A)140 adults and 72 children
Explanation
Step 1
Let x represents the number of childrend attending
Let y represents the number of adults attending
then
total cost for the children=4x
total cost for the adults=6y
if you raise 1128,
[tex]4x+6y=1128\text{ Equation(1)}[/tex]Now, 212 people attend,Hence
[tex]x+y=\text{212 Equation(2)}[/tex]Step 2
solve for x and y
a)isolate x in equation (2), then replace in equation (1)
[tex]\begin{gathered} x+y=212 \\ x=212-y \\ \text{now, replace} \\ 4x+6y=1128 \\ 4(212-y)+6y=1128 \\ 848-4y+6y=1128 \\ 2y+848=1128 \\ \text{subtract 848 in both sides} \\ 2y+848-848=1128-848 \\ 2y=280 \\ d\text{ivide boths ides by 2} \\ \frac{2y}{2}=\frac{280}{2} \\ y=140 \end{gathered}[/tex]it means 140 adults are attending
b)replace y=140 in equatin (2) to find x
[tex]\begin{gathered} x+y=212 \\ x+140=212 \\ \text{subtract 140 in both sides} \\ x+140-140=212-140 \\ x=72 \end{gathered}[/tex]so, the number of children is 72 and 72 children
46) The hundreds digit of the smallest six-digit number divisible by 12, 13,
14, 15 and 16 is
Answer: 2
Step-by-step explanation:
[tex]12=2^2 \times 3\\\\13=13\\\\14=2 \times 7\\\\15=3 \times 5\\\\16 =2^4\\\\\therefore \lcm(12, 13, 14, 15, 16)=2^4 \times 3 \times 5 \times 7 \times 13=21840[/tex]
Multiplying this by 5 to make it the smallest possible six-digit number, we get 109200, meaning the hundreds digit is 2.
Pls. Help me ;( thx ur the best
Answer:
**NEED USEFUL ANSWER ASAP, H.W QUESTION**
Given that hotter blackbodies produce more energy than cooler blackbodies, why do cooler red giants have much higher luminosities than much hotter white dwarfs?
Step-by-step explanation:
Write the standard form of the equation of the circle described below
Given:
Center ( 8, -4)
Radius (r) = 3
Find-:
Standard equation of a circle
Explanation-:
The standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where,
[tex]\begin{gathered} (h,k)=\text{ Center} \\ \\ r=\text{ Radius} \end{gathered}[/tex]So equation of circle is:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (h,k)=(8,-4) \\ \\ r=3 \end{gathered}[/tex][tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (x-8)^2+(y-(-4))^2=3^2 \\ \\ (x-8)^2+(y+4)^2=9 \end{gathered}[/tex]Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula,and solve the two equations for x and y.)midpoint (1,17), endpoint (-5,13)
The coordinates of a midpoint of a line delimited by two endpoints is:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ y_m=\frac{y_1+y_2}{2} \end{gathered}[/tex]Where (xm,ym) are the coordinates of the midpoint, (x1,y1) are the coordinates of the first endpoint and (x2,y2) are the coordinates of the second endpoint. We want to find (x2,y2), therefore:
[tex]\begin{gathered} 1=\frac{-5+x_2}{2} \\ 2=-5+x_2 \\ x_2=2+5=7 \end{gathered}[/tex][tex]\begin{gathered} 17=\frac{13+y_2}{2} \\ 34=13+y_2 \\ y_2=34-13 \\ y_2=21 \end{gathered}[/tex]The coordinates of the endpoint two are (7,21).
For each ordered pair, determine whether it is a solution to 7x - 4y = -5.(x,y)(-2,6) it is a solution yes or no(1,3) it is a solution yes or no(-3,4) it is a solution yes or no(4,2) it is a solution yes or no
If x=1, then:
[tex]\begin{gathered} 7(1)-4y=-5 \\ \Rightarrow-4y=-5-7=-12 \\ \Rightarrow y=\frac{-12}{-4}=3 \\ \\ y=3 \end{gathered}[/tex]therefore, a solution to the equation 7x-4y=-5 is (1,3)
Order the following from least to greatest: 0.232, 1.2, 1.09, 0, 3, 0.9
Answer:
0, 0.232 , 0.9 , 1.09, 1.2 , 3
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle? N O svē units O 4/3 units 10,5 units O 165 units M
The all the sided of the equlatral triangle have the same lentgth. All the angles of the triangles are 60 degrees.
