Answer:
The swimmer must move in the direction 338.2°
Step-by-step explanation:
Since the river flows due south at 1.2 miles per hour and the swimmer swims 3 miles per hour due east of the river, since their directions are perpendicular, the resultant speed is the hypotenuse of the triangle formed by the two perpendicular directions.
The direction of the resultant speed is thus θ = tan⁻¹( vertical component/horizontal component) where vertical component = 1.2 mph due south = -1.2 mph and horizontal component = 3 mph due east = + 3 mph
So, θ = tan⁻¹(-1.2 mph/+ 3mph)
θ = tan⁻¹(-1.2/3)
θ = tan⁻¹(-0.4)
θ = -21.8°
θ = -21.8° + 360° (since we are in the fourth quadrant- between east and south)
θ = 338.2°
So, the swimmer must move in the direction 338.2°.
which expression defines function h?
Answer:
[tex]h(x) = (\frac{f}{g})(x)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 3x^3 + 9x^2 -12x[/tex]
[tex]g(x) = x - 1[/tex]
[tex]h(x) = 3x^2 + 12x[/tex]
Required
What defines h(x)
Looking at the degree of f(x), g(x) and h(x), we have:
[tex]h(x) = (\frac{f}{g})(x)[/tex]
See proof
[tex]h(x) = (\frac{f}{g})(x)[/tex]
This gives:
[tex]h(x) = \frac{f(x)}{g(x)}[/tex]
[tex]h(x) = \frac{3x^3 + 9x^2 -12x}{x - 1}[/tex]
Factorize
[tex]h(x) = \frac{(3x^2 + 12x)(x - 1)}{x - 1}\\[/tex]
[tex]h(x) = 3x^2 + 12x[/tex]
What is the answer to 5/9 + 2/9? Lol please help me
Answer:
7/9
Step-by-step explanation:
Answer:
answer is 7/9
Step-by-step explanation:
5/9 + 2/9 = 7/9
Erin uses a spinner divided into four equal sections to decide which drink she’ll have with her lunch. The sections represent water, milk, lemonade, and tea. If she spins the spinner three days in a row, what is the probability that she drinks lemonade one day, tea one day, and water one day? Complete the steps below to find the sample space and solve the problem. PART A - Create a list of all the possible outcomes for three days of drink selections. Use the abbreviations W, M, T, and L to represent water, milk, tea, and lemonade. PART B - Based on the list you created in part A, how many possible outcomes are there? PART C - What is the probability that Erin drinks lemonade one day, tea one day, and water one day? PART D - What is the probability that Erin drinks water two days and lemonade one day?
Answer:
Part A
W W W M W W T W W L W W
W W M M W M T W M L W M
W W T M W T T W T L W T
W W L M W L T W L L W L
W M W M M W T M W L M W
W M M M M M T M M L M M
W M T M M T T M T L M T
W M L M M L T M L L M L
W T W M T W T T W L T W
W T M M T M T T M L T M
W T T M T T T T T L T T
W T L M T L T T L L T L
W L W M L W T L W L L W
W L M M L M T L M L L M
W L T M L T T L T L L T
W L L M L L T L L L L L
Part B
There are 64 possible outcomes. The sample size is 64.
Part C
To find the probability that Erin drinks lemonade one day, tea one day, and water one day, consider all the cases in which L, T, and W occur one time. Because the order doesn't matter in this scenario, these six outcomes from the list represent the desired event: W T L, T W L, T L W, W L T, L W T, and L T W.
The size of the sample space is 64. So, the probability that Erin drinks lemonade one day, tea one day, and water one day is 3/32.
Part D
To find the probability that Erin drinks water on two days and lemonade one day, we consider all the cases in which two Ws and one L occur. Because the order doesn't matter in this scenario, these three outcomes from the list represent the event: W W L, W L W, and L W W.
The size of the sample space is 64. So, the probability that Erin drinks water two days and lemonade one day is 3/64
Step-by-step explanation:
Construction crews are building a highway between the towns of Washington and Jefferson. Currently the highway is 16.25 miles long. Each month the total length increases by 4.5 miles. Which equation can be used to find y, the total length of the highway in miles after x months?
Noah invested $890 in an account paying an interest rate of 4 5/8% compounded
annually. Riley invested $890 in an account paying an interest rate of 5 1/4%
compounded continuously. To the nearest hundredth of a year, how much longer
would it take for Noah's money to triple than for Riley's money to triple?
