Answer:
a) X={BBB;BBG:BGG:GGG}
b) P(BBB)=0.125
c) P(BBB)=0.133
Step-by-step explanation:
The sample space states all the possible values that the random variable can take. In this case, the order does not matter, so the possible combinations for the random variable are:
X={BBB;BBG:BGG:GGG}
The probability p of having a boy is p=0.5, as it is equally likely to have a girl or a boy.
The probability that all 3 children are boys can be calculated multiplying 3 times the probability of having a boy. That is:
[tex]P(X=BBB)=p\cdot p\cdot \cdot p =p^3=0.5^3=0.125[/tex]
In the case that the chance of having a boy is p'=0.51, the probabiltity of having 3 boys become:
[tex]P(X=BBB)=p'^3=0.51^3=0.133[/tex]
given that a triangle LMN has side inches of 18.5 inches, 10, inches, and 15.5 inches, prove triangle LMN is aright triangle.
Answer:
LMN is not a right triangle.
Step-by-step explanation:
To verify that the lengths of a triangle for a right triangle, all we need to do is to check it they satisfy the Pythagoras Theorem.
Pythagoras Theorem:[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
The Hypotenuse is always the longest side.
Since no angle is given, the two other sides can be alternated.
Given lengths of triangle LMN: 18.5 inches, 10, inches, and 15.5 inches
[tex]LHS=18.5^2=342.25\\RHS=10^2+15.5^2=100+240.25=340.25\\Since \: LHS\neq RHS,\\$The triangle is not a right triangle.[/tex]
Complete the table for the given rule. Rule: y=3x
x y
? 15
10 ?
? 45
Answer:
x = 5, 15 y = 30
Step-by-step explanation:
y=3x is the rule, thus you can use it to find all values.
15 = 3x Divide 15 by 3 in order to isolate the variable
5 = x
y = 3(10) Multiply 3 by 10 in order to find y
y = 30
45 = 3x Divide 45 by 3 in order to isolate the variable
15 = x
Which statements are true? Check all that apply.
The area of the base of the pyramid, B, is 64 in.2
The area of the base of the pyramid, B, is 48 in.2
A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume three times as large as this pyramid.
A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume one third the volume of this pyramid.
The volume of the pyramid is 384 in.3
Answer:
a and c
Step-by-step explanation:
The statements that are true are:
The area of the base of the pyramid, B, is 48 in.2
A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume three times as large as this pyramid.
The volume of the pyramid is 384 in.3
What is a pyramid?A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.
The volume of a pyramid with a square base is given as:
Volume = 1/3 x base area x height
We have,
The area of the base of the pyramid is given by B = (1/2)bh, where b is the length of the base and h is the height of the pyramid.
We are not given the height of the pyramid, so we cannot determine the area of the base.
Therefore, the statement "The area of the base of the pyramid, B, is 64 in.2" is not true.
The area of the base of the pyramid is given as 48 in.2 in the problem statement. Therefore, the statement "
The area of the base of the pyramid, B, is 48 in.2" is true.
The volume of a square prism with dimensions 8 inches by 8 inches by 6 inches is V = lwh = 8 x 8 x 6 = 384 in.3.
The volume of the pyramid is also given as 384 in.3 in the problem statement.
Therefore, the statement "A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume three times as large as this pyramid" is true.
The correct statement is "A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume one-third the volume of this pyramid."
This statement is not true, since the volume of the pyramid is 384 in.3 and one-third of that volume is 128 in.3, which is not the volume of the prism given in the problem. Therefore, the statement is false.
Thus,
The statements that are true are:
The area of the base of the pyramid, B, is 48 in.2
A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume three times as large as this pyramid.
The volume of the pyramid is 384 in.3
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According to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent in 2011. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of eight mortgages was selected. What is the probability that exactly one of these mortgages is delinquent?
Answer:
The probability that exactly one of these mortgages is delinquent is 0.357.
Step-by-step explanation:
We are given that according to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent in 2011. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure.
