48 children and 96 adults
let x be the number of children then number of adults = 2x and
x + 2x = 144
3x = 144 ( divide both sides by 3 )
x = [tex]\frac{144}{3}[/tex] = 48
There are 48 children and ( 2 × 48 ) = 96 adults
There are 48 children and 96 adults in line.
Explanation:To find how many children and adults are in line, we can use algebraic equations and solve for each variable. Let's assume the number of children in line is x. Since there are twice as many adults as children, the number of adults in line would be 2x. According to the given information, the total number of people in line is 144. Therefore, we can set up the equation x + 2x = 144. Simplifying the equation, we get 3x = 144. Dividing both sides by 3, we find x = 48. So, there are 48 children and 2 * 48 = 96 adults in line.
What is the domain of the function represented by the mapping diagram below?
Answer:
Option C
{-1,3,5}
Step-by-step explanation:
A mapping is a subset of ordered pair (x,y) where x belongs to first set and y belongs to second set.
Hence a mapping is a subset of cartesian product AXB.
Here A = {-2,1,3,5} and
B = {2,4,6,8}
Ordered pair given by the mapping is
(-2,1) (3,6) and (5,8)
In other words, -2 is mapped on to 1, 3 to 6 and 5 to 8
Domain = set of elements in the I set which are mapped
= {-1,3,5}
Jenny has $2.40 deducted from her monthly allowanbevery time she forgets to do a chore. If she forgets three times in one month, what will be the charge in jenny's Total allowance
Answer: Charge in Jenny's Total allowance= $7.20
Step-by-step explanation:
Given : Jenny has $2.40 deducted from her monthly allowance every time she forgets to do a chore.
If she forgets three times in one month, then by using the MULTIPLICATION OPERATION the charge in Jenny's Total allowance will be :-
[tex]3\times\$2.40=\$7.20[/tex]
Hence, the charge in Jenny's Total allowance = $7.20
Find the perimeter of a square if the length of one side is given. Are the perimeter of the square and the length of its side directly proportional quantities? Explain.
2 in
All the sides of a square are equal.
Perimeter of a square = 4(measure of 1 side)
Therefore if a square contains 4 sides, and the measure of one side is 2 inches, the perimeter is 8 inches. (2x4)
The definition of directly proportional is when one substance increases at the same rate of another substance. When a number is plugged into our formula, the perimeter increases.
5. Draw the number line graph of -3.
6. What does |-9| equal?
7. Solve the equation y – 11 = -4.
8. Evaluate the expression a + b when a = 2.5 and b = -10.8.
9. Draw the number line graph of 0.4.
10. Insert < or > to make this statement true: -1.8 -2.5
Answer:
9, 7,-8.3,>
Step-by-step explanation:
5)-3 is marked exactly 3 units to the left of origin 0.
(since negative sign we mark on left of 0)
6) |-9| = absolute value of 9 = 9
7) y-11=-4
Add 11 to both the sides
WE get y =7 is the solution
8) a + b when a = 2.5 and b = -10.8.
= 2.5+(-10.8) = -(10.8-2.5) = -8.3
9) 0.4 is positive hence lies to the right of origin.
Partition the space between 0 and 1 into 10 equal subparts and mark 4th subdivision to get 0.4
10) -1.8>-2.5
2 times the difference between 49.6 and 37.5
A person invests $2,740 in an account that earns 4.3% annual interest. Find when the value of the investment reaches $7,000. If necessary, round to the nearest tenth. the investment will reach $7,000 in approximatelyyears.
So, to set up your equation is the hardest part. If you remember the basic format, you're set.
I(t) = P * (1+r%)^t
t= time and this will be our variable
Initial amount P = $2740
Rate = 4.3% which converts numerically into .043
I(t) = 7000
Before we get to find out how to find how many years it takes to get to $7000, set up the basic equation by plugging in what we know.
I(t) = $2740(1+4.3%)^t
I(t)=2740(1.043)^t
Now plug in for $7000 for I(t)
7000=2740(1.043)^t Divide both sides by 2740
7000/2740 = 2740/2740(1.043)^t
2.55474453=(1.043)^t
Now you can solve for t in two ways. You can either use the natural log or graph it on your graphing calculate and see when the two equations meet.
