The number of gallons required for 280 million cars is 1,555,556 gallons.
Given that, 1 ton makes 90 cars, there are 280 million cars needed
and 1 ton = 500,000 gallons of water.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of gallons of water needed for 280 million cars be x.
Now, 90 : 500,000 :: 280 : x
⇒ 90x=500,000 × 280
⇒ x = 14,00,00,000/90
⇒ x = 1,555,555.555≈1,555,556 gallons
Therefore, the number of gallons required for 280 million cars is 1,555,556 gallons.
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Some studies show that high school students are more successful when the school day begins after 9 am. To test this theory, Lake High School changes its school day start time from 7 am to 9 am. Which of the following methods would best describe the study above? A. controlled experiment B. experimental study C. survey D. observational study
The method that would best describe the study above is D. observational study
What is observational study?In observational studies, the impact of a risk factor, diagnostic test, treatment, or other intervention is observed without an attempt to alter who is or is not exposed to it. There are two categories of observational studies: cohort studies and case control studies.
Observational studies, often known as epidemiological studies, are those in which the researcher does not influence the study subjects but rather observes the associations that naturally exist between causes and outcomes. This was illustrated in the case regarding the students.
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Please Help with problem 27 part b, Algebra 1, in the attachment
Step-by-step explanation:
Using the formula c=6p+200 you can plug 350 in for c and solve for p
350=6p+200
-200 -200
150=6p
/6 /6
25=p
So, she can invite 25 people to her birthday party.
Simplify by combining like terms. 7s-s
The simplification by combining like terms of 7s -s is 6s.
According to the given question.
We have an expression 7s - s.
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression
7s - s.
Here 7s and s both are the like terms.
So, we subtract coeffcients of s to simplify the given expression.
Therefore, the simplification of the expression 7s - s is given by
7s - s
= 6s
Hence, the simplification by combining like terms of 7s -s is 6s.
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Use the Distance Formula to find the distance between the pair of points.
Q(-12,2), T(-9,6)
Using the distance formula the distance between and pair of points Q(-12,2) and T(-9,6) is 5 units
Given,
The points = Q(-12,2) and T(-9,6)
We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values in the equation
The distance = [tex]\sqrt{(-9--12)^{2}+(6-2)^{2} }[/tex]
[tex]=\sqrt{3^{2}+4^{2} } \\=\sqrt{9+16}\\ =\sqrt{25}[/tex]
=5 units
Hence, Using the distance formula the distance between and pair of points Q(-12,2) and T(-9,6) is 5 units
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Find the geometric mean between pair of numbers.
3 √2/7 and 5√2/7
The geometric mean between pair of numbers 3√2/7 and 5√2/7 is 0.78.
The geometric mean is the average or mean value that signifies the central tendency of a set of numbers. This is obtained by finding the product of their values.
Geometric mean (GM) is calculated as:
GM = [tex]\sqrt{x y}[/tex]
where x and y are the given two values.
According to the given condition, x = [tex]\frac{3\sqrt{2} }{7}[/tex] and y = [tex]\frac{5\sqrt{2} }{7}[/tex]
Substituting these values in the equation above,
∴GM = [tex]\sqrt{\frac{3\sqrt{2} }{7} \frac{5\sqrt{2} }{7} }[/tex]
= [tex]\sqrt{\frac{30}{49} }[/tex]
= 0.78.
Thus, the geometric mean between the given two numbers is 0.78.
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solve the system of equations using a matrix. x+3y=11 4x-y=31
Answer:
[tex] \sf \: x=8 and y=1[/tex]
Step-by-step explanation:
Let's solve your system by elimination.
x+3y=11;4x−y=31
Multiply the first equation by -4,and multiply the second equation by 1.
−4(x+3y=11)
1(4x−y=31)
Becomes:
−4x−12y=−44
4x−y=31
Add these equations to eliminate x:
−13y=−13
Then solve−13y=−13for y:
−13y=−13
−13y/−13=−13/−13
(Divide both sides by -13)
y=1
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
x+3y=11
Substitute1foryinx+3y=11:
x+(3)(1)=11
x+3=11(Simplify both sides of the equation)
x+3+−3=11+−3(Add -3 to both sides)
x=8
y = 8x + 3
The rate of change is 1 and the y-intercept is 4
Answer:
False
Step-by-step explanation:
The rate of change/slope of the linear equation is 8.
