The unit rate that relates the two quantities of distance and volume of gas is:
U = 30 miles per gallon.
How to describe this relation?To do so, we can find the unit rate.
This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.
Here we have the values:
10 gallons and 300 miles.
Then the unit rate is the quotient between these:
300miles/10 gallons = 30 miles per gallon
This says that with one gallon of gas you can travel 30 miles.
Learn more about the unit rate:
https://brainly.com/question/19493296
#SPJ1
Consider the graph of function f below. A diagonal curve declines through (negative 6, 7), (negative 5, 5), (negative 4, 3), (negative 3, 1), (3, negative 1, negative 3), (0, negative 5) and (1, negative 7) on the x y coordinate plane. The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g? A. g(x) = f(x) - 1 B. g(x) = f(x + 4) C. g(x) = f(x - 1) D. g(x) = f(x) + 4
The function g(x) is defined as follows:
D. g(x) = f(x) + 4.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The y-intercept for each function is given as follows:
f(x): y = -5.g(x): y = -1.Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:
g(x) = f(x) + 4.
More can be learned about translations at brainly.com/question/28174785
#SPJ1
Answer: D
Step-by-step explanation:
The function g(x) is defined as follows:
D. g(x) = f(x) + 4.
What is a translation?
A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).
Translation right a units: f(x - a).
Translation up a units: f(x) + a.
Translation down a units: f(x) - a.
The y-intercept for each function is given as follows:
f(x): y = -5.
g(x): y = -1.
Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:
g(x) = f(x) + 4.
Malden go company has a balance and its accounts payable control count of $10,500 on January 1, 2021. The subsidiary ledger contains three accounts Smith Company balance of $3000 white company balance of tMalden go company has a balance and it’s accounts payable control count of $10,500 on January 1, 2021. The subsidiary ledger contains three accounts Smith Company balance of $3000 white company balance of $2500 and Marina company during the January the following payable related transactions occurred
Answer:
6
Step-by-step explanation:
bc
which graph represents the linear equation y = 1/4 x + 1 on the coordinate plane
the line is passing through -2 for y and 4 for x
the line is passing through 2 for y and -4 for x
the line is passing through 1 for y and -5 for x
the line is passing through 1 for y and -4 for x
Answer:
the line is passing through 1 for y and -4 for x
Step-by-step explanation:
The function y = 1/4 + 1 contains all the information you need. The + 1 indicates the y intercept, so it is given. Since the slope of the line is 1/4, the graph would pass through (-4, 0) and (0, 1) as starting from a point would go up one unit and right 4 units.
Pam is visiting a historic town with an old-fashioned water well in the town square. She drops
a pebble into the well from a height of 27 feet above the surface of the water.
To the nearest tenth of a second, how long does it take for the pebble to hit the water?
Hint: Use the formula h = -16t² + 5.
seconds
The time taken for the pebble to hit the water is 1.41 seconds.
What is the time taken for the pebble to hit the water?The time taken for the pebble to hit the water is calculated by using the equation of the motion as follows;
h = -16t² + 5
where;
h is the height of fall during the motiont is the time of motionwhen the height is 27 ft, the time of motion is calculated as;
-27 = -16t² + 5
16t² = 5 + 27
16t² = 32
t² = 32/16
t² = 2
t = √2
t = 1.41 seconds
Thus, the time of motion is determined by applying the equation of motion as shown above.
Learn more about time of motion here: https://brainly.com/question/24739297
#SPJ1
Principle amount is 22,000. Interest rate is 4.5%.
1. Determine interest earned each year.
2. Write a recurrence relation to model the value of investment from year to year. Let Sn be the value after n years.
3. Determine value of interest after 5 years.
Answer:
1. $990
2. Sn = Sn-1 + (r/100) * Sn-1
3. $27,037.44
Step-by-step explanation:
1. The interest earned each year can be calculated using the simple interest formula:
Simple Interest = (Principal * Rate * Time) / 100
Here, Principal = $22,000, Rate = 4.5%, and Time = 1 year
So, the interest earned each year would be:
= (22,000 * 4.5 * 1) / 100
= $990
Therefore, the interest earned each year would be $990.
2. The recurrence relation to model the value of investment from year to year is:
Sn = Sn-1 + (r/100) * Sn-1
where Sn represents the value of the investment after n years, Sn-1 represents the value after n-1 years, and r represents the annual interest rate.