Answer:
3.37 years
Step-by-step explanation:
\text{Rate 1: }4\tfrac{5}{8}\%=4+5/8=
Rate 1: 4
8
5
%=4+5/8=
\,\,4.625\%\rightarrow 0.04625
4.625%→0.04625
\text{Rate 2: }5\tfrac{1}{4}\%=5+1/4=
Rate 2: 5
4
1
%=5+1/4=
\,\,5.25\%\rightarrow 0.0525
5.25%→0.0525
890\text{ tripled is }2670
890 tripled is 2670
\text{Calculate Tripling Time for Noah}
Calculate Tripling Time for Noah
\overline{\phantom{\text{Calculate Tripling Time for Noah}}}
Calculate Tripling Time for Noah
\text{Compounded Annually:}
Compounded Annually:
A=P(1+r)^t
A=P(1+r)
t
A=2670\hspace{35px}P=890\hspace{35px}r=0.04625
A=2670P=890r=0.04625
Given values
2670=
2670=
\,\,890(1+0.04625)^{t}
890(1+0.04625)
t
Plug in values
2670=
2670=
\,\,890(1.04625)^{t}
890(1.04625)
t
Add
\frac{2670}{890}=
890
2670
=
\,\,\frac{890(1.04625)^{t}}{890}
890
890(1.04625)
t
Divide by 890
3=
3=
\,\,1.04625^t
1.04625
t
\log\left(3\right)=
log(3)=
\,\,\log\left(1.04625^t\right)
log(1.04625
t
)
Take the log of both sides
\log\left(3\right)=
log(3)=
\,\,t\log\left(1.04625\right)
tlog(1.04625)
Bring exponent to the front
\frac{\log\left(3\right)}{\log\left(1.04625\right)}=
log(1.04625)
log(3)
=
\,\,\frac{t\log\left(1.04625\right)}{\log\left(1.04625\right)}
log(1.04625)
tlog(1.04625)
Divide both sides by log(1.04625)
24.2989=
24.2989=
Calculate Tripling Time for Riley
Compounded Continuously:
A=Pe^{rt}
A=Pe
rt
A=2670\hspace{35px}P=890\hspace{35px}r=0.0525
A=2670P=890r=0.0525
Given values
2670=
2670=
\,\,890e^{0.0525t}
890e
0.0525t
Plug in
\frac{2670}{890}=
890
2670
=
\,\,\frac{890e^{0.0525t}}{890}
890
890e
0.0525t
Divide by 890
3=
3=
\,\,e^{0.0525t}
e
0.0525t
\ln\left(3\right)=
ln(3)=
\,\,\ln\left(e^{0.0525t}\right)
ln(e
0.0525t
)
Take the natural log of both sides
\ln\left(3\right)=
ln(3)=
\,\,0.0525t
0.0525t
ln cancels the e
\frac{\ln\left(3\right)}{0.0525}=
0.0525
ln(3)
=
\,\,\frac{0.0525t}{0.0525}
0.0525
0.0525t
Divide by 0.0525
20.9259=
20.9259=
How much longer for Noah to triple:
24.2989-20.9259
24.2989−20.9259
3.373
3.373
Giving brainliest ; What is the mean of the data set? {20,1,14,14,9,8} Enter your answer in the box.
Answer:
11
Step-by-step explanation:
(20 + 1 + 14 + 14 + 9 + 8) / 6
= 66 / 6
= 11
Creating a parabola in stand form need help. I’m putting up 20 points for this
Step-by-step explanation:
Given that the triangles shown below are similar, what is the value of x? 32 20 H 48M P A. 96 B. 10.7 C. 24 D. 20
Answer:
I DONT SEE TRIANGLES
Step-by-step explanation:
In general, categorical data ___but do not___
O A. classify; measure
O B. measure; classify
O C. value; measure
O D. none of the above
Answer:
The answer is A Lma/o
Step-by-step explanation:
(10, 19), (-13, 9) find distance
Answer:
1,043 km
Step-by-step explanation:
hi hope you have a good dayy
Answer:
Distance between points (10, 19) and (-13, 9) is 25.0799
Step-by-step explanation:
Input Data :
Point 1 (xA, yA) = (10, 19)
Point 2 (xB, yB) = (-13, 9)
Formula : Distance between two points = √(xB − xA)^2 + (yB−yA)^2
Solution :
Distance between two points = √(−13−10)^2+(9−19)^2=
√(−23)^2+(−10)^2
= √529+100
= √629
= 25.0799
hope this helps and is right. p.s i really need brainliest :)
Pj spun the spinner 12 times. He landed on the number 3 four times. How does the theoretical probability compare to the experimental probability
Answer:She spun the arrow. 40 times and recorded the frequencies in the table. Based on the data, what is the probability that the next spin will land on H
Step-by-step explanation:
which features describe the graph of y^2/96^2 - x^2/40^2 = 1? select two options
◽️a focus at (104, 0)
◽️a focus at (0, - 96)
◽️a vertex at (- 40, 0)
◽️a vertex at (0, 96)
◽️the center at (0, 0)
Answer: d and e
Step-by-step explanation:
Edge 2021
The option describes graph 4. a vertex at (0, 96), and 5. the center at (0, 0) from the given equation [tex]\dfrac{y^2}{96^2} - \dfrac{x^2}{40^2} = 1[/tex]
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given equation is
[tex]\dfrac{y^2}{96^2} - \dfrac{x^2}{40^2} = 1[/tex]
From the given equation,
a = 40
b = 96
(h,k) = (0,0),
The vertices are at (0,96) and at (0, -96).