The expression for the hight of a equlatral triangle is,
[tex]\sin (60^0)=\frac{h}{l}_{}[/tex]Here, ''
what is the least common denominator for the two fractions 2 / 5 3 / 2
The multiples of the denominator of 2/5 is,
5,10,15,20,25....
The multiples of the denominator of 3/2 is,
2,4,6,8,10.....
Thus, the required least common denominator is 10.
Find the oth term of the geometric sequence 5,--25, 125,
Given the geometric progression below
[tex]5,-25,125,\ldots[/tex]The nth term of a geometric progression is given below
[tex]T_n=ar^{n-1},\begin{cases}a=\text{first term} \\ r=\text{common ratio}\end{cases}[/tex]From the geometric progression, we can deduce the following
[tex]\begin{gathered} T_1=a=5 \\ T_2=ar=-25 \\ T_3=ar^2=125 \end{gathered}[/tex]To find the value of r, we will take ratios of two consecutive terms
[tex]\begin{gathered} \frac{T_2}{T_1}=\frac{ar}{a}=\frac{-25}{5} \\ \Rightarrow r=-5 \end{gathered}[/tex]To find the 9th term of the geometric, we will have that;
[tex]\begin{gathered} T_9=ar^8=5\times(-5)^8=5\times390625 \\ =1953125 \end{gathered}[/tex]Hence, the 9th term of the geometric progression is 1953125
Place the numbers in the table to show them in order from least to greatest
Given the following question:
[tex]\begin{gathered} -\frac{3}{8},\frac{1}{8},-\frac{1}{4},-\frac{3}{5},\frac{1}{5} \\ \text{ Negatives go first} \\ -\frac{3}{8}>-\frac{3}{5}>-\frac{1}{4} \\ \frac{1}{5}>\frac{1}{8} \\ -\frac{3}{5}<\frac{-3}{8}<\frac{-1}{4}<\frac{1}{8}<\frac{1}{5} \end{gathered}[/tex]f(t) = 2t-3g(t) = t^3 + tFind (f •g)(0)
1) Given those functions, f(t) and g(t) let's find the composite function, for (f(g(0)) or (f •g)(0)
2) Let's pick the function f(t)
f(t) = 2t-3
And plug into that g(t), like this
f(g(t))= 2(t³ +t) -3
3) Finally, let's plug the value 0 into that composite function:
f(g(t))= 2(t³ +t) -3
f(g(0))= 2(0³ +0) -3 ⇒f(g(0))= 2(0) +3
f(g(0))= 3
(f •g)(0)=3
Using trigonometry functions find the value missing in the diagram round to the nearest whole number
Given a right angle triangle
As shown:
Given ∠58
the opposite side to the angle = 22
The adjacent side to the angle = x
So,
[tex]\begin{gathered} \tan 58=\frac{\text{opposite}}{\text{adjacent}} \\ \\ \tan 58=\frac{22}{x} \end{gathered}[/tex]solve for x:
[tex]x=\frac{22}{\tan 58}\approx13.747[/tex]round to the nearest whole number
So, the answer will be x = 14
Explain why (-1)^n = 1 for any even number n.How is this possible? I thought it would equal -1. Does that mean the answer is "not possible"?
The expression (-1)^n means the number -1 multiplies itself n times.
So for example if n = 2, we have that:
[tex](-1)^2=(-1)\cdot(-1)=1[/tex]For n = 3, we have:
[tex](-1)^3=(-1)\cdot(-1)\cdot(-1)=1\cdot(-1)=-1[/tex]For n = 4:
[tex](-1)^4=(-1)^2\cdot(-1)^2=1\cdot1=1[/tex]We can see that the result alternates from -1 and 1, and when n is odd, the result is -1, and when n is even, the result is 1.
So for any even number n, the result will be 1.
i need help with this question
Answer:
8%.
Step-by-step explanation:
The perimeter = 2(20 + 30)
= 100 cm.
The new perimeter = 2(20 + 0.05*20 + 30 + 30*0.10)
= 2(21 + 33)
= 2*54
= 108 cm.
Percent increases = 8%.
