The rate of change is 21.6 mpg.
The rate of change determines how one variable changes because of another variable. This rate value can be either positive or negative. Considering x as an independent variable and y as a dependent variable, the rate of change for these two variable is given by,
[tex]\text{rate of change}= \frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}[/tex]
From the given value, miles traveled is a dependent variable because it depends on the amount of gas. So the amount of gas is the independent variable.
Therefore, the rate of change is,
[tex]\begin{aligned}\text{rate of change}&=\frac{\Delta y}{\Delta x}\\&=\frac{\mathrm{259.2\;miles}}{1\mathrm{2\;gallons}}\\&=\mathrm{21.6\;mpg}\end{aligned}[/tex]
Therefore, the rate of change is 21.6 miles per gallon.
This formula is also used to calculate gas mileage.
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The complete question is -
Mariam uses 12 gallons of gas to drive 259.2 miles in her car. Find the rate of change.
a precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance. what assumptions are necessary? does the guarantee seem reasonable?
As per the given confidence interval, the value of P is lees than significant.
Confidence interval:
In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.
Given,
A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.
Here we need to find the assumptions of the given situation,
From the given question we have identified the following,
Reading of instruments = 353, 351, 351, and 355.
Confidence interval = 90% = 0.09
Number of units = 2.
Based on these details, the standard deviation of this temple is 0.7.
So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.
Therefore, P value was less than significant.
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2 divided by 5 over 6
Answer: 0.06 repeated, I'm sorry if it's wrong! I used a calculator.
Step-by-step explanation:
Calculating 2 divided by 5 / 6 should give you the answer 0.06666666666.
\frac{1}{6}f^3a=
6
1
\frac{1}{6}f^3a=
6
1
f
3
a=
\,\,D
D
Answer:
no
Step-by-step explanation:
\frac{1}{6}f^3a=
6
1
\frac{1}{6}f^3a=
6
1
f
3
a=
\,\,D
D
50POINTS
Do these pairs of values (x and y) represent two quantities that are
proportional?
xy
3 5
4 7
6 10
9 15
Answer:
D. No because not all of the pairs are simplified ratiosStep-by-step explanation:
The proportional relationship is:
y = kx, where k- constant of proportionalityLet's find the value of k for each pair and compare:
k = y/x1) x = 3, y = 5 ⇒ k = 5/32) x = 4, y = 7 ⇒ k = 7/43) x = 6, y = 10 ⇒ k = 10/6 = 5/34) x = 9, y = 15 ⇒ k = 15/9 = 5/3As we see thee of the pairs have same value of k, 5/3 and one is different 7/4.
The answer is no.
Answer choices given in the comment:
A. No because not all the pairs represent the same ratioB. Yes because the ratios 3/5 and 6/10 are equalC. Yes because as x increases y increasesD. No because not all of the pairs are simplified ratiosWhich of the expressions below means the
same as y/3
y+3
y-3
y÷3
3xy 3-y 3÷y
Answer:
y÷3
Step-by-step explanation:
y/3 is the same as y÷3
for corporation p to file a consolidated tax return with corporation s, p must own what percentage of s's voting stock?
For corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock
The consolidated tax return is defined as a single income tax return filed by an affiliated group of corporations that combines their tax liability.
The percentage is the ratio that can be represented as the fraction of hundred.
The voting stock is defined as the shares that give the stockholder, that is the right to vote on the policymaking of the corporation
Here, p must own 80% of s's voting stock
Hence, for corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock
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A math test with 26 questions is worth 100 points. There are multiple choice questions that are worth 2 points each and fill in the blank questions that are worth 5 points each. How many of each type of question is there?.
Answer:
Step-by-step explanation:
Please if possible, give an explanation.
Answer:
Step-by-step explanation:
put the day and the amount of money you made
Ursula wants to make 48 hotdogs for a party. If
a bag of 12 hotdog buns costs $1.50 each and a
package of 8 hotdogs costs $2 each, how much
will the 48 hotdogs cost altogether?
Answer:
Hotdogs: $12
Buns: $6
Altogether (Hotdogs plus Buns): $18
Step-by-step explanation:
She wants 48 hot dogs, and each package contains 8 hotdogs.
48/8 = 6
She'd have to buy 6 packages
6 packages x $2 each = $12
She'd be spending $12 on the hotdogs
She'd also have to get an equivalent amount of buns
Each bag has 12 buns. She needs 48 buns.
