the sum all the sides of that shape
True or false
Answer:
False
Step-by-step explanation:
The definition described is Perimeter
Area is found by multiplying the base by the height or the length by the width
The sales tax in Callie's town is
8.5%. Callie bought 3 DVDs for
$24.60 each and 1 book for $15.20
How much did she pay in sales tax?
Answer:
7.57
Step-by-step explanation:
Which expression shows a way to find 5 x 1,625?
A. 5 x (1+6+2 +5)
B. 5 x (1 x 6 x 2 x 5)
C. 5 (1,000 + 600 + 20 + 5)
D. 5 % (1,000 x 600 x 20 x 5)
Find the indicated limit, if it exists.
See file below.
Answer:
c
Step-by-step explanation:
The limit exists because it's continuous since they equal each other
when x approaches zero.
Substitute both expressions with x=0 and both of them will equal 2, so the limit should be 2.
A tent that sells for 250 is on sails for 20% discount what's the sale price of the tent
Step-by-step explanation:
Original price- $250
Discount 20% x 20
-----------
5000
Equals amount taken off $5000
Subtract original price -250
---------------
Sale Price 4750
Hope this helps! If this is not the answer please tell me!
What is -4/7 as an equivalent fraction
Answer:
There are many answers
Step-by-step explanation:
So, since we are finding the equivalent fraction there can be many answers
Here are 5 answers that can help you
• -8/14
• -12/21
• -16/28
• -40/70
• -24/42
What is the total surface area of the exterior of the box that Laura will cover? I’ll give points + brainalist
Answer:
The answer is B 100 in^2
Step-by-step explanation:
add 15+11+24 = 50 X 2 = 100
so yeah
good luck :D
You are wrapping a gift box that is 16 inches long, 7 inches wide, and 9 inches tall. Find the amount of wrapping paper you need to wrap the gift box to the nearest square inch.
... will make brainliest ...
Answer:
638 in.²
Step-by-step explanation:
Assuming you need to cover just the surface area of the box with no overlaps, and the shape is a rectangular prism, then you need to find the surface area of a rectangular prism.
SA = PH + 2LW
where
P = perimeter of base = 2(L + W),
H = height of prism
L = length of base
W = width of base
SA = 2(16 + 7)(9) + 2(16)(7)
SA = 638
A 3 foot wide painting should be centered on 13 foot wide wall how many feet should be on each side of the painting
Answer:
5 feet of wall should be on each side of the painting.
Step-by-step explanation:
Given that a 3 foot wide painting should be centered on 13 foot wide wall, to determine how many feet should be on each side of the painting, the following calculations must be performed:
(13 - 3) / 2 = X
10/2 = X
5 = X
Therefore, 5 feet of wall should be on each side of the painting.
1738.279 into 2 decimal places
Answer:
1738.28
Step-by-step explanation:
Given that
The number is 1738.279
We need to round off to 2 decimal places
Now as we know that
If the rounded number would be followed by 0, 1, 2, 3 or 4, so the number would be down
Let us suppose the number is 32 so it would be 30
If the rounded number would be followed by 5,6,7,8 or 9 so the number would be up
Let us suppose the number be 37 so it would be 40
Now as per the given case, the number is 1738.279
So after rounding to 2 decimal places, the number is 1738.28
Solve for x
3x +2 = 2x +7
Answer:
x ≈ − 1.25593754, 1.70270637
Step-by-step explanation:
Graph each side of the equation. The solution is the x-value of the point of intersection.
Find an expression which represents the sum of (8x+10y)
Answer:
Not sure of what your asking....
Step-by-step explanation:
equivalent to: 2(4x+5y)
Answer:
2(4x+5y)
Step-by-step explanation:
the sum of 8x+10y is 8x+10y
i guess you could make it even more complicated if you want
ln(8x)=ln(1/(10y))
ln(8x/(1/(10y)))
or you can just keep it simple
8x+10y = 2(4x+5y)
Access the hourly wage data on the below Excel Data File (Hourly Wage). An economist wants to test if the average hourly wage is less than $29.
