2.
To do the comparison, we'll use the following temperatures:
Day 1: 5°F
Day 2 : 1.5°F
Comparison of Day 1 and Day 2:
\(1.5F<5F\)or
\(5F>1.5F\)Comparison of days with absolute value:
\(1.5F<5F\)
or
\(5F>1.5F\)3.
The temperature that's the closest to 0 during the week is -0.5°F. Using absolute value, we can see that the distance from 0°F to -0.5°F is the smallest of all the temperature measurements.
4.
The temperature that's the farthest to 0 during the week is 5°F. Using absolute value, we can see that the distance from 0°F to 5°F is the biggest of all the temperature measurements.
5.
The coldest temperature is -4°F. This is the value that is farthest to the left of 0°F on the number line.
6.
The warmest temperature is 5°F. This is the value that is farthest to the right of 0°F on the number line.
A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, determine the velocity of the truck immediately after the collision.
Answer: The momentum of the truck before the collision is given by the formula:
p_i = m_i * v_i, where m_i is the mass of the object and v_i is its velocity.
The momentum of the truck before the collision is:
p_i (truck) = 3000 kg * 10 m/s = 30000 kg m/s
The momentum of the car before the collision is:
p_i (car) = 1000 kg * 0 m/s = 0 kg m/s
The total initial momentum of the system is the sum of the initial momenta of the truck and car:
p_i (total) = p_i (truck) + p_i (car) = 30000 kg m/s + 0 kg m/s = 30000 kg m/s
After the collision, the final momentum of the system is the sum of the final momenta of the truck and car:
p_f (total) = p_f (truck) + p_f (car)
Let's call the velocity of the truck after the collision v_f (truck). The final momentum of the truck is:
p_f (truck) = 3000 kg * v_f (truck)
The final momentum of the car is:
p_f (car) = 1000 kg * 15 m/s = 15000 kg m/s
Using the conservation of momentum, we can write an equation:
p_f (total) = p_i (total)
30000 kg m/s = p_f (truck) + p_f (car)
30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s
30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s
v_f (truck) = (30000 kg m/s - 15000 kg m/s) / 3000 kg = 7.5 m/s
So, the velocity of the truck immediately after the collision is 7.5 m/s.
Step-by-step explanation:
Deymarius drank 2/3 of a quart of water. Wesley drank 1/6 of a quart of water. how many quarts of water did they drink all together?
Answer:
5/6 quarts of water
Step-by-step explanation:
2/3 same as 4/6. 4/6 + 1/6 = 5/6
Fine the missing side lengths. Leave your answers as radicals in the simplest form.
Answer:
x = 3√3;
y = 3
Step-by-step explanation:
Use trigonometry:
\( \sin(30°) = \frac{y}{6} \)
Cross-multiply to find y:
\(y = 6 \times \sin(30°) = 6 \times 0.5 = 3\)
Use the Pythagorean theorem to find x:
\( {x}^{2} = {6}^{2} - {y}^{2} \)
\( {x}^{2} = {6}^{2} - {3}^{2} = 36 - 9 = 27\)
\(x > 0\)
\(x = \sqrt{27} = \sqrt{9 \times 3} = 3 \sqrt{3} \)
point a and b are placed on a number line. point a is located -20 and point b is 5 less than point a. where is point b located
Answer:
-25
Step-by-step explanation:
Please solve, will mark brainliest
Answer: I'm late but do you still need the answer?
Step-by-step explanation:
Ali used 2/7 of a foot of ribbon to attach a decoration to his rearview mirror. Now, he has 10/21 of a foot of ribbon left.
QUESTION: How much ribbon did Ali start with?
The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.
What are mathematical operations?The basic mathematical operations include addition, subtraction, division, and multiplication.
In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).
The quantity of ribbon attached to the rearview mirror = 2/7
The remaining quantity of ribbon after the attachment = 10/21
The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)
Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.
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O
Problem !. Draw the Logic Circuit for:
BD + BE + D'F
Problem 2. What is the boolean Expression of F5?
B
X
Y
Z
F5
The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.
To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.
Step 1: Apply De Morgan's laws
NOT (R AND NOT P) can be simplified as (NOT R) OR P.
Step 2: Distributive property
F5 = (P AND Q) OR ((NOT R) OR P)
Step 3: Apply associative property
F5 = (P AND Q) OR (P OR (NOT R))
Step 4: Apply absorption law
F5 = P OR (P OR (NOT R))
Step 5: Apply idempotent law
F5 = P OR (NOT R)
By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.
Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.
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The question probable may be:
Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:
F5 = (P AND Q) OR (R AND NOT P)
Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?
what is 0.105 as a fraction
0.105 is equivalent to the fraction 21/200 in lowest terms.
What is fraction?
A fraction is a number that represents a part of a whole. Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x.
To convert a decimal to a fraction, we need to write the digits after the decimal point as the numerator and the place value of the last digit as the denominator. In this case, the last digit is 5, which is in the hundredths place (two places to the right of the decimal point).
Therefore, we can write:
0.105 = 105/1000
However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 5:
105/1000 = (105 ÷ 5)/(1000 ÷ 5) = 21/200
Therefore, 0.105 is equivalent to the fraction 21/200 in lowest terms.
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what is x / 15 equals 5. what is x?
Answer:
x = 75
Step-by-step explanation:
x/15 = 5
Multiply each side by 15
15*x/15 = 5*15
x = 75
Answer:
x = 75
Step-by-step explanation:
Reverse the problem meaning you have to do multiplication
5 times 15 is 75
To check your work divided 75 by 15 and if it equals 5 it is correct
Hope this helped :]
\(4x - {x}^{3} \)
15 pieces of candy are given to s students from a bag of candy containing 310 pieces. There are 10 pieces left over.
(s x 15) ÷ 10 = 310
(s + 15) = 310 ÷ 10
(310 − 10) ÷ 15 = s
310 ÷ (s + 15) = 10
Answer:
C. (310 − 10) ÷ 15 = s
Step-by-step explanation:
The correct answer is C. (310 − 10) ÷ 15 = s. This is because we can use the following steps to find the equation:
First, we need to find how many pieces of candy were given out in total. Since there are 10 pieces left over in the bag, and the bag originally contained 310 pieces, we can subtract 10 from 310 to get 300 pieces given out.
Next, we need to find how many pieces of candy each student received. Since 15 pieces of candy were given to s students, we can divide 300 by 15 to get the number of students. This gives us 20 students.
Finally, we need to write an equation that relates the number of students (s) to the number of pieces of candy given out (300) and the number of pieces of candy per student (15). We can do this by using the inverse operations of subtraction and division. We can multiply both sides by 15 and then add 10 to both sides to get the equation:
(310 − 10) ÷ 15 = s
This equation can be used to find the number of students if we know the number of pieces of candy in the bag, the number of pieces left over, and the number of pieces per student.
But wait, there's more! If you act now, you can also get a bonus question for free! Here it is:
If s students each received 15 pieces of candy, and there are 10 pieces left over in the bag, how many cavities will they have after eating all the candy?
There are a few possible ways to approach this question, but here is one:
- First, we need to find how many pieces of candy each student ate. Since they received 15 pieces each, and there are no leftovers, we can assume they ate all of them. So each student ate 15 pieces.
- Next, we need to find how many cavities each piece of candy causes. This may vary depending on the type and quality of the candy, but let's assume that each piece causes 0.1 cavities on average. This means that for every 10 pieces of candy, one cavity is formed.
- Finally, we need to multiply the number of pieces each student ate by the number of cavities each piece causes, and then add up all the results for all the students. This will give us the total number of cavities for the whole group. We can use this formula:
c = (15 × 0.1) × s
where c is the number of cavities and s is the number of students.
Using this formula, we can plug in the value of s that we found
c = 1.5 × 20
c = 30
✧☆*: .。. That's all folks, have fun with math! (✧ω✧) .。.:*☆✧
the scale of a map says that 4 centimeters represents 5 km what is the actual number of kilometers that is represented by 16 cm on the map
This question is about proportions. So we can build the following table:
Centimeters Km
4 5
16 x
So we have the following equation
\(\frac{4}{5}=\text{ }\frac{16}{x}\)this equation is equivalent to
\(\frac{x}{16}\text{ = }\frac{5}{4}\)So multyplying by 16 on both sides we get
\(x\text{ = }\frac{16\cdot5}{4}\text{ = 4}\cdot5\text{ = 20}\)So 16 cm are 20 km.
Find the distance d from across the river. Assume the triangles are similar and the ratio of d to 90 feet is the same as the ratio of 90 ft to 30 feet.
Since the triangles are similar, we will use the idea of proportion to find the
distance d across the river.
