Answer:
Step-by-step explanation:
I'm going to use Physics here for this concept of vectors. Here are some stipulations I have set for the problem (aka rules I set and then followed throughout the problem):
** I am counting the 50 m as 2 significant digits even though it is only 1, and I am counting 200 as 3 significant digits even though it is only 1. 1 sig dig doesn't really give us enough accuracy, in my opinion.
** A bearing of .25 degrees is measured from the North and goes clockwise; that means that measured from the x axis, the angle is 89.75 degrees. This is the angle that is used in place of the bearing of .25 degrees.
** Due east has an angle measure of 0 degrees
Now let's begin.
We need to find the x and y components of both of these vectors. I am going to call the first vector A and the second B, while the resultant vector will be C. Starting with the x components of A and B:
[tex]A_x=50cos(89.75)[/tex] so
[tex]A_x=.22[/tex]
[tex]B_x=200cos(0)[/tex] so
[tex]B_x=200[/tex] and we need to add those results together. Due to the rules for adding significant digits properly, the answer is
[tex]C_x=200[/tex] (and remember I am counting that as 3 sig fig's even though it's only 1).
Now for the y components:
[tex]A_y=50sin(89.75)[/tex] so
[tex]A_y=50[/tex] (which I'm counting as 2 sig fig's)
[tex]B_y=200sin(0)[/tex] so
[tex]B_y=0[/tex] and we need to add those results together.
[tex]C_y=50[/tex]
Now for the resultant magnitude:
[tex]C_{mag}=\sqrt{(200)^2+(50)^2}[/tex] and that gives us a final magnitude of
[tex]C_{mag}=206[/tex] m
Now for the angle:
Since both the x and y components of the resultant vector are in quadrant 1, we don't need to add anything to the angle to get it right, so
[tex]tan^{-1}(\frac{50}{200})=14[/tex]
The girl is 206 meters from her starting point at an angle of 14 degrees
Jane spent 3 hours exploring a mountain with a dirt bike. First, she rode 48 miles uphill. After she reached the peak she rode for 15 miles along the summit. While going uphill, she went 5 mph slower than when she was on the summit. What was her rate along the summit?
Answer: [tex]25\ mph[/tex]
Step-by-step explanation:
Given
Jane took 3 hours
First she rode 48 miles with let say with [tex]x[/tex] mph
then she rode 15 miles with speed [tex](x+5)[/tex] mph
Equate the time in each ride and equate it to total time
[tex]\Rightarrow 3=\dfrac{48}{x}+\dfrac{15}{x+5}\\\\\Rightarrow 3x(x+5)=48(x+5)+15x\\\\\Rightarrow 3x^2+15x=48x+48\times 5+15x\\\\\Rightarrow 3x^2-48x-240=0\\\\\Rightarrow (x-20)(x+4)=0\\\\\text{Neglecting the negative value as speed cannot be negative}\\\\\Rightarrow x=20\ mph[/tex]
So, her along the summit is [tex]x+5=25\ mph[/tex]
The figure that will be formed if two 45° 45° 90° setsquares are put together is _________.
The population of a town is 157,220 and is decreasing at a rate of 0.8% each year. Predict the population in 5 years (round to the nearest whole number).
Answer:
151,031
Step-by-step explanation:
If the population of a town is decreasing at 0.8% each year, the new population of the town will be [tex]100\%-0.8\%=99.2\%[/tex] of what it was last year. To find 99.2% of something, multiply it by 0.992. Therefore, we can write the following equation:
[tex]f(x)=157,220\cdot 0.992^x[/tex], where [tex]f(x)[/tex] is the population of the town [tex]x[/tex] years after the town had a population of 157,220.
Substitute [tex]x=5[/tex] into this equation to get the projected population after 5 years:
[tex]f(5)=157,220\cdot 0.992^5, \\f(5)=151031.019048,\\f(5)\approx \boxed{151,031}[/tex]
Therefore, in 5 years, the population should be 151,031.
Daniela buys records for $9 each
if daniela buys 4 records how much money will she spend?