The curves open upward and downward.
c² = a² + b²
c² = 40² + 96²
c² = 10816
c = 104
Therefore the foci are at (0, -104) and (0, 104).
Hence, the option describes the graph
4. a vertex at (0, 96) is correct.
5. the center at (0, 0) is correct.
Learn more about equations here;
https://brainly.com/question/27056029
#SPJ2
Find the measure of the missing angles. Help please
Answer:
< 1 = 92º
< 2 = 24º
< 3 = 35º
< 4 = 35º
< 5 = 81º
Step-by-step explanation:
< 1 = 180 - 88 = 92
< 3 = 64 corresponding angle due to parallel lines
< 2 = 180 - (92 + 64) = 24
< 4 = 180 - (64 - 81) = 35
< 5 = 180 - (64 + 35) = 81
If y varies inversely as x, and y= 12 as x=2, how do you find the y for the x-value of 6?
Answer: X=4 and y=4
Step-by-step explanation:
Answer:
x =4
Explanation: As x and y are inversely proportional, the equation can be represented as x=k/y.
Substituting x=2 and y=12, we get 2=k/12=> k=12⋅2 => k=24.Equation can be represented as x=24/y. So, when y=6, we get x=24/6 => x=4
What is the radius of the circle? Hurrry
Answer:
8 in
Step-by-step explanation:
Given,
Diameter ( circle ) = 16 in ( from the diagram )
To find : Radius ( circle ) = ?
Formula : -
Radius ( circle ) = Diameter ( circle ) / 2
Radius ( circle )
= 16 / 2
= 8 in
Why would the volumes of the two figures be the same?
Answer:
They would sill be the same because just because the other shape is lopsided doesn't mean its different than the other. They can me moved left or right but they will still have the same volume.
Step-by-step explanation:
As 3D shearing transformations preserves the volume of figure, the volumes of the two figures would be the same.
What is shearing transformation in geometry?"Shearing is the process of slanting a three- dimensional geometrical object in 3-D space either in x, y, or in the z-direction."
For given example,
We can observe that figure 2 is a result of shearing transformation on figure 1.
We know, a three-dimensional shearing transformation preserves the volume of solid figures.
This means, the volume of both the figures is same.
Also, we can observe that the length, width and height of the both figures are equal.
Therefore, the volumes of the two figures would be the same.
Learn more about shearing transformation here:
https://brainly.com/question/23834102
#SPJ2
2(x + 4)2 = 20 solve by square roots
Answer:
x = − 4 ± √ 10,
Step-by-step explanation:
2(x + 4)² = 20
=> 2(x + 4) (x + 4) = 20
=> 2x + 8 (x + 4) = 20
=> 2x² + 8x + 8x + 32 = 20
=> 2x² + 16x + 32 = 20
=> 2x² + 16x + 12 = 0
=> Now solve using the quadratic formula:
x = − 4 ± √ 10,
Radical form: − 4 ± √ 10,
Decimal form: -0.84, -7.16
Hope this helps!
HELPPPPPPP SUMMMMBODYYY
B or A. I'm not sure, because i learned this 5 years ago, but it is a or b. the only reason i dont know which one is because i forgot what a filled in dot, versus a circle means. on point 3 on your number line, there's a circle, and there's a dot on answer A and answer B respectively. if memory serves, it should be B
Four students explain how to find the measure of ZRST in this diagram.
S
75°
53 R
т
Which student correctly explains how to find the measure of ZRST given the angle measures shown?
