Kim drives 378 miles and uses 18 gallons of gasoline. At that rate, how many miles can she go on 24 gallons of gas?
How many degrees are in each interior angle of a regular pentagon? 50 72 108 120
The answer 108 degrees.
Answer: [tex]108^{\circ}[/tex]
Step-by-step explanation:
The sum of all the angles in a regular polygon with sides n , is given by :-
[tex]S_n=180^{\circ}(n-2)[/tex]
Now, the sum of all the angles in a regular pentagon with 5 sides will be :-
[tex]S_5=180^{\circ}(5-2)=180^{\circ}(3)=540^{\circ}[/tex]
We know that all the interior angles of a regular polygon are equal .
Therefore, the measure of each interior angle in a pentagon is given by :-
[tex]x=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]
Hence, the measure of each interior angle in a pentagon=[tex]108^{\circ}[/tex]
Which property justifies this statement? If 4x=20, then x=5. Division Property of Equality Reflexive Property of Equality Substitution Property of Equality Subtraction Property of Equality
Answer:
Option 1 - Division Property of Equality
Step-by-step explanation:
Given : If [tex]4x=20[/tex], then x=5.
To find : Which property justifies this statement?
Solution :
The equation is [tex]4x=20[/tex]
To make variable separate we have to remove 4 which is in multiple of variable x.
So, We divide both side by 4,
Applying division property of equality,
We can divide both sides of an equation by the same number and preserve equality.
[tex]\frac{4x}{4}=\frac{20}{4}[/tex]
[tex]x=5[/tex]
Therefore, The property justifies the statement is 'Division Property of Equality'.
So, Option 1 is correct.
Change each fraction to a decimal. If the division doesn’t end, round your answer to the nearest hundredth. a. 3⁄4 b. 7⁄16 d. 3⁄5 e. 7⁄40 f. 51⁄20
Answer:
a = 0.75
b= 0.4375
d= 0.6
e=0.175
f= 2.55
Step-by-step explanation:
By simple division method, the following answers can be calculated:
a.
=[tex]\frac{3}{4}[/tex]
=0.75
b.
= [tex]\frac{7}{16}[/tex]
=0.4375
d.
= [tex]\frac{3}{5}[/tex]
=0.6
e.
= [tex]\frac{7}{40}[/tex]
=0.175
f.
=[tex]\frac{51}{20}[/tex]
=2.55
Thus, the answer are :
a = 0.75
b= 0.4375
d= 0.6
e=0.175
f= 2.55
Answer:
A.0.75 B.0.4375 C. 14.4 D. 0.6 E. 0.175 F. 2.55
Step-by-step explanation:
compute the following: 8C3 5C2
56×10= 560 so the answer is 560
A variable is: an instruction for the compiler a location in memory where a value can be stored a description of a value (such as a number or character) none of the above.
Final answer:
A variable is a name assigned to a quantity that can take on various values, and is used by mathematicians, economists, and statisticians in different contexts to represent data or elements of an equation.
Explanation:
A variable is the name given to a quantity that may assume a range of values. Mathematicians and economists often use variables in equations to represent different aspects of a problem or scenario. For example, in the equation of a line, commonly expressed as y = mx + b, the variables are 'x' and 'y'. Here, 'x' typically represents values on the horizontal axis, and 'y' represents values on the vertical axis, while 'b' is the y-intercept, and 'm' is the slope of the line. To understand how an equation with variables functions, we can look at a numerical example.
In statistics, variables can also refer to characteristics or measurements that can be determined for each member of a population. These variables can be numerical or categorical. A numerical variable, such as 'X' representing the number of points earned by a math student, allows for mathematical calculations like averaging. A categorical variable, like 'Y' indicating a person's political party affiliation, places individuals into categories and doesn't lend itself to mathematical operations like averaging.
The Garcias have $12,000 in a saving account. The bank pays 3.5% interest on saving accounts, compounded monthly. Find the balance after 3 years?
To find the balance after 3 years in a savings account with $12,000 and a 3.5% interest rate compounded monthly, we can use the formula for compound interest.
