You're going on a 1211-mile trip, and your car gets about 29 miles per gallon. Gas prices along your route average $3.10. Estimate the cost of gasoline for this trip by rounding the distance to 1200 miles, the mileage to 30 miles per gallon, and the cost of gas to $3.00 per gallon. Calculate the answer without using estimation and compare the two results. (Round your answers to the nearest cent.)
Using proportions, it is found that:
Without estimation, the cost is of $129.46.With estimation, the cost is of $120.For the estimation, the mileage was rounded up while the cost was rounded down, hence the estimated cost is less than the actual cost.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Without the estimate, the number of gallons used is:
1211/29 = 41.76 gallons.
Hence the cost is:
41.76 x 3.10 = $129.46.
With the estimate, the number of gallons used is:
1200/30 = 40 gallons.
Hence the cost is:
40 x 3 = $120.
For the estimation, the mileage was rounded up while the cost was rounded down, hence the estimated cost is less than the actual cost.
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A cricketer scored 12 runs short of a century. How many runs did he score?
Answer:
it's 88
Step-by-step explanation:
a century = 100
so 100-12 =88
Is 4:6 and 8:12 equivalent to each other
Answer:
YES!
Step-by-step explanation:
ratios are like fractions, and fractions are basically division problems. SO, if you divide 4 by 6 you get .66666666, and if you divide 8 by 12 you ALSO get .66666666, soooooo yes they are equivalent!
A pilot flew a plane from an altitude of 4500 feet to an altitude of 6300 feet. What was the change in altitude?
The required change in altitude is 900ft
Calculating change in altitudeFrom the question, we are given the following parameters
Initial height =5400ft
Final height = 6300ft
Determine the change in altitude
Change in altitude = Final - Initial
Change in altitude = 6300ft - 5400ft
Change in altitude = 900ft
Hence the required change in altitude is 900ft
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Find the difference between the largest and the smallest of the four numbers below.
10,743.93
234.018
324.1
23.107
Answer:
10720.823
Step-by-step explanation:
largest number is 10743.93 and the smallest number is 23.107. subtracting 23.107 from 10773.93 to get 10743.93
If a// b and m 1 = 90° then m 2 =
Slope m2=90°
The slope of a line, also known as the gradient is defined as the value of the steepness or the direction of a line in a coordinate plane. Slope can be calculated using different methods, given the equation of a line or the coordinates of points lying on the straight line.
given that, since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.
so we can conclude since m1=90° the m2 is also = 90°
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Answer:
M2 slope = 90°
Step-by-step explanation:
The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches.
Given that parallel lines must have the same angle from the horizontal and that slope is a measurement of that angle, parallel lines must therefore have the same slope, therefore lines with the same slope are parallel.
We can then deduce that if m1=90°, m2 must also be 90°.
PLS HELP!! 25 POINTS + BRAINLIEST
Answer:
A. 5/4n - 3/8
Step-by-step explanation:
-5n/2 + 1/4 + 15/4n - 5/8
15/4n - 10/4n + 2/8 - 5/8
5/4n - 3/8
Rewrite y =
1/4x+3,
solving for x. What feature of the line can easily be found using the rearranged equation?
The solution of the equation for x is x = 4y - 12
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to rewrite the equation of the function?The function y is given as
y = 1/4x + 3
As a general rule, we start by writing y as a variable (say y = f(x)).
So, the equation of the function becomes
y = 1/4x + 3
The next step is to switch/swap the positions of x and y in the above equation y = 1/4x + 3 (in this case, it is not necessary)
So, the equation remains the same
y = 1/4x + 3
The next step is to make x the subject of the formula in the above equation y = 1/4x + 3
The equation becomes
1/4x = y - 3
This is done by subtracting 3 from both sides of the equation.
So, we have:
1/4x = y - 3
Multiply through the sides of the equation by 4
So, we have
x = 4y - 12
Express as an inverse function
f-1(x) = 4x - 12 --- this is not compulsory
So, the solution of the equation for x is x = 4y - 12
Hence, the rewuired solution of the equation for x is x = 4y - 12
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A naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet.
If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet then 145 is the position of the submarine relative to the surface of the ocean now.
What is Equation?
Two expressions with an equal sign is called as Equation.
If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet. we need to find the position of the submarine relative to the surface of the ocean now.
