To solve this problem, we need to use vector addition to find the resultant velocity of Julia.
Let's assume that the east direction is the positive x-axis and the south direction is the negative y-axis.
The velocity of Julia in still water is 8 km/hr in the positive x-axis direction.
The velocity of the river is 3 km/hr in the negative y-axis direction.
To find the magnitude and direction of Julia's velocity, we need to find the resultant velocity vector, which is the vector sum of her velocity in still water and the velocity of the river.
Using the Pythagorean theorem, the magnitude of the resultant velocity can be calculated as:
|V| = √(Vx² + Vy²)
where Vx is the x-component of the resultant velocity and is equal to Julia's velocity in still water, and Vy is the y-component of the resultant velocity and is equal to the velocity of the river.
Vx = 8 km/hr
Vy = -3 km/hr
|V| = √(8² + (-3)²) = √(64 + 9) = √73 km/hr
The direction of the resultant velocity can be calculated as:
θ = tan⁻¹(Vy / Vx)
θ = tan⁻¹(-3 / 8) = -20.56°
The negative sign indicates that the resultant velocity vector makes an angle of 20.56° below the positive x-axis (east direction).
Therefore, the magnitude of Julia's velocity is approximately 8.54 km/hr, and the direction of her velocity is 20.56° below the positive x-axis (east direction).
Need help on all three of these 4,5,6
The answers are given below:
Mean: μ = 60, Standard deviation: σ = 10
Mean: μ = 50, Standard deviation: σ = 8
Mean: μ = 49, Standard deviation: σ = 7.5
How to solveFor a normal distribution, the empirical rule states:
99.7% of the data is within 3 standard deviations (σ) of the mean (μ)
68% of the data is within 1 standard deviation of the mean
95% of the data is within 2 standard deviations of the mean
99.7% data between 30 and 90:
μ - 3σ = 30, μ + 3σ = 90
Mean: μ = 60, Standard deviation: σ = 10
68% data between 42 and 58:
μ - σ = 42, μ + σ = 58
Mean: μ = 50, Standard deviation: σ = 8
95% data between 34 and 64:
μ - 2σ = 34, μ + 2σ = 64
Mean: μ = 49, Standard deviation: σ = 7.5
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(5 1/2, - 7 1/2) and (5 1/2, - 1 1/2)
Answer:
Step-by-step explanation:
1) -2
2) 0
Please mark me Brainliest!!! <3 <3 <3
add [-6 -22] + [-3 2 1]
Answer:
-349
Step-by-step explanation:
1)[-6-22]+[-321]
2)(-28)-321
3)-349
A person places $34300 in an investment account earning an annual rate of 2%, compounded continuously. Using the formula � = � � � � V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 17 years.
The amount of money in the account after 17 years is approximately $49,222.26.
Describe Investment?Investment is the act of allocating resources, such as money or time, with the expectation of generating a return or profit in the future. Investment can take many forms, such as investing in stocks, bonds, real estate, or businesses.
Investment is an important tool for individuals and businesses to build wealth and achieve financial goals. By investing in assets that appreciate in value or generate income, investors can increase their net worth and achieve long-term financial stability.
When making investment decisions, investors typically consider factors such as risk, return, liquidity, and diversification. Risk refers to the possibility of losing money, while return refers to the potential profit or income generated by the investment. Liquidity refers to how easily an investment can be converted into cash, while diversification refers to spreading investment across multiple assets to reduce risk.
Using the formula [tex]V= Pe^{rt}[/tex], where P = $34300, r = 0.02, and t = 17, we can find the value of the account after 17 years:
V = 34300 * [tex]e^{0.02*177[/tex]
V ≈ $49,222.26
Therefore, the amount of money in the account after 17 years is approximately $49,222.26.
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Jason conducted a survey amongst his friends to determine the amount of hours they watch TV each week. Here is the table that Jason found.
What statement is NOT true about the frequency chart?
Only 3 people did not watch TV each week.
The largest group of people were the ones who watched 1 hour per week.
70% of the people spent less than 1 hour watching TV a week
30% watch 2 hours or more on TV a week
The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week".
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week". This is because according to the table, the percentage of people who spent less than 1 hour watching TV is 50%, which means that half of the people surveyed watched less than 1 hour of TV each week.
Therefore, The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week".
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A(r(t))=\pi(0.25+2t+4t^2)
Explanation:
To write a composite function, we apply one function to another given function. In this case, we want to find area in terms of time; this means that the function A(r) gets applied to the function r(t).
