Answer:
the total surface area of the prism is 245.67
Step-by-step explanation:
Given;
height of the triangular prism, h = 8
length of the triangular bases, = 7, 8, and 9
The total surface area of the prism is calculated as;
T.S.A = ph + 2B
Where;
p is the perimeter of the base
B is area of the base
P = 7 + 8 + 9 = 24
Area of the base can be calculated using Hero's formula;
[tex]S = \frac{7+8+9}{2} = 12\\\\Base \ area (B) = \sqrt{12(12-7)(12-8)(12-9)} = 26.833[/tex]
T.S.A = (24 x 8) + 2 x 26.833
T.S.A = 192 + 53.666
T.S.A = 245.67
Therefore, the total surface area of the prism is 245.67
Sarah invested $2,500 in an account paying an interest rate of 2.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 14 years?
Answer:
sorry 2458946547165874%
Step-by-step explanation:
Caleb has a board that measures 10 feet in length. How many 1/3 foot-long pieces can Caleb from the board?
Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)
Answer:
0.9544 = 95.44% probability of the resulting sample proportion being within .04 of the true proportion
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
20% of the residents in a certain state support an increase in the property tax. Sample of 400.
This means that [tex]p = 0.2, n = 400[/tex]
Mean and standard deviation:
Mean [tex]\mu = p = 0.2[/tex]
Standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.2*0.8}{400}} = 0.02[/tex]
How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?
This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16. So
X = 0.24
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.24 - 0.2}{0.02}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 0.16
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.16 - 0.2}{0.02}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability of the resulting sample proportion being within .04 of the true proportion
.) Suppose college students produce 650 pounds of solid waste each year, on average. Assume that the distribution of waste per college student is normal with a mean of 650 pounds and a standard deviation of 20 pounds. What is the probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
Answer:
0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
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.
Mean of 650 pounds and a standard deviation of 20 pounds.
This means that [tex]\mu = 650, \sigma = 20[/tex]
What is the probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste?
Less than 620:
pvalue of Z when X = 620. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{620 - 650}{20}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
More than 700:
1 subtracted by the pvalue of Z when X = 700. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 650}{20}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
Total:
0.0668 + 0.0062 = 0.073
0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
The measure of an angle is 42.89. What is the measure of its supplementary angle?
Answer:
The supplementary angle is 137.11.
Step-by-step explanation:
180-42.89 = 137.11
Hope this helps!
PLEASE PLEASE HELP!! A ferris wheel with a radius of 38 feet rotates at a rate of 8 revolutions per minute. The height above the ground of the carriage labeled C below is a function of time, t, in minutes
Solve for x in the triangle. Round your answer to the nearest tenth
Answer:
9.1
Step-by-step explanation:
Tangent 33=x/14
x=14*Tan 33
x=9.1(nearest tenth)
find the slope
!!HELP QUICKLY PLEASE!!
A bag contains 4 white,5 blacks and 2 blue balls. 3 balls are drawn one after the other without replacement from the bag .what is the probability that they are of different color
Answer:
24/99
Step-by-step explanation:
From the question given above, the following data were obtained:
White (W) balls = 4
Black (B) balls = 5
Blue (Bl) balls = 2
Probability that they are of different color =?
Next, we shall determine the total number of balls in the bag. This can be obtained as follow:
White (W) balls = 4
Black (B) balls = 5
Blue (Bl) balls = 2
TOTAL = 4 + 5 + 2 = 11 balls
Next, we shall determine the possible outcome of draw. This can be obtained as follow.
The possible outcome could be:
WBLB or WBBL or BBLW or BWBL or BLBW or BLWB
Next we shall determine the probability of each of outcomes.
Since the ball is drawn without replacement, it means the total number of ball will reduce after each draw.