The submarine initial position=310 feet.
To pass above an underwater mountain, or seamount, it rose =165 feet.
The position of submarine is
310-165
=145 feet.
Therefore the position of the submarine relative to the surface of the ocean now is 145 feet.
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Sixty-one percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?
The unusual outcomes for the binomial distribution are given as follows:
0 or 1 employee making judgements.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In the binomial distribution, a measure is considered unusual if it is more than 2.5 standard deviations from the mean.
For this problem, the parameters are given as follows:
n = 8, p = 0.61.
Hence the mean and the standard deviation are given by:
E(X) = np = 8 x 0.61 = 4.88.[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8(0.61)(0.39)} = 1.38[/tex]The bounds of usual outcomes are:
4.88 - 2.5 x 1.38 = 1.43.4.88 + 2.5 x 1.38 = 8.33.Hence outcomes of less than 1 employee making judgements would be unusual.
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Solve the equation
2^2x+1 + 2^x+2 = 12-2^x
Therefore the value of x is 2.
Given 2²ˣ ⁺ ¹ + 2ˣ ⁺ ² = 12 * 2ˣ
2²ˣ ⁺ ¹ + 2ˣ ⁺ ² = 12 * 2ˣ
We can write this as follows
aˣ ⁺ ⁿ = aˣ * aⁿ
2²ˣ * 2 + 2ˣ * 2² = 12 * 2ˣ
2ˣ * 2ˣ * 2 + 2ˣ * 2² = 12 * 2ˣ
By taking common terms aside we get
2ˣ * 2 (2ˣ + 2) = 12 * 2ˣ
By canceling the like terms we get
2ˣ + 2 = 6
2ˣ = 6 - 2
2ˣ = 4
2ˣ = 2²
∴ x = 2
Therefore the value of x is 2.
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HELP ME OUT PLEASE!!!!!
Answer:
y = -1/6x - 7/3
Step-by-step explanation:
slope = rise/run
(y2 - y1) / (x2 - x1)
ordered pairs: (-2,-2) and (4,-3)
-3 - (-2) = -1
4 - (-2) = 6
-1/6 = -1/6
m = -1/6
find b
take one ordered pair
y = mx + b
-3 = (-1/6)(4) + b
-3 = -4/6 + b
-3 + 4/6 = -2 2/6
-2 2/6 = -14/6
-14/6 = -7/3
b = -7/3
given the function f(t)=2(T)-3,what is f(7)
Answer: 11
Step-by-step explanation:
f(t)=2(t)-3
f(t)=2t-3
f(7)=2(7)-3
f(7)=14-3
f(7)=11
How do I graph -2x + 6 < 4 and 3(x + 1) < 12 on a number line?
Step-by-step explanation:
u first have to simplify a bit so u expand giving u -2x+6 less than 4 u then group like terms giving u -2x less than 4-6 amounting to -2x less than-2 u then divide both side by negative two to make x stand alone giving u positive 1 when u get Yr answer because u divided by a negative answer the sign changes to greater than
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 40 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer: The LARGEST angle has a measure of
degrees.
The measure of the largest angle is 84°
How to compute the value?It should be noted that the total angles on a triangle is 180°.
Let the smallest angle = x
Second angle = x + 40
Third angle = 3x
Therefore 3x + x + x + 40 = 180
5x = 180 - 40
5x = 140
x = 140/5
x = 28
Therefore, the largest angle will be:
= 3x
= 3 × 28°
= 84°
Therefore, the measure of the largest angle is 84°
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El área total de la superficie de un cilindro circular recto es 196 centímetros cuadrados. Si el radio de la base y la altura del cilindro tienen la misma longitud, encuentre la longitud de un radio.
--
The total surface area of a right circular cylinder is 196
The length of the radius when the total surface area of a right circular cylinder is 196 cm² is 7√π cm.
How to illustrate the information?It should be noted that the total surface area will be calculated thus,:
= 2πr(h + r)
It was stated that the radius and the.lebgth are the same and that the area is 196. This will be:
2πr(r + r)
= 2πr(2r)
= 4πr²
Therefore, 4πr² = 196
πr² = 198/4
πr² = 49
πr² = 49
r² = 49/π
r = 7√π
Therefore, the length of the radius when the total surface area of a right circular cylinder is 196 cm² is 7√π cm.