A random sample of eight mortgages was selected.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 8 mortgages
r = number of success = exactly one
p = probability of success which in our question is % of U.S.
mortgages those were delinquent in 2011, i.e; 8%
LET X = Number of U.S. mortgages those were delinquent in 2011
So, it means X ~ [tex]Binom(n=8, p=0.08)[/tex]
Now, Probability that exactly one of these mortgages is delinquent is given by = P(X = 1)
P(X = 1) = [tex]\binom{8}{1}\times 0.08^{1} \times (1-0.08)^{8-1}[/tex]
= [tex]8 \times 0.08 \times 0.92^{7}[/tex]
= 0.357
Hence, the probability that exactly one of these mortgages is delinquent is 0.357.
Eitan sells a mean of $8000 worth of merchandise with a standard deviation of $1500 each month.
Each month, Eitan earns a base salary of $2000 plus a commission of 30% of his sales. He calculates his total
salary according to this formula:
[total salary) = commission + base salary]
What will be the mean and standard deviation of the distribution of Eitan's total monthly salary?
Answer:
t = $4400 +/- $450
mean = $4400
standard deviation = $450
Step-by-step explanation:
Given;
Base salary b = $2000
Sales s = $8000 +/- $1500
Commission c = 30% sales = 0.3 × s
Total Salary t = base salary + commission = b + c
Commission c = 0.3×s = 0.3×($8000 +/-$1500)
c = $2400 +/- $450
Total salary t = b + c
Substituting the values;
t = $2000 + ($2400 +/- $450)
t = $4400 +/- $450
mean = $4400
standard deviation = $450
Help fast it’s geometry
Answer:
a-area-22
a-perimeter-19
b-area-98
b-perimeter-42
Step-by-step explanation:
for the sides just add the numbers 2x
for the area multiply the numbers
hope this helps
Which expressions are equivalent to the one below? Check all that apply. log 2-log 6 A.log(2)+log(1/6) B.log 2 C.log 3 D.log(1/3)
The equivalent expression to log(2) - log(6) is D. log(1/3), since subtraction in logarithms indicates division, making the expression log(2/6) which simplifies to log(1/3).
Explanation:The question asks which expressions are equivalent to log(2) - log(6). According to the properties of logarithms, the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers (log a - log b = log(a/b)). Therefore, log(2) - log(6) = log(2/6) = log(1/3).
Hence, the only equivalent expression from the given options is D. log(1/3). Option A is incorrect because log(2) + log(1/6) would imply multiplication, not division. Option B is just log(2) without subtraction. Option C, log(3), does not represent the given difference.
The number of miles y in a measure varies directly as the number of kilometers x. Write a direct variation equation that can be used to convert kilometers to miles, if 5 kilometers is about 3.1075 miles.
Answer:
[tex]y = 0.6215x[/tex]
Step-by-step explanation:
I am going to model an equation in the following format:
[tex]y = ax[/tex]
In which y is the number of miles, given the distance in kilometers x.
a is the slope, that is, how many miles each kilometer has.
5 kilometers is about 3.1075 miles.
So
5 km - 3.1075 miles
1 km - a miles
5a = 3.1075
a = 3.1075/5
a = 0.6215
So
[tex]y = 0.6215x[/tex]
In the number 4,444.444, how does the 4 in the hundreds place compare to the 4 in the place to its left?
Answer:
The four in the hundreds place on the right is bigger because it is a whole number and the 4 behind the decimal on the left is smaller because it is a decimal.
Step-by-step explanation:
1. Prove that quadrilateral DOGS is
a parallelogram. The coordinates
of DOGS are D(1, 1), (2, 4),
G(5, 6), and S(4,3).
-108
-6
-4
4
6
8
10
S doo
Page
1
1
2
-
+
Answer:
DOGS is a parallelogram.
Step-by-step explanation:
Given the quadrilateral DOGS with coordinates D(1, 1), O(2, 4), G(5, 6), and S(4,3).
To prove that it is a parallelogram, we need to show that the opposite lengths are equal. That is:
|DO|=|GS||OG|=|SD|Using the Distance Formula
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For D(1, 1) and O(2, 4)
[tex]|DO|=\sqrt{(2-1)^2+(4-1)^2}=\sqrt{1^2+3^2}=\sqrt{10} \:Units[/tex]
For G(5, 6), and S(4,3).