That is;
\(\frac{d}{90}=\frac{90}{30}\)cross-multiply
30d =8100
Divide both-sie of the equation by 30
d =270ft
2. A shipping box should weigh 1.0 pound. If
there is a 10% error on the weight, what is the
range of acceptable weight?
A. 1.0 - 1.10
B. 0.9 - 1.0
C. 1.10 - 1.20
D. 0.9 - 1.10
Answer:
10% of 1 is .1
D. .90 - 1.10 lb
Answer:
The answer is D
Step-by-step explanation:
The answer is D because you don't know if the added 10% or took away 10%
Imagine a clock with the hour hand at 12 and the minute hand at 2. Does the angle formed by the two hands have a measure greater than, less than, or equal to 1/4 turn?
The angle formed by the two hands have a measure less than 1/4 turn
How to relate the measure of the angle to 1/4 turn?From the question, we have the following parameters that can be used in our computation:
A clock with the hour hand at 12 and the minute hand at 2
The turn represented by the above is represened as
Turn = (2 * 30)/360
When simplified, we have
Turn = 1/6
Next, we have
Angle at the turn = 1/4
1/6 is less than 1/4
This means that the angle formed by the two hands have a measure less than 1/4 turn
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hi! what’s the square root of 82 rounded to the nearest tenth?
Answer:
9.1
Step-by-step explanation:
I went into my calculator and typed in \(\sqrt{82}\) and I was given:
9.055385...
So to round the nearest tenth, you look at the tenths place (which is 0) and go one number behind that (which is 5). Since the number behind the tenths place is 5 or higher, you round up to 1
if anyone could help me with one of these it'd be greatly appreciated
The value of a collectible toy is increasing exponentially. The two points on the graph
show the toy's initial value and its value 3 weeks afterward.
The question is incomplete. Here is the complete question.
Part A
The value of a collectible toy is increasing exponentially. The two points on the graph show the toy's initial value and its value 3 weeks afterward.
Express the toy's value t, in dollars, as a function of time w in weeks after purchase.
Part B
Write an expression to represent the toy's value 10 days after purchase
Answer and Step-by-step explanation: An exponential function is of the form: \(y=ab^{x}\)
Part A
Translating to the question, the toy's value as a function of time is
\(t=ab^{w}\)
To determine constants a and b, we use points given by graph.
First, (0,5) to find a:
\(5=a.b^{0}\)
a = 5
Now, (3,10) to determine b:
\(10=5b^{3}\)
\(b=\sqrt[3]{2}\)
b = 1.26
The toy's value as a function of time in weeks is \(t=5.(1.26)^{w}\)
Part B
Since, the function is in weeks:
1 week = 7 days
w weeks = 10 days
\(w = \frac{10}{7}\)
Replacing w:
\(t=5.(1.26)^{w}\)
\(t=5.(1.26)^{10/7}\)
Expression that represents toy's value after 10 days is \(t=5.(1.26)^{10/7}\).
look at attachment!!!!
Answer:
x = 5
Step-by-step explanation:
We know that BD = 2x - 1 and BC + CD = BD. Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:
BC + CD = BD
x - 3 + 7 = 2x - 1
x + 4 = 2x - 1
x + 5 = 2x
5 = x
Thus, x = 5
Checking the validity of our answer:
We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:
5 - 3 + 7 = 2(5) - 1
2 + 7 = 10 - 1
9 = 9
Thus, our answer is correct.
Consider a game in which a player rolls one die. If an even number comes up, the player wins the number of dollars showing on the die. If an odd number comes up, the player loses the number of dollars showing on the die. Calculate the expected value for this game. Is the game fair? (Assume that there is no cost to play the game.)
Answer:
Yes
Step-by-step explanation:
Winning numbers: 2, 4, 6
Losing numbers: 1, 3, 5
The even numbers are greater.
The average even (winning) number is 4.
The average odd (losing) number is 3.
You can win half a dollar on average.
Equation: (1/6)(-1)+(1/6)(2)+(1/6)(-3)+(1/6)(4)+(1/6)(-5)+1/6(6) = 0.5
Express (x+5)^2 as a trinomial in standard form.
Answer:
x² + 10x + 25
Step-by-step explanation:
(x + 5)(x + 5)
using FOIL method
First x•x = x²
Outside x•5 = 5x
Inside 5•x = 5x
Last 5•5 = 25
add like terms together.
