Answer:
D. The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).
The hypothenus is the distance travelled by the plane which is 83 meters (h)
The height of the tower is 98 Meters
We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.
According to Pythagorean theorem
(x^2) + (y^2) = h^2
y = √ (h^2) - (x^2)
y = √ (83^2) - (42^2)
y= √(6889 - 1764)
y= 71.59 Meters
The height from the plane's position to the top of the tower will be
Height difference = 98 - 71.59 = 26.41 Meters
So the plane should go about 27 Meters higher to clear the tower
Find a • b. a = 5i + 7j, b = -4i + 3j (5 points)
<1, 10>
<-20, 21>
1
41
Answer:
[tex]a\cdot b[/tex] = 1
Step-by-step explanation:
Given that,
Vector [tex]a=5i+7j[/tex]
Vector [tex]b=-4i+3j[/tex]
We need to find [tex]a{\cdot} b[/tex] means the dot product of a and b. So,
[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)[/tex]
We know that,
[tex]i{\cdot}i, j{\cdot}j,k{\cdot}k=1\ \text{and}\ i{\cdot}j= j\cdot i=0[/tex]
So,
[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)\\\\=5i{\cdot}(-4i)+5i{\cdot} 3j+7j\cdot(-4i)+7j\cdot 3j\\\\=-20+21\\\\=1[/tex]
So, the value of [tex]a\cdot b[/tex] is 1.
Answer:
1
Step-by-step explanation:
The Colonel spots a campfire at a bearing N 59∘59∘ E from his current position. Sarge, who is positioned 242 feet due east of the Colonel reckons the bearing to the fire to be N 34∘34∘ W from his current position.
Determine the distance from the campfire to each man, rounded to the nearest foot.
Colonel is about............................ feet away from the fire
Sarge is about............................... feet away from the fire
Answer:
i. Colonel is about 201 feet away from the fire.
ii. Sarge is about 125 feet away from the fire.
Step-by-step explanation:
Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.
The total angle at the campfire from both the Colonel and Sarge = [tex]59^{0}[/tex] + [tex]34^{0}[/tex]
= [tex]93^{0}[/tex]
Thus,
<CAB = [tex]90^{0}[/tex] - [tex]59^{0}[/tex] = [tex]31^{0}[/tex]
<CBA = [tex]90^{0}[/tex] - [tex]34^{0}[/tex] = [tex]56^{0}[/tex]
Sine rule states;
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]
i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;
[tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{b}{Sin 56^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]
[tex]\frac{b}{0.8290}[/tex] = [tex]\frac{242}{0.9986}[/tex]
cross multiply,
b = [tex]\frac{0.8290*242}{0.9986}[/tex]
= 200.8993
Colonel is about 201 feet away from the fire.
ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{a}{Sin 31^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]
[tex]\frac{a}{0.5150}[/tex] = [tex]\frac{242}{0.9986}[/tex]
cross multiply,
a = [tex]\frac{0.5150*242}{0.9986}[/tex]
= 124.8073
Sarge is about 125 feet away from the fire.
In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=10 and BC=2, what is the area of the shaded region? Answer as a decimal, if necessary. Little confused on this one.
Answer:
10 units²
Step-by-step explanation:
Consider the unshaded region to consists of 2 triangles, ∆AED and ∆BEC, which are both of equal dimensions. Their bases and heights are both the same. Both triangles are embedded inside a rectangle ABCD.
Area of the shaded region = Area of rectangle - area of the 2 triangles.
Area of rectangle = l*w
l = 10
w = 2
[tex] Area_R = 10*2 = 20 units^2 [/tex]
Area of the 2 triangles = 2(½*b*h)
b = 2
h = 5
[tex]Area_T = 2(\frac{1}{2}*2*5)[/tex]
[tex] Area_T = 1*2*5 = 10 units^2 [/tex]
Area of shaded region = 20 - 10 = 10 units²
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9 } A= {1, 2, 3, 4} and B= {4, 5, 6, 7}. Draw the Venn diagram of A ∩B. Answer with full explanation and diagram will be marked as brainliest for sure!!!
Step-by-step explanation:
Its mean the same number for both A and B which is only 4.