[tex]|GS|=\sqrt{(4-5)^2+(3-6)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{10}\:Units[/tex]
For O(2, 4) and G(5, 6)
[tex]|OG|=\sqrt{(5-2)^2+(6-4)^2}=\sqrt{(3)^2+(2)^2}=\sqrt{13}\:Units[/tex]
For S(4,3) and D(1, 1)
[tex]|SD|=\sqrt{(1-4)^2+(1-3)^2}=\sqrt{(-3)^2+(-2)^2}=\sqrt{13}\:Units[/tex]
Since:
|DO|=|GS||OG|=|SD|Then, quadrilateral DOGS is a parallelogram.
What is the volume of this rectangular prism? The length is 5 1/2. The width is 1 3/8. The height is 1 2/3.
Answer:
12 29 /48 in mixed number form,
≈ 12.6 as a rounded decimal
Step-by-step explanation:
Multiply all three numbers together for the volume.
mariam measured the distance for 8 wavelengths of visible light as 5,600 nanometers. what is the distance for 1 wavelength
Answer:
700 nanometers
Step-by-step explanation:
8 wavelengths had a combined length of 5,600 nanometers.
We want to find the wavelength (in nm) of 1 of those wavelengths.
We will assume all of them are same wavelength. So, we can basically divide the total of 8 wavelengths by 8 to get 1 wavelength. Thus:
5600/8 = 700
Hence,
1 wavelength distance is 700 nanometers (or 700 nm)
A jar contains 6 marbles numbered 1 through 6. An experiment consists of randomly selecting a marble from the jar, observing the number drawn, and then randomly selecting a card from a standard deck and observing the suit of the card (hearts, diamonds, clubs, or spades).
How many outcomes are in the sample space for this experiment?
Answer:
24 Outcomes
Step-by-step explanation:
The sample space of an event is the set of all possible outcomes.
A jar contains 6 marbles numbered 1 through 6
Sample Space of Selecting a Marble from the Jar =6
A standard deck contains 4 Suits
Sample Space of Selecting a Card and Observing the Suit = 4
Theorem(The Fundamental Counting Principle)
If there are “x” ways for one event to happen, and “y” ways for a second event to happen, then there are “x * y” ways for both events to happen.
Therefore the Sample Space of randomly selecting a marble from the jar, observing the number drawn, and then randomly selecting a card from a standard deck and observing the suit of the card is given as:
Sample Space of Selecting a Marble X Sample Space of Selecting a Card and observing the Suits
= 6 X 4
=24
There are 24 Outcomes in this experiment.
In one region of the Caribbean Sea, daily water temperatures are normally distributed with a mean of 77.9 degrees Fahrenheit and a standard deviation of 2.4 degrees Fahrenheit. What temperature separates the lowest 59.5% of temperatures from the rest?
Answer:
The temperature that separates the lowest 59.5% of temperatures from the rest is 83.66 degrees Fahrenheit.
Step-by-step explanation:
Mean temperature = u = 77.9
Standard Deviation = [tex]\sigma[/tex] = 2.4
Since the distribution is normal and we have the value of population standard deviation, we will use the concept of z-score to find the desired value.
We have to find the value that separates lowest 59.5% of the temperature from the rest. This means our desired value is above 59.5% of the data values.
From the z-table we can find a z-score which is above 59.5% of the values and then convert it to its equivalent temperature using the formula.
From the z-table, the z-score which is above 59.5% of the value is:
z = 0.24
The formula for z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the values we have:
[tex]0.24=\frac{x-77.9}{2.4}\\\\ 5.76=x-77.9\\\\ x=83.66[/tex]
This is our data value equivalent to a z-score of 0.24. Just like 59.5% of z values were below 0.24, in the same manner, 59.5% of temperatures are below 83.66 degrees Fahrenheit.
Therefore, the temperature that separates the lowest 59.5% of temperatures from the rest is 83.66 degrees Fahrenheit.
Which question is a statistical question?
