The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .
In the question ,
it is given that ,
the airplane covers the distance of 560 miles in 2 hours with the wind,
So , the speed of the airplane with the wind is 560/2 = 280 miles per hour
also given that
airplane covers the distance of 560 miles in 2.5 hours against the wind ,
So , the speed of the plane with the wind = 560/2.5 = 224 miles per hour .
let the speed of the airplane be "a" miles per hour ,
and let the speed of the wind be "b" miles per hour ,
So , equation of speed with the wind is denoted by
a + b = 280
and the equation of speed against the wind is denoted by
a - b = 224
Adding both the equations , we get
2a = 504
a = 504/2
a = 252 miles per hour
and b = 280 - 252 = 28 miles per hour .
Therefore , The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .
Learn more about Speed here
https://brainly.com/question/19064729
#SPJ4
[tex]3x-8\geq 7[/tex]
Answer:
x ≥ 5
Step-by-step explanation:
3x - 8 ≥ 7 ( add 8 to both sides )
3x ≥ 15 ( divide both sides by 3 )
x ≥ 5
8. Angles x and y are located in the first quadrant
such that sin x=5/3 and cos y=5/13
a) Determine an exact value for cosx.
b) Determine an exact value for siny.
sin y =12/13 but can't find cos x as sin x can't exceed from 1.
It can be solved by using identities of trigonometry.
What are the trigonometric identities?
These are the equivalent ways to define trigonometric functions.
Basic identities are:
sin²x + cos²x = 1
1 + tan²x = sec²x
1 + cot²x = cosec²x
For cos x:
cos²x = 1 - sin²x
= 1 - (5/3)²
= 1- (25/9)
= -16/9
i.e. not possible
For sin y:
sin²y = 1 - cos²y
= 1 - (5/13)²
= 1 - 25/169
= 144/169
So, sin y = ±(12/13)
but as mentioned x and y are in 1st quadrant ,
so, sin y = 12/13.
Learn more about trigonometric identities from the given link:
https://brainly.com/question/24496175
#SPJ1
8. You are selling concessions at a local swim meet. Hot dogs are being sold for
$1.00 and soda is being sold for $0.50. At the end of the day you made $150.
Let x represent the number of hotdogs sold and y represent the number of
sodas sold. Write an equation that can be used to find the number of hotdogs
and sodas sold at the swim meet.
a. Standard Form:
b. Slope-Intercept Form:
c. If you sold 40 hot dogs how many sodas did you sell?
d. Using the Standard Form, identify the x-intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sold.
e. Using the Standard Form, identify the y-intercept of the graph and explain
how the y-intercept relates to the number of hot dogs and sodas sold.
The equation that can be used to find the number of hotdogs
and sodas sold at the swim meet.
a)x+0.50y=150
b) y=-2x+300
c)Number of soda sold y =220 if hot dog is 40.
d) x intercept=150. It is related to the total earnings of soda and hot dogs sold.
f) y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.
What is x-intercept and y-intercept?
An equation's or a function's graph that contacts the x axis is said to have a "X intercept." This is comparable to a point having a value of zero. Given that it is located on the horizontal axis, this is sometimes referred to as the horizontal intercept. The y value at the point where the line meets the y axis is known as the y intercept. By examining the graph and identifying the point that crosses the y axis, we may determine the y intercept. This point's x coordinate will always be 0. It will be recorded as (0,y). Given that it is on the vertical axis, this is also referred to as a vertical intercept.
Let us take number of hot dogs sold as x and number of soda sold as y.
Cost of one hot dog = $1.00
Cost of one soda = $0.50
Then , cost of x number of hot dogs sold = 1x
cost of y number of soda sold = 0.50y
Then, . At the end of the day you made $150.
=> 1x+0.50y= 150
a) standard form of the equation is ,
=> x+0.50y=150 ------->1
b) x+0.50y=150
=> x+[tex]\frac{1}{2}[/tex]y=150
=>2x+y=150*2
=>2x+y=300
Then slope intercept form is y=-2x+300------->2
c) Number of hot dogs sold x=40 and put into 2 ,
then , y=-2(40)+300
=> y=-80+300
=>y=220
Number of soda sold y =220
d) To find x intercept put y=0 into 1 , then
=> x+0=150
=>x=150
Here x intercept=150. It is related to the total earnings of soda and hot dogs sold.
e)To find y intercept put x=0 into 1,
=> 0+0.50y=150
=> y = 150/0.50
=> y =300
Here y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.