In order to do this, we replace r with r(t). We already know that r(t)=0.5+2t; this means we replace r with 0.5+2t:
A(r(t))=π(0.5+2t)²
To simplify this, we simplify the squared term:
A(r(t)) = π(0.5+2t)(0.5+2t)
A(r(t)) = π(0.5*0.5+0.5*2t+2t*0.5+2t*2t)
A(r(t)) = π(0.25+t+t+4t²)
A(r(t)) = π(0.25+2t+4t²)
Answer:
So the composite function that gives the area of a circle in terms of time is:
A(r(t)) = π(0.25+2t+4t²)
Triangle QRS is shown below. Use the information given to determine the measure of ∠ R.
Angel Q= 38.2
Angel S= 52.7
Angel R=??
I’m so confused please help!
Answer: r=89.1
Step-by-step explanation: It has been given that,
PQ=PR
So, it is an isosceles triangle, hence ∠Q=∠R. let it be x
Now, we know that the sum of the angles of a triangle = is 180
∘
.
So,
∠P+∠Q+∠R=180
38.2+52.7+x=180
90.9+x=180
taking 90.9 in RHS it becomes -, so
x=180-90.9
x=89.1
2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Part A
Which equation can be solved to predict the number of times Harris will spin a sum less than 10?
A) 3/500 = x/15
B) 12/500 = x/15
C) 12/15 = x/500
D) 3/15 = x/500
QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?
_______
The equation that can be solved to predict the number of times Harris will spin a sum less than 10 is B) 12/500 = x/15
Harris should expect to spin a sum of 10 or greater 240 times.
How to explain the equationIt should be noted that to predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of experiments (500).
The possible sums that can be obtained are: 5, 6, 7, 8, 9, 10, 11, and 12. The probability of getting a sum less than 10 is the sum of the probabilities of getting each of these outcomes, which is:
P(sum less than 10) = P(1 and 4, 1 and 5, 2 and 4, 2 and 5, 3 and 4, 3 and 5)
= 6/15 * 2/5
= 4/25
Multiplying this probability by the total number of experiments (500), we get:
Number of times Harris will spin a sum less than 10 = (4/25) * 500 = 80
Therefore, the correct equation to predict the number of times Harris will spin a sum less than 10 is: 12/500 = x/15
Part B: Based on the information, the possible outcomes that give a sum of 10 or greater are: 10, 11, and 12. The probability of getting a sum of 10 or greater is the sum of the probabilities of getting each of these outcomes, which is:
P(sum of 10 or greater) = P(1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, 6 and 4, 7 and 3, 8 and 2, 9 and 1, 8 and 3, 7 and 4, 6 and 5)
= 12/15 * 3/5
= 36/75
= 12/25
Multiplying this probability by the total number of experiments (500), we get:
Number of times Harris should expect to spin a sum of 10 or greater = (12/25) * 500 = 240
Therefore, Harris should expect to spin a sum of 10 or greater 240 times.
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Question Catherine randomly selects 10 books off of her bookshelf. She records the number of pages in the books in the table below. Use a calculator to create a histogram of the data, and then interpret the plot. Set Xmin to 100, Xmax to 250, and Xscl to 25. Number of Pages 227 142 165 180 145 162 121 195 160 174
1. Data is approx bell-shaped and symmetric
2. Median is between 150 to 175
What is a Histogram?A histogram is a graphical representation of a frequency distribution of a set of continuous data. It is used to display the shape of the data and to show how frequently certain values occur within a given range or interval.
In a histogram, the x-axis represents the range or interval of the data, and the y-axis represents the frequency of occurrence of values within each interval.
The data is divided into a set of bins or intervals, and the height of each bar on the histogram represents the number of data points that fall within that particular bin. The bars of the histogram are typically drawn adjacent to each other, with no gaps between them, to emphasize the continuity of the data.
Therefore, from the histogram used to represent the given data, it can be seen that the data is symmetric and also the median has the values between 150 to 175
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Karen needs to find a courier to deliver a package the first courier charges a fee of $20 plus $2 per pound the second charges $12 plus $3 per pound karen determines that given her packages weight the two courier services are equivalent in terms of cost. how much will it cost? what is the weight?
Answer:
Step-by-step explanation:
Let's call the weight of Karen's package "w" in pounds.
For the first courier, the cost is given by:
Cost = 20 + 2w
For the second courier, the cost is given by:
Cost = 12 + 3w
We know that these costs are equivalent, so we can set them equal to each other:
20 + 2w = 12 + 3w
Simplifying this equation, we get:
8 = w
So the weight of Karen's package is 8 pounds.