White (W) balls = 4
Black (B) balls = 5
Blue (Bl) balls = 2
TOTAL = 11
P(WBLB) = 4/11 × 2/10 × 5/9 = 40/990
P(WBLB) = 4/99
P(WBBL) = 4/11 × 5/10 × 2/9 = 40/990
P(WBBL) = 4/99
P(BBLW) = 5/11 × 2/10 × 4/9 = 40/990
P(BBLW) = 4/99
P(BWBL) = 5/11 × 4/10 × 2/9 = 40/990
P(BWBL) = 4/99
P(BLBW) = 2/11 × 5/10 × 4/9 = 40/990
P(BLBW) = 4/99
P(BLWB) = 2/11 × 4/10 × 5/9 = 40/990
P(BLWB) = 4/99
Finally, we shall determine the probability that they are of different color. This can be obtained as follow:
P(WBLB) = 4/99
P(WBBL) = 4/99
P(BBLW) = 4/99
P(BWBL) = 4/99
P(BLBW) = 4/99
P(BLWB) = 4/99
Probability that they are of different color =?
Probability that they are of different color = P(WBLB) + P(WBBL) + P(BBLW) + P(BWBL) + P(BLBW) + P(BLWB)
= 4/99 + 4/99 + 4/99 + 4/99 + 4/99 + 4/99
= (4 + 4 + 4 + 4 + 4 + 4)/99
= 24/99
Thus, the probability that they are of different color is 24/99
Plz help What is 2x+x
Answer:
The correct answer is 3x
Step-by-step explanation:
Add 2x and x
~Hoped this helped~
~Brainiliest, please?~
What is the mode of the data set?
A. 8
B. 9
C. 10
D. 5
Answer:
A: 8
Step-by-step explanation:
The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. ... The mode can be the same value as the mean and/or median, but this is usually not the case
Question 6 (5 points)
Which of the following statements is true for 6.24?
O A) It's irrational because 6.24 =
68/33
OB) It's irrational because 6.24 =
= 60/25.
OC) It's rational because 6.24 = 68/33.
OD) It's rational because 6.24 =
66/25.
Answer:
C
Step-by-step explanation:
it's rational because 6.24 can be 68/33
sorry if I'm wrong!!
find-5/6÷(-1/2) write the answer in the lowest terms.
Answer:
[tex]\dfrac{-5}{3}[/tex]
Step-by-step explanation:
We need to solve the given expression in the lowest form i.e.
[tex]\dfrac{5}{6}\div (-\dfrac{1}{2})[/tex]
We know that,
[tex]\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{a}{b}\times \dfrac{d}{c}[/tex]
So,
[tex]\dfrac{5}{6}\div (-\dfrac{1}{2})=\dfrac{5}{6}\times (-2)\\\\=\dfrac{-5}{3}[/tex]
So, the lowest form is equal to [tex]\dfrac{-5}{3}[/tex].
Mr.Bhal has a circular wading pool with a radius of 3.5 feet. He bought a larger pool witha diameter of 21 feet. The measurements of each pool are shown below. How many times the circumference of the old pool is the circumference of the new pool?
Answer: i think c
Step-by-step explanation:
HELPP!!
Explain how to find the difference between two integers using the difference.
WILL GIVE BRAINLIEST
Answer:
Hope this will help you.
HURRY I NEED HELP!!!
Answer: 6 plus 15 and give me brainlest
Step-by-step explanation:
Answer:
complementary angles add to 90°
create an equation for both of the angles:
90= 3x + 10 + x
solve for x by combining like terms:
90= 4x + 10
solve for x by removing 10 from both sides:
80= 4x
solve for x by dividing by 4 on both sides:
20=x
and you get your answer of x=20
To check your answer plug in 20 for x in the equation above:
90= 3(20) + 10 + 20
90= 60 + 30
90=90
PLEASE HELP DEW IN 1 hour
Answer: B
Step-by-step explanation:
2(—2) + 10 = 6.
2(0) + 6 = 6.
2(2) + 2 = 6.
2(4) + (—2) = 6
6. A hypothesis test in which rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution is called _______ Group of answer choices A one-tailed test A two-tailed test The null hypothesis The alternative hypothesis g
Answer:
A two-tailed test.
Step-by-step explanation:
ANOVA is a short term or an acronym for analysis of variance which was developed by the notable statistician Ronald Fisher. The analysis of variance (ANOVA) is typically a collection of statistical models with their respective estimation procedures used for the analysis of the difference between the group of means found in a sample. Simply stated, ANOVA helps to ensure we have a balanced data by splitting the observed variability of a data set into random and systematic factors.
In Statistics, the random factors doesn't have any significant impact on the data set but the systematic factors does have an influence.