48 buns /12 per bag = 4 bags
She would need to buy 4 bags of buns
$1.50 per bag x 4 bags = $6
She'd be spending $6 on buns
Adding the amount she spends on both the buns and hotdogs, she spends $18
Which of the following statements about the changing features of the family is not true of todays Commonwealth Caribbean societies?
A) men and women choose their own partners
B) husband and wives usually treat each other as equals
C) parents are becoming more autocratic
D) generally, families have fewer children
The statement about the changing features of the family that is not true of todays Commonwealth Caribbean societies is C. parents are becoming more autocratic.
How to illustrate the information?It should be noted that nowadays, men and women choose their own partners, husband and wives usually treat each other as equals and generally, families have fewer children
While role changes are often difficult, many positive things can occur as a result. Families may learn to work better together and support one another. Learning new tasks can help children gain confidence. Families may discover that, despite the changes, life can still be enjoyable.
In conclusion, the correct option is C.
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What's the
degree measure of
NEED HELP ASAP
The measure of ∠x is 190°
Define Exterior angle
The Exterior Angle is the angle between any side of a shape, and a line extended from the next side. The sum of the exterior angles of a triangle is 360°.In the given diagram, all angles marked is an exterior angle
And, we know sum of exterior angle is 360°
So, now just equate the given values to 360 degree
x + 60 + 110 = 360
x + 170 = 360
x = 360 - 170
x = 190°
Hence, the measure of ∠x is 190°
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−64÷(−8)
solve and show how you solved
Determine which postulate can be used to prove that the triangles are congruent.
The postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.
First, let us understand the congruency of the triangle:
When two triangles have the same sides and angles, they are congruent. That is, one's three sides are equal to the other's three sides, and one's three angles are equal to the angles of the other.
In triangles ABD and CBD;
Side BD = side BD (common)
∠ABD = ∠CBD (90 degrees)
Side AB = side CB (common)
For this triangle pair, the postulate that fit are:
SAS since the two sides and the included angle are equal in both triangles.
Thus, the postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.
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define your variables and set up a system of equations, then solve
Solving by the system of linear equations, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.
What do you mean by system of linear equations?
A system of linear equations consists of two or more equations, each of which has two or more variables, and all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy each of the system's linear equations is necessary to identify the system's unique solution.
Let, the cost per pound of peanut be $x and for M&M's be y
so, according to the question, we are getting two linear equations,
$8x + $5y = $55.27..................(i)
$6x + $4y = $42.70....................(ii)
Solving this two systems of linear equations , x=$3.79 and y=$4.99
Hence, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.
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What is the quotient and remainder when 2x3 + x2 − 10x − 11 is divided by x + 1?
The quotient of the division is 2x² - x - 11 and 0 is the remainder.
Given,
The expression; 2x³ + x² - 10x -11 ÷ x + 1
We have to find the quotient and remainder
One of the arithmetic operations carried out on two given polynomials is to divide them. In this, the divisor is typically a polynomial of lower degree than the dividend.
Lets solve ;
2x³ + x² - 10x -11 / x + 1 (2x²)
= -x² - 10x - 11 / x + 1 (-x)
= -11x - 11 / x + 1 (-11)
= 0
Here,
The quotient = 2x² - x - 11
Remainder = 0
That is,
The quotient of the division is 2x² - x - 11 and 0 is the remainder.
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Simplify: 2√2 + 3√5 in the calculus topic, surds.
The radical expression 2√2 + 3√5 cannot be simplified
How to simplify the expression?From the question, we have the following parameters that can be used in our computation:
2√2 + 3√5
The above expression is a radical expression
The radicals in the expression are √2 and √5
The numbers 2 and 5 do not have common factors
This means that 5 cannot be expressed in terms of 2, and vice versa
So, we cannot simplify the given expression 2√2 + 3√5
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The distance between Bills house and his aunts house is 835 miles.About how many miles would he drive if he made 4 one-way trips?
Answer:
3340 miles
Step-by-step explanation:
Multiply 4x835=3340 miles
Under a dilation, the point (2, 6) is moved to (6, 18). What is the scale factor of the dilation? enter your answer in the box.
Under a dilation, the point (2, 6) is moved to (6, 18). the scale factor of the dilation is 3
We know that if we transform point (x,y) by using dilation with scale factor k then the coordinate of the image will be (kx,ky).