A. How many theaters are there in my city
B. How many students in my class like classical movies
C. How many movies do the students in my class watch in a month
D. How many students in my class watch movies on weekdays
Answer:
C. How many movies do the students in my class watch in a month
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Using polynomial regression fit a cubic equation to the following data: x 3 4 5 7 8 9 11 12 y 1.6 3.6 4.4 3.4 2.2 2.8 3.8 4.6 Plot the data and the cubic equation. Along with the coefficients, determine r2 and sy/x.
Final answer:
Fitting a polynomial regression model involves determining coefficients that minimize the sum of squared differences between observed and predicted values. After plotting the data, the cubic model is fitted using statistical software. The coefficients, r-squared, and standard error of the estimate are then calculated to assess the model's accuracy.
Explanation:
The process of fitting a polynomial regression model involves finding the coefficients that minimize the sum of the squares of the differences between the observed values and the values predicted by the model. For a cubic equation, we will be fitting a model in the form y = a + bx + cx2 + dx3, where a, b, c, and d are the coefficients that need to be determined from the data.
To fit a cubic equation to the data and assess the goodness-of-fit, we usually perform the following steps:
Scatter plot: Draw a scatter plot of the given data points to visualize the trend and the relationship between x and y.Polynomial regression: Use a statistical software or a calculator with polynomial regression capability to fit the cubic model to the data.Plot the cubic equation: Alongside the scatter plot, plot the regression curve represented by the cubic equation.Calculate the coefficients and r-squared (r2): Obtain the values of the coefficients and the coefficient of determination, which shows the proportion of the variance in the dependent variable explained by the regression model.Calculate standard error of the estimate (sy/x): Compute the standard error to get an idea of the typical distance between the actual data points and the estimated regression curve.The calculation of r2 (r-squared) is important because it tells us the strength of the relationship between the independent and dependent variables. An r2 value of 0.72, for instance, would indicate that 72% of the variability in the dependent variable can be explained by the model. The r2 value cannot be negative because it represents the proportion of variance explained, which is inherently non-negative.
Coefficient of determination is the square of the correlation coefficient (r), and since the correlation coefficient ranges between -1 and +1, its square will always be non-negative as well.
Whats the answer of (X+9)^2=25?
Answer:
x=-4,x= -14
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x2+18x+81=25
Step 2: Subtract 25 from both sides.
x2+18x+81−25=25−25
x2+18x+56=0
Step 3: Factor left side of equation.
(x+4)(x+14)=0
Step 4: Set factors equal to 0.
x+4=0 or x+14=0
x=−4 or x=−14
========================================================
Explanation:
Apply the square root to both sides
(x+9)^2 = 25 leads to x+9 = 5 or x+9 = -5
This is because (-5)^2 = 25 and (5)^2 = 25. This is the plus/minus you often see with quadratics.
Solve x+9 = 5 to get x = -4. We subtract 9 from both sides to get this.
Solve x+9 = -5 to get x = -14
That's why the two answers are x = -4 and x = -14.
------
To check our answers, we plug those x values into the original equation and simplify. We should get the same thing on both sides
(x+9)^2 = 25
(-4+9)^2 = 25 ... replace x with -4
(5)^2 = 25
25 = 25 ... So x = -4 has been confirmed
and,
(x+9)^2 = 25
(-14+9)^2 = 25 ... replace x with -14
(-5)^2 = 25
25 = 25 ... and x = -14 has been confirmed
What is 5 4/9 take away 1 7/9
Answer:
4 13/9 - 1 7/9
3 6/9
3 2/3
Step-by-step explanation:
The answer would be 3.6 because I simplified my answer into decimal. Hope this helps! If you have any other questions, please ask me. Stay safe! And have a good day!
A cat weighs 8 1/4 pounds.
How many ounces does the cat weigh?
a 33 oz
b 66 oz
c 132 oz
d 264 oz
The correct answer is c. 132 oz. To convert the cat's weight of 8 1÷4 pounds to ounces, multiply by 16.
Converting Pounds to Ounces
The cat weighs 8 1/4 pounds. To find out how many ounces this is, we need to convert pounds to ounces. We know from the conversion rate that 1 pound equals 16 ounces.