Basically, the analysis of variance (ANOVA) procedure is typically used as a statistical tool to determine whether or not the mean of two or more populations are equal through the use of null hypothesis or a F-test.
Hence, the null hypothesis for an analysis of variance (ANOVA) requires that all treatments or samples should be generated from populations having the same mean.
A hypothesis test in which rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution is called a two-tailed test.
Zoom in for a better look BUT HELP PLS ITS MY FINALS! I RLLY NEED HELP
Answer:
C.
Step-by-step explanation:
The word biodiversity means the variety of life and in this case, bats
Ecosystem 1 has the most variety bc it has the most number of different varieties of bats observed
hope this helps <3
What is the measure of the unknown angle?
Answer:
24
Step-by-step explanation:
x+120+36=180
x+156=180
x=180-156
x=24
i dont understand what im doing wrong
Answer:
8
Step-by-step explanation:
-2 x -2 = 4
4 - (-28 / 7 = -4)
4- -4 = 8
Find the value of x to the nearest tenth! HELP ME!!!!!!!!!!!!! (PICTURE IS BELOW)
Answer:
11.4
Step-by-step explanation:
By Pythagoras Theorem:
[tex]x^{2} = {7}^{2} + ( {4}^{2} + {8^{2}}) \\ \\ x^{2} = 49+(16 + 64)\\ \\ x^{2} = 49+80\\ \\ x^{2} = 129 \\ \\ x = \sqrt{129} \\ \\ x = 11.3578167 \\ \\ x = 11.4[/tex]
Jackie says that 200 ÷ 18 = 25. Is Jackie correct? Explain.
Answer:
Wrong
Step-by-step explanation:
200%18=11.11111111
Answer: Jackie is incorrect
Step-by-step explanation:
Because 200/18 = 11.1111111111
(02.01)Polygon ABCD slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees, what is the measure of angle A'?
A-75 degrees
B-100 degrees
C-105 degrees
D-180 degrees
Sonya paid $4.39 for a hero. She paid $0.95 for an orange and $1.67 for a drink. What is the total amount Sonya paid for all three items?
Is this sequence arithmetic? 6,11,16,21
Answer: Yes, it is.
Step-by-step explanation:
Sorry, I just know the answer because I just did this in school. Like- right now
(help?)
Look at the model.
Which of the following statements of equality is true? [png]
Answer:
H
Step-by-step explanation:
Answer:
H
Step-by-step explanation:
3 times 2 and x in each row
which equals to 6 and 3x
132 beads is split into 96 beads and 36 beads. in simplest form , what is the ratio of the split
Answer:
16:6
Step-by-step explanation:
96:36
Highest common factor is 6
divide both sides by 6
16:6
Suppose that in the production of 60-ohm radio resistors, nondefective items are those that have a resistance between 58 and 62 ohms and the probability of a resistor’s being defective is The resistors are sold in lots of 200, with the guarantee that all resistors are nondefective. What is the probability that a given lot will violate this guarantee? (Use the Poisson distribution.)
Answer:
The probability that a given lot will violate this guarantee is [tex]1 - e^{-200x}[/tex], in which x is the probability of a resistor being defective.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The probability of a resistor’s being defective is x:
This means that [tex]\mu = nx[/tex], in which n is the number of resistors.
The resistors are sold in lots of 200
This means that [tex]n = 200[/tex], so [tex]\mu = 200x[/tex]
What is the probability that a given lot will violate this guarantee?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = 0) = \frac{e^{-200x}*(200x)^{0}}{(0)!} = e^{-200x}[/tex]
So
[tex]P(X \geq 1) = 1 - e^{-200x}[/tex]
The probability that a given lot will violate this guarantee is [tex]1 - e^{-200x}[/tex], in which x is the probability of a resistor being defective.
In two or more complete senteces compare the number of x-intercepts in the graph of f(x)=x^2 to the number of x-intercepts in the graph of g(x)=x^2-7. Be sure to include the transformation that occured between the parent function f(x) and its image g(x)
Answer:
Step-by-step explanation:
f(x) = x² is an up-opening parabola with vertex (0,0). There is one x-intercept, and that is the vertex.
g(x) = x²-7 is the equivalent to f(x) shifted down 7 units. Since the vertex is below the x-axis and the parabola opens upwards, it intercepts the x-axis at two points.