Given: under a dilation, the point (2, 6) is moved to (6, 18)
Here (x,y)=(2,6) and (kx,ky)=(6,18)
x = 2
kx = 6
k = 6/x
k = 6/2
k = 3
Similarly taking y into account
y = 6
ky = 18
k = 18/y
k = 18/6
k = 3
Hence, Under a dilation, the point (2, 6) is moved to (6, 18). the scale factor of the dilation is 3
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Hey, can anyone help me with this maths question please? Will mark brainliest!
Answer:n1=-9,n2=10
Step-by-step explanation:
How to solve for k=x/y?
Answer:
Step-by-step explanation:
k=x÷y
Multiply both sides of the equation by y.
ky=x
Swap sides so that all variable terms are on the left-hand side.
x=ky
Hollie says, "when you cube root a
number, the answer is always smaller."
Show she is wrong.
When you cube root a number, the answer is always smaller. This is true.
What is a number's cube root?The cube root, denoted by, is the inverse of the cube of a number. For example, 216, or the cube root of 216, equals 6 because multiplying 6 three times yields 216. In other words, because 6³ = 216.
A number's cube root is a value that, when multiplied by itself three times, yields the original value. For example, the cube root of 27 is 3, denoted as 3³ because multiplying 3 by itself three times yields 3 x 3 x 3 = 27.
In this case, we have showed that the answer will be smaller than the original number.
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Parallelogram ABCD has vertices A(1,1) , B(17,1) , C(22,13) , and D(6,13) what is the perimeter in units of parallelogram ABCD
The perimeter of the parallelogram ABCD is, 58 units.
What is perimeter?
The length of a shape's boundary taken as a whole is referred to as its perimeter. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.
Consider the given vertices, A(1, 1), B(17, 1), C(22, 13), D(6, 13).
The perimeter of parallelogram is the sum of all sides of parallelogram.
So, first to find the length of each side of parallelogram, using the distance formula,
[tex]d = \sqrt{(x_2 -x_1)^2+(y_2-y_1)^2}[/tex]
So,
[tex]AB = \sqrt{(17-1)^2+(1-1)^2}=\sqrt{16^2-0} = 16\\ BC = \sqrt{(22-17)^2+(13-1)^2} = \sqrt{5^2+12^2}= \sqrt{25+144}=13\\ CD = \sqrt{(6-22)^2+(13-13)^2} = \sqrt{16^2+0}=16\\ AD = \sqrt{(6-1)^2+(13-1)^2}=\sqrt{5^2+12^2} =\sqrt{25+144}=13[/tex]
Therefore, the perimeter of the parallelogram ABCD is,
P = AB + BC + CD + AD
P = 16 + 13 + 16 + 13
P = 58
Hence, the perimeter of the parallelogram ABCD is, 58 units.
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Determine the inverse of the function f (x) = 3(x − 4)2 + 5.
inverse of f of x is equal to 4 minus the square root of the quantity of the quantity x minus 5 end quantity over 3 end quantity such that the domain of f (x) is x ≥ 4
inverse of f of x is equal to 4 minus the square root of the quantity of the quantity x minus 5 end quantity over 3 end quantity such that the domain of f (x) is x ≤ 4
inverse of f of x is equal to 4 minus the square root of the quantity x over 3 minus 5 end quantity such that the domain of f (x) is x ≥ 4
inverse of f of x is equal to 4 minus the square root of the quantity x over 3 minus 5 end quantity such that the domain of f (x) is x ≤ 4
Question 4(Multiple Choice Worth 2 points)
(02.06 MC)
Determine the inverse of the function f(x) = log2(3x + 4) − 5.
f inverse of x is equal to 2 to the power of x plus 3 all over 2
f inverse of x is equal to the quantity x plus 5 end quantity squared minus 4 all over 3
f inverse of x is equal to 2 to the power of the quantity x plus 5 end quantity minus 4 all over 3
f inverse of x is equal to 2 to the power of the quantity x minus 5 end quantity plus 4 all over 3
Question 5(Multiple Choice Worth 2 points)
(02.06 MC)
Given the graph of f(x), determine the range of f−1(x).
Rational function with one piece increasing from the left in quadrant 2 asymptotic to the line y equals 1 and passing through the point 2 comma 2 and asymptotic to the line x equals 3 and another piece increasing from the left in quadrant 4 asymptotic to the line x equals 3 passing through the point 4 comma 0 asymptotic to the line y equals 1.