The y-intercept is the point where x has no value and y does.
And in the linear equation y = 8x+3, the y-intercept is 3.
Therefore, false.
- Thanks.
Exponential function f is represented by the table.
x -2 -1 0 1 2 f
(x) -62 -30 -14 -6 -2
Function g is represented by the equation.
g(x) = -20 (1/2)^x + 10
Which statement correctly compares the two functions on the interval [-2, 1]?
A. Only function f is increasing, and both functions are negative.
B. Only function f is increasing, and only function f is negative.
C. Both functions are increasing, but function g increases at a faster average rate.
D. Both functions are increasing, but function f increases at a faster average rate.
Answer:
I believe the correct answer to this question is D.
Step-by-step explanation:
You can use Desmos (graphing calculator) to graph the equation to verify it. :)
Write in point-slope form an equation of the line through each pair of points. (1,9) and (6,2)
The equation of the line in point-slope form, which passes through the pair of points located at (1 , 9) and (6 , 2), is y - 9 = -7/5(x - 1).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (1 , 9) and (6 , 2).
m = (y2 - y1)/(x2 - x1)
m = (2 - 9)/(6 - 1)
m = -7/5
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = -7/5 and (x1 , y1) = (1 , 9)
(y - 9) = -7/5(x - 1)
y - 9 = -7/5(x - 1)
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Membership at the Get Moving Gym requires new members to pay an
enrollment fee of $99 and purchase a key card for $16, in addition to the
regular monthly fee of $29.
Write an equation that represents the cost C for membership for m months.
What is the cost of a 2-year membership?
$811.00
$2,789.00
$795.00
$1,179.00
Answer:
C=115+29m
Step-by-step explanation:
C=115+29(24)
C=£811
so the first option
Four students participate as a team in a 1000 m wacky relay race. In a wacky
relay race, the students each run a portion of the 1000 m length, but they do not
run equal lengths. Andrea and Billie run 1
8
and 1
5
of the total length, respectively.
Carol runs the average of what Andrea and Billie run. Dana runs the remainder
of the length.
Determine the fraction of the total length that Dana runs.
Answer: 14/40 or 7/20
Step-by-step explanation: We need to set the fraction's denominators equal to each other and their LCM is 40 so Andrea ran 1/8 which =5/40. Billie ran 1/5 which =8/40. 5/40+8/40=13/40/ Carol ran both Andrea's and Billie's length combined so that's another 13/40 = 26/40. The whole length is 40/40 so 40/40-26/40=Dana's length which =14/40 or 7/20
Select the correct answer. histogram is plotted between x-axis (ranging from 0 to 5) and y-axis (ranging from 1 to 7). the histogram exhibits negative skewness. what type of skew is observed in this histogram? a. symmetry b. zero skew c. negative skew d. positive skew
Answer:
C. Negative skew
Step-by-step explanation:
I did the test and got it right, plato / edmentum
Which two segments have the same length?
The two segments having the same length are line VW and line YZ. Option D
What is a number line?A number line can simply be defined as a straight line with numbers that are placed at equal intervals or segments along its length.
It is also known as a visual picture or representation of numbers.
From the number line shown, we have the following deductions;
Line XY = 10- 3 = 7Line YZ = 18 - 10 = 8Line WX = 3 --3 = 3 + 3 = 6Line VW = -2 --10 = -2 +10 = 8From the above solutions, we can see that line
Line VW is equal in length to line YZ
Thus, the two segments having the same length are line VW and line YZ. Option D
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Solve y3 = −125.
please please help
Answer:
pretty sure it's -5
Step-by-step explanation:
the cubed root if 125 is 5 so you just make it negative
Answer:
y = 5
Step-by-step explanation:
Let's solve your equation step-by-step.
[tex] y{}^{3}=125[/tex]
Step 1: Take cube root.
[tex] \sf \: y= {(125)} ^ {( \frac{1}{3} )}[/tex]
y=5
200,150,112.5,...
next three terms?? explanation??
The next three terms of the sequence are 84.375, 63.28, 47.46
What are the next three terms?In order to determine the next three terms, the relationship between the numbers have to be determined.