To learn more about x-intercept and y-intercept refer the below link
https://brainly.com/question/18176433
#SPJ1
What is the equation of a parabola that passes through the points (−5, −10), (−3, 2), and (2, −3)?.
The equation of the parabola is y = -x² - 2x + 5
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k - p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
The equation of the parabola with the points
A ( -5 , -10 ) , B ( -3 , 2 ) and C ( 2 , -3 )
So , from the equation of parabola ,we get
y = ax² + bx + c
Substituting the values of x and y , in the equation of point A , we get
-10 = a ( -5 )² - 5b + c
-10 = 25a - 5b + c be equation (1)
Substituting the values of x and y , in the equation of point B , we get
2 = a ( -3 )² - 3b + c
2 = 9a - 3b + c be equation (2)
Substituting the values of x and y , in the equation of point C , we get
-3 = a ( 2 )² + 2b + c
-3 = 4a + 2b + c be equation (3)
By the method of brute force , we can solve the equations and derive the equation for the parabola
So , the equation for the parabola will be
y = -x² - 2x + 5
Now , substituting the values of x and y from the points , we get
For point A ( -5, -10 )
-10 = - 25 + 10 + 5
-10 = -10
Therefore , the equation is TRUE
Now , substituting the values of x and y from the points , we get
For point B ( -3, 2 )
2 = -9 + 6 + 5
2 = 2
Therefore , the equation is TRUE
Now , substituting the values of x and y from the points , we get
For point C ( 2 , -3 )
-3 = -4 - 4 + 5
-3 = -3
Therefore , the equation is TRUE
Hence , the equation of the parabola is y = -x² - 2x + 5
To learn more about equation of parabola click :
https://brainly.com/question/24042022
#SPJ1
the annual rainfall in a certain region is approximately normally distributed with mean 41.4 inches and standard deviation 5.5 inches. round answers to the nearest tenth of a percent. a) what percentage of years will have an annual rainfall of less than 43 inches?
The probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.
How to calculate the probability?
Given
μ = 41.4
σ = 5.5
First, we need to find the z score when the rainfall 43 inches. So:
z = (x - μ) / σ
z = (43 - 41.4) / 5.5
z = 0.2909
Then, to find out the probability we need to find P(z < 0.2909) in the z score table. So, we get 0.6141 or in percentage is 61.41%.
Thus, the probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.
Learn more about probability here:
brainly.com/question/29057124
#SPJ4
what is the reciprocal of 5 1/3
Answer:
Step-by-step explanation:
reciprocal of 51/3 is 3/16
Hi you need to change 5 1/3 from mixed number to improper fraction 51/3=(5x3)+1 /3 =16/3
The reciprocal of 16/3 is 3/16
can you substitute y=2x+4 and 6x-3y=-12
Answer: x=0 y=4
Step-by-step explanation:
6x - 3(2x + 4) = 12
6x - 6x - 12 = 12
0 = 0
therefore, x = 0
substitute x=0 into y = 2x + 4
y = 2(0) + 4 = 4
a 2013 study by pediatricians investigates whether it is better to give children the diphtheria, tetanus and pertussis (dtap) vaccine in the thigh or the arm. the pediatricians collected the data from two different random samples. the first random sample was collected from children who were given the vaccine in the thigh. the second random sample was collected from children who were given the vaccine in the arm. pediatricians recorded whether the children had a severe reaction or not. no severe reaction severe reaction thigh observed expected 4758 4750.9 30 37.1 arm observed expected 8840 8853.1 76 68.9 reference: jackson, l.a., peterson, d., nelson, j.c., et al. (13 co-authors). 2013. vaccination site and risk of local reactions in children one through six years of age. pediatrics 131: 283-289. pediatricians conducted a chi-square test of independence. the chi-square test statistic for this datais 2.0609 with a p-value of 0.1511. what can the pediatricians conclude? group of answer choices there is a statistically significant association between vaccine location and severe reaction. pediatricians have strong evidence that the severe reactions to vaccine depend on location of the vaccine. there is not enough evidence to conclude that there is an association between vaccine location and severe reaction. the pediatricians cannot make a conclusion. the conditions for use of the chi-square test are not met.
Ther right option is that there is not enough evidence to conclude that there is enough association between vaccine location and severe reaction.