Money spent( )
Answer:
36
Step-by-step explanation:
9×4=36 so money spent will be 36 dollars
please help with this on the images
Answer:
52%
7 more
Step-by-step explanation:
There are 5*5 = 25 boxes in the grid
13 are shaded
13/25 = 13/25 *4/4 = 52/100 = 52% are shaded
We want 80% shaded
80/100
Divide top and bottom by 4
20/25
We need 20 shaded and have 13 shaded
20-13 = 7
We need to shaded 7 more
The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion differs from 30%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.5. Find the P-value for a two-tailed test of hypothesis.
Answer:
The appropriate answer is "0.0124".
Step-by-step explanation:
Given:
Test statistics,
z = 2.5
By using the z-table,
p value for one tailed test will be:
= 0.0062
For two-tailed test,
⇒ [tex]p \ value = 2\times 0.0062[/tex]
[tex]=0.0124[/tex]
Finish the following table for the given function with x as the independent variable
Answer:
hi?
Step-by-step explanation:
The price of an item changed from $175 to $150. Later, the price decreased to $125. Which of the two decreases was larger in percentage and how much is it?
Answer:
The second decrease is larger at 16 1/6% decrease
Step-by-step explanation:
175 to 150
Take the original price minus the new price divided by the original price
(175 -150) /175 =25/175 = 1/7 =.142857143 = 14.28 % decrease
150 to 125
Take the original price minus the new price divided by the original price
( 150-125)/150 = 25/150 = 1/6 =.16666 = 16 1/6 % decrease
The second decrease is larger at 16 1/6% decrease
Two boys are running track. They decide to start in the northwest corner and go opposite directions around the rectangular track. If the width of the track is 150 yards and the diagonal is 240 yards, what is the length of the track?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The length of the rectangular track is 187.35 yards.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the width of the track is 150 yards and the diagonal of the track is 240 yards. The length of the track is,
(Diagonal)² = (Length)² + (Width)²
240² = Length² + 150²
Length = √(240²-150²)
Length = 187.35 yards
Hence, the length of the rectangular track is 187.35 yards.
Learn more about Pythagoras' Theorem:
https://brainly.com/question/14461977
#SPJ2
PLEASE HELP!! Angle K has a measure of 83° and is reflected across the line y = 2 to get angle K'.
What is the measure of angle K'?
Enter your answer as the correct value, like this: 42
Answer:
[tex]K' = 83^o[/tex]
Step-by-step explanation:
Given
[tex]K = 83^o[/tex]
Reflection: [tex]y= 2[/tex]
Required
K'
The general rule is that, reflection does alter measurements (angles or lengths).
So, this means that K' will have the same measure as K.
i.e.
[tex]K' = K[/tex]
[tex]K' = 83^o[/tex]
What is the area of this polygon
Answer:
51
Step-by-step explanation:
1. Approach
One is given the polygon, (ABCDE); the problem asks one to find the area of this polygon. The most logical step to take is to divide this polygon into easier parts, find the area of each part, and then add up the area to find the total area of the figure.
One way to divide this figure up is to draw the line (AC). This will create the triangle (ABC) and rectangle (ACDE).
2. Find the area of (ABC)
The formula to find the area of a triangle is the following:
[tex]A=\frac{b*h}{2}[/tex]
Where (b) is the base of the triangle, and (h) is the height. The base of the triangle (ABC) is (AC), which has a measure of (6) units. The height of the triangle is the distance from the base of the triangle to the vertex opposite the base. This measurement is (3) units. Substitute these values into the formula and solve for the area:
[tex]A=\frac{b*h}{2}[/tex]
Substitute,
[tex]A=\frac{6*3}{2}\\\\A=\frac{18}{2}\\\\A=9[/tex]
3. Find the area of (ACDE)
The formula to find the area of a rectangle is as follows:
[tex]A=b*h[/tex]
The base of the rectangle is the segment (AE), with a measure of (7) units. The height of the rectangle is the segment (AC) with a measurement of (6) units. Substitute these values into the formula and solve for the area:
[tex]A=7*6\\\\A=42[/tex]
4. Find the area of the total figure
To find the area of the total figure, add up the area of the triangle, and the area of the rectangle:
[tex]9+42= 51[/tex]
choose the equation that satisfies the data in the table
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
See this attachment
option D is correctReview the data you collected for the angles in Question 2. Notice that ∠CFB is one of four angles formed by the two intersecting chords. What relationship do you observe that could help you determine the measure of any of the four angles created by two intersecting chords? Write the relationship as an equation.