Using this recurrence relation, we can calculate the value of the investment for different years:
- S1 = 22,000 + 990 = 22,990
- S2 = 22,990 + (4.5/100) * 22,990 = 24,026.55
- S3 = 24,026.55 + (4.5/100) * 24,026.55 = 25,103.46
And so on...
3. To determine the value of the investment after 5 years, we can simply substitute n = 5 in the recurrence relation:
S5 = S4 + (r/100) * S4
= S3 + (r/100) * S3 + (r/100) * S3
= S2 + (r/100) * S2 + (r/100) * S2 + (r/100) * S2
= S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1
Substituting values from previous calculations:
S1 = 22,000 + 990 = 22,990
So,
S5 = 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990
= $27,037.44
Therefore, the value of the investment after 5 years would be $27,037.44.
find the margin of error given the values of C, stigma, and n.
c= 0.95, stigma=3.4, n=100
E=?
The margin of error is E = 0.67.
To find the margin of error
We can use the formula:
E = z* (σ / sqrt(n))
Where
E is the margin of errorz* is the z-score corresponding to the desired level of confidence Cσ is the population standard deviation (also known as the population parameter) n is the sample sizeIn this case, we are given that C = 0.95, σ = 3.4, and n = 100. We can use a standard normal distribution table to find the z-score that corresponds to a 95% confidence level, which is approximately 1.96.
Substituting the values:
E = 1.96 * (3.4 / sqrt(100))
E = 1.96 * 0.34
E = 0.6664
Rounding to two decimal places, the margin of error is approximately 0.67.
Therefore, the margin of error is E = 0.67.
Learn more about margin of error here : brainly.com/question/24289590
#SPJ1
the price of a shirt was $25, but it is now on sale for $20. what is the percent decrease in price?
ACTIVITY 1: Determine whether each of the following is a proposition or mere sentence. It is a
Proposition if the given is either true or false and Mere Sentence if the given can be both true and
false at the same time.
Answer:
number 1111q
Step-by-step explanation:
the answer is 1
The trajectory of a golf ball hit from a tee on the ground at an angle of 40 degrees with an initial speed of 50 meters per second can be modeled by the parabola f(x) = 0.84x − 0.0033x^2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground.
Therefore, the horizontal distance the golf ball travels before hitting the ground is approximately 254.55 meters.
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.
Here,
The equation of the parabolic trajectory of the golf ball is given by:
f(x) = 0.84x - 0.0033x²
where x is the horizontal distance travelled by the ball and f(x) is the corresponding height at that distance. To find the highest point of the trajectory, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:
x = -b / 2a
where a and b are the coefficients of the quadratic term and the linear term in the equation of the parabola, respectively. In this case, we have:
a = -0.0033 and b = 0.84
Substituting these values into the formula, we get:
x = -0.84 / 2(-0.0033)
= 127.27
So the horizontal distance at the highest point of the trajectory is approximately 127.27 meters. To find the height of the highest point, we substitute this value of x into the equation of the parabola:
f(127.27) = 0.84(127.27) - 0.0033(127.27)²
f(127.27) ≈ 21.67
So the highest point of the trajectory is approximately 21.67 meters above the ground.
To find the horizontal distance the golf ball travels before hitting the ground, we need to find the two values of x where the height of the ball is zero (i.e., where the ball hits the ground). We can set f(x) = 0 and solve for x:
0 = 0.84x - 0.0033x²
0.0033x² = 0.84x
x = 0 or x = 254.55
So the golf ball hits the ground twice, once at x = 0 (i.e., where it was hit from the tee) and once at x ≈ 254.55 meters.