1) Circle the tables that represent y as a function of x.хХ-31X-10у-5515-3y3608-2-4- 1-2-2-5- 1290у-1-1- 1-11-2-52-5
The answer is the last table
The answer is the last table
Complete the sentence. The amount of time it takes to complete a puzzle is most likely to be a function of the .
"The ammount of time it takes to complete a puzzle is most likely to be a function of the number of pieces in the puzzle."
Can someone help me with this geometry question I don’t know if I’m right or wrong?
Given:-
A circle has a central angle 135 degrees.
The radius of the circle is 24.
To find the arc length.
So now we use the formula,
[tex]s=r\theta[/tex]Now we convert 135 degrees to radians. so we get,
[tex]135=\frac{135}{180}\times\pi[/tex]So now we substitute the value. so we get,
[tex]\begin{gathered} s=24\times\frac{135}{180}\times\pi \\ s=18\pi \end{gathered}[/tex]So the required value is,
[tex]18\pi[/tex]So the correct option is OPTION D.
A sample of 25 measurements at breaking strength of cotton thread gave a mean of 7.4 and a standard deviation of 1.2 gms. Find 95% confidence limits for the mean breaking strength of cotton thread.
Answer:
(6.9296, 7.8704)
Explanation:
Given:
• Sample Mean = 7.4
,• Sample Standard Deviation = 1.2
,• n = 25
First, determine the standard error.
[tex]S.E.=\frac{\sigma}{\sqrt{n}}=\frac{1.2}{\sqrt{25}}=\frac{1.2}{5}=0.24[/tex]At 95% confidence limits, Z=1.96.
Using the formula below:
[tex]\bar{x}-Z_{\frac{\alpha}{2}}(S.E)<\mu<\bar{x}+Z_{\frac{\alpha}{2}}(S.E)[/tex]The limits is calculated below:
[tex]\begin{gathered} 7.4-(1.96\times0.24)<\mu<7.4+(1.96\times0.24) \\ 7.4-0.4704<\mu<7.4+0.4704 \\ 6.9296<\mu<7.8704 \end{gathered}[/tex]At 95%, the confidence limits for the mean breaking strength of cotton thread is (6.9296, 7.8704).
Which has quotient of 0.5
An example of a fraction that has a quotient of 0.5 is 2/4.
What is a quotient?A quotient is a quantity created by the division of two numbers in mathematics. The quotient is widely used in mathematics and is also known as the integer component of a division, a fraction, or a ratio.
In mathematics, the quotient is the number that is produced when two integers are divided. It is essentially the outcome of the division procedure. In arithmetic division, four primary terms are used: divisor, dividend, quotient, and remainder.
In this case, 2/4 = 0.5. This is the quotient.
Note that the information is incomplete and.an overview was given.
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In the expression 27 = 9x3-4x2, explain why 27 = 9 is the first operation you would do.
You follow the rule
PEMDAS
When doing order of operation questions.
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Note: You can interchange M and D. Also A and S.
Thus, in the expression shown, we can do the division first.
27 and 9
What is eight plus four minus three equal?
Answer:
9
Step-by-step explanation:
8+4-3=9
im pretty sure 8+4-3=9
4. You are making guacamole for a familygathering. Your first trip to the store, youpurchased 5 avocados and 3 pounds of tomatoesfor $13.30. The head count changed, and youwent back for an additional 3 avocados and 8pounds of tomatoes, spending another $22.55.What is the price per avocado and pound oftomatoes?
hello
to solve this question, we need to write an equation expressing the word problem and solve for the price of each item.
