Answer:
Let's call the number of seats in the first aircraft "x", the number of seats in the second aircraft "y", and the number of seats in the third aircraft "z".
From the problem statement, we know that:
x = y + 88 (the first aircraft has 88 more seats than the second aircraft)
z = 2y - 103 (the third aircraft has 103 seats less than twice the seating capacity of the second aircraft)
x + y + z = 1909 (the total number of seats in all three aircraft is 1909)
We can substitute the first equation into the third equation to get:
y + 88 + 2y - 103 = 1909
3y = 2000
y = 666 (the number of seats in the second aircraft)
Now that we know the number of seats in the second aircraft, we can use the first and second equations to find the number of seats in the other two aircraft:
x = y + 88 = 666 + 88 = 754 (the number of seats in the first aircraft)
z = 2y - 103 = 2(666) - 103 = 1229 (the number of seats in the third aircraft)
So, the first aircraft has 754 seats, the second aircraft has 666 seats and the third aircraft has 1229 seats.
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Answer: The first aircraft has 265 seats, the second aircraft has 177 seats and the third aircraft has 248 seats.
Step-by-step explanation:
Let's call the number of seats for the first aircraft x, the number of seats for the second aircraft y, and the number of seats for the third aircraft z.
From the problem, we know the following:
x = y + 88 (the first aircraft has a capacity of 88 more seats than the second aircraft)
z = 2y - 103 (the third aircraft has 103 seats less than twice the seating capacity of the second aircraft)
x + y + z = 1909 (the total number of seats for all three aircraft is 1909)
We can use the first equation to substitute for x in the second and third equations:
y + 88 = y + 88
2y - 103 = z
Now we have a system of equations:
y + 88 + y + 2y - 103 + z = 1909
4y + z = 2000
We can use the first equation to find y:
y = (1909 - 88 - 103) / 4 = 709 / 4 = 177
Now we can substitute this value of y back into the first equation to find x:
x = y + 88 = 177 + 88 = 265
and substitute it back into the second equation to find z:
z = 2* 177 - 103 = 248
So the first aircraft has 265 seats, the second aircraft has 177 seats and the third aircraft has 248 seats.
in the accompanying diagram parallel lines ab and cd are cut by transversal ef. If e m<2= 72, what is m1
The measure of m<1 is 108 degrees from the provided figure.
Line geometry involving transversalsA line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Lines are therefore one-dimensional objects, even if they can exist in spaces with two, three, or more dimensions.
From the diagram, we have the following parameters
m<2 = 72 degrees
Required parameters
The measure of angle m<1
From the figure, the sum of the interior angle is equivalent to 180 degrees, that is:
m<1 + m<2 = 180
m<1 = 180 - m<2
m<1 = 180 - 72
m<1 = 108 degrees
Hence the measure of m<1 from the given figure is 108 degrees.
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During the 2005 football season, Team Tackle beat Team Sack by 19 points. If their combined scores totaled 37, find
the individual team scores.
Team Tackle's score was
Team Sack's score was
points.
points.
Team Tackle's score was 28 points. And team Sack's score was 9 points.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
During the 2005 football season, Team Tackle beat Team Sack by 19 points. If their combined scores totaled 37.
Let 'x' be the Tackle's score and 'y' be the Sack's score. Then the equations are given as,
x + y = 37 ...1
x = y + 19 ...2
From equations 1 and 2, then we have
y + 19 + y = 37
2y = 18
y = 9
Then the value of 'x' is given as,
x = 9 + 19
x = 28
Team Tackle's score was 28 points. And team Sack's score was 9 points.
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Charise can pick 1/3 pound of berries in 15 minutes.
How many pounds of berries can she pick in 4 hours at the same unit rate?
Answer:
Step-by-step explanation:
To convert minutes to hours, we divide by 60, since there are 60 minutes in an hour.
So 4 hours is equal to 4 * 60 = 240 minutes
Charise can pick 1/3 pound of berries in 15 minutes. This is her unit rate. To find out how many pounds of berries she can pick in 4 hours, we need to multiply this unit rate by the number of 15-minute intervals in 4 hours.
240 minutes / 15 minutes = 16 (four-hour intervals)
So the amount of berries Charise can pick in 4 hours is:
1/3 pound/15 minutes * 240 minutes = (1/3) * 16 = 16/3 = 5.333 pounds of berries.
Answer:
5 1/3 pounds of berries----------------------------------
Charise can pick 1/3 pound of berries in 15 minutes.