To know more about equation,
https://brainly.com/question/28243079
#SPJ1
I will give 30 points to whoever answers
|x +3| if x >5
|x +3| if x >2
|x +3| if x =2
|x − 3| if x >5
|120+x| if x < −120
|x − 120| if x < −120
|x − (−12)| if x > −12
|x − (−12)| if x < −12
|x − (−12)| if x = −12
|x ÷ 3| if x >0
|x ÷ 3| if x <0
|x ÷ 3| if x =0
These are absolute value expressions evaluated under different conditions:
How to solve|x + 3| if x > 5:
Here x is greater than 5, so x + 3 will also be positive. In this case, |x + 3| = x + 3.
|x + 3| if x > 2:
Similar to the above, x is greater than 2, so x + 3 will be positive. Thus, |x + 3| = x + 3.
|x + 3| if x = 2:
In this case, x + 3 = 2 + 3 = 5, and the absolute value of 5 is just 5. Thus, |x + 3| = 5.
|x - 3| if x > 5:
If x is greater than 5, then x - 3 will be positive. Hence, |x - 3| = x - 3.
|120 + x| if x < -120:
Since x is less than -120, 120 + x will be negative. But the absolute value of a negative number is its positive counterpart, so |120 + x| = -(120 + x).
Read more about absolute value expressions here:
https://brainly.com/question/28644610
#SPJ1
what is y= -2/9x +2 in standard form?
Answer:
2x+9y=18
Step-by-step explanation:
Write a form of 1 that you can use to rationalize the denominator of the expression.
A form of 1 that you can use to rationalize the denominator of the expression 8/(∛4), the rationalizing factor is 9.
Describe Rationalization?In mathematics, rationalization refers to the process of eliminating radical or irrational expressions from the denominator of a fraction. This is done by multiplying both the numerator and the denominator of the fraction by a suitable expression that will result in a rational denominator.
The resulting fraction has a rational denominator, which makes it easier to work with and manipulate algebraically. Rationalization is a useful technique in algebra, trigonometry, and calculus, and is often used to simplify expressions and solve equations.
To rationalize the denominator of the expression 8/(∛4), we need to multiply the numerator and the denominator by a rationalizing factor that will eliminate the radical in the denominator.
Since the root 4 is equal to 2, we can rewrite the expression as:
8/3²
The square of 3 is 9, so we can use 9 as the rationalizing factor.
Multiplying the numerator and denominator by 9, we get:
(8/3²) x (9/9) = 72/9
Simplifying, we get:
72/9 = 8
Therefore, the rationalizing factor is 9.
To know more about factor visit:
https://brainly.com/question/21649943
#SPJ1
pleaseeeee i need helppp in this
The resulting matrix formed by performing R2 -> 4R1 + R2 on M is given as follows:
[tex]M = \left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]M = \left[\begin{array}{ccc}-4&3&1\\-2&-3&r\end{array}\right][/tex]
The rows of the matrix are given as follows:
R1: -4, 3 and 1.R2: -2, -3 and 4.Hence the row 2 of the resulting matrix has the elements given as follows:
Column 1: 4 x -4 - 2 = -18.Column 2: 4 x 3 - 3 = 9.Column 3: 4 x 1 + 4 = 8.More can be learned about operations with matrices at brainly.com/question/16901354
#SPJ1
Hi can someone please help me? Look in the picture. I’ll give brainly if you explain :)
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
Step-by-step explanation:
C (Wait for another defendant, check with him and write this answer)
The Frequency table shows The time it look students in PE class to run in 1 mile
3.) The quantity of students that are in the P.E class would be = 31 students.
4.) The number of students that ran 1 mile in under 9 minutes would be = 6 students.
How to determine the quantity of students from the frequency table?For question 3.)
To calculate the quantity of students, all the values in the frequency column is added together. That is;
Total number of students= 6+2+8+6+9 = 31 students.
For question 4.)
To calculate the number of students that ran 1 mile in less than 9 minutes would be the time range of 8.00-8.59 minutes = 6 students.
Learn more about frequency table here:
https://brainly.com/question/29213586
#SPJ1
Find the circumference and area of the circle.
Answer:
9.38
Step-by-step explanation:
I did the math
The length of circumference of this circle is 21.9911 inches.
The area of this circle is, approximately, 38.4845 (in²).
Step-by-step explanation:For the circumference.1. Formula.The circumference of the circle can be easily found by utilizing the "π" (pi) number.This number is one of the most recognizible and emblematic numbers in math because it's the value of the ratio between any circle's length of circumference to it's diameter. Therefore, another way to express π is:
[tex]\sf \pi =\dfrac{s}{d}[/tex], where "s" is the length of the circumference of a circle, and "d" is the diameter of that same circle.
The value of π is not a variable, it is a constant for all circles, and it's, approximately, 3.141592653589793238... But don't worry, majority of calculator, if not all of them, have a button with the π so you can just click on it and have that value written automatically.