Answer:
The measure of an angle created by two intersecting chords is half the sum of the measure of the intercepted arc and the measure of the arc vertically opposite to the angle. In this case, I can write m∠CFB = 1/2(m∠CAB + m∠EAD) because the measure of an intercepted arc is equal to the measure of its corresponding central angle.
Explanation:
sample answer from edmentum
In a function, y varies inversely with x. The consistent of variation is 4. Which table could represent the function?
Answer:
none of the tables shown
Step-by-step explanation:
Inverse variation is
xy = k where k is the constant
xy = 4
in the top table
-2*2 = -4 so it cannot be the first table
In the middle table
-2 * -8 = 16 so it is not the middle table
In the bottom table
-2 *4 = -8 so it is not the bottom table
There must be a table not shown
If F is conservative, find all potential functions f for F so that F = ∇f. (If F is not conservative, enter NOT CONSERVATIVE. Use C as an arbitrary constant.)
Answer: some parts of your question is missing below is the missing data
Determine if the given vector field F is conservative or not. F = −6e^y, (−6x + 3z + 9)e^y, 3e^y
answer:
F is conservative
F = -6xe^y + ( 33 + 9 ) e^y + C
Step-by-step explanation:
The Potential functions for F so that F = ∇f.
F = -6xe^y + ( 33 + 9 ) e^y + C
attached below is a detailed solution
The length of a rectangle is 3 times the width. The perimeter of the rectangle is 64 cm. Show the equation that would be used to find the dimensions of the rectangle.
Answer:
64 = 2(3x + x)
Step-by-step explanation:
Perimeter of the rectangle = 64 cm
Width of the rectangle = x
Length of the rectangle = 3x
Perimeter of a rectangle = 2(length + width)
The equation is
64 = 2(3x + x)
64 = 6x + 2x
64 = 8x
x = 64/8
x = 8 cm
Width of the rectangle = x = 8 cm
Length of the rectangle = 3x
= 3(8 cm)
= 24 cm
Examine circle O, where chords AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are congruent.
Point P lies on AB¯¯¯¯¯¯¯¯ and point Q lies on CD¯¯¯¯¯¯¯¯.
Angles APO and DQO are right angles.
The diagram as described in the problem.
Which congruence statement is true?
CD≅AP
QD≅QO
OP≅OQ
OP≅AB
Answer:
Option 3
Step-by-step explanation:
Given:
AB ≅ CD
Point P lies on AB and point Q lies on CD.
∠APO = ∠DQO = 90°
By theorem, if two chords in a circle are equal in measure, then they will be equidistant from the center.
Therefore, OP and OQ will be congruent.
Option (3) will be the answer.
Caroline earns $49000 a year, and her friend Jennifer earns $51000 a year but doesn't belong to a health fund. The tax rule this year is $40000 and above pay $5000 plus 40 cents in the dollar in tax on anything over $40000 per annum and $50000 and above pay $ 9000 plus 30 cents in the dollar in tax on anything over $ 50,000per annum, plus 2% of her income if he is not in a health fund.
Answer:
Caroline has to pay $8600 taxes
Jennifer has to pay $10320 taxes
Step-by-step explanation:
I guess the question is who has to pay how much taxes, right ?
Caroline earns $49000, and I guess, she belongs to a health fund.
she has to pay $5000 for the first $40000.
and for the remaining $9000 she has to pay $0.40 per dollar.
that means 9000×0.4 = $3600
and no penalties for no health fund.
so altogether $5000 + $3600 = $8600 taxes
Jennifer earns $51000 and did not belong to a health fund.
she has to pay $9000 for the first $50000.
and for the remaining $1000 she had to pay $0.30 part dollar.
that means 1000×0.3 = $300
and 2% of the total income because no health fund
51000×0.02 = $1020
so, altogether $9000+$300+$1020 = $10320 taxes
if the mean of x1,x2,x3 and x4 is 6 then find the mean of x1+10,x2+8,x3+16 and x4+2
Answer:
f the mean of this set is equal to 20, we can write down the below equation,
20 = (x1 + x2 +x3 + .... + x10)/10
x1 + x2 + x3 + ... x10 = 200
Then we can also write an equation for the mean of the given numbers as below,
Mean = [(x1+4) + (x2+8) + (x3+12) + .... + (x10+40)]/10
= (x1 + x2 + x3 + ... + x10 + 4 + 8 + 12 + ... + 40)/10
Then we can use above equation (1) to replace x1 + x2 + x3 + ... + x10 by 200
Mean = (200 + 4 + 8 +12 + 16 + 20 + 24 + 28 + 32 + 36 + 40)/10
= 420/10
= 42
If you remember Arithmetic Progressions you can simply add together the above number set.