There are 4 of 15 minutes in an hour and we need to calculate it for 4 hours.
4*4 = 16 of 15 minutesShe picked:
1/3*16 = 16/3 = 5 1/3 pounds of berriesIf a cubic millimeter of blood contains 5.2 x10^6 red blood cells, how many red blood cells are contained in 40 cubic millimeters of blood? Write your answer in scientific notation.
The amount of red blood cells contained in 40 cubic millimeter is 1.08×10⁸
What is proportion?A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
For example If Mary is paid for a job $50 per day.
How much will she earn in 10 days.
She will earn 50×10 = $ 500 in 10 days
Similarly, 1 cubic millimeter contains 5.2× 10⁶ red blood cells
then, 40 cubic millimeter will contain 40× 5.2×10⁶
= 108×10⁶ = 1.08 × 10⁸ red blood cells
Therefore the amount of red blood cells contain in 40cubic millimeter of blood is 1.08× 10⁸
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ANYONE GOOD AT MATH HELP IF YOU CAN , PLEASE WILL GET BRAINLIEST!
Answer:
[tex]f \left( g \left( f \left( 1 \right) \right) \right)=45[/tex]
[tex]g \left( f \left( g \left( 0 \right) \right) \right)=3[/tex]
We had to use the equation on the first problem as the graph does not show the value of function f(x) when x = -6.
Step-by-step explanation:
When calculating composite functions, work from the inside out.
Given composite function:
[tex]f \left( g \left( f \left( 1 \right) \right) \right)[/tex]
First use the graph to find f(1):
f(1) = -4[tex]\implies f \left( g \left( f \left( 1 \right) \right) \right)= f \left( g \left(-4\right)\right)[/tex]
Now use the graph to find g(-4):
g(-4) = -6[tex]\implies f \left( g \left(-4\right)\right)=f(-6)[/tex]
As the graph does not show the value for f(x) when x = -6, we need to use the equation:
[tex]\implies f(-6)=(-6)^2-2(-6)-3=45[/tex]
Therefore:
[tex]f \left( g \left( f \left( 1 \right) \right) \right)=45[/tex]
------------------------------------------------------------------------------
Given composite function:
[tex]g \left( f \left( g \left( 0 \right) \right) \right)[/tex]
First use the graph to find g(0):
g(0) = -2[tex]\implies g \left( f \left( g \left( 0 \right) \right) \right)=g \left( f \left( -2 \right) \right)[/tex]
Now use the graph to find f(-2)
f(-2) = 5[tex]\implies g \left( f \left( -2 \right) \right)=g \left(5 \right)[/tex]
Finally, use the graph to find g(5):
g(5) =3Therefore:
[tex]g \left( f \left( g \left( 0 \right) \right) \right)=3[/tex]
We had to use the equation on the first problem as the graph does not show the value of function f(x) when x = -6.
compute
3.04*21.5-9.12/3.8
The required simplified value of the given expression is given as 62.96.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression
= 3.04 × 21.5 - 9.12 / 3.8
= 65.36 - 2.4
= 62.96
Thus, the required simplified value of the given expression is given as 62.96.
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HELP I NEED HELP I NEED HELP I NEED HELP
Answer:
A is an Irregular Polygon
B is Neither a Polygon
C is an Irregular Polygon
D is a Regular Polygon
E is a Regular Polygon
The information in the table is linear.
true or false
The table is not linear.
Ethan sold exactly eight TVs this quarter. Frank sold exactly twice as many TVs as Gina. Gabriel sold more TVs than Ethan. Gina sold exactly three more TVs than Gabriel and Ethan combined. Which statement must be true? Gabriel and Gina combined sold more TVs than Frank. Frank sold more than 40 TVs. Gina sold more than twice as many TVs as Ethan. Gina sold exactly twice as many TVs as Gabriel. Ethan, Gabriel, Gina, and Frank combined sold more than 80 TVs.
Gina sold more than twice as many TVs as Ethan, because 19 > (2 * 8)
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Ethan sold exactly eight TVs this quarter.
Ethan TV = 8
Gabriel sold more TVs than Ethan, hence:
Gabriel TV (G) > 8
Gabriel TV > 8
Gina sold exactly three more TVs than Gabriel and Ethan combined
Gina TV = Gabriel TV + 8 + 3
Gina TV > 8 + 8 + 3
Gina TV > 19
Frank sold exactly twice as many TVs as Gina, hence:
Frank TV = 2 * Gina TV
Frank TV > 2 * 19
Frank TV > 38
Gina sold more than twice as many TVs as Ethan.