Carolyn and Paul are playing a game starting with a list of the integers $1$ to $n.$ The rules of the game are: $\bullet$ Carolyn always has the first turn. $\bullet$ Carolyn and Paul alternate turns. $\bullet$ On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list. $\bullet$ On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed. $\bullet$ If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers. For example, if $n=6,$ a possible sequence of moves is shown in this chart: \begin{tabular}{|c|c|c|} \hline Player & Removed \# & \# remaining \\ \hline Carolyn & 4 & 1, 2, 3, 5, 6 \\ \hline Paul & 1, 2 & 3, 5, 6 \\ \hline Carolyn & 6 & 3, 5 \\ \hline Paul & 3 & 5 \\ \hline Carolyn & None & 5 \\ \hline Paul & 5 & None \\ \hline \end{tabular} Note that Carolyn can't remove $3$ or $5$ on her second turn, and can't remove any number on her third turn. In this example, the sum of the numbers removed by Carolyn is $4+6=10$ and the sum of the numbers removed by Paul is $1+2+3+5=11.$ Suppose that $n=6$ and Carolyn removes the integer $2$ on her first turn. Determine the sum of the numbers that Carolyn removes.
Answer:
The sum of the numbers that Carolyn removes is 5.
Step-by-step explanation:
The provided instruction for the game are:
Carolyn always has the first turn. Carolyn and Paul alternate turns.On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list.On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed.If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers.The value of n is supposed as 6.
And it is also provided that Carolyn removes the integer 2 on her first turn.
The table displaying the outcomes of the game are as follows:
Player Removed Remaining
Carolyn 2 1, 3, 4, 5, 6
Paul 1 3, 4, 5, 6
Carolyn 3 4, 5, 6
Paul 6 4, 5
Carolyn None 4, 5
Paul 4, 5 None
The sum of the numbers that Carolyn removes is:
S = 2 + 3 = 5
Thus, the sum of the numbers that Carolyn removes is 5.
I believe the answer is 8, but I am not sure.
100 students are interviewed to see which of biology, chemistry or physics they prefer.
59 of the students are girls. 35 of the girls like biology best.
2 of the boys prefer physics.
6 out of the 30 who prefer chemistry are girls.
What percentage of the students prefer biology?
Answer:
50%
Step-by-step explanation:
Girls Boys
total: 59 total: 41
- Chemistry 35 - Physics 2
= 24 = 39
- Chemistry ( 30 - 6 ) 24
= 15
Total boys and girls for Biology = 35 + 15 = 50
% = 50/100*100
= 50%
Hope it helps and also mark it as brainliest!!!!1.
The ratio of the numbers of sides of two regular polygons is 1:2 .If each interior angle of the first
polygon is 1200 then the measure of each interior angle of the second polygon
is
(1)1400
(2)1350
(3)1500
(4)1600
first polygon
ext. angle=180°-120°
=60°
[tex]ext \: ang = \frac{360}{n} [/tex]
n=360°/60°
n=6
second polygon
n=2(6)=12
ext. ang= 360°/n = 360°/12° = 30°
int. ang = 180°-30°= 150°
answer is C
If the ratio of the numbers of sides of two regular polygons is 1:2 and each interior angle of first angle is 120° then the measure of each interior angle of the second polygon is 150° which is option 3).
What is regular polygon?A regular polygon is a polygon whose all sides are equal to each other.
How to find interior angle?We have been given ratio of sides of two polygon that is 1:2 and the interior angle of first polygon that is 120 degrees.
Exterior angle will be 180-120=60°
We know that exterior angle =360/n where n is the sides of the polygon.
60=360/n
n=360/60
n=6
Number of sides of other polygon=2*6=12
Exterior angle=360/n
=360/12
=30
Interior angle=180-30=150°
Hence the interior angle of the second polygon is 150 degrees.
Learn more about regular polygon at https://brainly.com/question/1592456
#SPJ2
On the maturity date of a $10,800, 6-month, 8% note, the borrower sends a check that includes the principal and all of the interest due on the note. What is the amount of the borrower's check?
Answer: $ 11,232.00
Step-by-step explanation:
Given: Amount = $ 10,800
Interest Rate = 8% =0.08
Time in Months= 6.00
Formula :
Interest on Note = (Amount)× (Interest Rate) × ((Time in Months) /12)
= (10800)× (0.08)× (6/12)
= $432
The amount of the borrower's check =(Amount + Interest on Note)
= $ (10,800+432)
= $ 11,232.00
Hence, The amount of the borrower's check = $ 11,232.00
A population consists of 100 elements. We want to draw a simple, random sample of 20 elements from this population. On the first selection, the probability of any particular element being selected is ____.