Given that,
Children who received the vaccine in the thigh received the first random sample. Children who received the immunization in the arm provided the second random sample.
The chi-square test yields a chi square is 2.0609 with a P value of 0.1511 meaning, the chi square test is not statistically significant.
A,B is therefore out.
C is not also right.
D is what we get when we cannot reject null hypothesis.
Therefore, We cannot conclude that there is dependence.
Learn more about null hypothesis :
brainly.com/question/28920252
#SPJ4
This graph shows the height in inches, h, of a bamboo plant t months after it had been planted
4.1 Write an equation that describes the relationship between t and h.
4.2 After how many months will the Bamboo plant be 66 inches tall?
The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
A linear function is a function that varies linearly with respect to the changing variable.
4.1)
The linear equation is given as y = mx + c
Here, m is the slope while c is the y-intercept.
Given line has a y-intercept of 12.
Slope m = (12 - 24)/(0 - 4) = 3
Thus, h = 3t + 12
4.2)
Time is taken to bamboo to 66 inches tall,
66 = 3t + 12
3t = 54
t = 3 months.
Hence "The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months".
For more about the linear function,
brainly.com/question/21107621
#SPJ1
the garden table and a bench cost $582 combined. the garden table costs $68 less than the bench. what is the cost of the bench?
Answer:
$325
Step-by-step explanation:
t +b = 582
t = b - 68
b - 68 + b = 582
2b = 582 + 68
2b = 650
2/2 b = 650 / 2
b = 325
PLEASE HELPPPPP ASAPPPP I NEED THIS MATH DONE! WILL GIVE BRAINLIST
Answer: __________________________________________
3x + 9
Answer: 3x + 9
Step-by-step explanation:
The shapes below are mathematically similar.
X
9 cm
Calculate the length of side x.
8 cm
12 cm
Not drawn
to scale
The length of side x is 6cm
We need to find the scale factor of the shapes below are mathematically similar.
it can be found using the two bases given.
The base of the smaller triangle is 9 and that of large triangle is 12
9/12 = 3/4
The smaller triangle is 3/4 of the larger one.
Multiply the known side by 3/4
X = 8 x 3/4 = 6
X= 6
Therefore, the length of side x is 6cm
To learn more about scale factor refer here
https://brainly.com/question/15891755
#SPJ1
Write the equation of the line that passes through the points (3, -8) and(9, 9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
3
What is the area of the composite figure?
12.5cm
20cm
500
490.62
245.31
745.31
25cm
4
27
Answer: 745.31 cm²
Total area of the figure can be obtained by adding area of the semi circle and rectangle.
The radius of the semi circle is given as 12.5cm and it's area is equal to (πr²)/2
I hope you understand It's simple!
Graph equations that represent the growth rates of hamburgers sold
and wraps sold in the same coordinate plane. Compare the steepness
of the graphs. What does this mean in the context of the problem?
(a) Hamburgers sells faster than Wraps ,
(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .
In the question ,
it is given that
the rate at which the hamburgers are selling = 160 hamburgers per hour ,
we need to find the rate at which the wraps are selling
From the table ,
we can see that the wraps are sold in an Arithmetic Progression ,
So , at 60 minutes the wraps sold = 2.5 + (n-1)d
= 2.5 + 59×2.5
= 2.5 + 147.5
= 150
So , after one hour , number of wraps sold is 150 and the number of hamburgers sold is 160 .
Similarly , after 2 hours , the number of wraps sold will be 300 and number of hamburgers sold will be 320 .
So, the hamburgers sells faster than wraps .
the slope(steepness) of the hamburgers = (number of hamburgers sold)/60
= 160/60
= 2.667
the slope(steepness) of the wraps = (number of wraps sold)/60
= 150/60
= 2.5
from the above data , we can see that the steepness of hamburgers is more ,
which means that the hamburgers sells faster than wraps .
the equation that denotes the number of hamburgers sold is y = 2.667x
the equation that denotes the number of wraps sold is y = 2.5x
where x is time in minutes .
The graph that represents the growth rate of hamburger and wraps is shown below .
Therefore , (a) Hamburgers sells faster than Wraps ,
(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .
Learn more about Equations here
https://brainly.com/question/15685060
#SPJ1
cos²x + 2 cosx - 3=0
The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .
In the question ,
it is given that ,
the quadratic equation is cos²x + 2 cosx - 3 = 0 ,
let cosx = a ,
So , the equation becomes , a² + 2a - 3 = 0
writing the factors using the splitting the middle term method ,
we get ,
a² [tex]+[/tex] 3a -a - 3 = 0
a(a + 3) -1(a [tex]+[/tex] 3) = 0
(a - 1)(a [tex]+[/tex] 3) = 0
which means a - 1 = 0 or a + 3 = 0
a [tex]=[/tex] 1 or a [tex]=[/tex] -3 ,
Substituting a = cosx , we get
cosx [tex]=[/tex] 1 or cosx [tex]=[/tex] -3 ,
Therefore , The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .
The given question is incomplete , the complete question is
Solve the given quadratic equation for Cosx , cos²x + 2 cosx - 3 = 0 .
Learn more about Quadratic Equation here
https://brainly.com/question/1863222
#SPJ1
you are synthesizing a chip composed of random logic with an average activity factor of 0.1. you are using a standard cell process with an average switching capacitance of 450 pf/mm2 . estimate the dynamic power consumption of your chip if it has an area of 70 mm2 and runs at 450 mhz at vdd
The dynamic power consumption of your chip if it has an area of 70 mm² and runs at 450 MHz at vdd = 0.9V is 1.08 W.
It is given that,
The average activity factor = 0.1
The Average switching capacity = 450 pF/mm²
We know that,
p = aCV²f
putting the values in the above equation:
= 0.1× (450e⁻¹² × 70) × (0.9)² × 450e⁶
= 1.08 W
Learn more about Dynamic Power consumption:
https://brainly.com/question/14587975
#SPJ4
at gumdrops galore candy store, miguel and his sister each fill a bag with gumdrops. miguel's bag of black gumdrops weighs 3 8 of a pound. miguel pays for both his gumdrops and his sister's red gumdrops. in all, miguel buys 7 8 of a pound of gumdrops. he wants to know how much his sister's red gumdrops weigh. use an equation to find the weight of his sister's red gumdrops. to write a fraction, use a slash ( / ) to separate the numerator and denominator.
Miguel's sister's red gumdrops weigh 0.5 pounds.
Formulate based on the conditions stated: [tex]\frac{3}{8} + x = \frac{7}{8}[/tex]
Unknown terms should be moved to the left side of the equation: [tex]x = \frac{7}{8} - \frac{3}{8}[/tex]
Numerators written over common denominator: [tex]x = \frac{7-3}{8}[/tex]
Determine the total or difference: [tex]x = \frac{4}{8}[/tex]
Remove the connecting element: [tex]x = \frac{1}{2}[/tex]
get the outcome: or x = 0.5 or 50%
A fraction is a mathematical symbol representing any quantity of equal parts, and it also represents a portion of a whole. In common English, the word "fraction" is used to describe the quantity of parts of a particular size. Fractions speed up and simplify calculations by making it easier to divide and evaluate numbers.
To learn more about fractions: https://brainly.com/question/1622425
#SPJ4
Simplify
1-(cos^2)theta/(sin^2 )theta
A. 1
B. sin^2 theta
C. cos^2 theta
D. tan^2 theta
What is the y-intercept of g(x) = -|x +6|+ 4
Answer: -2
Step-by-step explanation:
since g(x) is a function, x needs to be 0 in order to find the y-intercept. so we plug in 0 to the function. -|0+6|+4=-2 so the y-intercept is -2
The 3rd term of a a G.P is 18 and the 7th term is 32/9. Find the G.P
The G.P. of a term is 256/243.
To find out the G.P. for the 3rd term:
Let us consider the 1st term to be 'a'.
So, [tex]ar^{2}=18[/tex] ....... Equation (1)
Also [tex]ar^{6} = \frac{32}{9}[/tex] ..... Equation (2)
Dividing (2) by (1), we get,
[tex]\frac{ar^{6}}{ar^{2}} = \frac{32}{162}[/tex]
[tex]r^{4}[/tex] = 16/81.
r = 2/3.
Putting r in equation (1) than we will get
a = 81/2.
So, 10th term = [tex]ar^{9}[/tex]
= (81/2) ×(512/19683)
= 256/243.
Hence the answer is the G.P. of a term is 256/243.