Step-by-Step Calculation
First, convert the mixed number 8 1÷4 to an improper fraction: 8× 1÷4 = 33÷4.Then, convert this fraction to pounds: 33÷4 pounds.Now, convert pounds to ounces by multiplying by 16 (since there are 16 ounces in a pound): 33÷4 × 16 = 33 × 4 = 132 ounces.Thus, the cat weighs 132 ounces, so the correct answer is c. 132 oz.
Earlier, we considered data from the GSS on numbers of close friends people reported having. The mean for this variable is 7.44, with a standard deviation of 10.98. Let's say that you decide to use the GSS data to test whether people who live in rural areas have a different mean number of friends than does the overall GSS sample. Again, treat the overall GSS sample as the entire population of interest. Let's say that you select 40 people living in rural areas and find that they have an average of 3.9 friends. What is the z statistic for this sample
Answer:
The z statistic for this sample is -2.04.
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 7.44[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 7.44[/tex]
The z-statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the population mean(the hypothesis tested), [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
In this problem:
[tex]X = 3.9, \mu = 7.44, \sigma = 10.98, n = 40[/tex]. So
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.9 - 7.44}{\frac{10.98}{\sqrt{40}}}[/tex]
[tex]z = -2.04[/tex]
The z statistic for this sample is -2.04.
Find the sum of the first 10 terms.
8,20,32,44...
Answer:
8,20,32,44,56,68,80,92,104,116,128
Step-by-step explanation
Just keep adding 12
Answer: 620
Step-by-step explanation:
This is a progression but we need to find out whether it is Arithmetic Progression or an exponential or geometric progression.
From the quest, 8, 20, 32, 44, this is not an exponential function but an arithmetic progression because, when you subtract the first time from the second term , the common difference is 12.
20 - 8 = 12, so this is an arithmetic progression as said earlier. Now to find the sum of the first ten terms of the series, we apply the formula which is
S10 = n/2{(2a + ( n - 1 )d}, where n = 10, and a = 8 the first term and d the common difference = 12.. Now substitute for the values
S10 = 10/2{(2 x 8 + ( 10 - 1 )12}
= 5( 16 + 9 x 12)
= 5( 16 + 108 )
= 5( 124 )
= 620.
Therefore, the sum of the 10 terms of the series is 620.
But we can also solve it using other means . To solve this we first find the last term which is the 10th term using this formula
T10 = a + ( n - 1 )d
= 8 + (10 -1)12
= 8 + 9 x 12
= 8 + 108
= 116.
Now with this we could put this in the equation below.
S10 = n/2( a + L ) where L is the last term calculated above. Now we substitute to get the sum.
S10 = 10/2( 8 + 116)
= 5( 8 + 116 )
= 5( 124)
= 620.
I could have explained how we arrived at the formula above but the time could not permit, I will discuss that in the next lecture if I come across such question.
Two cars start moving from the same point. One travels south at 60miles/hour and the other travels west at 25 miles/hour. At what rate is the distance between the cars increasing two hours later
Answer:
The distance between the cars is increasing at a rate of 65miles/hour
Step-by-step explanation: Please see the attachments below
The exercise involving data in this and subsequent sections were designed to be solved using Excel.
The following estimated regression equation was developed for a model involving two independent variables.
y=40.7+ 8.63x1+ 2.71x2
After x2 was dropped from the model, the least-squares method was used to obtain an estimated regression equation involving only x1 as an independent variable. y=42.0+9.01x1
a. In the two independent variable cases, the coefficient x1 represents the expected change in (Select your answer: y, x1, x2) corresponding to a one-unit increase in (Select your answer: y, x1, x2) when (Select your answer: y, x1, x2) is held constant.
In the single independent variable case, the coefficient x1 represents the expected change in (Select your answer: y, x1, x2) corresponding to a one-unit increase in (Select your answer: y, x1, x2).
b. Could multicollinearity explain why the coefficient of x1 differs in the two models? Assume that x1 and x2 are correlated.
Answer:
Step-by-step explanation:
Hello!