let x represent the cost of avocados
let y represent the cost of tomatoes
[tex]\begin{gathered} 5x+3y=13.30\ldots\text{.equation 1} \\ 3x+8y=22.55\ldots\text{.equation 2} \end{gathered}[/tex]from equation 1, let's make xthe subject of formula
[tex]\begin{gathered} 5x+3y=13.30 \\ 5x=13.30-3y \\ \text{divide both sides by 5 to solve for x} \\ x=\frac{13.30-3y}{5} \\ \text{this is equation 3} \end{gathered}[/tex]put equation 3 into equation 2
[tex]\begin{gathered} 3x+8y=22.55 \\ 3(\frac{13.30-3y}{5})+8y=22.55 \\ \frac{39.9-9y}{5}+8y=22.55 \\ \text{solve for y} \\ \frac{39.9-9y+40y}{5}=22.55 \\ \frac{39.9+31y}{5}=22.55 \\ 39.9+31y=22.55\times5 \\ 39.9+31y=112.75 \\ 31y=112.75-39.9 \\ 31y=72.85 \\ y=\frac{72.85}{31} \\ y=2.35 \end{gathered}[/tex]since y = 2.35, let's put that in either equation 1 or 2
from equation 2
3x + 8y = 22.55
put y = 2.35 and solve for x
[tex]\begin{gathered} 3x+8y=22.55 \\ y=2.35 \\ 3x+8(2.35)=22.55 \\ 3x+18.8=22.55 \\ 3x=22.55-18.8 \\ 3x=3.75 \\ x=\frac{3.75}{3} \\ x=1.25 \end{gathered}[/tex]from the calculations above, the price per avocado and pound of tomatoes are $1.25 and $2.35 respectively
Debra the trainer has two solo workout plans that she offers her clients: plan A and plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did plan A and 3 who did plan B. On Thursday there were 7 clients who did plan A and 9 who did plan B. Debra trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 12 hours. How long does each of the workout plans last?
The solo plans Debra offers her clients are plan A and plan B. Each client can only do one plan .
According to the question the plan only ran on wednesday and thursday.
Wednesday = plan A has 5 client and plan B has 3 clients.
Thursday = plan A has 7 client and plan B has 9 clients.
On wednesday she trained her client for 6 hours.
On thursday she trained her client for 12 hours.
let
x = hour of plan A workout for each client
y = hour of plan B workout for each client
[tex]\begin{gathered} 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}\mathrm{}(i) \\ 7x\text{ + 9y = 12}\ldots\ldots\ldots\text{.(2)} \\ 3y\text{ = 6 - 5x} \\ y\text{ = }\frac{6}{3}\text{ - }\frac{5}{3}x \\ y\text{ = 2 - }\frac{5}{3}x \\ 7x\text{ + 9(2 - }\frac{5}{3}x\text{) = 12} \\ 7x\text{ + 18 - }\frac{45}{3}x\text{ = 12} \\ 7x\text{ + 18 - }15x\text{ = 12} \\ -8x\text{ = 12 - 18} \\ -8x\text{ = - 6} \\ x\text{ = }\frac{6}{8} \\ x\text{ = }\frac{3}{4} \\ 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}(i) \\ 5(\frac{3}{4})\text{ + 3y = 6} \\ \frac{15}{4}\text{ + 3y = 6} \\ 3y\text{ = 6 - }\frac{15}{4} \\ 3y\text{ = }\frac{24-15}{4} \\ 3y\text{ = }\frac{9}{4} \\ y\text{ = }\frac{9}{4}\text{ }\times\text{ }\frac{1}{3} \\ y\text{ = }\frac{9}{12} \\ y\text{ = }\frac{3}{4} \end{gathered}[/tex]on wednesday plan A lasted for 5 * 3/4 = 15/4 hrs and plan B lasted for 3 * 3/4 = 9/4 hrs
On thursday plan A lasted for 7* 3/4 = 21/4 hrs and plan B lasted for 9 * 3/4 = 27/4 hrs
Each of the work out lasted for 3/4 hrs = 0.75 hrs
Solve the following quadratic equation by factoring. If needed, write your answer as a fraction reduced to lowest terms
The given equation is
[tex]y^2-5y-36=0[/tex]For solving it we will factorize the number 36 as 9 x 4 which on subtraction gives 5 and on multiplication gives 36.
Then, we have
[tex]\begin{gathered} y^2-(9-4)y-36=0 \\ y^2-9y+4y-36=0 \\ y(y-9)+4(y-9)=0 \\ (y-9)(y+4)=0 \\ y-9=0\text{ and y+4=0} \\ y=p\text{ and y=-4} \end{gathered}[/tex]Hence, the values of y are 9 and -4.