To find the cost, we can plug this weight into either of the equations above:
For the first courier:
Cost = 20 + 2(8) = 36
For the second courier:
Cost = 12 + 3(8) = 36
So it will cost Karen $36 to deliver her package, and the weight of the package is 8 pounds.
Write a system of linear equations for the graph below.
00
X
08
Answer:
y = 3/2x -5
y= 3/2x -7
Step-by-step explanation:
since the two lines are parallel (never touch) they have the same slope, so find the slope of one of the lines (rise over run). Then, to find the y-intercept for the equations, simply look at where each of the lines cross the y-axis.
~lmk if u got Qs
What generalization can you make about the equations?
A whole number by a unit fraction is the same as
About the equation [tex]7 * 3 = 21[/tex], the generalization we can make is that dividing a whole number by a unit fraction is the same as multiplying a whole number by the denominator of the unit fraction.
What is considered as generalization in mathematics?We use generalizations to describe the pattern they see in the relationship of a specific group of numbers. It's a pattern that holds true every time.
In mathematics, generalization can be defined as a statement that is true for an entire class of objects, the process by which we obtain a general statement, or the method by which knowledge is transferred from one setting to another.
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Two buses leave a station at the same time and travel in opposite directions. One bus travels 18 miles hour faster than the other. If the two buses are 768 miles apart after 6 hours, what is the rate of each bus?
Answer: the slower bus travels at 55 miles per hour and the faster bus travels at 73 miles per hour.
Step-by-step explanation:
distance = rate x time
768 = 6x + 6(x + 18)
Simplifying this equation, we can distribute the 6 on the right-hand side:
768 = 6x + 6x + 108
Combining like terms, we get:
768 = 12x + 108
Subtracting 108 from both sides:
660 = 12x
Dividing both sides by 12:
x = 55
So the slower bus is traveling at 55 miles per hour. To find the speed of the faster bus, we can add 18:
x + 18 = 55 + 18 = 73
Answer: one is 55 and the other is 73
Step-by-step explanation:
lets say x is for the slower bus. for every hour the become x+x+18
and this is happening for 6 hours so its is 6(2x+18)=768
x=55
x+18=73
find the slop of a line (-3,5)(5,9)
Answer:
Slope = 0.5
Step-by-step explanation:
Slope of a Line passing through two points [tex](x_1 , y_1)[/tex] and [tex](x_2 ,y_2)[/tex] equal [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Since our Line passes through the two points ( -3 , 5 ) and ( 5 , 9 )
Then the Slope = [tex]\frac{9-5}{5-(-3)}=\frac{4}{8} =0.5[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{Slope\ formula\ is :\mathtt{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}\rightarrow \dfrac{rise}{run} = slope}[/tex]
[tex]\textsf{Your labels :}\\\\\mathtt{y_2 \rightarrow 9}\\\mathtt{y_1 \rightarrow 5}\\\\\mathtt{x_2\rightarrow 5}\\\mathtt{x_1\rightarrow-3}[/tex]
[tex]\textsf{Your equation should look like : }\mathtt{slope = \dfrac{9 - 5}{5 - (-3)}}[/tex]
[tex]\textsf{Solving for your answer should be :}[/tex]
[tex]\mathtt{slope = \dfrac{9 - 5}{5 - (-3)}}[/tex]
[tex]\mathtt{slope = \dfrac{9 - 5}{5 + 3}}\\\textsf{(We got a positive (+) symbol because double negatives }(-)\textsf{ make a positive!})[/tex]
[tex]\mathtt{slope = \dfrac{4}{8}}}[/tex]
[tex]\mathtt{slope = \dfrac{4\div2}{8\div2}}[/tex]
[tex]\mathtt{slope = \dfrac{2}{4}}[/tex]
[tex]\mathtt{slope = \dfrac{2\div2}{4\div2}}[/tex]
[tex]\mathtt{slope = \dfrac{1}{2}}[/tex]
[tex]\large\textsf{Thus your \boxed{\textsf{answer}} should most likely be :}\\\\\\\large\boxed{\mathtt{slope = \dfrac{1}{2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
two glasses can hold the same amount of liquid. Glass A is 1/2 filled and glass B is 1/3 filled. If the liquid in Glass B is poured into Glass A, what fraction of Glass A will then be filled?
A 5/6
B 4/5
C 3/4
D 1/5
After answering the provided question, we can conclude that As a result, function option A) 5/6 is the correct answer.
what is function?A function appears to be a hyperlink between two sets of numbers in mathematics, where each member of the first set (referred as the domain) corresponds to a certain representative of the second set (called the range). In other utterance, a function takes input from a set and produces output by another. Inputs are frequently represented by the variable x, and outputs are represented by the variable y. A function can be represented by a formula or a graph. The method y = 2x + 1 is an example of a conceptual model in which each value assigned to x yields a value of y.