Answer: The inverse of the function f(x) = 4(x-3)² + 2 is
The given function is:
f(x) = 4(x - 3)² + 2
To find the inverse of the function:
Make x as the subject of the formula
Replace x by and replace f(x) by x
Therefore, the inverse of the function is:
Step-by-step explanation:
Mari cella has a bag containing 35 nickels and quarters. The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions?
A nonregular hexagon has five exterior angle measures of 55, 60, 69, 57, and 57. What is the measure of the interior angle adjacent to the sixth exterior angle?
62
128
118
108
The measure of the interior angle adjacent to the sixth exterior angle of the heaxagon is 118°.
What is an interior angle?Interior angles are those that lie inside a polygon.
To calculate an interior angle of a hexagon, we use the formula below.
Formula:
a = 360-(b+c+d+e+f)............ Equation 1Where:
a = The sixth exterior angleb = 55°c = 60°d = 69°e = 57°f = 57°Substitute these values into equation 1
a = 360-(55+60+69+57+57)a = 360-298a = 62°Recall that, the sum of an interior and exterior angle is 180°
a'+a = 180............... Equation 2Where:
a = Interior angle of the sixth exterior angle.Substitute the value of a into equation 2
a' = 180-62a' = 118°Hence, the value of the interior angle is 118°.
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(9,−7) after a dilation by a scale factor of 4 centered at the origin?
The image of the coordinates after a dilation of (9, −7) by a scale factor of 4 centered at the origin include the following: (36, -28).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage (9, -7) by using a scale factor of 4 centered at the origin as follows:
Coordinate A (9, -7) → Coordinate A' (9 × 4, -7 × 4) = Coordinate A' (36, -28).
In conclusion, the coordinates of the image after a dilation are (36, -28).
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make x the subject of the formular 6x+a=5(x+t)
The value of x is (5t-a) when the formula is 6x+a=5(x+t).
According to the question,
We have the following information:
6x+a=5(x+t)
Now, from this formula, we have to mark the value of x or in other words, we have to find the value of x.
Now, multiplying 5 into the bracket on the right hand side:
6x+a = 5x+5t
Subtracting 5x from both sides of the equation:
6x-5x+a = 5t
x+a = 5t
Subtracting a from both sides of the equation, we will get the final value of x in terms of t and a:
x = 5t-a
Hence, the value of x is (5t-a) when the formula is 6x+a=5(x+t).
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Question 4 please help it's important
A matrix is a form of writing items in rows and columns.
The matrice B is
[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]
The value of [tex]b_{11}[/tex] = 9
The value of [tex]b_{22}[/tex] = 15
The value of [tex]b_{31}[/tex] = -3
The value of [tex]b_{32}[/tex] = -18
What is a matrix?A matrix is a form of writing items in rows and columns.
[tex]\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right][/tex]
We have,
[tex]A=\left[\begin{array}{ccc}3&-2\\4&5\\-1&-6\end{array}\right][/tex]
B = 3A
We will multiply 3 with all the items in matrices A.
[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]
This is in the form of
[tex]B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{array}\right][/tex]
Now,
The value of [tex]b_{11}[/tex] = 9
The value of [tex]b_{22}[/tex] = 15
The value of [tex]b_{31}[/tex] = -3
The value of [tex]b_{32}[/tex] = -18
Thus,
The matrice B is
[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]
This is in the form of
[tex]B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{array}\right][/tex]
The value of [tex]b_{11}[/tex] = 9
The value of [tex]b_{22}[/tex] = 15
The value of [tex]b_{31}[/tex] = -3
The value of [tex]b_{32}[/tex] = -18
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if the zeroes of the quadric polynomial 2x^2-5x+k are reciprocal to each other then find the value of k
Answer:
The value of k is 1.
Step-by-step explanation:
Answer:
The value of k=1
Step-by-step explanation:
Triangle xyz was translated up 2 and right 3 units, creating triangle cab. Which relationship between the parts of the two triangles must be true?.
Triangle xyz was translated up 2 and right 3 units, creating triangle cab.
To find out the relationship between the parts of the two triangles must be true:
YZ ≅ AB
A translation is known as a rigid transformation. This is because it preserves congruence. Since CAB is created from XYZ, this tells us that:
X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.
Since the triangles are congruent, the corresponding pieces are congruent as well.
Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.
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