Answer:
x^2 + 25 + 10x
= x^2 + 10x + 25
Step-by-step explanation:
( x + 5 )^2
Formula : -
( a + b )^2 = a^2 + b^2 + 2ab
Here,
a = x
b = 5
( x + 5 )^2
= x^2 + 5^2 + 2 ( x ) ( 5 )
= x^2 + 25 + 10x
Shaikha sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Khalid sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What system of equations can be used to find the price of a package of sugar cookies and a package of oatmeal cookies? (sugar cookies: x and oatmeal cookies: y )
Answer:
The system that can be used is:
\(10x + 2y = 56\)
\(9x + 3y = 60\)
Step-by-step explanation:
We have that:
x is the price of a package of sugar cookies, y is the price of a package of oatmeal cookies.
Shaikha sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56.
This means that:
\(10x + 2y = 56\)
Khalid sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60.
This means that \(9x + 3y = 60\)
System that can be used:
The system that can be used is:
\(10x + 2y = 56\)
\(9x + 3y = 60\)
What is the equation in point slope form of the line that is perpendicular to the given line and passes through the point(2,5)?
Answer:
Step-by-step explanation:
To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:
Find the slope of the provided line.
The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.
Substituting the values, the equation of the perpendicular line becomes:
y - 5 = (-1/m)(x - 2)
Simplifying the equation further, we can rewrite it in point-slope form:
y - 5 = (-1/m)x + (2/m)
Friday's temperature was 15° warmer than Tuesday's temperature. Find the temperature
on Friday if the temperature on Tuesday was 69°
Answer:
the answer is 84 degrees
Step-by-step explanation: add 15 degrees to 69 degrees
What are prime number
A prime number is a special number because it means that it only has one factor pair and that factor pair is always 1 and the number itself.
In other words, prime numbers are the numbers
divisible by 1 and the number itself.
For example, let us take 2.
2 has only two factors and those are 1 and 2 so it's prime.
Similarly, 7 is also a prime number because it has only two factors
and these are 1 and the number itself which is 7.
Answer:
A number that is only divisible by itself and 1
Step-by-step explanation:
please help me out here I need it
Step-by-step explanation:
it is the 3rd one I know this as I substituted all values of x into each equation and got the answer for y
Answer:
y=2X2-5x+5
Step-by-step explanation:
Find the pair of numbers that completes the factorization. x^2 - 3x - 40 = (x +?)(x-?)
a- 5,8
b- 4,10
c- 10,4
d- 8,5
answer
a. 5,8
explanation
use numbers in each answer choice
+5 * -8 = - 40
+5 -8 = -3
Consider the form \(x^2+bx+c\). Find a pair of integers whose product is \(c\) and whose sum is \(b\). In this case, whose product is -40 and whose sum is -3.
\(\longrightarrow\boxed{\bold{(-8,5)}}\)
Write the factored form using these integers.
\((x-8) \ (x+5)\)
1\2(x-12)=4 what is this
Answer:
1/2x=10
x=20
Step-by-step explanation:
x=5 because 1/2x-6=4
Move the other side and divide 1/2 by 10. dividing by 1/2 is the same as multiplying by 2 so the answer is 20
Answer:
x = 20
Step-by-step explanation:
\(\sf \dfrac{1}{2}*(x-12)=4\\\\Multipy \ the \ entire \ equation \ by 2\\\\ 2*\dfrac{1}{2}(x - 12) =2*4\\\\\)
x - 12 = 8
Add 12 to both sides,
x = 8 + 12
\(\sf \boxed{x = 20}\)
4(3 + 5) - 3 x 9² ?
Answer:
- 211Step-by-step explanation:
4(3 + 5) - 3 x 9² =4(8) - 3(81) =32 - 243 =- 211Find the 3rd term in the expansion of ( 5 � − 7 � ) 3 (5x−7y) 3 in simplest form.
The third term in the expansion of the expression (5x - 7y)³ is 735xy².
Given expression is,
(5x - 7y)³
We have to expand this.
We know that,
(a + b)³ = a³ - 3a²b + 3ab² - b³
Using this,
(5x - 7y)³ = (5x)³ - (3 × (5x)² × 7y) + (3 ×(5x) × (7y)²) - (7y)³
= 125x³ - (3 × 25x² × 7y) + (3 × 5x × 49y²) - 343y³
= 125x³ - 525x²y + 735xy² - 343y³
Here the third term is 735xy².
Hence the third term is 735xy².
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