If you closely look above, you can find that there is an Arithmetic Progression : 4, 8, 12, ... , 40
Here we want the addition of 10 terms. So we can use,
Sn = n/2(a+l)
S10 = 10/2(4+40)
= 220
Then you can easily get the answer,
Mean = (200 + 220)/10
= 42
The mass of 5 m' of copper is 44 800 kg. Work out
the density of copper.
Expand and Simplify
10a-(3a+7)
Which coordinate pair identifies a point in the third quadrant of the coordinate plane? A) (0, 5) B) (1, −5) C) (1, 5) D) (−1, −2)
(IF YOU USE THIS QUESTION FOR POINTS I WILL REPORT YOU)
(NVM IT'S (-1,-2)
Answer:
Me need my points :D
Step-by-step explanation:
Solve the equation P=s+t+r for s.
Answer:
[tex]\huge\boxed{\boxed{s=P-t-r}}[/tex]
Step-by-step explanation:
[tex]P=s+t+r\qquad|\text{subtract}\ t\ \text{and}\ r\ \text{from both sides}\\\\P-t-r=s+t+r-t-r\\\\P-t-r=s\Rightarrow\boxed{s=P-t-r}[/tex]
A cylindrical roller is 4m long. Its diameter is 1.4m. How many metres does it travel in 500 revolution?
Step-by-step explanation:
the answer is in the image above
Question 3
1 pts
Students from Mr. Caldwell's Spanish class are saving money for a summer
trip to Barcelona, Spain. Each student needs to raise $1,080 to be able to
attend the trip. This amount represents an increase of 12.5% over the cost of
the trip last year. How much did the trip to Barcelona cost last year?
O $850
$960
$1,215
$1,030
Answer:
$960
Step-by-step explanation:
Let the original amount be = x
Percentage increase is equal to = 12.5%
final amount = original amount + increase
final amount = x + 0.125x
final amount = 1.125x
final amount = 1080 = 1.125x
and then solve for x
[tex]x = \frac{1080}{1.125} \\ \\ x = 960[/tex]
so in the end x is equal to $960
Solve the equation: 1080 = 1.25x
solve the formula for a
(q&c in picture)
Answer:
C
Step-by-step explanation:
Subtract Vot from the given equation
s - Vo*t = 1/2 a t^2 Multiply by 2
2(s - Vo*t) = at^2 Divide by t^2
2(s - Vo*t) / t^2 = a
Looks like C is the answer.
HELPASAP
A circle with an arc length of ____ centimeters is intercepted by a central angle of 3pi/4 radians has a radius of ____ centimeters.
1st Blank Options: 12pi, 4pi, 2pi
2nd Blank Options: 3, 16, 24
Answer:
add an attachm3nt to make iy clear
Which function is shown in the graph below? Please hurry I’m being timed!!!
Heidi solved the equation
3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below:
3x + 12 + 2 = 2 + 5x – 20
3x + 14 = 5x – 18
14 = 2x – 18
32 = 2x
16 = x
Answer:
The answer is correct
Step-by-step explanation:
3(x + 4) + 2 = 2 + 5(x – 4)
3x + 12 + 2 = 2 + 5x - 20
3x + 14 = 5x - 18
-2x = -32
x = 16
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM JUST NOT SMART
PLEASE GIVE EXPLANATION
Answer:
Ellipse
[tex]✔ \: \: : { \sf{ {x}^{2} + {y}^{2} = 1 }}[/tex]
Step-by-step explanation:
[tex]{ \sf{circle : \: {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0}} \\ { \sf{parabola : \: {y}^{2} = 4ax }} \\ { \sf{hyperbola : \: {x}^{2} - {y}^{2} = 1 }}[/tex]