In your calculator you can set up:
ln(2.55474453)/ln(1.043) = t which is the method I prefer since it's much simpler
t=22.278528
but you can also graph it in your ti-84
with
y1=2.55474453
y2=(1.043)^x
and find where they intersect on the graph.
either way it'll be the same answer
Given: △KPS
m∠P=105°, m∠S=30°
PS=12
Find: PK.
split ∠ P into a ∠45° and a ∠60° with altitude PO. ΔPOK is isosceles and ΔPOS is 30-60-90. PO=6=KO Pk=6√2
Answer:
PK= 8.5
Step-by-step explanation:
The sum of interior angles in a triangle is 180 degree
[tex]m<k+m<p+m<s=180[/tex]
[tex]m<k+105+30=180[/tex]
[tex]m<k+135=180[/tex]
Subtract 135 from both sides
[tex]m<k=45[/tex]
Now use sine rule
[tex]\frac{sin A}{a} =\frac{sin B}{b}[/tex]
[tex]\frac{sin K}{PS} =\frac{sin S}{PK}[/tex]
[tex]\frac{sin(45)}{12} =\frac{sin(30)}{PK}[/tex]
Cross multiply
[tex]PKsin(45)}=12sin(30)[/tex]
[tex]PK =\frac{12sin(30)}{sin(45)}[/tex]
PK= 8.5
What is the GCF of the expression 4x2 + 3x?
A.x
B.3x
C.4x
D.x2
The greatest factor that will divide into the 2 terms is x.
Its A.
The GCF of the given polynomial expression is the monomial x
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here: The polynomial expression as 4x²+3x
Greatest Common Factor (GCF) The GCF for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial.
4x²+3x=x(4x+3)
Thus the greatest polynomial that divides or is a factor the expression is given by x
Hence, The GCF of the given polynomial expression is the monomial x
Learn more about a polynomial expression here:
https://brainly.com/question/11536910
#SPJ2
If manuel deposits 25% of 130 into a savings how much is the amount of his deposit
What Number has the dame valué as 12 tens
A softball team scored 8 runs, 5 runs, 13 runs, 8 runs, and 11 runs in its last five games. What is the range of the number of runs scored in the five games
The range is the difference between the highest number and the lowest number.
The lowest number is 5, the highest number is 13.
The range is 13 - 5 = 8 runs.
The correct answer for the range is: "5 to 13 runs" with a median of 8 and here is why:
The range of a set of numbers is what values could have or could be based on the lowest and highest values. The range is not the same as the average or the median. 5 runs was the least amount of runs that happened during one game and 13 was the most in another.
The average is calculated by adding all of the numbers added together and then divides by how many numbers that you added together.
The median is found by removing the lowest number and then the highest number. You repeat this process until you are left with only one number.
There are other things to find as well, but I think you understand now
Range: 5-13 ; 8
Average: 9
Median: 8
Also here is the definition from Dictionary.com on what range is:
range rānj/Submit
noun
1.the area of variation between upper and lower limits on a particular scale.
ex: "the cost is thought to be in the range of $1-5 million a day"
What are the end behavior and the possible discontinuity of
2x+4/x^2-1?
So, The discontinuity would be at 1, since plugging in one for x would yield a zero in the denominator (It would be a non-removable one).
End Behavior: [tex]\lim_{x \to \infty} f_x = 0 \\\\ \lim_{x \to -\infty} f_x = 0[/tex]
(Zero is a the horizontal asymptope)
Given sample set A= {1,2,3,4,5} how many items are in the complement of set B if set B= all numbers greater than 2? (30 pts)
Alright, so first we need to establish two things.
First, the compliment of a set is like the extreme opposite; everything that is not in set B will be in the complement.
Second, we need to find out what B is.
Okay, so B is everything that is greater than 2, that's given. That includes 3, 4, and 5. B = {3, 4, 5}. There are three items in this set.
The numbers that aren't included are 1 and 2. The complement of B, let's call this C I guess, is C = {1, 2}. There are 2 items in this set.
The answer, I believe, is two. Hope this helps!
Which exponent makes this statement true? 1/5^9= 5^?
Answer:
The exponent -9 makes the given statement true.
Step-by-step explanation:
We have been given an incomplete mathematical statement and we need to figure out the exponent for 5 on the right hand side to complete the statement.
The given incomplete statement is [tex]\frac{1}{5^{9}}=5^{?}[/tex].