To learn more about Probability click here https://brainly.com/question/24756209
#SPJ9
PLEASE HELP, NEEDED ASAP
Answer:
a) x=5
b) x=4
Step-by-step explanation:
4x-3=2x+7
-2x. -2x
2x-3=7
+3. +3
2x=10
x=5
2x+6=7x-14
-2x. -2x
6=5x-14
+14. +14
20=5x
/5. /5
4=x
Hopes this helps please mark brainliest
Jo flips a coin {h, t}; then rolls a 6-sided die {1, 2, 3, 4, 5, 6}. How many possible outcomes are in the sample space of this experiment?.
The possible outcomes in the sample space of this experiment are
{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}
Jo flips a coin sample space for a coin = {h, t}
and rolls a 6-sided die sample space for a die = {1,2,3,4,5,6}
at a time coin is tossed and the die is rolled
the possible outcomes in the sample space of this experiment are
{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}
To learn more about Sample space:
https://brainly.com/question/19268954
#SPJ4
which statement can you use to conclude that quadrilateral xyzw is a parallelogram
The statement can you use to conclude that quadrilateral xyzw is a parallelogram
The statement to conclude that quadrilateral XYZW is a parallelogram is
XY = WZ and XW = YZ
Quadrilateral :
A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.
Parallelogram :
A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other , where the pair of parallel sides are equal in length.
So we can conclude that :
XY is parallel to WZ and XW is parallel to YZ .
so ,
XY = WZ and XW = YZ is the conclusion .
Hence , the answer is XW = YZ and XY = WZ
To learn more about quadrilateral and parallelogram click here
https://brainly.com/question/1190071
#SPJ9
Two similar bottles are shown. The smaller bottle can hold 500 ml of water. How much water can the larger bottle hold?
Smaller bottle length=15cm
Larger bottle length=21cm
The larger bottle will be able to hold a volume of 1372ml
What is Volume of similar object?If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.
This shows that the ratio of the cube of length of the bottle is equal to the the ratio of their volumes
the length of the smaller bottle = 15, the cube of the length= 15^3= 3375
the length of the larger volume = 21, the cube of the length is 21^3=9261
therefore 3375/9261= 500/x
x is the volume of the larger bottle
therefore x= 500×9261/3375
x= 1372ml.
therefore the volume of the larger bottle is 1372ml
learn more about volume of similar shapes from
https://brainly.com/question/16246860
#SPJ1
The sum 691 + 208 is closest to the sum
A. 600 + 200
B. 700 + 200
C. 700 + 300
D. 900 + 200
Answer:
B. 700+200
Step-by-step explanation:
691+208=899
A. 600+200=700
B.700+200=900
C.700+300=1000
D.900+200=1100
B is closest to 899
Answer:
700+200
Step-by-step explanation:
we round these numbers to the closest hundreds by looking at the tenth place
5 or more we round up
4 or less we let it rest and round down
691 since it is 9 in the tenths place we round up to 700
208 since the tenths place is 0 we round down to get 200
700+200 is the answer hopes this helps please mark brainliest
question is in the pic .
The set of ordered pairs that represent dilation factor of -3 is
c. A' (-3, -18) B' (-18, -18) C' (-3, -6)
How to find the coordinates of the imageDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
From the graph the coordinates are read and following the given transformation rule we have
preimage image
A (1, 3) → (2 * -3, 4 * -3) → A' (-3, -8)
B (6, 6) → (4 * -3, 4 * -3) → B' (-18, -18)
C (1, 6) → (3 * -3, 2 * -3) → C' (-3, -6)
Learn more about transformation here:
https://brainly.com/question/29393610
#SPJ1
8 points
Megan and Desmond each added the same amount of water to their aquariums. Megan mixed
5 mL of a chemical solution with every gallon of water for her aquarium. Desmond mixed
8 mL of the chemical solution with every 2 gallons of water for his aquarium.
Which of these statements is true?
A Megan used more solution per gallon of water than Desmond, because 5:1 is greater
than 8: 2.
B Megan used more solution per gallon of water than Desmond, because 5 mL is greater
than 2 mL.
C Desmond used more solution per gallon of water than Megan, because 8 mL is greater
than 5 mL.
D Desmond used more solution per gallon of water than Megan, because 8:2 is greater
than 5: 1.
what is 10 + 10 i need some help
Answer:20
Step-by-step explanation: my man
Answer:
20
Step-by-step explanation:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10
+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10
= 20
19) Over the past 4 hours the temperature fell 37.5°F. On average, how much did the temperature fall per hour?
Answer:
if you don't mind is there a starting number or a chart so i can calculate and solve this for you!