A Amy says to use vertical angles to find the measure of ZSRT and add this measure to 75º.
® Brett says to use complementary angles to find the measure of ZSRT and add this measure to 75º.
© Cate says to use vertical angles to find the measure of ZSRT, add this measure to 75º. and then subtract
from 180
D Dylan says to use complementary angles to find the measure of ZSRT, add this measure to 75°, and then
subtract the sum from 180°
Answer:
To find the angle RST we have to first find SRT As the exterior angle adjoined with SRT =53°
so the SRT = Outer angle adjoined with angle SRT
angle SRT = 53° [°.° vertically opposite angles are equal]
Angle SRT + Angle STR + Angle RST = 180°
=>53° + 75° + Angle RST =180°
=> 128° + Angle RST = 180°
=> Angle RST =(180-128)°
= 52°
SO NO. C IS correct what Cate says is absolutely right
Ill give brainliest to first person to answer CORRECTLY! I don't have all day.
34 + 2 ⋅ 5 = ____
Answer:
180
Step-by-step explanation:
34+2=
36
36 . 5=
180
Answer:
44
Step-by-step explanation:
2x5=10
10+34=44
hope this helped :3
Practice:
Complete the table:
a. 1
b. -1
c. 2
d. 0
Please select the best answer from choices provided
Answer:
D. 0
Step-by-step explanation:
I calculated logically
The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
MIN X1 + X2 + X3 + X4
s.t. X1 + X4 ≥ 12 ........(on duty during shift 1)
X1 + X2 ≥ 15 ........(on duty during shift 2)
X2 + X3 ≥ 16 ........(on duty during shift 3)
X3 + X4 ≥ 14 ........(on duty during shift 4)
X1, X2, X3, and X4 ≥ 0
Given the optimal solution: X1* = 13, X2* = 2, X3* = 14, X4* = 0, how many workers would be assigned to shift 2?
a. 13
b. 12
c. 14
d. 15
e. 2
Answer:
d. 15
Step-by-step explanation:
Putting the values in the shift 2 function
X1 + X2 ≥ 15
where x1= 13, and x2=2
13+12≥ 15
15≥ 15
At least 15 workers must be assigned to the shift 2.
The LP model questions require that the constraints are satisfied.
The constraint for the shift 2 is that the number of workers must be equal or greater than 15
This can be solved using other constraint functions e.g
Putting X4= 0 in
X1 + X4 ≥ 12
gives
X1 ≥ 12
Now Putting the value X1 ≥ 12 in shift 2 constraint
X1 + X2 ≥ 15
12+ 2≥ 15
14 ≥ 15
this does not satisfy the condition so this is wrong.
Now from
X2 + X3 ≥ 16
Putting X3= 14
X2 + 14 ≥ 16
gives
X2 ≥ 2
Putting these in the shift 2
X1 + X2 ≥ 15
13+2 ≥ 15
15 ≥ 15
Which gives the same result as above.
1. If the function f can be expressed with
the equation f(x) = -x2 – 3x - 10, find the
value of f(-2)
Answer:
f(-2) = -8
Step-by-step explanation:
Plug in x=-2 into the function:
f(x) = -x² - 3x - 10
f(-2) = -(-2)² - 3(-2) - 10
f(-2) = -4 - (-6) - 10
f(-2) = -4 + 6 - 10
f(-2) = 2 - 10
f(-2) = -8
Find the remainder when x3 - 2x2 + x + 1 is divided by (x - 2).?
Answers are 0-5 5-10 10-15 15-20 20-25
what is 4/7 times 4/4 in simplest form
struggling with homework!!
Answer:
40
Step-by-step explanation:
if 20% were Caesar and 20 divided by 5 is 4, then every four salads sold is five percent.
Identify the domain of the function shown in the graph.
10-
8
8
4
2
-8-8-4
-2
-2-
2
4
8
8
10 12
4
-B
-8
-10
Answer:
domain means x- component I hope you you can identify the domain
A limousine company charges $1.50 per mile plus a mandatory $25 tip. Ms. Warwick gave the limousine driver a total of $62.50. What is the total miles driven and the equation to solve it?
Answer:
25 total miles the equation is 1.50x+25=62.50
Step-by-step explanation:
Answer:25 MILES driven
subtract 25 from 62.50 which is 37.50.
Then: Divide 37.50 to 1.5 which is 25.
Step-by-step explanation:
Write 0.000 376 in standard form.
Answer:
0.000376 in standard form
=3.76×10^-4