Explanation:To find the balance after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amountP is the principal amount (initial balance)r is the annual interest rate (as a decimal)n is the number of times interest is compounded per yeart is the number of yearsPlugging in the given values:
P = $12,000r = 0.035n = 12 (monthly compounding)t = 3 yearsThe formula gives us:
A = $12,000(1 + 0.035/12)^(12*3)
Calculating this expression will give us the balance after 3 years.
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Adam earns a base pay plus a commission for each car he sells at Crazy Carl's Cool Cars. His monthly salary is modeled by the function f(c) = 250c + 500. If Adam doesn't sell a car, how much money does he earn for the month?
Answer: 500
Step-by-step explanation:
Since, The monthly salary is modeled by the function,
f(c) = 250 c + 500.
According to the question,
Adam earns a base pay plus a commission for each car he sells at Crazy Carl's Cool Cars.
In the given function c is a variable.
Thus, c must show the number of cars.
Thus, the base pay must be free from any variable.
In the above expression 500 is free from the variable c therefore, 500 is the base pay of Adam.
⇒ f(c) is the total earning by Adam after selling a car.
If he Does not sell any car then c=0,
f(0) = 250×0+500 = 500
Therefore, if he does not sell any car then his earning is 500.
How many students had a shoe size greater than the mean shoe size?
What is the slope of the line perpendicular to the line represented by the equation 2x+4y=12?
An is planning a birthday party for her younger sister at a skating rink. the cost of admission is $3.50 per adult and $2.25 per child., and there is a limit of 20 people. jan has $50 to spend. how many adults and how many children can jan invite?
Write a quadratic function (f) whose zeros are −8 and 2.
Two buses leave towns 1631km apart at the same time and travel toward each other. one bus travels 17 /kmh slower than the other. if they meet in 7 hours, what is the rate of each bus?
2. For the circle with equation , answer each question.
(a) What are the coordinates of the center?
(b) What are the radius and diameter of the circle?
(c) Graph the circle.
John Gray bought a basic car for $32,750.00, with options that cost $375.00. There's a 6% sales tax in his state and a combined $50.00 license and registration fee. What was John's total cost
Answer:
The total cost of the car be $35162.5 .
Step-by-step explanation:
As given
John Gray bought a basic car for $32,750.00, with options that cost $375.00.
Cost of the car = Car cost + Option cost
= $32750 + $375
= $33125
As given
There's a 6% sales tax in his state .
6% is written in the decimal form.
[tex]= \frac{6}{100}[/tex]
= 0.06
Sales tax price = 0.06 × 33125
= $ 1987.5
As given
A combined $50.00 license and registration fee.
Than
Total cost of the car = Cost of the car + Sales tax price + license and registration fee.
= $33125 + $ 1987.5 + $ 50
= $35162.5
Therefore the total cost of the car be $35162.5 .
Find the value of the variable.
I need help with this math question!!
Simplify 0.4i−i.
The simplification of the given expression is 0.6i.
What are complex numbers?Complex numbers are those numbers that contain the imaginary and the real part.
A Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
where r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Usually the simplification involves proceeding with the pending operations in the expression.
We need to simpify the 0.4i - i
= i(0.4-1)
= 0.6i
Therefore, the simplification of the given expression is 0.6i.
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Witch of the following is closest to 27.8 X 9.6 is it 280, 2800, 300, or 3000
Which statements are true about the ordered pair (−4, 0) and the system of equations?
{2x+y=−8
x−y=−4
Select each correct answer.
The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
If sinθ = -1/2 and θ is in Quadrant III, then tanθ = _____.
Answer: [tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]
Step-by-step explanation: Given that
[tex]\sin\theta=-\dfrac{1}{2}[/tex] and [tex]\theta[/tex] lies in Quadrant III.
We are to find the value of [tex]\tan \theta.[/tex]
We will be using the following trigonometric identities:
[tex](i)~sin^2\theta+\cos^2\theta=1,\\\\(ii)~\dfrac{\sin\theta}{\cos{\theta}}=\tan \theta.[/tex]
We have
[tex]\tan\theta\\\\\\=\dfrac{\sin\theta}{\cos\theta}\\\\\\=\dfrac{\sin\theta}{\pm\sqrt{1-\sin^2\theta}}\\\\\\=\pm\dfrac{-\frac{1}{2}}{\sqrt{1-\left(\frac{1}{2}\right)^2}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\sqrt{1-\frac{1}{4}}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\frac{\sqrt3}{2}}\\\\\\=\pm\dfrac{1}{\sqrt3}.[/tex]
Since [tex]\theta[/tex] lies in Quadrant III, so tangent will be positive.
Thus,
[tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]
The sum of two right angles always, sometimes, never results in a straight angle. Justify answer
Adding two right angles, each being 90 degrees, always results in a straight angle, which is 180 degrees, so this is always true.
Explanation:The sum of two right angles always results in a straight angle. This can be justified with a basic understanding of angles in a flat plane. A right angle is 90 degrees and a straight angle is 180 degrees. So, if you add two right angles together (90 + 90), you get 180, which is the measure of a straight angle. Hence, this is always true, regardless of the vectors or other elements you are working with. It's also important to note that in broader geometric terms, this statement is also always true: two angles that add up to form a straight line (180 degrees) are referred to as supplementary angles.
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Describe how the variability of the x bar distribution changes as the sample size increases
The standard deviation decreases and the sampling distribution becomes more normal as the sample size increases in x bar distribution.
The variability of the x bar distribution changes as the sample size increases. As the sample size increases, the standard deviation of the sampling distribution of the means will decrease, approaching the standard deviation of X. The sampling distribution of the mean becomes more normal as the sample size grows, showing less variability.
Fifty randomly selected individuals were timed completing a tax form. the sample mean was 23.6 minutes; the sample standard deviation was 2.4 minutes. a 99% confidence interval for the mean time required by all individuals to complete the form is about:
HELP!!! I GIVE LOTS OF POINTS!! THE ANSWER IS NOT 3!!!!!!!!
In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in.
the answer would be 6 i did my calculations on paper then misplaced it but checked answer and it said 6
Which equation could generate the curve in the graph below?y=3x^2-2x+1
Twice the smallest of three consecutive odd integers is nine more than the largest. find the integers.
The required Integers are 13, 15, 17
What are the Integers?
Integers are the collection of whole numbers and negative numbers.
Given that twice the three consecutive odd Integers is nine more than the largest.
Let the numbers be x , x+2 , x+4
According to question
2x = 9+x+4
x = 13
Hence the Integers are 13, 15, 17
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Tristan jogs a route that is 7/10 mile. If he wants to jog between 2 and 3 miles, how many times should he plan to run the route? Circle the letter for all that apply.
A. 2 times
B 3 times
C. 4 times
D. 5 times
Answer:
B 3 times
C. 4 times
Step-by-step explanation:
For Tristan to jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.
Considering the options given
A. 2 * 7/10 = 1.4 miles (this is not within the range)
B. 3 * 7/10 = 2.1 miles (this is within the range)
C. 4 * 7/10 = 2.8 miles (this is within the range)
D. 5 * 7/10 = 3.5 miles (this is not within the range)
Brainliest for a math answer
A Springer Spaniel weighs 20 kilograms 490grams. A Cocker Spaniel weighs 7,590 grams less than a Springer Spaniel. A Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. What is the difference, in grams, between the weights of the Newfoundland and the Springer Spaniel?
To find the difference in weight between the Newfoundland and the Springer Spaniel, subtract the weight of the Springer Spaniel from the weight of the Newfoundland.
Explanation:To find the difference in weight between the Newfoundland and the Springer Spaniel, we need to subtract the weight of the Springer Spaniel from the weight of the Newfoundland. The Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. So, we first need to find the weight of a Cocker Spaniel by subtracting 7,590 grams from the weight of the Springer Spaniel. We then add this weight to the weight of the Newfoundland to get the final answer. Let's calculate:
The weight of the Cocker Spaniel = Weight of Springer Spaniel - 7,590gThe weight of the Newfoundland = Weight of Cocker Spaniel + 52kg 656gFinally, the difference in weight between the Newfoundland and the Springer Spaniel is the weight of the Newfoundland - weight of the Springer SpanielWe can now substitute the given values into these equations and solve.
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Marcia can make 5 candles in an hour. Kevin can make only 4 candles in an hour, but he already has 7 completed candles. Explain to Marcia how she can use a system of equations to determine when she will have the same number of candles as Kevin. Use complete sentences.