Fun fact: This number doesn't really have an end for its decimal figures because it's irrational.
2. Rewrite the formula.So now, taking the equation of π presented previously, we can rewrite the equation by solving it for "s", which is our variable of interest for this first parth. This is the process of that rewritting:
[tex]\sf \pi(d) =\dfrac{s}{d}(d)\\ \\\\\pi(d) =s\\ \\ \\s=\pi(d)[/tex]
3. Calculate.We're given the diameter of this circle, which is 7 inches. Now, substitute letter "d" on the formula by "7 inches" and calculate:
[tex]\sf s=\pi(7(in))=\boxed{\sf 21.9911(in)}.[/tex].
Remember that π is an irrational number, so any calculation involving it will result in an irrational answer aswell, unless the π is cancelled by another π.
The length of circumference of this circle is 21.9911 inches.
-------------------------------------------------------------------------------------------------------
For the area.1. Formula.These are the most commonly used formulas for the area of circles:
[tex]\sf1) A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
[tex]\sf2) A=\dfrac{\pi d^{2}}{4}[/tex]; where "d" si the diameter of the circle.
Remember that the difference between the radius and diameter is just that the radius is half of the diamaterer. So, technically, everytime you have either the diameter of the radius, you can get both of the parameters.
2. Calculate.Let's use the area formula that directly involves diameter to avoid any conversions.
Substitute letter "d" by the length of the diameter (7 inches).
[tex]\sf A=\dfrac{\pi d^{2}}{4}=\dfrac{\pi (7(in))^{2}}{4}=\pi \dfrac{49}{4} (in^{2} )=\boxed{\sf 38.4845(in^{2} )}.[/tex]
Therefore, the area of this circle is, approximately, 38.4845 (in²).
-------------------------------------------------------------------------------------------------------
Learn more about calculating the area and parameters of different shapes here:https://brainly.com/question/31651027
https://brainly.com/question/31638424
https://brainly.com/question/31637968
-2(-2/3) x 3/5
Write in simplest form .
Answer:
4/5
Step-by-step explanation:
S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B = the number is Between 12 and 25
O = number is Odd
L = number is a Less than 25
Which events are independent.
After considering all the given options we conclude that the number is atleast 21 and the less than 25, which is Option C.
It is given to us that two events are independent if they take place then one event does not trigger the probability of the other event.
Now if the taking place of a certain event triggers the other event then it is referred as dependent
For the given case, we have four events A, B, Q and L.
A = the state when the given number is At least 21
B = is the sate when the given number is Between 12 and 25
Q = is the sate when the given number is Odd
L = is the state when the given number is a Less than 25
It is clearly visible that events A and L are independent due to the number being at least 21, it doesn't affect whether it's less than 25 or not. So, events B and Q are independent because if we know that a number is between 12 and 25, it doesn't affect whether it's odd or not.
Hence, option C) A and L is correct.
To learn more about probability
https://brainly.com/question/13604758
#SPJ1
The complete question is
S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B= the number is Between 12 and 25
Q = number is Odd
L= number is a Less than 25
Which events are independent.
Question options:
A) A and B
B) A and O
C) A and L
D) Band O
E) Land B
F) Land O
G) None of the 2 events are independent
Find the missing side lengths. Leave your answers as radicals in simplest form.
The value of m and n are 2√3 and 4√3/3 respectively.
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
There are special angles in trigonometry, examples are; 60° , 30° and 90°. This angles have exact values and can be calculated without using calculator.
Tan 60 = n/2
√3 = n/2
n = 2√3
cos 60 = 2/m
√3/2 = 2/m
m√3 = 4
m = 4/√3
= 4√3/3
Therefore the value of m and n are 2√3 and 4√3/3 respectively.
learn more about trigonometric ratio from
https://brainly.com/question/24349828
#SPJ1
The components of v = 210i + 300i represent the respective number of gallons of regular and premium gas sold at a station. The components of w = 2.8i + 2.99i represent the respective prices per gallon for each kind of gas. Find Vw and describe what the answer means in practical terms.
The station earned $1485 in revenue from selling the gas.
In this problem, we are given two vectors, v and w, representing the number of gallons of gas sold at a station and the corresponding prices per gallon, respectively. We are asked to find the dot product of these two vectors, which is a scalar quantity known as the "Vw". We will then interpret the meaning of this dot product in practical terms.