Isabella earns interest at an annual rate of 10% compounded annually on her savings account. She deposits $2,000 into her account. What is the total amount of money Isabella will have in her account after 2 years? (Use the formula to calculate compound interest: A = P(1 + r)')
As it indicates on the text, compound interest is represented by the following expression:
[tex]\begin{gathered} A=P(1+r)^t \\ \text{where,} \\ A=\text{ Amount} \\ P=\text{ Principal} \\ r=\text{ interest rate in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Then, substituing the information given:
[tex]\begin{gathered} A=2,000(1+0.1)^2 \\ A=2,420 \end{gathered}[/tex]Isabella will have $2,420 after 2 years.
Which ordered pair represent points on the graph of this exponential function?f(x) = 2^x+1A(1, 3)B(-4, -7)C(-2, -3)D(4, 9)
Answer:
[tex]A(1,3)[/tex]Step-by-step explanation:
To determine which of the given ordered pairs belongs to the given function, substitute each x-value and see if the y-value is correct.
[tex]\begin{gathered} f(1)=2^1+1 \\ f(1)=3 \\ \\ f(-4)=2^{-4}+1 \\ f(-4)=\frac{17}{16} \end{gathered}[/tex][tex]\begin{gathered} f(-2)=2^{-2}+1 \\ f(-2)=\frac{5}{4} \\ \\ f(4)=2^4+1 \\ f(4)=17 \end{gathered}[/tex]Therefore, the only point that represents points on the given function is A(1,3)
Find all the zeros of the following function.
f(x)=x^4+8x²-9
The zeros of the function are
(Use a comma to separate answers as needed. Express complex numbers in terms of i.)
All the zeros of following function f(x)=x4−8x2−9 are 3, -3, i, -i
What do you mean by the roots of function?A number x that reduces the value of a function f to 0 is known as its root in mathematics: f(x) = 0.
Roots are actual objects since polynomials are functions as well.
Every polynomial with complex coefficients has at least one (complex) root, according to the fundamental theorem of algebra.
f(x)=x4−8x2−9
You should set (x4 - 8x2 - 9) to 0.
x4−8x2−9=0
Learn what x's value is.
Put u=x2 in the equation's place.
As a result, applying the quadratic formula will be straightforward.
u2−8u−9=0
Consider the equation x2+bx+c.
Write out the factored form (u-9)(u+1) = 0.
The answer is the set of all numbers that add up to (u9)(u+1)=0.
u=9,−1
If u=x2 has a genuine value, change it to x2=9, x2= -1
In the case of these equations, x = +3, -3, and -i, +i .
The whole solution is made of of the solution's positive and negative components.
x4- 8x2- 9 = 0 has a solution.
is x=3,−3, i,−i
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X 즈 - + 3 = 15 -4someone help me confused
First we have to transfer the number 3 the other side of equal sign as follows,
[tex]\begin{gathered} \frac{x}{-4}=15-3 \\ \frac{x}{-4}=12 \end{gathered}[/tex]Now, we need to transfer (-4) to the other side of the equal side by multiplying with the number 12.
[tex]\begin{gathered} \frac{x}{-4}=12 \\ x=12\ast(-4) \\ x=-48 \end{gathered}[/tex]Thus, the answer of the x is (-48).
the perimeter of the rectangle belowis 112 units. Find the value of y
Question:
Solution:
The perimeter of a rectangle is the sum of the lengths of its sides. According to this, we get the following equation:
[tex]P\text{ = 2(4y+2)+2(5y)}[/tex]since P = 112, we obtain:
[tex]112\text{ = 2(4y+2)+2(5y)}[/tex]Applying the distributive property, we obtain:
[tex]112\text{ = 8y+4+10y}[/tex]this is equivalent to:
[tex]18y\text{ = 112-4}[/tex]that is:
[tex]18\text{ y = 108}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{108}{18}=6[/tex]that is:
[tex]y\text{ = 6}[/tex]so that, we can conclude that the correct answer is:
[tex]6[/tex]A group of friends' dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill,
including tax and tip, rounded to the nearest cent?
O $150.57
O $154.29
o $154.67
O $156.43
Their total dinner bill including sales tax rate is 8% and 18% tip will be $156.43 by using the concept of percentages and addition.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
What is sales tax?A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.
Here,
$122.75 dollars to be paid without tax and tip,
=8% of $122.75
=$9.82.
=122.75+9.82
=$132.57
=18% of 132.57
=$23.86
=132.57+23.86
=$156.43
Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.
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