When examined, it can be seen that the next number is 75% of the previous number
150 / 200 = 75%
112.50 / 150 = 75%
The next number would be 75% of 112.50 = 112.50 x 0.75 = 84.375
The second number would be 75% of 84.375 = 0.75 x 84.375 = 63.28
The third number would be 75% of 63.28 = 0.75 x 63.28 = 47.46
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Find the lengths of the sides (x=5)
Answer:
−87.5
Step-by-step explanation:
3×5−4×7×5+2×4×5−5÷2=-87.5
Construct a true table. Use tea for true enough for falls
Truth Table is used to perform logical operations in Maths. These operations comprise boolean algebra or boolean functions. It is basically used to check whether the propositional expression is true or false, as per the input values. This is based on boolean algebra.
A truth table is a breakdown of a logic function by listing all possible values the function can attain. Such a table typically contains several rows and columns, with the top row representing the logical variables and combinations, in increasing complexity leading up to the final function.
Here we construct truth table for And operation -
see attachment below -
So because we don't have statements on either side of the "and" symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p.
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IF AB = 7, AD = 25 and CD = 10, find BC
The measure of the length of BC from the expression is 8
Addition postulateThe segment addition postulate in geometry is the axiom which states that a line segment divided into smaller pieces is the sum of the lengths of all those smaller segments.
Given the following segments
AB = 7
AD = 25 and:
CD = 10
Using the addition postulate below:
AB+BC+CD = AD
Substitute the given parameters
7+BC+10 = 25
17+BC = 25
Subtract 17 from both sides
17+BC-17 = 25 - 17
BC = 8
Hence the measure of the length of BC from the expression is 8
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Find the distance between the pair of points. Round to the nearest tenth.
A(5,1) and C(-3,-3)
Distance between the pair of points A(5,1) and C(-3 ,-3) is equal to
8.9 units (nearest tenth).
As given in the question,
Given points are A (5, 1) and C( -3,-3)
Distance between the pairs of points = [tex]\sqrt{(y_{2}-y_{1})^{2} + (x_{2}-x_{1})^{2} }[/tex]
=[tex]\sqrt{(-3-1)^{2} + (-3-5)^{2} }[/tex]
= [tex]\sqrt{16 + 64}[/tex]
= [tex]\sqrt{80}[/tex]
= 8.9 units (nearest tenth)
Therefore, distance between the pair of points A(5,1) and C(-3 ,-3) is equal to 8.9 units (nearest tenth).
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What’s this I need help asap
Answer:
see attached photo for the graph
How many periods can you use for an n period moving average? question 1 options: 1)
The periods that you can use for an n period moving average is 3.
What is the n period moving average?The term n period moving average is the type of average that an investor can use to determine the trends in investments and the equities market. This type of average helps the traders to be able to understand the moving trends in the market and also to be able to make forecasts.
The period of the moving average spans across the times that the stock would last. This is determined by the equities market. Hence we can say that number of periods that you can be able to substitute for n to obtain the period moving average is 3.
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Factor x^2+2x-16=2x?
Answer:
Step-by-step explanation:
x^2+2x-16-2x = x^2 - 16
= ( x - 4) ( x+ 4)
State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
A vector is in ₋standard ₋position when the initial point is at the origin.
Given statement 'A vector is in standard position when the initial point is at the origin.' is True.
In given question,
We have been given a statement 'A vector is in ₋standard ₋position when the initial point is at the origin.'
We know that the tail of a vector is the initial point of the vector.
And the head of a vector is the final point of the vector with an arrowhead.
The definition of standard position of vector is: "When a vector is in a standard position the head of the arrow is at a point (x, y) and the tail of the arrow is at the origin."
Therefore, given statement 'A vector is in standard position when the initial point is at the origin.' is True.
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The prime factor decompositions of two numbers,
A and B, are shown below.
A = 26 x 33 x 5
B = 23 x 34 x5x7
Work out the
a) lowest common multiple (LCM) of A and B.
b) highest common factor (HCF) of A and B.
Give your answers as products of their prime
factors in index form.
