Answer:
45 km/h and 9 km/hStep-by-step explanation:
Let the rate of boat in still water be b and the speed of the current be c
Speed downstream = b + cSpeed upstream = b - cWe got equations for time:
108/(b - c) = 3 ⇒ b - c = 36108/(b + c) = 2 ⇒ b + c = 54Add up the equations:
b - c + b + c = 36 + 542b = 90b = 45 km/hThen finding the values of c
c = 45 - 36 = 9 km/hOn a standardized test, Jose scored an 87 and Mia scored a 74. The distribution of test scores for the population is normal with a population mean of 76.28 and a population standard deviation of 7.02.
What percentage of people received a higher score than Jose?
Using the normal distribution, it is found that 6.3% of people received a higher score than Jose.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.In this problem, the mean and the standard deviation are given by, respectively: [tex]\mu = 76.28, \sigma = 7.02[/tex].
The proportion of people who received a higher score than Jose is one subtracted by the p-value of Z when X = 87, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{87 - 76.28}{7.02}[/tex]
[tex]Z = 1.53[/tex]
[tex]Z = 1.53[/tex] has a p-value of 0.937.
1 - 0.937 = 0.063.
6.3% of people received a higher score than Jose.
More can be learned about the the normal distribution at https://brainly.com/question/24663213
WILL GIVE BRAINLIEST(If it helps me) SO PLEASE HELP
A weight loss organization has a new member who weighs 210 pounds. After 6
months the member hopes to weigh 162 pounds.
a. Write a linear model that represents the member's weight loss goal.
b. According to the linear model, how much should the member weight after 9
months?
c. What is the slope of this function? What does the slope represent in this scenario?
Answer:
Our calorie calculator will tell you how many calories you ... If you would like to lose or gain weight, you can also enter ... Here is the backstory on the following fantastic ...
Step-by-step explanation:
make me as brain liest
Enter the improper fraction as a mixed number.
32/9
Answer:
[tex]\3[/tex]3 [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
The weight of an object on Planet X is twice that of its weight on Earth and one third of its weight on Planet Y. If an object on Earth weighs 100 units, what is its weight on Planet Y?
Answer:
33.3333333333
Step-by-step explanation:
100 divided 1/3 = 33.3333333333
hope it helped
Please type out the correct one for me out of those 2 thanks <4
Answer:
1.2n=0.45n+1.5
Step-by-step explanation:
WILL MARK BRAINLIEST Solve the following problems. Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it. b Given: FD ⊥ AB ∠A ≅ ∠B Prove: ∠F ≅∠CEF
Sum of the interior angles of any triangle equal 180° .
So ;
A + B + ECB = 180°
A = B = μ
So : 2μ + ECB = 180°
→ ECB = 180° - 2μ
_________________________________
ECF + ECB = 180°
ECF + 180° - 2μ = 180°
ECF = 180° - 180° + 2μ
ECF = 2μ
_________________________________
∆ ADE :
A + D + E = 180°
μ + 90° + E = 180°
E = 180° - 90° - μ
E = 90° - μ
_________________________________
AED + AEF = 180°
90° - μ + AEF = 180°
AEF = 180° - 90° + μ
AEF = 90° + μ
_________________________________
AEF + FEC = 180°
90° + μ + FEC = 180°
FEC = 180° - 90° - μ
FEC = 90° - μ (( # ))
_________________________________
∆ BDF :
B + D + F = 180°
μ + 90° + F = 180°
F = 180° - 90° - μ
F = 90° - μ ((★))
_________________________________
((#)), ((★)) say :
FEC = 90° - μ
F = 90° - μ
So : F =~ FEC
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
what is [tex]\frac{w}{3}[/tex] + [tex]\frac{5}{6}[/tex] = [tex]\frac{1}{12}[/tex]
my answer was w = - [tex]\frac{9}{4}[/tex]
18. Your neighbor's yard is in the shape of a triangle, with dimensions 120 ft, 84 ft,
and 85 ft. Is the yard an acute, obtuse, or a right triangle? Explain.
The yard is obtuse!