Answer:
1/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event /total outcome
Since the population consists of 100 elements, the total outcome of event = 100.
If random sample of 20 element is drawn from the population, the expected outcome = 20
On the first selection, the probability of any particular element being selected = 20/100 = 1/5
find out what's wrong with this graph
Answer:
The y-axis is upside down, meaning that instead of the values increasing as they go up, they decrease.
determine each unknown addend ___ + 41=-18
Answer:
-59
Step-by-step explanation:
x+41=-18
x= -18-41
x = -59
PLEASE HELP ME!!! The students in Suzanne's school are painting a rectangular mural outside the building that will be 15 feet by 45 feet. To prepare they are create a scale drawing that represents 20% of the given dimensions. What is the length and width of the scale drawing?
Answer:
length of scale drawing = 9 feet
width of scale drawing = 3 feet
Step-by-step explanation:
Actual dimension 15 feet by 45 feet.
length = 45 feet
width = 15 feet
Dimension on drawing is 20% of actual dimension.
20% = 20/100
Thus,
20% of 15 feet = 20/100 * 15 feet = 3 feet
20% of 45 feet = 20/100 * 45 feet = 9 feet
Thus, length of scale drawing = 9 feet
width of scale drawing = 3 feet
If the true mean is 50 and we reject the hypothesis that μ = 50, what is the probability of Type II error? Hint: This is a trick question.
Answer:
Zero
Step-by-step explanation:
Given that:
the true mean is 50 and we reject the hypothesis that μ = 50
The probability of the Type II error will be zero, given that we reject the null hypothesis. This has nothing to do with if it is true or false.
Type II error is occurs when you accept a false null hypothesis. The probability of this error is denoted by beta which relies on sample size and population variance.
The probability of rejecting is equal to one minu beta. i.e it is the researchers goal to reject a false null hypothesis.
Do not use spaces in your answer. Solve for x. -5x + 12x - 8x = -24 x = ___ a0
Answer:
[tex]\Huge \boxed{x=24}[/tex]
Step-by-step explanation:
[tex]-5x + 12x - 8x = -24[/tex]
Combine all like terms.
[tex](-5+ 12- 8)x = -24[/tex]
[tex]-x=-24[/tex]
Multiply both sides by -1.
[tex]x=24[/tex]
Answer:
x must be 24
Step-by-step explanation:
I assume you meant " -5x + 12x - 8x = -24
Combine the x terms on the left side, obtaining -x = -24.
Then x must be 24
Question 2 (1 point)
Saved
A year ago, Rebecca purchased 100 shares of Havad stock for $20 per share.
Yesterday, she placed a limit order to sell her stock at a price of $33 per share before
the market opened. The stock's price opened at $23 and slowly increased to $26 in
the middle of the day, before declining to $22 by the end of the day. The stock did
not pay any dividends over the period in which Rebecca held it. Given Rebecca's
initial investment of $ 20 per share, her return is
Answer:
Rebecca does not have a return yet because the stock was not sold since there was a limit order at $33.
However, the value of her investment can be put around $2,400 (100 x $24 average price).
Step-by-step explanation:
Price of Havad Stock bought a year ago = $20
No. of shares = 100
Limit order selling price = $33
Stock prices during the limit order day = $23, $26, and $22
The stock cannot be sold, since its price did not reach $33.
Rebecca's limit order is an order to buy or sell her stock in Havad at $33 or better. Since her order is a sell limit order, it can only be executed at the limit price of $33 or higher. Unfortunately, the price of the stock did not reach the limit order on that particular day. This implies that her limit order is not guaranteed to execute.
Find the missing term in the
geometric sequence.
13,[ ? ],208
Answer:
110.5
Step-by-step explanation:
208=13+(3-1)d
208=13+2d
-13. -13
195=2d
÷2. ÷2
97.5=d. (d means difference)
13(first term)+97.5=110.5
Answer: 676
Step-by-step explanation: r/13=208/r
r²=2704
r=52
13x52=676
What is the lateral area of the drawing is it a 200 km.b. 425.c.114d.1021km
Answer:
114 km
Step-by-step explanation:
Each side is an isosceles trapezoid, so ED=2 since you would need to add 2 to each end of the bottom line to get the top line. Now use Pythagorean Theorem to get ED^2+AD^2=AE^2. Plug in your numbers to solve for AE. This is the height of each trapezoid. Then use your formula for the area of a trapezoid, (B1+B2)h/2, to get the area of each side, then multiply by 4 to get the lateral area since there are 4 sides. Remember lateral area is just the sides, then surface area is when you include the area of the two bases.