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Points of discontinuity, holes, vertical asymptotes, and horizontal asymptote. (Please show work)
Discontinuities are points where the function is undefined. Holes are points where the graph has a break in it. Vertical asymptotes are lines on a graph where the function approaches infinity and horizontal asymptotes are lines on a graph where the function approaches a limit.
What is rational functions?The theory used in this question is the theory of rational functions. This theory is used to identify points of discontinuity, holes, vertical asymptotes, and horizontal asymptotes in rational functions.
In the given question,
2. f(x) = x-2/x-4
Points of discontinuity: x = 4
Holes: None
Vertical Asymptote: x = 4
Horizontal Asymptote: None
3. f(x)= 3x-3/x2-1
Points of discontinuity: x = 1
Holes: None
Vertical Asymptote: x = 1
Horizontal Asymptote: y = 0
4. f(x) = x²+5x+6/x²+6x+9
Points of discontinuity: None
Holes: None
Vertical Asymptote: None
Horizontal Asymptote: y = 1
5. f(x) = (x+3)(x-2)/(x-2)(x+1)
Points of discontinuity: None
Holes: x = -1, x = 2
Vertical Asymptote: x = -1, x = 2
Horizontal Asymptote: y = 1
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Please help
The water is 7 meters deep 2 meters from the shore.
How deep is the water 45 meter from
the shore?
Answer: 157.5
Step-by-step explanation:
5s+7s fatorise this answer
Answer:
s(5+7)
Step-by-step explanation:
Since 's' is the Highest Common Factor that will go outside the brackets.
[tex]s(5+7).[/tex]
Step-by-step explanation:1. Write the expression.[tex]5s+7s[/tex]
2. Find a common term between the 2 elements.As you can tell, a common term between "5s" and "7s" is variable "s". Hence, we may factorize using that variable.
3. Divide by "s" ans express as a factor.[tex]s(\frac{5s+7s}{s} )\\\\s(\frac{5s}{s} +\frac{7s}{s} )\\ \\s(5+7)[/tex]
4. Conclude.Final answer: [tex]s(5+7)[/tex].
a map is drawn with a centimeter representing 25 miles. if the distance between two towns is 4 centimeters on the map, what is the actual distance between the two towns?
Answer:
1 cm - 25 miles
4 cm - 25 x 4 = 100 miles
The required distance is 100 miles.
It takes you 53 minutes to bike 15 miles. At that same rate, about how long does it take you to bike 100 miles?
Answer:
795
Step-by-step explanation:
you mutiply 53 x 15 which gives you 795
Answer:
You have to take the 53 and divide it by 15 which gives you 3.53 repeating so than take 3.53 and multiply by 100 and that gives you 353 minutes as you answer
Step-by-step explanation:
Below is a diagram of the dotted cube with edges of length 5. Suppose vectors u=⟨5,0,0⟩, v=⟨0,5,0⟩, and w=⟨0,0,5⟩. Find the following vectors.
The vectors generated by means of operations with canonical vectors:
(5, 5, 10) (- 5, 5, 0) (- 15, - 5, - 10) (10, 15, 15)How to perform operations with vectors
Herein we find three canonical vectors, one for each orthogonal axis, from which we need to perform operations to generate new vectors. There two fundamental operations:
Vector sums
(a, b, e) + (c, d, f) = (a + c, b + d, e + f)
Vector multiplication by a scalar
α · (a, b, c) = (α · a, α · b, α · c)
Where:
a, b, c, d, e, f - Vector componentsα - ScalarIf we know that U = (5, 0, 0), V = (0, 5, 0) and W = (0, 0, 5), then the following operations are below:
Case 1
U + V + 2 · W
(5, 0, 0) + (0, 5, 0) + 2 · (0, 0, 5)
(5, 0, 0) + (0, 5, 0) + (0, 0, 10)
(5 + 0 + 0, 0 + 5 + 0, 0 + 0 + 10)
(5, 5, 10)
Case 2
U + T = V
T = V - U
T = (0, 5, 0) - (5, 0, 0)
T = (0 - 5, 5 + 0, 0 + 0)
T = (- 5, 5, 0)
Case 2b
R = U + V + W
R = (5, 0, 0) + (0, 5, 0) + (0, 0, 5)
R = (5 + 0 + 0, 0 + 5 + 0, 0 + 0 + 5)
R = (5, 5, 5)
Case 3
T - 2 · R
(- 5, 5, 0) - 2 · (5, 5, 5)
(- 5, 5, 0) + (- 10, - 10, - 10)
(- 5 - 10, 5 - 10, 0 - 10)
(- 15, - 5, - 10)
Case 3b
S = U + W
S = (5, 0, 0) + (0, 0, 5)
S = (5 + 0, 0 + 0, 0 + 5)
S = (5, 0, 5)
Case 4
U + V + W + R + S + T
(5, 0, 0) + (0, 5, 0) + (0, 0, 5) + (5, 5, 5) + (5, 0, 5) + (- 5, 5, 0)
(5 + 0 + 0 + 5 + 5 - 5, 0 + 5 + 0 + 5 + 0 + 5, 0 + 0 + 5 + 5 + 5 + 0)
(10, 15, 15)
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Hi- can someone help me with 4 of these questions? I used a calucator to help but it didn't give me the right answer, (the questions are the pictures)
Answer: first one is D 15 1/2
second one is B 11 2/8
Third one is C (already had the correct answer)
fourth answer would be A 3 2/12
Step-by-step explanation:
hope this helps
The table describes the quadratic function p(x).