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53
4. Consider the rational number and the irrational number √78.
6
(a) Use your calculator to write out the (b) Which number is greater? Justify.
decimal expansion for both. If necessary,
use the repeating decimal bar.
53
6
√√78=
Difference between mixed farming and mixed cropping
PLEASE HELP ME!!!!!!How is the product of a complex number and a real number represented on the complex plane?
Consider the product of −2+8i and 5.
Drag a value or phrase into each box to correctly complete the statements.
The complete paragraph is shown:
The complex number - 2 + i 8 has modulus of 2√17. When - 2 + i 8 is multiplied by 5, the modulus of the product of 10√17.
Multiplying a complex number by a real number is a scalar of a complex number. The quadrant location of the complex number and its product with the real number are the same.
How to make operations with complex numbers
In this problem we have a paragraph, in which we must fill the blanks with the results of operations with complex numbers. The modulus of a complex number is found by using the Pythagorean theorem:
r = √[(- 2)² + 8²]
r = √(4 + 64)
r = √68
r = 2√17
And the product between the real number and the complex number is done by distributive property:
5 · (- 2 + i 8)
5 · (- 2) + i (5 · 8)
- 10 + i 40, whose modulus is 10√17.
Graphically speaking, the scalar of a complex number remains in the same quadrant of the complex plane.
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HELP WITH NUMBER 5 FOR 20 POINTS
Answer:
5
Step-by-step explanation:
that is hte anwers
What is the difference between adjusting entries and correcting entries? explain
Answer:
In short, the difference between adjusting entries and correcting entries is that adjusting entries bring financial statements into compliance with accounting frameworks, while correcting entries fix mistakes in accounting entries.
The number of students in mathletes increased from 20 to 28. what was the percent of increased
Step-by-step explanation:
Use the formula for finding out how what percent it is. (new amount ÷ old amount)28 ÷ 20 = 1.4Since you want to know how much it increased, subtract 11.4 - 1 = 0.4Convert 0.4 into a percentage.0.4 = 40%Answer:
The number of students increased by 40%
What is the answer at the A - B i don't know how to do this so I want answer or explanations The
Answer:
where is the question bro?
Step-by-step explanation:
write three rations equivalent to 3/10
Answer:
6/20, 9/30, 12/40
Step-by-step explanation:
Original fraction: 3/10
How I got: 6/20
3 x 2 = 6
10 x 2 = 20
How I got: 9/30
3 x 3 = 9
10 x 3 = 30
How I got: 12/40
3 x 4 = 12
10 x 4 = 40
(i) Write down the largest possible two digit number that can be made with two of the digits.
Answer:
85
Step-by-step explanation:
use the largest digit in the tens place, that is 8
use the next largest digit in the units place, that is 5
the largest 2- digit number is 85
(ii)
514 is the closest to 500 ( 14 units away )
485 is also close ( but 15 units away )
so 514 is the closest to 500
Answer: i) 85 & ii) 514
Step-by-step explanation:
Here, 8>5>4>1
So,
i) 85
ii) 514
Select the correct answer form each drop-down menu.
Given: m/WOZ = 90°
Prove: m/WOX = 90°
X
W
N
Complete the proof.
Suppose m/WOX # 90°. By the
✓ZWOXis supplementary to ZWOZ. Therefore,
m/WOX + m/WOZ = 180°. By the assumption and the substitution property of equality. 90° +m/WOZ 180°. Using the
subtraction property of equality, the measure of angle WOZ
✓90°, which contradicts the given. Therefore, the
assumption is not true, and m/WOX = 90°.
4
Reset
Next. Answer?
The complete proof are;
Suppose m ∠WOX ≠ 90°. By the definition of linear pair of straight line ∠ WOX is supplementary to ∠WOZ.
Therefore, m ∠WOX + m ∠WOZ = 180°.
By the assumption and the substitution property of equality.
90° + m ∠WOZ = 180°.
Using the subtraction property of equality, the measure of angle WOZ is equal to 90°, which contradicts the given.
Therefore, the assumption is not true and m ∠WOX = 90°.
What are Supplementary angles?
The two angles are called supplementary angles when sum of both angles are 180 degree.
Given that;
m ∠WOZ = 90°
Now, The proof of m ∠WOX = 90° is given as;
Suppose m ∠WOX ≠ 90°.