[tex]\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Explanation :-}}}}}}[/tex]
Determination of acute angled triangle:-When the square of the longest side is less than the sum of the squares of two shorter sides then the triangle is acute angled.Determination of right angled triangle:-When the square of the longest side is equal to the sum of the squares of two shorter sides then the triangle is right angled .Determination of obtuse angled triangle:-When the square of the longest side is more than the sum of the squares of two shorter sides then the triangle is obtuse angled.[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
Final answer ⤵️Longest side = 120 feetShorter side = 85 feetShortest side = 84 feet[tex] \sf \longrightarrow \: {120}^{2} > {85}^{2} + {84}^{2} [/tex]
[tex] \sf \longrightarrow \:14400> 7225 + 7056[/tex]
[tex] \sf \longrightarrow \:14400> 14281[/tex]
[tex] \qquad \mathbb{TRUE}[/tex]
Thus, The triangle is obtuse angled...~
We need angle
Apply law of cosines
[tex]\\ \rm\Rrightarrow c^2=a^2+b^2-2abcos\gamma[/tex]
[tex]\\ \rm\Rrightarrow 2abcos\gamma=a^2+b^2-c^2[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{a^2+b^2-c^2}{-2ab}[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{120^2+84^2-85^2}{-2(120)(84)}[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{14400+7056-7225}{-20160}[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{14231}{-20160}[/tex]
[tex]\\ \rm\Rrightarrow cos\gamma=-0.714[/tex]
[tex]\\ \rm\Rrightarrow \gamma=cos^{-1}(-0.714)[/tex]
[tex]\\ \rm\Rrightarrow \gamma=135.56°[/tex]
The yard is obtuse
Jocelyn and linda own a bakery. they had 388 custoners this week, 55 fewer than last week. write and algebraic equation for the number of customers they had last week (Let c be the number of costumers they had last week.)
Answer:
c - 55 = 338
Step-by-step explanation:
fifty-five fewer than the number last week is 338
c - 55 = 338
algebraic equation: c - 55= 338
Hope it helps!!!Brainliest pls!!!help please:) its a quick question
20 pointss
Answer:
1rst one
Step-by-step explanation:
Answer:
1st
Step-by-step explanation:
Bonds with a face value of $744000 and a quoted price of 98.5 have a selling price of
Answer:
67.91
Step-by-step explanation:
How many solutions does the following equation has
Answer:
I think only 1 but not 100% sure
Step-by-step explanation:
Answer:
One solution
Step-by-step explanation:
Combine like terms and simplify.
20z - 5 - 12z = 10z + 8
⇒ z(20 - 12) - 5 = 10z + 8
⇒ z(8) - 5 = 10z + 8
⇒ 8z - 5 = 10z + 8
Subtract 8z both sides.
⇒ 8z - 8z - 5 = 10z + 8 - 8z
⇒ -5 = 2z + 8
Subtract 8 both sides.
⇒ -5 - 8 = 2z + 8 - 8
⇒ -13 = 2z
⇒ -13/2 = 2z/2
⇒ -6.5 = z
Thus, there is 1 solution.
Please teach me how to solve part b, thank you.
Part (a)
The locus is the set of points that satisfy the given conditions. Namely that the point P needs to be 1 unit from the line given.
Think of a median along a highway. Then imagine the two shoulders of the road. The locus describes the two parallel lines that are to this given median. In other words, the median is y = x+2 and the road shoulders are unknown for now.
Though we do know that parallel lines have equal slopes (but different y intercepts).
Therefore, the answers to the next section will be of the form y = x+k for some real number k.
=============================================================
Part (b)
Use your favorite graphing tool to plot y = x+2. I recommend GeoGebra since I use it all the time, and it's what I used to make the drawing below. Desmos is another tool you can use. Both are free.
Note that point A(0,2) is on the line y = x+2. The line perpendicular to y = x+2 and goes through (0,2) is y = -x+2. From here, plot a circle centered at (0,2) with radius 1. The equation of this circle is x^2 + (y-2)^2 = 1
The intersection points of the circle and y = -x+2 will provide starting points, so to speak, for the two shoulder lines I mentioned in part (a).