x p(x)
−4 24
−3 9
−2 0
−1 −3
0 0
1 9
2 24
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 3
p(x) = 2(x + 1)2 − 3
p(x) = 3(x − 1)2 − 3
p(x) = 3(x + 1)2 − 3
Step-by-step explanation:
[tex]p(x) = 3 {(x + 1)}^{2} - 3[/tex]
One pair of segments in the figure above is parallel. Based on the appearance of the lines, which statement about the figure is true?
AB I BC
AB I CD
AB I AD
AD I BC
Answer:
Step-by-step explanation:
Ad and BC because they are 2 lines going in the same place , they are the same
At a gym you swim every four days run every five days and cycle every 12 days if you did all three activities they have and how many days will you do all three activities again
Answer:
Just find the LCM of all the days.
LCM of 4,5 and 12 is 60
Therefore, u will have to do all the activities again after 60 days.
I have added a screenshot.
The probability that people aged between 34 to 65 have a certain disease is 0.95.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, A stem-leaf diagram of people of different ages having a certain disease.
The probability that people have a certain disease between 35 and 64 years of age is,
= P(35 - 44) + P(45 - 54) + P(55 - 64).
= 0.14 = 0.39 + 0.42.
= 0.95.
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I just need this question left pls help
By using the fact that the sum of the interior angles must be 180°, we wil see that:
x = 110°.
How to find the value of x?First, remember that the sum of the interior angles of a triangle is alway equal to 180°.
We also can see that the interior angle that is adjacent to x can be written as:
a = 180° - x
Then the sum of the interior angles will give:
30° + 80° + (180° - x) = 180°
30° + 80° - x = 0
110° - x = 0
110° = x
That is the value of x.
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Are the two triangles below similar? If so, write a similarity statement, and stay with similar to criteria can be used to prove it.
Similarity statement-
1. PNK DKG
2. PNK GDK
3. PNK KGD
4. The triangles are not similar
Criteria-
1. AA
2. SAS
3.SSS
4. Not applicable, the triangles are not similar
The two triangles below show the property of similarity.
The first property is the Side.
The side PN is similar to the side DG.
The second property his angle.
∠PNK = ∠DGK = 90°
The third property would be side as well.
Side NK is similar to the side GK.
Thus, the two triangles are similar.
Similarity is the mathematical property of triangles, wherein two triangles are called similar if they have either two congruent angles and one similar side, or two similar sides in ratio with one another and a congruent angle.
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A triangle ABC has coordinates for A (-4, 1).
Triangle A'B'C' has coordinates for A' (0-3)
What is the translation?
How many units right or left and how many units up or down?
Choose the best answer from the options below:
A
B
C
D
4 right, 4 down
4 left, 4 up
You have 1 hour to answer this question or you will be logged out.
4 left, 4 down
4 right, 4 up
The solution is Option A.