The Least Common Multiple (LCM) of A and B is 11,741,730 and the Highest Common Factor (HCF) of A and B is 10
What is LCM and HCF?The least common multiple is also known as LCM (or) the lowest common multiple in math. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.
The highest common factor of two or more numbers is the highest number among all the common factors of the given numbers. It is also known as HCF.
So, Given numbers LCM of A and B can be calculated by
Listing all prime factors for each number.
Prime Factorization of A is:
2 x 3 x 5 x 11 x 13
Prime Factorization of B is:
2 x 5 x 7 x 17 x 23
The new superset list is
2, 3, 5, 7, 11, 13, 17, 23
Multiply these factors together to find the LCM.
LCM = 2 x 3 x 5 x 7 x 11 x 13 x 17 x 23 = 11741730
Now, Given numbers HCF of A and B can be calculated by
The factors of A are: 1, 2, 3, 5, 6, 10, 11, 13, 15, 22, 26, 30, 33, 39, 55, 65, 66, 78, 110, 130, 143, 165, 195, 286, 330, 390, 429, 715, 858, 1430, 2145, 4290
The factors of B are: 1, 2, 5, 7, 10, 14, 17, 23, 34, 35, 46, 70, 85, 115, 119, 161, 170, 230, 238, 322, 391, 595, 782, 805, 1190, 1610, 1955, 2737, 3910, 5474, 13685, 27370
Then the greatest common factor is 10.
Therefore, LCM of A and B is 11741730 and HCF of A and B is 10.
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i need help with this please please please !asap !
Answer:
18
7b² + 12b + 19 + -------
b - 1
Step-by-step explanation:
(7b³ + 5b² + 7b - 1) ÷ (b - 1)
1 | 7 5 7 -1
↓ 7 12 19
----------------------
7 12 19 18
18
7b² + 12b + 19 + -------
b - 1
I hope this helps!
A bald eagle flies 43.2 meters in 3 seconds. Part C: At these rates, what is the difference in the distances, in kilometers, flown by these two birds after 3 hours of flight?
PLEASE PLEASE PLEASE HELP ASAP
The difference between the distances flown by these birds is 150 Km.
We have a graph given in the question.
We have to find the difference in the distances flown by these two birds after 3 hours of flight.
What is the general equation of a line ?The general equation of a line is -
y = mx + c
According to the question -
The slope of the line is -
m = 400/5 = 80
The y - intercept of the line is 0. Therefore → c = 0.
Therefore, the equation of the line will be -
y = 80x
The distance covered by Bird 1 →
D[1] = initial distance + 80 x 3 = 250 + 240 = 490 Km.
The distance covered by Bird 2 →
D[2] = initial distance + 80 x 3 = 400 + 80 x 3 = 400 + 240 = 640 Km.
Therefore, difference between the distances flown by these birds -
D[2] - D[1] = 640 - 490 = 150 Km.
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[ The given question is incomplete. A graph is attached at the end of answer which is also a part of the question]
Help Please
An employee earns $17.55 per hour after receiving a 8% raise. What was the employee's hourly pay before raise? Round your answer to the nearest cent. The employee's pre-raise salary was $____.
Answer:
Step-by-step explanation:
17.55 x 0.92 = $16.15
Y=3x + 1 and 5x = y + 3
How to solve this type of simultaneous equation?
Answer:
(2, 7 )
Step-by-step explanation:
y = 3x + 1 → (1)
5x = y + 3 → (2)
substitute y = 3x + 1 into (2)
5x = 3x + 1 + 3
5x = 3x + 4 ( subtract 3x from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
substitute x = 2 into (1)
y = 3(2) + 1 = 6 + 1 = 7
solution is (2, 7 )
Question is below in the image. Please explain. Thanks
Answer:
E
Step-by-step explanation:
Substituting x=0 into 1-x², we get:
[tex]\lim_{x \to 0} f(1-x^2)=\lim_{x \to 1} f(x)[/tex]
which does not exist.
Find the indicated measure. Round to the nearest tenth.
The area of a circle is 201 square meters. Find the radius.
Radius = 799.877cm
or = 7.99877m(in meters)
Explanation
Radius of a circle from area: if you know the area A, the radius is r = √(A / π).
➟ r = √(201/3.142)
➟ r = √63.98
➟ r = 7.99877m