Let us rewrite the left hand side of the expression by moving the exponential term to the numerator using exponent property. As per this property, if we shift an exponential term from denominator to numerator (or vice versa), the sign of exponent changes.
Therefore, we get:
[tex]5^{-9}=5^{?}[/tex]
Now that we have common bases on both the sides, we can equate the exponents. And upon equating the exponents, we can see that the 'question mark' should be replaced by -9 in order for statement to be true.
Therefore, exponent -9 on the right hand side will make the statement true.
Answer:
1/5^9 = 5^-9
Step-by-step explanation:
What are the first four terms of the sequence shown below?
an = n^3 + ^2
A.
1, 2, 3, 4
B.
1, 12, 15, 20
C.
2, 12, 36, 80
D.
5, 10, 15, 18
[tex]a_{n} = n^{3} + n^{2}[/tex]
[tex]a_{1} = 1^{3} + 1^{2}[/tex]
= 1 + 1
= 2
[tex]a_{2} = 2^{3} + 2^{2}[/tex]
= 8 + 4
= 12
[tex]a_{3} = 3^{3} + 3^{2}[/tex]
= 27 + 9
= 36
[tex]a_{4} = 4^{3} + 4^{2}[/tex]
= 64 + 16
= 80
Answer: C
intellectual property law deals with
A: Plans for buildings
B: Concepts with monetary value.
C: Use of historic texts
D: Complex disputes between businesses and suppliers.
Answer:
B: Concepts with monetary value
Step-by-step explanation:
for future reference the exact meaning of intellectual property law is the rules for securing and enforcing legal rights to inventions, designs, and artistic works. it is obviously easy to draw the connections from the meaning to the answer B.
Intellectual property law protects intangible creations with monetary value, fitting best with answer B: Concepts with monetary value. It includes patents, trademarks, copyrights, and trade secret law, and is essential for creators and inventors to capitalize on their work.
Intellectual property law deals with the protection of intangible creations that have monetary value, such as art, written work, research findings, and ideas.
The correct answer to the question provided is B: Concepts with monetary value.
Intellectual property includes patents, trademarks, copyrights, and trade secret law which allow inventors and creators to produce, publish, and sell their work and inventions while preventing others from using them without authorization or compensation.
Countries across the globe have distinct laws protecting intellectual property, and organizations like the World Intellectual Property Organization (WIPO) strive to harmonize these laws internationally. Intellectual property is nonexcludable and non rivalrous in nature, often leading to positive externalities and offering private benefits to creators and inventors.
How does cot(x)sin(x)=cos^3(x)+cos(x)sin^2(x)?
[tex]\cot(x)\sin(x)=\cos^3(x)+\cos(x)\sin^2(x)[/tex]
[tex]R=\cos(x)[\cos^2(x)+\sin^2(x)]=\cos(x)\cdot1=\cos(x)\\\\L=\dfrac{\cos(x)}{\sin(x)}\cdot\sin(x)=\cos(x)\\\\L=R\\\\\text{used:}\\\\\sin^2x+\cos^2x=1\\\\\cot x=\dfrac{\cos x}{\sin x}[/tex]
Write an equation in slope-intercept form for the line that is parallel to y = −7x − 8 and that passes through the point (7, −8).
A. y = −7x − 56
B. y=1/7x-9
c. y = −7x + 41
D. y=1/7x-8
The slope intercept from of equation is y= -7x + 41.
what is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
A line that passes through points (7, −8). and parallel to y = −7x − 8
Now, the slope of given parallel line is -7 and slope of line which is to parallel also of have the same slope.
So, slope of parallel line = -7
Now, using slope intercept form
y -a = m( x- b)
y - (-8)= (-7)(x-7)
y +8 = -7x + 49
y= -7x + 71
Hence, the slope intercept from of equation is y= -7x + 41
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
Simplify the expression. Write the answer using scientific notation.
(9x10^5)(3x10^10)
a. 2.7x10^16
b. 1.2x10^51
c. 1.2x10^16
d. 2.7x10^51
Answer:
2.7 x 1016
Step-by-step explanation:
that's the answer
A bucket holds 4 quarts of popcorn. If 1/3 cup of corn kernels make 2 quarts of popcorn, how many buckets can be filled with the popcorn made from 4 cups of Kernels?