Both Glass A and Glass B initially hold the same amount of liquid. Assume that the total amount of liquid that each glass can hold is equal to 6 units.
As a result, Glass A is initially filled with 3 units of liquid (1/2 of 6 units) and Glass B is initially filled with 2 units of liquid (1/3 of 6 units).
When the liquid from Glass B is poured into Glass A, the total amount of liquid in Glass A increases to 5 units (3 units + 2 units), and the glass is now completely filled.
So, after pouring the liquid from Glass B into it, the fraction of Glass A that is filled is 5/6.
As a result, option A) 5/6 is the correct answer.
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Find the total surface area of this cylinder. Give your answer to 1 decimal place. 18 cm Feedback 24 cm
In light of this, the cylinder's total surface area falls between approximately 1017.9 cm²and 1357.2 cm².
Define the cylinder's entire surface area.A cylinder's total surface area is equal to the sum of all of its faces' surface areas. The cylinder's total surface area—the sum of its curved and circular areas—has a radius of "r" and a height of "h." The entire surface area of the cylinder is calculated as follows:
Define cylinder:Total Surface Area of Cylinder = 2r (h + r) square units.
The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. It is seen as a prism since its base is a circular. It is frequently used as a container and can either be solid or hollow 13.
The following formula can be used to get a cylinder's total surface area:
A = 2πr² + 2πrh
where r is the cylinder's base's radius, h is the cylinder's height, and is a mathematical constant roughly equal to 3.14159.
Yet, we can locate a variety of potential surface areas using the provided information. With the assumption that the radius is equal to the feedback's half (9 cm), we can
after which, we can determine the surface area as follows:
A = 2π(9)² + 2π(9)(18) (18)
A= 2π(81) + 2π(2916)
A ≈ 1017.9 cm²
The surface area can be calculated as follows if we assume that the radius is equal to two-thirds of the feedback (i.e., r = 12 cm):
A = 2π(12)² + 2π(12)(18) (18)
A ≈ 1357.2 cm²
Complete question is given below:
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*Write the slope-intercept equation of the function f whose graph satisfies the given conditions.
The graph of f passes through (-12,7) and is perpendicular to the line that has an x-intercept of 1 and a y-intercept of -3.
What is the equation of the function ?
Answer: Slope-intercept form : y-y₁=m(x-x₁)
Passes through (-12, 7)
Slope = -5/3
m = slope
Simply plug everything in :)
y - y₁ = m(x - x₁)
y - 7 = -5/3(x + 12)
Simplify.
y - 7 = -5/3x - 20
Add 7 to both sides.
y = -5/3x = -13
~Hope I helped~
Step-by-step explanation:
A triangular piece of land has base 2 meter and height 10meter. if the land is 15 dolar per square meter what is its value
Answer:
150.00
Step-by-step explanation:
a = 1/2bh
a = 1/2(2)(10)
a = 10 [tex]m^{2}[/tex]
10x15 = 150
Helping in the name of Jesus.
find the segment CB, knowing that the angle α is 25° and the segment AB is 8 cm.
After calculating the value of CB, we get a result of 3.45 cm. This means that the segment CB is 3.45 cm, given that the angle α is 25° and the segment AB is 8 cm.
CB = 8 cm * tan(25°)
≈ 3.45 cm
To find the segment CB, we need to use the tangent of the angle α (25°). We also need to know the length of the segment AB, which is 8 cm. To solve for CB, we use the equation CB = 8 cm * tan(25°). After calculating the value of CB, we get a result of 3.45 cm. This means that the segment CB is 3.45 cm, given that the angle α is 25° and the segment AB is 8 cm.
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I think you need to make an equation. Help Me!
Answer: h = 7
Step-by-step explanation:
63 = 1/2 * 18 * h
63 = 9 * h
63 = 9h
*Divide 9 on both sides.
7 = h
Point B (8, -3) has been transformed. After a reflection over the x-axis, what is the coordinate of point B’?
The coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.
What is Reflection in geometry?A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.
When a point is reflected over the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.
Therefore, to find the coordinates of point B' after reflecting point B over the x-axis, we simply need to change the sign of the y-coordinate of point B.
Starting with point B at (8, -3), reflecting over the x-axis changes the sign of the y-coordinate, so the new point B' is at:
B' = (8, 3)
Therefore, the coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.
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Find the perimeter of 2cm, 4cm, 2cm, 5cm, 4cm, 1cm
Answer:
Step-by-step explanation:
The perimeter is the distance around the edge of the shape.