You have two regression models:
The multiple regression model that was estimated is y=40.7+ 8.63x1+ 2.71x2
The Simple regression model that was estimated is y=42.0+9.01x1
a.
MRmodel the 8.63 represents the modification in the estimated mean of Y when X₁ increases one unit and X₂ remains constant.
SRmodel the 9.01 represents the modification in the estimated average of Y when X₁ increases one unit.
b.
Yes, since both variables X₁ and X₂ are correlated, the effect that X₁ has over Y is directly affected by the precence of X₂
I hope you have a nice day!
Lo que tú y yo ganamos suman $400. Si tu ganaras $80 más y yo $80
menos, tendríamos la misma cantidad de dinero. ¿Cuánto tenemos cada
uno?
Answer:
$280 y $120
Step-by-step explanation:
Primero haces una ecuación. Entonces puedes adivinar y verificar o usar la ecuación. Solía adivinar y comprobar.
¡Espero que esto haya ayudado!
Morgan throws a ball up into the air. The height of the ball above the ground, in feet, is modeled by the function h(t)=-16t+24t, where t represents the time, in seconds, since the ball was thrown. What is the appropriate domain for this situation?
The appropriate domain for this situation is all non-negative real numbers or the interval [0, ∞).
Explanation:The appropriate domain for this situation can be determined by considering the values that the independent variable, t, can take in the given function. In this case, the function is h(t) = -16t^2 + 24t, where t represents the time since the ball was thrown.
Since time cannot be negative in this context, the domain of the function is t ≥ 0. This means that the appropriate domain for this situation is all non-negative real numbers or the interval [0, ∞).
A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1000 bacteria present after 20 minutes. Write the exponential equation representing this scenario modeled as a continuous growth model.
The exponential equation that represents the growth of the bacteria over time, considering the given initial and future population sizes and the time that has passed, is P(t) = 360 × e^[(ln(1000/360)/15)t]. This formula adjusts the rate of growth to match the change from 360 bacteria to 1000 bacteria over a 15-minute period.
Explanation:In this situation, we are dealing with a phenomenon commonly seen in biology called exponential growth which can be modeled mathematically. For this case, we can use the exponential growth formula, P(t) = P_0 × e^(rt), where P(t) is the future population size, P_0 is the initial population size, r is the growth rate, and t is the time that has passed.
Firstly, we know the initial population size (P_0) is 360 bacteria. The population size after 15 minutes (from 5 minutes to 20 minutes is 15 minutes) is 1000 bacteria. Therefore, if we plug in these values, we have 1000 = 360 × e^(15r).
To solve for r, we start by dividing both sides by 360 which results in 1000/360 = e^(15r). Taking the natural logarithm (ln) of both sides to isolate the exponential part, we get ln(1000/360) = 15r. Finally, divide by 15 yielding r = ln(1000/360)/15.
Therefore, the exponential equation representing this scenario is P(t) = 360 × e^[(ln(1000/360)/15)t], showing the population P(t) of the bacteria at any time t.
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An open box is made from a 30-cm by 70-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 1536 cm2. What is the length of the sides of the squares?
To find the length of the sides of squares cut from a piece of tin to create an open box, we use the dimensions of the tin and the area of the box's base to set up and solve a quadratic equation.
Explanation:The student is asking for the length of the sides of the squares that are cut out from a piece of tin to create an open box. Given that the tin measures 30 cm by 70 cm, and the area of the base of the resulting box is 1536 cm2, we can set up an equation to solve for the side length of the squares.
Let's denote the side length of the squares as x. After the squares are cut out, the length and width of the base of the box will be (70 - 2x) and (30 - 2x) respectively. The area of the base is given by:
Area = length × width
1536 cm2 = (70 - 2x)(30 - 2x)
By expanding this and solving the quadratic equation for x, we can find the length of the sides of the squares cut from each corner of the tin.