Answer:
6 buckets
Step-by-step explanation:
Look at the ratio:
1/3 cup kernels : 2 quarts popcorn
2/3 cup kernels : 4 quarts popcorn : 1 bucket . . . . multiply by 2
2 cups kernels : 3 buckets . . . . . . . . . . . . . . . . . . . . .multiply by 3
4 cups kernels : 6 buckets popcorn . . . . . . . . . . . . multiply by 2
Mark left 3/8 of pizza in the refrigerator. On friday he ate 1/2 if what is left of the pizza. What fraction of the entire pizza did he eat on friday?
3/16 because 3/8 is equal to 6/16 and half of that is 3/16.
Answer:
Mike ate [tex]\frac{3x}{16}[/tex]th portion of the pizza on Friday.
Step-by-step explanation:
Let us consider the quantity of pizza = x
If Mike left [tex]\frac{3x}{8}[/tex] of the pizza in the refrigerator.
On Friday he ate [tex]\frac{1}{2}[/tex] the portion of pizza he ate = [tex]\frac{3x}{8}\times \frac{1}{2}[/tex]
= [tex]\frac{3x}{16}[/tex]
Therefore, Mike ate [tex]\frac{3x}{16}[/tex]th portion of the pizza on Friday.
How do I solve this
You start from right to left, the third number is always the hundred place, the second number (6 in your case) is the tens place, and 5 is in the ones place. So your correct answer is 3 or B
A car uses 7litres of pétrole to coker 28km . How many litres of pétrole does hé use to coker 64km
28/7=4km is car journey covered by car in 1l
64/4=16l
The car would use 16 liters of petrol to cover 64 km.
Explanation:To find out how many liters of petrol the car uses to cover 64 km, we can set up a proportion using the given information. Since the car uses 7 liters of petrol to cover 28 km, we can say that the fuel consumption rate is 7 liters per 28 km. To find out the fuel consumption rate for 64 km, we can set up the proportion:
7 liters / 28 km = x liters / 64 km
Cross-multiplying, we get 28x = 7 * 64.
Dividing both sides by 28, we get x = 7 * 64 / 28 = 16 liters. Therefore, the car would use 16 liters of petrol to cover 64 km.
Learn more about fuel consumption rate here:https://brainly.com/question/28809733
#SPJ12
Select the multiplication sentence that applies the associative property of multiplication to the example. Example: (4 × 5) × 2 = 40 A. 4 × (5 + 2) = 28 B. 4 + (9 × 4) = 40 C. 4 × (5 × 2) = 40 D. (4 + 5) × 2 = 18
C. 4 x (5 x 2) = 40 hope that helps
Answer : option C
A. 4 × (5 + 2) = 28
Associative property of multiplication . Here we have 5+2 so it does not comes under Associative property of multiplication
B. 4 + (9 × 4) = 40
Here we have 4 + . there is a + sign inbetween. so it does not comes under Associative property of multiplication
C. 4 × (5 × 2) = 40
Here we have 4 times 5 times 2. so it comes under Associative property of multiplication
D. (4 + 5) × 2 = 18
Here we have 4 + 5 so it does not comes under Associative property of multiplication
Give an example of a real world situation for which there could be a positive correlation
Find the y-intercept of the line below.
Show work
3x - 7y + 2 = 0
a) -7
b) 2/7
c) -2/7
d) 2
Ryan spent $26.33 on 8 gallons of gas how much would he spend for 20 gallons
First divide 26.33 with 8 to find the cost per gallon
26.33/8 = ~3.29 (rounded).
Each gallon of gas costs $3.29
Next, multiply the cost per gallon with the amount of gallons, 20 in this case.
20 x 3.29 = 65.80
$65.80 is your answer
~Rise Above the Ordinary
Washington Elementary has 232 students Washington High has six times as many students how many students does Washington High have
Lisa's penny bank is
7
10
full. After she removes
240
pennies, it is
1
2
full. How many pennies can Lisa's bank hold?
If x=-2 and y=6 is a solution of equation 3ax+2by=6, then find the value of b
[tex]\text{Substitute the values of x and y to the equation}\\\\x=-2,\ y=6,\ 3ax+2by=6\\\\3a(-2)+2b(6)=6\\\\-6a+12b=6\qquad|\text{add 6a to both sides}\\\\12b=6a+6\qquad|\text{divide both sides by 12}\\\\b=\dfrac{6a}{12}+\dfrac{6}{12}\\\\\boxed{b=\dfrac{1}{2}a+\dfrac{1}{2}}[/tex]