[tex]P=2+4+2+1+4+5=18cm[/tex]
30*8000(5-)1800=?
1500(800-)15000*18000=?
Answer:
1) 2160000000
2) 3.24 * 10^14
Step-by-step explanation:
30*8000(5-)1800
240000 * 5 * 1800
1200000 * 1800
2160000000
1500(800-)15000*18000
1200000 * 15000 * 18000
18000000000 * 18000
3.24 * 10^14
How do we write 2.5million?
Answer:
2,500,000
Step-by-step explanation:
To write 2.5 million, you can write it as 2,500,000. This is because one million is equal to 1,000,000. So, 2.5 million is equal to 2,500,000.
Answer:
2500000 <--- in numbers
Two million and five hundred thousand OR Two and a half million
What is the measurement of the fourth angle of a quadrilateral if the other angle’s measure 80 degrees 120 degrees and 65 degrees?
the measurement of the fourth angle of the quadrilateral is 95 degrees.
To find the measurement of the fourth angle of a quadrilateral when the measures of three angles are given, we can use the fact that the sum of the measures of the angles in a quadrilateral is 360 degrees.
Let's denote the measure of the fourth angle as x. Then we can write an equation:
80 + 120 + 65 + x = 360
Simplifying this equation, we get:
x = 360 - 80 - 120 - 65 = 95
Therefore, the measurement of the fourth angle of the quadrilateral is 95 degrees.
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Which of the following is not a perfect square trinomial?
Group of answer choices
A. x^2+16x+64
B. x^2+7x+49
C. x^2+10x+25
D. 4x^2+16x+16
Answer:
B
Step-by-step explanation:
[tex]x^{2} +7x+49[/tex] is a prime equation.
Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not exist, enter DNE.)
The calculated value of the derivative f'(x) at x = -2/3 if f(x) = 5x√(x + 1) is f'(-2/3) = 0
How to find the value of the derivativeGiven the function
f(x) = 5x√(x + 1)
Factor out 5
So, we have
f(x) = 5[x√(x + 1)]
The derivative is then calculated using the following chain rule
f'(x) = 5[du/dx * dy/du]
When differentiated, we have
f'(x) = 5[√(x + 1) + x/2[√(x + 1)]]
This gives
f'(x) = 5[3x + 2/2[√(x + 1)]]
So, we have
f'(x) = [15x + 10]/[2√(x + 1)]
Substitute -2/3 for x
f'(-2/3) = [15(-2/3) + 10]/[2√((-2/3) + 1)]
Evaluate
f'(-2/3) = [0]/[2√1/3]
Evaluate the quotient
f'(-2/3) = 0
Hence, the value of the derivative is 0
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Weekly wages at a certain factory are
normally distributed with a mean of $400 and
a standard deviation of $50. Find the
probability that a worker selected at random
makes between $450 and $550.
250 300 350 400 450 500 550
P=[?]%
Hint use the 68-95-99.7 rule.
Enter
Answer:
First, we need to standardize the values using the formula:
z = (x - mu) / sigma
where x is the value, mu is the mean, and sigma is the standard deviation.
For $450: z = (450 - 400) / 50 = 1
For $550: z = (550 - 400) / 50 = 3
Using the 68-95-99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Since we are interested in the probability of a worker making between $450 and $550, we need to find the area under the normal curve between z = 1 and z = 3.
Using a standard normal table or calculator, we can find that the area under the curve between z = 1 and z = 3 is approximately 0.1359.
Therefore, the probability that a worker selected at random makes between $450 and $550 is 13.59% (rounded to two decimal places).
Step-by-step explanation:
I need help with this question
The revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016. 2. The revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.
What is fraction and percentage?A factor is a number that represents how two quantities are related to one another. It is frequently used to indicate how much one amount exceeds or falls short of another. For instance, if a business's revenue. On the other hand, a percentage is a technique to represent a portion or ratio of something as a fraction of 100. For instance, if a company made money.
The given revenue for the two years is $138200 and $164900.
The factor of the two revenue is:
factor = 164900 / 138200 = 1.193
Hence, the revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016.
percentage = (164900 / 138200) * 100% = 119.3%
Therefore, the revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.
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Help with math problems
The expressions whose solutions are represented by the graph are:
A. 5 - X > 4
D. 6x - 7 > 5
Which expressions have solutions on the graph?The mathematical expressions, whose solutions are represented by the graph are those that fall within the shaded region of the graph. For instance, in the mathematical expression, 5 - x > 4, the shaded region points to 4 and values greater than it.
So, this expression satisfies the condition and can be described as a solution represented by the graph.
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