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Jose rides his bicycle for 5 minutes to travel 8 blocks .He rides for 10 minutes to travel 16 blocks
Answer:
Step-by-step explanation:
A: 8
B: 15
C: 40
(A) The rides in 5 minutes are 8, (B) the time to cover 24 blocks is 15 minutes, and (C) in 25 minutes Jose rides 40 blocks.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Jose rides his bicycle for 5 minutes to travel 8 blocks
Speed = distance cover / time taken
Speed = 8/5
Now, at the same speed
A) Distance covered in 5 minutes
8/5 = Distance/5 ⇒ Distance = 8 blocks.
B) Time taken in 24 blocks
8/5 = 24/Time ⇒ Time = 15 minutes.
C) Distance covered in 25 minutes
8/5 = Distance/25 ⇒ Distance = 40 blocks.
Hence "The rides in 5 minutes are 8, the time to cover 24 blocks is 15 minutes and in 25 minutes Jose rides 40 blocks".
Options are missing in the given question
Correct options are in the table and ask the same question as answered.
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The area of a figure is 13 square inches. If all the dimensions of the figure are multiplied by 4, the area of the figure will be multiplied by _____. 2 4 8 16
Answer:
option D.
Step-by-step explanation:
Given,
Area of a figure = 13 in²
All dimension is multiplied by 4.
Area of the figure will be multiplied by = ?
We know that,
[tex]Area\ \alpha \ (Length)^2[/tex]
If length is multiplied by 4.
[tex]Area\ \alpha \ 4^2 (L)^2[/tex]
Where L is the dimension of the figure.
[tex]Area\ \alpha \ 16 (L)^2[/tex]
Area of the figure will be multiplied by 16.
Hence, correct answer is option D.
Suppose that the random variable X represents the amount of electrical energy used (in kwH) in a month for residents in Virginia. The historical amount of electrical energy used in a month for residents is 102 kwH. The following data (in kwH per month) were recorded from a random sample of 8 residents: 111 113 145 105 90 100 150 88(a) Calculate the mean and sample variance of X. (b) What is t statistic with this problem?
Answer:
a)[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]\bar X = 112.75[/tex]
[tex]s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
[tex] s^2 = 540.5[/tex]
b) [tex] t = \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}[/tex]
And if we replace we got:
[tex] t = \frac{112.75-112}{\frac{23.249}{\sqrt{8}}}= 0.0912[/tex]
Step-by-step explanation:
Part a
For this case we have the following data: 111 113 145 105 90 100 150 88
We can calculate the mean with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X = 112.75[/tex]
And the sample variance can be calculated with this formula:
[tex]s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
And replacing we got:
[tex] s^2 = 540.5[/tex]
Part b
For this case we want to check is the true mean is equal to 102 or no, the t statistic is given by:
[tex] t = \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}[/tex]
And if we replace we got:
[tex] t = \frac{112.75-112}{\frac{23.249}{\sqrt{8}}}= 0.0912[/tex]
To answer the student's question, the sample mean of electrical energy usage is calculated to be 112.75 kwH. The sample variance requires computing the squared differences of each data point from the mean, summing them up and dividing by n-1. The t-statistic can then be calculated using the historical mean, the sample mean, and the sample standard deviation.
Explanation:To calculate the mean of the sample data, we sum all the sample values and divide by the number of observations. The sample data for electrical energy usage in kwH per month are: 111, 113, 145, 105, 90, 100, 150, and 88. The sum of these values is 902 kwH, and with 8 residents in the sample, the mean (μ) is 902 kwH / 8 = 112.75 kwH.
The sample variance (s²) is calculated by taking the sum of squared differences from the mean and dividing by the sample size minus one. First, we find the squared differences for each data point: (111-112.75)², (113-112.75)², (145-112.75)², (105-112.75)², (90-112.75)², (100-112.75)², (150-112.75)², and (88-112.75)², which then summed up give us the total sum of squares. Dividing this total by 7 (n-1), we obtain the sample variance.
For the t statistic, we would need the hypothesized population mean to compare our sample mean against. However, we can calculate the t-value if we assume the historical mean provided (102 kwH) is the population mean we are testing against. The t-statistic is calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(n)). In this scenario, n=8 and we would need the sample standard deviation, which is the square root of the variance we calculated earlier. Once these values are obtained, the t-statistic can be computed.