To find the dot product of v and w, we will use the formula:
Vw = v . w = (210)(2.8) + (300)(2.99)
Vw = 588 + 897 = 1485
Therefore, the value of Vw is 1485.
Practical terms: The dot product of two vectors is a scalar quantity that represents the "projection" of one vector onto the other. In this case, the dot product Vw represents the total revenue earned by selling regular and premium gasoline at the given station.
The components of v represent the number of gallons of regular and premium gas sold, while the components of w represent the respective prices per gallon for each kind of gas. Multiplying the number of gallons sold by the price per gallon gives the total revenue earned for each type of gas. Adding these two values together gives the total revenue earned for both types of gas.
Therefore, the dot product Vw represents the total revenue earned by selling all the gas at the given station. In practical terms, this means that the station earned $1485 in revenue from selling the gas.
To know more about Dot Product here
https://brainly.com/question/29097076
#SPJ1
2
A farmer places beehives containing bees in her orchard to pollinate the plants. The table
below shows the ratio of the number of beehives to the number of acres in the orchard.
BEEHIVES PER ACRE
A 38
B 40
C 44
Number of
Beehives
48
Number of
Acres
3 9
12
If the bees pollinate the plants at a constant rate, how many acres will be pollinated by the
bees in 18 beehives?
8 24 32
18
?
The number of acres pollinated by the bees in 18 beehives is 48 acres.
A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
x: number of beehives.
y: number of acres.
From the table, the constant is obtained as follows:
3k = 8
k = 8/3
Hence the equation is of:
y = 8x/3.
The number of acres that will be pollinated by 18 beehives is then given as follows:
y = 8(18)/3
y = 48 acres.
Therefore, the number of acres pollinated by the bees in 18 beehives is 48 acres.
To learn more about the proportional relationship visit:
brainly.com/question/12917806.
#SPJ1
What is the answer for this problem and tell me how it is correct.
Answer:
Step-by-step explanation:
D is the correct answer.
Answer:
D
Step-by-step explanation:
By reading the graph, place the art museum at location (5,5). Then check all the locations to see which statement is true.
A is not true because the art museum is located 4 units east and 1 unit north from the coliseum.
B is not true because the art museum is located 3 units east and 3 units north of the smith's tower.
C is not true because the art museum is located 1 unit east and 2 units north of the state capital.
This is why D is the correct answer.
Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.42cm
7.42cm and a standard deviation of 0.36cm. Using the empirical rule, what percentage of the apples have diameters that are between 6.34cm and 8.5cm
The percentage of percentage of the apples have diameters that are between 6.34cm and 8.5cm is given as follows:
99.7%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The measures of 6.34 cm and 8.50 cm are the bounds exactly within three standard deviations of the mean, hence the percentage is given as follows:
99.7%.
More can be learned about the Empirical Rule at brainly.com/question/10093236
#SPJ1
Find the sum of the arithmetic sequence: 7+11+15+19+...+83+87.
The sum of the arithmetic sequence is 987
What is arithmetic sequence?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.
For example, the sequence, 2,4,6,8,10... is an arithmetic sequence.
The sum of an arithmetic sequence is given as;
Sn=n/2[2a+(n−1)d]. Where d is the common difference and a is the first term.
the last term is 87
therefore;
87= 7+(n-1) 4
87= 7+4n-4
91-7 = 4n
84 = 4n
n = 84/4
n = 21
therefore 87 is the 21st term
Sn=n/2[2a+(n−1)d]
= 21/2(2×7+(21-1)4
= 21/2 ( 14+80)
= 21×94/2
= 987
therefore the sum of the arithmetic sequence is 987
learn more about Arithmetic sequence from
https://brainly.com/question/6561461
#SPJ1
I also need help on finding the pvalue
The claim is: Testing if the time spent completing the obstacle course is improved by the energy drink
The null and the alternate hypotheses are added below
Stating the null and the alternate hypothesisFrom the question, we have the following parameters that can be used in our computation:
The table
Also, we have the following statistical question
Is there sufficient evidence at α = 0.05 to conclude that the students did better the second time?
This means that the null hypothesis are
H1: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.
The alternate hypothesis is the opposite of the null hypothesis
So, we have
H2: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.