The approximate locations of those points are:
B = (0.71, 1.29)
C = (-0.71, 2.71)
From here, it shouldn't be too hard to find the y = mx+b forms of the locus lines. Let me know if you need help with that, or if you need me to check your answers.
Side note: Why is it called a locus? I'm not sure, but my gut feeling tells me it has to do with the insects of a similar sounding name (locus the math term and locust the insect). Imagine millions of them forming various shapes in the sky, similar to how many points are used in the 2D plane to create various curves.
On the graph of f(x)=sinx and the interval [2π,4π), for what value of x does f(x) achieve a minimum?
Answer:
Step-by-step explanation:
The minimum value of sinx is -1 when x = 3π/2, 7π/2, ...
In [2π, 4π), x = 7π/2
The function f(x)=sin(x) achieves its minimum value of -1 at x=3π.
The function f(x)=sin(x) is a periodic function with a period of 2π, meaning it repeats every 2π units. Within the interval [2π,4π), which is one period of the function, the minimum value of sin(x) occurs at x=3π.
This is because at x=3π, the sine function reaches its minimum value of -1. As you move further away from 3π, the sine function starts increasing again.
So, within the interval [2π,4π), the function f(x)=sin(x) achieves its minimum value of -1 at x=3π.
To know more about function:
https://brainly.com/question/30721594?
#SPJ3
Choose the expression that represents a quadratic expression.
O 6x4 - 5x3 + 3x2 -7x - 8
O 5x3 + 3x2 -7x - 8
© 2x2 + 3x - 1
© 3x - 1
Answer:
[tex]2x {}^{2} + 3x - 1[/tex] option(c)
Step-by-step explanation:
[tex]its \: 2x {}^{2} + 3x - 1 \\ because \: the \: highest \: power \: of \: the \: unkown \: is \: 2[/tex]
436 +2312 leaving your answer in base 4 and 8728-3456 leaving your answer in base 9
Emma buys two identical bottles of shampoo. She uses of 3/8 one of them at home, and uses 7/10
of all the remaining shampoo while she is on holidays. In total, how much shampoo remains?
Answer:
Step-by-step explanation:
she uses 3/8's of one of them and 7/10 of the other one. first, you need to make the denomanators the same number. so the answer is 3/16 of the starting amount
What type of decimal is this fraction: 11/20
1.Group of answer choices
2.repeating
3.neither
4.both
5.terminating
Answer:
I think the answer is repeating because it'd be
0.55
Solve for x and graph the solution on the number line below.
The solution to both inequality is [tex]x>-1[/tex] and [tex]x\leq 7[/tex].
We have equation [tex]-2>-4x-6[/tex] and [tex]-34\leq -4x-6[/tex]
Let us solve the inequality
[tex]-2>-4x-6\\-2+6>-4x\\4>-4x\\x>-1[/tex]
Now, let us solve the inequality
[tex]-34\leq -4x-6\\-34+6\leq -4x\\-28\leq -4x\\x\leq 7[/tex]
Learn more:https://brainly.in/question/9995212
Reflection of point P (3,-1) over the line y=x is
Answer:
(-3,-1)
Step-by-step explanation:
please help
A bank employee combines the constant function f(t)=5000 and the linear function g(t)=250t to create the function h(t)=f(t)+g(t), where h(t) represents the value, in dollars, of an account earning simple interest after t years.
Based on the function h(t), what will be the account value 5 years after the account is opened?
A.) $5,250
B.) $6,250
C.) $25,250
D.) $26,250
Answer:
B. $6,250
Step-by-step explanation:
Given data
constant function f(t)=5000
linear function g(t)=250t
new function= h(t)=f(t)+g(t)
the new value will be
5000+250t
substituting t = 5 in the linear function we have
=5000+250(5)
=5000+1250
=6250
the answer is $6250
the answer is option B
which choices are correctly written in a scientific notation ? select the four correct answers
Answer:
34
Step-by-step explanation:
Answer:B,D,F,G
Step-by-step explanation:
A car rental company charges a daily rate of $41 plus $0.10 per mile for a certain car. Suppose that you rent that car tor a day and your bill (before taxes) is $86. How many miles did you drive?