By the definition of linear pair of straight line ∠ WOX is supplementary to ∠WOZ.
Therefore,
⇒ m ∠WOX + m ∠WOZ = 180°.
By the assumption and the substitution property of equality.
⇒ 90° + m ∠WOZ = 180°.
Using the subtraction property of equality, the measure of angle WOZ is equal to 90°, which contradicts the given assumption.
Therefore, The assumption is not true and m ∠WOX = 90°.
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can someone help me with this
The cost per passenger for no wind conditions is $199 and 33 cents
Ground speed, 'x' = 500 ± 0 = 500 miles/h;
Cost per passenger is given by;
C(x) = 100 + x/15 + 33000/x;
Put x = 500;
C(500 miles/h) = 100 + 500/15 + 33000/500
C(500 miles/h) = $199.33
The cost per passenger for no wind conditions = $199 and 33 cents;
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A restaurant has 11 2/5 pounds of pasta to make casserole dishes. Each casserole requires 2 2/3 pounds pasta. How many casseroles can be made?
Answer:
Step-by-step explanation:
4.275
112/5 / 22/3
Find the sum of 2.53 x 1019 and 3.197 x 1017.
2.56197 x 1019
3.2223 x 1019
2.56197 x 1036
3.2223 x 1036
Taking into account the scientific notation, the result of the sum is 2.56197×10¹⁹.
Scientific notationScientific notation is a quick way to represent a number using powers of base ten.
The numbers are written as a product:
a×10ⁿ
where:
a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.n is an integer, which is called an exponent or an order of magnitude. Represents the number of times the comma is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.Sum in scientific notationYou want to add the following two numbers in scientific notation:
2.53×10¹⁹3.197×10¹⁷When the numbers to be added do not have the same base 10 exponent, the base 10 power with the highest exponent must be found. In this case, the highest exponent is 19.
Then all the values are expressed as a function of the base 10 exponent with the highest exponent. In this case: 3.197×10¹⁷= 0.03197×10¹⁹
Taking the quantities to the same exponent, all you have to do is add what was previously called the number "a". In this case:
2.53×10¹⁹ + 0.03197×10¹⁹= (2.53 + 0.03197)×10¹⁹= 2.56197×10¹⁹
Finally, the result of the sum is 2.56197×10¹⁹.
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Which type of compound inequality is 3|y+7|-16>5
-union
-hole
-disjunction
-intersection
y < -14ory > 0
Rearrange variables to the left side of the equation: 3|y+7| >5+16
Calculate the sum or difference: 3 |y+7| >21
Divide both sides of the inequality by the coefficient of the variable: |y+7| >[tex]\frac{21}{3}[/tex]
Reduce the fraction: |y+7|>7
Convert the absolute inequality to standard inequality: y+7 >7ory +7 < -7
:y < -14ory > 0
Find the union: y < -14ory > 0
A variable in mathematics is a sign and placeholder for any mathematical object (from the Latin variabilis, "changeable"). A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
A variety of issues are resolved by algebraic calculations that treat variables like explicit integers in a single computation. The quadratic formula, for instance, can be used to solve any quadratic equation by exchanging the variables in the quadratic formula for the numerical values of the coefficients in the equation.
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Question 5 (1 point)
Match the expressions that are equivalent.
Column A
1/32
32
2
1/2
64
1/64
Column B
a. (2^3)(2^2)
b. 2^(-2) x 2^(-3)
C. (2^3) x (2^-3)
d. (2^2)^3
e. 2^2/2^3
f. 2^3/2^2
It should be noted that the correct matching of the expressions illustrated will be:
a. (2^3)(2^2) = 32
b. 2^(-2) x 2^(-3) = 1/32
C. (2^3) x (2^-3) = 1
d. (2^2)^3 = 64
e. 2^2/2^3 = 1/2
f. 2^3/2^2 = 2
How to illustrate the information?It should be noted that (2^3)(2^2) will be:
= 2³ × 2²
= 8 × 4
= 32
b. 2^(-2) x 2^(-3) will be illustrated as:
= 1/4 × 1/8
= 1/32
C. (2^3) x (2^-3)
= 8 × 1/8
= 1
d. (2^2)^3
= 4³
= 64
e. 2^2/2^3
= 4 / 8
= 1/2
f. 2^3/2^2
= 2³ / 2²
= 8 / 4
= 2
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