What is the name of a number that can be written in the form a + bi where a and b are nonzero real
numbers? (1 point)
a pure imaginary number
an imaginary unit
a real number
a complex number
Answer:
Complex numbers
Step-by-step explanation:
Given
[tex]a + bi[/tex]
Required
Determine the type of number in that form
Numbers written in [tex]a + bi[/tex] are referred to as complex numbers
Where [tex]a \neq 0[/tex]; [tex]b\neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]
Note that a and b can either integers or non integers and a and be can also be positive or negative
The following are valid examples of complex numbers
[tex]2 + 3i[/tex]
[tex]2.4 - 5i[/tex]
[tex]-3 - i[/tex]
and lots more..
15 POINTS AND BRAINLIEST JUST HELP ME PLZZZZZ 4x^2 + 28x + 49 = 0 Rewrite equation (x + __ )^2 = __
Answer:
[tex]\boxed{(x+7)^2 =-3x^2-14x}[/tex]
Step-by-step explanation:
[tex]4x^2 + 28x + 49 = 0[/tex]
[tex]\sf Subtract \ 3x^2 \ and \ 14x \ from \ both \ sides.[/tex]
[tex]4x^2 + 28x + 49 -3x^2-14x= 0-3x^2-14x[/tex]
[tex]x^2 + 14x + 49 = -3x^2-14x[/tex]
[tex]\sf Factor \ left \ side \ of \ the \ equation.[/tex]
[tex](x+7)^2 =-3x^2-14x[/tex]
Answer:
(x+7)² = -3x² -14x
Step-by-step explanation:
4x^2 + 28x + 49 = 0
Subtract 3x² and 14x from each sides.
x^2 + 14x + 49 = -3x² -14x
Next step will be factoring.
(x+7)² = -3x² -14x
Help me please ?! ❤️❤️
Answer:
Hey there!
Point K has coordinates of (-2, -5)
Hope this helps :)
Answer:
Point K
Step-by-step explanation:
Since they're asking us to find (-2,-5) first we need to move 2 points to the left and then 5 points down.
Emile is a long-distance trucker. In one week he drives miles from his home in Fort Lauderdale, FL, to Benson, NC. He then drives miles to Barstow, CA, and continues driving miles to Bakersfield, CA. From there, Emile drives miles to Seattle, WA. Estimate the total distance Emile travels by first rounding each distance to the nearest hundred. Do not put units in your answer.
Answer:
Estimated total distance is 1,900 miles.
Step-by-step explanation:
We begin by adding each distance traveled by Emile:
1. Fort Lauderdale, FL, to Benson, NC = 748 miles
2. Barstow, CA, to Bakersfield, CA = 130 miles
3. Bakersfield, CA. to Seattle, WA = 1030 miles
Total miles = 1,908.
Therefore, in one week Emile's total distance to the nearest hundred is 1,900.
Note: the distances where gotten via Google Map.
which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 9xy³ -4y⁴ -10x²y² + x³y + 3x⁴ + 2x²y² - 9y⁴
Answer:
3x^4+(x^3)y-8x^2y^2+9xy^3-13y^4
Step-by-step explanation:
3x^4+(nothing)=3x^4
x^3y+(nothing)=x^3y
-10x^2y^2=2x^2y^2=-8x^2y^2
9xy^3+(nothing)=0
-4y^4-9y^4=-13y^4
Add it all up and write the terms by descending order of exponent value, and u get my answer.
A museum curator is hanging 7 paintings in a row for an exhibit. There are 4 Renaissance paintings and 3 Baroque paintings. From left to right, all of the Renaissance paintings will be hung first, followed by all of the Baroque paintings. How many ways are there to hang the paintings
Answer:
144 ways
Step-by-step explanation:
Number of paintings = 7
Renaissance = 4
Baroque = 3
We are hanging from left to right and we will first hang Renaissance painting before baroque painting.