Hourly EDUC EXPER AGE Gender
Wage
37.85 11 2 40 1
21.72 4 1 39 0
34.34 4 2 38 0
21.26 5 9 53 1
24.65 6 15 59 1
25.65 6 12 36 1
25.45 9 5 45 0
20.39 4 12 37 0
29.13 5 14 37 1
27.33 11 3 43 1
28.02 8 5 32 0
20.39 9 18 40 1
24.18 7 1 49 1
17.29 4 10 43 0
15.61 1 9 31 0
35.07 9 22 45 0
40.33 11 3 31 1
20.39 4 14 55 0
16.61 6 5 30 1
16.33 9 3 28 0
23.15 6 15 60 1
20.39 4 13 32 0
24.88 4 9 58 1
23.88 5 4 28 0
37.65 6 5 40 1
15.45 6 2 37 0
26.35 4 18 52 1
19.15 6 4 44 0
16.61 6 4 57 0
18.39 9 3 30 1
25.45 5 8 43 0
28.02 7 6 31 1
23.44 4 3 33 0
17.66 6 23 51 1
26.33 4 15 37 0
34.34 4 9 45 0
35.45 6 3 55 0
37.43 5 14 57 0
35.89 9 16 36 1
20.39 4 20 60 1
31.81 4 5 35 0
35.45 9 10 34 0
37.66 5 4 28 1
23.87 6 1 25 0
36.35 7 10 43 1
25.45 9 2 42 1
23.67 4 17 47 0
26.02 11 2 46 1
23.15 4 15 52 0
24.18 8 11 64 0
a) Choose the null and the alternative hypotheses for the test.
A. H0:μ≥29;HA:μ<29
B. H0:μ=29;HA:μ≠29
C. H0:μ≤29;HA:μ>29
b) Use the Excel function Z. TEST to calculate the p-value. Assume that the population standard deviation is $6.
c) At α = 0.01 what is the conclusion?
A. Do not reject H0; the hourly wage is not less than $29.
B. Do not reject H0; the hourly wage is less than $29.
C. Reject H0; the hourly wage is not less than $29.
D. Reject H0; the hourly wage is less than $29.
Answer:
A. H0:μ≥29;HA:μ<29
Pvalue < 0.01
D. Reject H0; the hourly wage is less than $29
Step-by-step explanation:
The null hypothesis will negate the claim which will be the hypothesis to be tested. Therefore, since the claim is to test if hourly wage is less Than 29 ; then the null will be that hourly wage is equal to or greater than 29
H0:μ≥29;HA:μ<29
The Pvalue measure the probability that the extremity of our finding against a certain α level. The Pvalue obtained using the Excel function should be 0.00058
When Pvalue is < α ; We reject the null hypothesis
Hence, Reject H0; the hourly wage is less than $29 and conclude that hourly wage is less Than $29
Help pls no links I'll give you briliantest
Answer:
Surface area of cube = 6a²
Side of cube = 5/2
Surface area of cube = 6 (5/2)² = 6 (25/4)
= 37.5 unit²
∛≅≅≅≅≅≅≅≅≅≅≅≅≅≅≅≅≅≅[tex]\geq \neq \neq \neq \neq \neq[/tex]
Sorry, I won't understand
The scores of individual students on the ACT Exam are modeled as normally distributed with a mean of19.6 and a standard deviation of 5.0. At Voldemort High, 64 seniors take the test. Assume the individualscores at this school are modeled using the same distribution as national scores. What is the samplingdistribution of the sample average score for this random sample of 64 students
Answer:
The sampling distribution of the sample average score for this random sample of 64 students is approximately normal, with mean 19.6 and standard deviation 0.625.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 19.6 and a standard deviation of 5.0.
This means that [tex]\mu = 19.6, \sigma = 5[/tex]
What is the sampling distribution of the sample average score for this random sample of 64 students?
By the Central Limit Thoerem, the sampling distribution of the sample average score for this random sample of 64 students is approximately normal, with mean 19.6 and standard deviation [tex]s = \frac{5}{\sqrt{64}} = \frac{5}{8} = 0.625[/tex]