The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the coordinate of the triangle be represented as A
Now , the coordinate A = A ( -4 , 1 )
Now , the coordinate of the triangle after translation is A' ( 0 , -3 )
when there is a translation of the coordinate A by 4 units to the right , we get
A to 4 units right = A ( -4 + 4 , 1 )
The new coordinate of A = A ( 0 , 1 )
Now , A to 4 units down , we get
The coordinate of A' = A' ( 0 , 1 - 4 )
The coordinate of A' = A' ( 0 , -3 )
Hence , the translated coordinate is A' ( 0 , -3 )
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The function is defined below.
H(x)= x+2/x^2+4x+4
Find all values of that are NOT in the domain of H.
If there is more than one value, separate them with commas.
Answer:
The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In the case of the function H(x) = x+2/x^2+4x+4, we need to find the values of x for which the denominator x^2+4x+4 is not equal to zero.
x^2+4x+4 = 0
(x+2)^2 = 0
The denominator is always non-zero as the square of any real number is always positive. Therefore, the function H(x) = x+2/x^2+4x+4 is defined for all real values of x. Therefore, the function H(x) does not have any values that are not in its domain.
Step-by-step explanation:
Find the volume of the combined solid from the figure.
Answer:
1734
Step-by-step explanation:
We can simply solve the volume of the 2 different cubes. The bigger cube's volume is 15*12*8 = 1440. The volume of the small cube is 6*7*(15-4-4)=294.
So the total volume should be 1734
Answer:
1944 cm³
Step-by-step explanation:
Two rectangular parallelepipeds:
Upper: 12 x 7 x 6 = 504 cm³
Lower: 12 x 15 x 8 = 1440 cm³
Total: 504 + 1440 = 1944 cm³
Find the sum of the first seven terms of the geometric sequence series having the following information: 2-8+32- … +a n
Answer:
6554-------------------------------
From the given information we can see:
The first term is a = 2,Common ratio is r = - 4Use the equation for the sum of the first n terms:
Sₙ = a(rⁿ - 1)/(r - 1)S₇ = 2((-4)⁷ - 1)/(-4 - 1) = 6554Answer:
[tex]S_7=6554[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given geometric series:
[tex]2-8+32-...+a_n[/tex]
The first term (a) of the sequence is 2:
[tex]\implies a=2[/tex]
To find the common ratio (r), divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{-8}{2}=-4[/tex]
To find the sum of the first 7 terms, substitute the found values of a and r into the formula, along with n = 7:
[tex]\implies S_7=\dfrac{2(1-(-4)^7)}{1-(-4)}[/tex]
[tex]\implies S_7=\dfrac{2(1-(-16384))}{5}[/tex]
[tex]\implies S_7=\dfrac{2(16385)}{5}[/tex]
[tex]\implies S_7=\dfrac{32770}{5}[/tex]
[tex]\implies S_7=6554[/tex]
simplify the expression 8h + (-7.7d) -14 +5d - 3.3h
The expression 8h + (-7.7d) -14 +5d - 3.3h can be simplified as
4.7h - 2.7d - 14
What is a Linear Expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power (1). In other words, none of the exponents can be greater than 1.
For example, x² is a variable raised to the second power, but x is a variable raised to the first power.
5 is an example of a constant.
8h + (-7.7d) -14 +5d - 3.3h
Taking like terms
8h - 3.3h + 5d - 7.7d - 14
4.7h - 2.7d - 14
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Shop a charges $275.00 for an oil change and has a gross oil profit of 39.1%. What is the profit per lube
The profit from Lube for Store A would be = $8.31.
What is the profit per unit?Unit profit can be obtained by subtracting the cost of the product from the selling price.
Data and calculations:
Selling price for oil change = $275
Percentage of total oil revenue = 39.1%
Cost of oil per gallon = $21.25
Selling price per gallon = $29.56 ($21.25 x $1,391)
Total income = $8.31 ($29.56 - $21.25)
Therefore, the profit from Lube for Shop A would be= $8.31.
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Complete question:
Shop A charges $275.00 for an oil change and has a gross oil profit percent of 39.1% for its total oil gross profit %. Shop B charges $275.00 for an oil change and has a gross oil profit percent of 28.4% for its total oil gross profit %. Both shops pay $21.25 per gallon of oil. What is the Profit per Lube for Shop A?
what is the rate of interest per annum at which 8000 will yield 1650 after 10years
Step-by-step explanation:
annual interest = 1650
10
= 165
[tex] \frac{165}{8000} \times 100 = 2.0625\%[/tex]
Which of the following equations is correctly calculated?
-18 ÷ -2 = -9
-24 ÷ 3 = 8
-5 × -5 = 25
6 × -2 = 12