If t < s and s < r, what is the relationship between the values t and r?
Answer:
r is much larger compared to t.
r is much larger compared to the largness of s to r.
Step-by-step explanation:
Find the sum. Enter your answer in the box.
3 + (–4)
Answer:
the answer is -1
Step-by-step explanation:
Answer:
The answer is -1
Step-by-step explanation:
If you have 3 and you take away 4, so you end up with a negative number. or what you can do is also just flip the numbers around so subtract 4 minus 3 and put a negative sign when the first number is less than the second one!!
Hope this helps!!!!
2. Consider the line
y = 3/5x -8
What is the
slope of the line perpendicular to this line?
Answer:
The slope of the perpendicular line is [tex]-\frac{5}{3}[/tex]
Step-by-step explanation:
The product of the slopes of the perpendicular lines is -1That means to find the slope of a perpendicular line to a given line, reciprocal its value, and reverse its signEx: If the slope of a line is [tex]\frac{1}{3}[/tex], then the slope of the line perpendicular to it is -3Let us solve the question
∵ The equation of a line is y = [tex]\frac{3}{5}[/tex] x - 8
→ The form of the equation is y = m x + b, where m is the slope
∴ The slope of the line is [tex]\frac{3}{5}[/tex]
→ To find the slope of the line perpendicular to it reciprocal it and
reverse its sign
∵ The reciprocal of [tex]\frac{3}{5}[/tex] is [tex]\frac{5}{3}[/tex]
→ Change its sign from positive to negative
∴ The slope of the perpendicular line is [tex]-\frac{5}{3}[/tex]
If = 14,700,-473,4644,84 . Then, Z is what
The equation is an illustration of the subtraction equation
The value of z in the equation is -473449784
What are equations?Equations are expressions that have equal values, when compared
How to determine the value of z?The equation to determine the value of z is given as:
z = 14,700,-473,4644,84
Evaluate the difference
z = -473449784
Hence, the value of z in the equation is -473449784
Read more about equations at:
https://brainly.com/question/2972832
Whats the height of the rectangular prism
Answer:
length l = 32.25 m
width w = 8223.75 m
height h = 12.5 m
diagonal d = 8223.82273 m
total surface area Stot = 736831.875 m2
lateral surface area Slat = 206400 m2
top surface area Stop = 265215.938 m2
bottom surface area Sbot = 265215.938 m2
volume V = 3315199.22 m3
Step-by-step explanation:
Determine the length and width of a rectangle if the perimeter is 42 and the length
is six more than twice the width.
Answer: The width would be 5 and the length would be 16
Step-by-step explanation:
If the length is 5… double that up, and you get 10. Six more than ten is 16… double that and you get 32. And then if you add 32+10 you get your total of 42 for the perimeter.
What's the exact area and the exact perimeter of square EFGH shown in the coordinate plane?
Using the distance between two points to find the length of the side of the square, it is found that:
The area is of 50 square units.The perimeter is of [tex]20\sqrt{2}[/tex] units.Hence, option A is correct.The distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
In this problem, the length of the side of the square can be found as the distance between points G and H, that is, the distance between (0,5) and (-5,0), hence:
[tex]l = \sqrt{(0 - (-5))^2 + (5 - 0)^2} = \sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}[/tex]
The area of a square of side length l is given by:
[tex]A = l^2[/tex]
Hence:
[tex]A = (5\sqrt{2})^2 = 50[/tex]
The area is of 50 square units.
The perimeter of a square of side length l is given by:
[tex]P = 4l[/tex]
Hence:
[tex]P = 4(5\sqrt{2}) = 20\sqrt{2}[/tex]
The perimeter is of [tex]20\sqrt{2}[/tex] units.
You can learn more about distance between two points at https://brainly.com/question/18345417
Answer:
IT'S A
Step-by-step explanation: