Answer:
Definition: The average speed over the course of mobion can be calculated using the formula Total Distance Traveled Average Speed = Time of Travel A car fravels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles per hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of the car for the whole trip? 20.0 mph 37.5 mph 40.0 mph 45.0 mph 80.0 mph QUESTION 13 Wriat is the height h, of the equilateral triangle shown below? Aak Sareend Sabmit ro save and submit. Click Save AlAnseers to save all ansuers Save
Average speed of the whole trip is equals to 37.5 mph.
What is average speed?
" Average speed is defined as the ratio of the total distance travelled to the total time taken."
Formula used
Average speed = [tex]\frac{Total distance travelled }{Total time taken}[/tex]
According to the question,
Total distance travelled = 300miles
Speed for first 150 miles = 30 miles per hour
For, 30 miles = 1hour
⇒150 miles = 5 hours
Speed for remaining 150 miles = 50 miles per hour
For, 50 miles = 1hour
⇒150 miles = 3 hours
Substitute the value in the formula to get average speed,
Average speed = [tex]\frac{300miles}{(5 + 3)hours}[/tex]
[tex]=\frac{300}{8}\\ \\= 37.5 miles per hour[/tex]
Hence, average speed of the whole trip is equals to 37.5 mph.
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S is a subset within a universal set, u. if s = {x, y, 4, 9, ?}, which could describe u?
The set that best describes the universal set U is; U = {keys on a keyboard }
How to determine mathematical sets?We are told that S is a subset within a universal set U.
Now, from the subset S = (x, y, 4, 9, ?), we will need to find among the given sets the one that describes the best set.
From the subset, we see that the Universal set will be keys on a key board due to the fact that the keys on a keyboard will have alphabets, numbers and punctuation marks mentioned in the set.
Therefore U = {keys on a keyboard } will be the correct answer.
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For her job, natasha spent a total of n minutes processing id card applications and driver's license applications. it takes natasha 15 minutes to process and id card aplication and 20 minutes to process a driver's license application. what is the value of n
Step-by-step explanation:
if I understand the question, write an equation for n in terms of i for number of Id cards an d for number driver license.
n = 15i + 20d
The value of n for a total minutes processing id card applications and driver's license applications would be 35 minutes.
Used the concept of addition that states,
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that,
For her job, Natasha spent a total of n minutes processing id card applications and driver's license applications.
And, it takes Natasha 15 minutes to process an id card application and 20 minutes to process a driver's license application.
Now by the given condition, we get;
n = 15 minutes + 20 minutes
n = 35 minutes
Therefore, the value n is 35 minutes.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given expression:-
2.3p – 10.1 = 6.5p – 4 – 0.01p
The same expression will be calculated as:-
Multiply the given expression by 100 we will get our answer.
E = 100 (s 2.3p – 10.1 = 6.5p – 4 – 0.01p )
E = 230p – 1010 = 650p – 400 – p
Therefore the correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.
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One possible integer of x for which 1/4 < k/10 < 1/3 is true?
Answer:
[tex]\fbox {x = 3}[/tex]
Step-by-step explanation:
Decimal form of the lower and higher limits :
1/4 = 0.251/3 = 0.33...Hence, the best one which lies in the middle of the limits would be 0.3.
Now, equate the middle part :
x/10 = 0.3x = 3HELP I REALLY NEED HELP
Answer: 72 inches squared
Step-by-step explanation:
So, the real floor of a classroom is 36 feet by 32 feet.
And the scale drawing, has length of the classroom equal to 9 inches.
What is the area in square inches of the floor in the scale drawing
1 foot = 12 inches
The length of the classroom, measured in feet, has been multiplied by 12, to get converted in inches. After that, it has been divided by a number, a proportion, to get to 9 inches.
36feet * 12 / x = 9 inches
432 inches / x = 9 inches
Now, to solve for x, we can cross-multiply
432 inches = 9x inches
Divide 9 inches on both sides.
x = 48
To solve the exercise, we need to calculate the floor's area in the scale drawing.
We have the length = 9 inches.
Now, let's calculate the width
Width = 32 feet * 12 / 48
Width = 384 inches / 48
Width = 8 inches
Area = Length * Width
Area = 9 inches * 8 inches
Area = 72 inches squared
Hope I helped!
Set up a proportion to solve for x in the following similar triangles
Answer:
[tex] \frac{18}{12} = \frac{24}{x - 2} [/tex]
AP Calculus AB Question from A, P .E* X
(Will give branliest if correct)
If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)
What is the domain of a function as a result of a binary operator
Binary operators are operators that involves two functions, there are four binary operators: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division. First, we determine the domains of the functions f(x) and g(x):
f(x):
Domain - [-3, 3]
g(x):
Domain - (- ∞, + ∞)
If we divide f(x) by g(x), then we must take g(x) = 0 into account, since it leads to indetermination. In this case, x = 1/3. Then, the domain of the resulting function:
(f/g)(x):
Domain - [-3, 1/3) ∪ (1/3, 3]
If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)
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one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?
Answer:
3 months
Step-by-step explanation:
When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. which equation represents this situation? 6x2 5x - 4 = 0 6x2 5x 4 = 0 62x 5 x = 4 6 x2 5x = 4
Answer:
The answer would be 6x^2 + 5x - 4 = 0
Why is it just as likely that the cube will show an even number as an odd number?
Name
Two-Variable Statistics
Relationship between Two Categorical Variables - Marginal and Joint Relative Frequency -
Part 2
Warm Up
Complete the table and calculate the percent for each total.
The completed table is given below,
the percentage of girls in the class is 47.62%,
the percentage of boys in the class is (100-47.62)% = 52.38%,
the percentage of students that love Math is 36.5%,
the percentage of students that love Reading is 22%, and
the percentage of students that love Science is 41.27%
To make comparison and statistical analysis easier, numerical data is systematically and logically represented in tabulations as rows and columns. Grouping relevant data together makes comparison easier and aids in statistical analysis and interpretation.
To put it another way, tabulation is the process of organizing data and presenting it in a tabular format. Depending on the type of categorization, it might be double, complicated, or simple.
The below table yields that
The total number of students is 315
The fraction of girls in the class is 150/315 = 0.4762
So, the percentage of girls in the class is 47.62%
Hence the percentage of boys in the class is (100-47.62)% = 52.38%
The fraction of students that love Math is 115/315 = 0.365
So, the percentage of students that love Math is 36.5%
The fraction of students that love Reading is 70/315 = 0.22
So, the percentage of students that love Reading is 22%
The fraction of students that love Science is 130/315 = 0.4127
So, the percentage of students that love Science is 41.27%
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I want to verify my work answer for the below SSAT question.
Thank you
Cindy throws a rock in the air. The rock's height, y, in feet, with respect to time, x, in seconds can be modeled by the function y=-2x^2+10x+28. When does the rock hit the ground in seconds
My work:
y=-2x^2+10x+28
0= -2(x^2-5x-14) (While knowing that the zero is supposed to be there, I don't understand why 0= -2(x^2-5x-14) )
(x-7)(x+2)
(-7,+2)
I put 2 as the answer, but when checking it was 7?
What part did I do wrong?
Answer:
7
Step-by-step explanation:
You were correct in setting the equation equal to 0 because the problem is asking for when the rock hits the ground and in this problem, you may assume that the ground is y=0, unless the problem says otherwise.
Ok so where you went wrong is that when you factored out and got
(x-7)(x+2), which is correct, you forgot to set these equal to zero (because your actual equation is set to zero). So you should have
x-7 = 0
and
x+2 = 0
and this gives the actual answers +7 and -2. And since time cant be negative its 7 seconds.
This was a silly mistake and happens a lot more often than you think, so I wouldn't worry too much but make sure you practice more, better to lose points on harder questions than easy ones.
Good luck with your exam !
Answer:
7 seconds
Step-by-step explanation:
Given function:
[tex]y=-2x^2+10x+28[/tex]
where:
y = height above the ground (in feet)x = time (in seconds)To find the time when the rock hits the ground, set the equation to zero and solve for x.
First, simplify by factoring out the common term -2:
[tex]\implies -2(x^2-5x-14)=0[/tex]
Divide both sides by -2:
[tex]\implies x^2-5x-14=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=1 \cdot -14=-14[/tex]
[tex]\implies b=-5[/tex]
Therefore, the two numbers that multiply to -14 and sum to -5 are: -7 and 2
Rewrite b as the sum of these two numbers:
[tex]\implies x^2-7x+2x-14=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x-7)+2(x-7)=0[/tex]
Factor out the common term (x - 7):
[tex]\implies (x+2)(x-7)=0[/tex]
Therefore:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-7=0 \implies x=7[/tex]
As time cannot be negative, the rock hits the ground in 7 seconds.
Which of the following is a factor of x^3-7x-6?
A. X+3
B. X+4
C. X-2
D. X+1
What is the additive inverse of x=-1317, and verify -(-x) = x ?
Answer:
1317 is the additive inverse of x = -1317.
Step-by-step explanation:
Additive inverse of a number which when added to the original number gives zero as the result.
Additive inverse of x = -1317
-1317 + 1317 = 0
1317 is the additive inverse of x = -1317.
Verification of -(-x) = x
L. H. S
-(-x) = -{-(-1317)}
= - 1317
R. H. S
x = -1317
Thus, L.H.S. = R.H.S
-(-x) = x
Verified
Graph of y = log(-x)?
Answer:
lklklkj
Step-by-step explanation:
67890-
Solve for x :
[tex]\qquad \rightarrow\bf 4x + 9x + 2x = 30[/tex]
I Need explanation
Answer:
x=2
Step-by-step explanation:
combine like terms to get 15x=30. divide by 15 on both sides to get x=2
Answer:
x=2
Step-by-step explanation:
1. Simplify the expression
4x+9x+2x=30
Simplify the arithmetic:
15x=30
2. Isolate the x
15x=30
Divide both sides by 15:
[tex]\frac{15x}{15}=\frac{30}{15}[/tex]
Simplify the fraction:
[tex]x=\frac{30}{15}[/tex]
Find the greatest common factor of the numerator and denominator:
[tex]x=\frac{2\cdot 15}{1\cdot 15}[/tex]
Factor out and cancel the greatest common factor:
[tex]x=2[/tex]
Why learn this
Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?
Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.
Terms and topics
Linear equations with one unknownHow many other states have a similar law? all 50 states 48 states 40 other states 52 states
Answer:
all 50 states
Step-by-step explanation:
What is the nth term rule of the linear
sequence
below?
1, 7, 13, 19, 25, . ..
Answer:
Un= 1+(n-1)6
Step-by-step explanation:
a = 1
d= 7-1= 13-7= 6
and using the formula, Un= a+(n-1)d
PLEASE HELP ASAP!! Kate is trying to convert an area from meters squared to centimeters squared. She multiplied the area she had by 100 and got the wrong answer. What should she have multiplied the original area by?
1,000
1,000,000
100
10,000
Answer:
1m=100cm
1m squared=100cm×100cm
1msquared= 10000cm squared
She has to multiply 10000 to convert square centimetres to square meters. Hence option D is correct.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
We know that 1 meter is equal to 100 cm now for a 1-meter square the centimetres will be calculated as,
1m=100cm
1m squared=100cm×100cm
1msquared= 10000cm squared
Hence option D is correct.
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Sarah transfer 450 from her saving account to her checking account she uses the check register to record her transaction but will her new balance.
After transferring $450 from the savings account to the checking account, the updated balance in :
the savings account is =previous balance-$450the checking account= previous balance +$450Calculation of the new balance?All of that is based on the notion that Sarah's savings and checking accounts are distinct from one another.
Assume that, Sarah's savings account balance was 'x' and checking account balance was 'y'.
She transferred $450 from the savings to the checking account.
∴Updated savings account balance= x-450 units
∴Updated checking account balance= y+ 450 units.
Therefore, it can be concluded that the current value of Sarah's savings account would be the amount >$450, and the updated value of her checking account would be the balance <$450 if she transferred $450 from her savings account to her checking account.
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Solve the equation.
–3x + 1 + 10x = x + 4
x = x equals StartFraction one-half EndFraction
x = x equals StartFraction 5 Over 6 EndFraction
x = 12
x = 18
Answer:
x = 1/2
Step-by-step explanation:
-3x + 1 + 10x = x + 4 [given]7x + 1 = x + 4 [combine like terms]6x + 1 = 4 [subtract x from both sides]6x = 3 [subtract 1 from both sides]x = 1/2 [divide both sides by 6)Answer:x = 1/2
Step-by-step explanation: Just took the test on EDGE!!
3 *(x-7)*(x+7)-(x-1)*(3x+2)=13
The value of x will be 158. The value of x is obtained by simplifying the equation.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Identity used;
(x+a)(x-a) = x² - a²
Given expression;
3(x-7)(x+7) - (x-1)(3x+2) = 13
Solving the equation step by step;
[tex]\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158[/tex]
Hence, the value of x will be 158.
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Marcia bought a car for £34500 and sold it for £29700. what was her percentage loss?
can i have an explanation please :)
Answer:
cost of car = 34500
selling price = 29700
amount of loss = 34500 - 29700 = 4800
loss percentage = (loss amount ÷ cost price ) * 100
= 13.913 ≈ 14% loss
Hi! 6 questions, find the slope of the line through the given points, ty! They should be practice questions
Answer:
3. undefined (vertical line)
4. 1
7. -4
8. 3
11. undefined (vertical line)
12. -1/3
Step-by-step explanation:
You can use the slope formula to calculate the slope which is (y2-y1)/(x2-x1)
3. (-4 - (-2)) / (6-6) denominator is 0 here so the slope is undefined (vertical line)
4. (7 - 1) / (-2 - (-4)) = 6 / 6 = 1
7. (1 - (-7)) / (2 - 4) = 8 / -2 = -4
8. (-1 - 5) / (0 -2 ) = -6 / -2 = 3
11. (3 - 0) / (-6 - (-6)) = 3 / 0 = undefined (vertical line
12. (2 - 3) / (-5 - (-2) = 1 / -3 = -1/3
Select the two binomials that are factors of 49x^2 - 36
A. 7x + 12
B. 7x - 3
C. 7x + 6
D. 7x - 6
By definition of the subtraction of squares, the binomial 49 · x² - 36 have the following two factors: 7 · x + 6, 7 · x - 6 (Correct choices: C, D)
How to find the factors of subtraction of squares
A subtraction of squares is a binomial which satisfies the following property:
a² - b² = (a - b) · (a + b) (1)
If we know that a² = 49 · x² and b² = 36, then we have the following factors:
49 · x² - 36 = (7 · x - 6) · (7 · x + 6)
By definition of the subtraction of squares, the binomial 49 · x² - 36 have the following two factors: 7 · x + 6, 7 · x - 6 (Correct choices: C, D)
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The function gives the mass, m, of a radioactive substance remaining after h half-lives. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?
The equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52 milligram remains
How to determine the equation?The missing information in the question is:
[tex]f(t)=m(0.5)^{\frac th}[/tex]
When the mass is 50 mg, it means that:
m = 50
So, we have:
[tex]f(t)=50(0.5)^{\frac th}[/tex]
When 10 years remain in the life of the substance, it means that:
t = 10
So, we have:
[tex]f(t)=50(0.5)^{\frac {10}h}[/tex]
The half life is 5.3. So, we have
[tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex]
Evaluate the equation
f(t) = 13.52
Hence, the required equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52 milligram remains
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Answer:c
Step-by-step explanation:
Ms. Kilicoglu wants to buy a total of 45 volleyballs and basketballs. She has $435 to spend. Each volleyball costs $8 and each basketball costs $11. How many of each type of ball can she purchase?
An equation is formed when two equal expressions. Ms. Kilicoglu will buy 20 volleyballs and 25 basketballs.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let x be the number of volleyballs and y be the number of basketballs. Therefore, the total number of balls can be written as,
x + y = 45
x = 45 - y
Each volleyball costs $8 and each basketball costs $11. Also, Ms. Kilicoglu has only $435, therefore,
8x + 11y = 435
8(45 - y) + 11y = 435
360 - 8y + 11y = 435
3y = 75
y = 25
Substitute the value of y in the first equation,
x + y = 45
x + 25 = 45
x = 20
Hence, Ms. Kilicoglu will buy 20 volleyballs and 25 basketballs.
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Cos(5 π/3)=___
A. √3/2
B. -√2/2
C. 1/2
D. √2/2
Answer:
i think the answer is C. 1/2
a tank 2m tall stands on the top of a concrete pillar. From point P on the same horizontal ground as the foot of the pillar, the angles of elevation of the top T and bottom B of the tank are 49 degress and 42 degrees respectively. Calculate correct to one decimal place the height of the pillar
Answer:
2
[tex]3 \times 3[/tex]
A television has increased in price by 5%
the new price is £194.25. what was the original price?
Answer:
let the original price be X
now new price = original price + increment
increment = 5 % of X = X/20
new price = 194.25
now, 194.25 = X + X / 20 = 21X / 20
X = 194.25 * 20 / 21
X = 185
original price = 185