For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24
For baroque we have 3! Ways of doing so. 3x2x1 = 6
We have 4!ways x 3!ways
= (4x3x2x1) * (3x2x1) ways
= 144 ways
Therefore we have 144 ways to hang the painting.
PLEASE HELP!
Suppose there is a strong positive correlation between mand n. Which of the
following must be true?
A. An increase in m causes n to increase.
B. When m increases, n tends to decrease.
C. When m increases, n tends to increase.
D. An increase in m causes n to decrease.
Answer:
A an increase in m cause n to increase
Step-by-step explanation:
a positive correlation means they will travel in the same direction when one is affected.
Answer:
Option A: An increase in m causes n to increase.
Step-by-step explanation:
A Positive correlation is a relationship between two variables in which both variables move with the same ratio. A positive correlation exists when one variable increases as the other variable increases, or vice-versa.
A perfect positive correlation means that both variables move by the exact same percentage.
Therefore, if there is a strong positive correlation between m and n then V increases and, w tends to increase.
Hope this helped :)
The first side of a triangle measures 3 in. less than the second side, the third side is 2 in. more than the first side, and the perimeter is 20 in. Set up an equation that relates the sides of the triangles in terms of the perimeter of the triangle.
Answer:
P = 3x - 4
Step-by-step explanation:
Side 1 = x - 3
Side 2 = x
Side 3 = 2 + (Side 1) = 2 + x - 3 = x - 1
Perimeter = 20 in
Perimeter = Side 1 + Side 2 + Side 3
Perimeter = (x - 3) + (x) + (x - 1)
Perimeter = x - 3 + x + x - 1
Perimeter = 3x - 3 - 1
Perimeter = 3x - 3 - 1
Perimeter = 3x - 4
P = 3x - 4
3
Select the correct answer.
Which equation represents the line that is parallel to y= 2 and passes through (-1,-6)?
OA x=-1
OB
X= 2
OCy= -6
OD. y= 2x - 4
Reset
Next
Hey there! I'm happy to help!
Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.
We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.
If the line we are looking for is flat; it stays at the same y-value the entire time. We see that the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.
I hope that this helps! Have a wonderful day!
Answer:
Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.
We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.
If the line we are looking for is flat; it stays at the same y-value the entire time. We see that the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.
Step-by-step explanation:
; ) BELIEVE IN YOURSELF!!!!!!!!!!!!!!!!!
Henry takes out a $650 discounted loan with a simple interest rate of 12% for a period of 7 months. How much money does Henry receive into his bank account when the loan is drawn down? Give your answer to the nearest cent.
Answer:
$546
Step-by-step explanation:
Given
Amount, P = $650
Rate, R = 12%
Period, T = 7 months
Required
Determine the amount paid.
We'll solve this using simple interest formula, as thus
[tex]I = \frac{PRT}{100}[/tex]
Substitute values for T, R and P
[tex]I = \frac{\$650 * 12 * 7}{100}[/tex]
[tex]I = \frac{\$54600}{100}[/tex]
[tex]I = \$546[/tex]
Hence, Henry's withdrawal is $546
domain and range A) D: (–7, –2], (–1, 3] R: (–10, 9.2] B) D: [–7, –2], [–1, 3] R: [–10, 9.2] C) D: (–7, 3] R: (–10, 9.2] D) D: (–7, –2), (–1, 3) R: (–10, 9.2)
Answer:
[tex]\Large \boxed{\mathrm{C) \ D: (-7, 3] \ R: (-10, 9.2]}}[/tex]
Step-by-step explanation:
The domain is the set of all possible x values.
The range is the set of all possible y values.
For the domain, we observe the graph, the graph will contain all the x values shown on the x-axis.
[tex]\mathrm{D= (-7,3] }[/tex]
For the range, we observe the graph, the graph will contain all the y values shown on the y-axis.
[tex]\mathrm{R= (-10,9.2] }[/tex]
What are the zeros of the quadratic function represented by this graph?
У
A
6
2
X
-6
- 2
6
2-
-6-
A.
1 and 3
OB.
-3 and -1
C.
-3 and 1
D. -1 and 3
Look where the parabola crosses the x axis. This is where the x intercepts are located. The term "x intercept" is the same as "root" and also the term "zero".
in the diagram, find the values of a and b.
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