Lastly, the claim is that
Testing if the time spent completing the obstacle course is improved by the energy drink
Read more about test of hypothesis at
https://brainly.com/question/14701209
#SPJ1
Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is µg =0. Compute the value of the t test statistics. Round intermediate
calculations to four decimal places as needed and final answers to three decimal places as needed.
x 9 6 7 5 12
y 6 8 3 6 7
A.t= 2.890
B.t= 1.292
C. t=0.578
D. t=0.415
Answer: To compute the t-test statistic for the paired sample data, we need to first calculate the sample mean difference and the sample standard deviation of the differences. Then we can use the formula:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the standard error of the mean difference is calculated as:
standard error = sample standard deviation / sqrt(sample size)
Let's first calculate the sample mean difference:
x 9 6 7 5 12
y 6 8 3 6 7
The differences between each pair of x and y values are:
(9-6), (6-8), (7-3), (5-6), (12-7) = 3, -2, 4, -1, 5
The sample mean difference is the average of these differences:
sample mean difference = (3 - 2 + 4 - 1 + 5) / 5 = 1.8
Next, we need to calculate the sample standard deviation of the differences. To do this, we first calculate the deviations of each difference from the sample mean difference:
(3 - 1.8), (-2 - 1.8), (4 - 1.8), (-1 - 1.8), (5 - 1.8) = 1.2, -3.8, 2.2, -2.8, 3.2
The sample standard deviation of the differences is the square root of the sum of the squared deviations divided by (n-1):
sample standard deviation = sqrt[(1.2^2 + (-3.8)^2 + 2.2^2 + (-2.8)^2 + 3.2^2) / 4] = 3.153
Finally, we can calculate the t-test statistic:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the hypothesized mean difference is 0, and the standard error of the mean difference is:
standard error = sample standard deviation / sqrt(sample size) = 3.153 / sqrt(5) = 1.410
Substituting the values, we get:
t = (1.8 - 0) / 1.410 = 1.277
Rounding the final answer to three decimal places, we get:
t = 1.277
Therefore, the correct option is B. t = 1.292.
Carolina wants to save $900 to go to Puerto Rico. She saves $45 each week. Her
brother gives her $180. Which equation determines how many weeks she must
save.
Answer:
45w + 180 = 900
45w = 720
w = 16 weeks
Line n is perpendicular to the x-axis and passes through the point (–3,–7).
Write the equation for line n.
What is the slope of line n?
The equation for line n that is perpendicular to the x-axis and passes through the point (–3,–7) is x = -3, and its slope is undefined.
Since line n is perpendicular to the x-axis, it is parallel to the y-axis. Therefore, its slope is undefined since the y-axis is a vertical line with no defined slope.
To write the equation for line n, we know that the y-coordinate of every point on the line will be constant since the line is parallel to the y-axis. We also know that the line passes through the point (-3,-7), so we can write the equation as:
x = -3
This means that for any value of y, the x-coordinate will always be -3. Graphically, this represents a vertical line passing through the point (-3,-7) and parallel to the y-axis.
To learn more about equation of line perpendicular to x-axis click on,
https://brainly.com/question/29444523
#SPJ1
Let u = - 4i + j v = 4i - 2j and w = - 2j
Find the specified scalar or vector.
5u(3v - 4w)
The result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.
In linear algebra, we often use scalars and vectors to perform various operations. Scalars are just ordinary numbers that can be used to multiply or divide vectors. On the other hand, vectors are quantities that have both magnitude and direction.
In this problem, we are given three vectors, u, v, and w, and we are asked to find the result of multiplying 5u by the difference between 3v and 4w.
First, let's calculate 3v - 4w. Since v = 4i - 2j and w = -2j, we can substitute these values to get,
3v - 4w = 3(4i - 2j) - 4(-2j)
= 12i - 6j + 8j
= 12i + 2j
Next, we need to find the scalar product of 5u and 12i + 2j. To find the scalar product of two vectors, we need to multiply the corresponding components and add up the products.
Therefore: 5u(3v - 4w) = 5u(12i + 2j)
= 5(-4i + j)(12i + 2j)
= -20i(12i) + 5i(2j) + 60j(i) - 10j(j)
= -240i + 10j + 60j + 10
= -240i + 70j + 10
So, the result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.
To know more about Scalar or Vector here
https://brainly.com/question/28518744
#SPJ1