Help please. Catching up on missed work from being out due to medical issues. Thank you in advance!
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Let B be the number of cups of boiling water that we should mix with I cups of ice to get 3 cups of 110°F water.
Therefore, we can set the following equation:
[tex]\begin{gathered} B+I=3, \\ 220B+32I=110\cdot3. \end{gathered}[/tex]Subtracting B from the first equation we get:
[tex]\begin{gathered} B+I-B=3-B, \\ I=3-B\text{.} \end{gathered}[/tex]Substituting the above equation in the second one we get:
[tex]220B+32(3-B)=330.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 220B+96-32B=330, \\ 188B+96=330. \end{gathered}[/tex]Subtracting 96 to the above equation we get:
[tex]\begin{gathered} 188B+96-96=330-96, \\ 188B=234. \end{gathered}[/tex]Dividing the above equation by 188 we get:
[tex]\begin{gathered} \frac{188B}{188}=\frac{234}{188}, \\ B\approx1.24. \end{gathered}[/tex]Substituting B=1.24 at I=3-B we get:
[tex]I=3-1.24=1.76.[/tex]Answer:
[tex]\begin{gathered} 1.26\text{ cups of boiling water.} \\ 1.74\text{ cups of ice.} \end{gathered}[/tex]Related Questions
The lines shown below are perpendicular. If the green line has a slope of 23/1,what is the slope of the red line?-510-9-1051015XOA. 3/4OB.4/3O C.-4/3O D. -3/4MIN
Answers
Solution
Step 1
Two lines are perpendicular if the product of their slope = -1
Step 2
[tex]m1\times m1=\text{ -1}[/tex]Step 2
[tex]\begin{gathered} m1\text{ = }\frac{3}{4} \\ \\ \frac{3}{4}m2\text{ = -1} \\ \\ 3m_2\text{ = -4} \\ \\ m_2\text{ = }\frac{-4}{3} \end{gathered}[/tex]Solve negative a minus eight ninths equals one third for a. a equals 5 over 9 a equals negative 5 over 9 a equals 11 over 9 a equals negative 11 over 9
Answers
8/9 - 1/3
To subtract these two fractions, first find a common denominator.
The common denominator will be the
least common multiple for the two denominators.
In this case, the least common multiple of 9 and 3 is 9.
So to subtract, a denominator of 9 is needed in each fraction.
8/9 already has 9 in the denominator so it stays the same.
To get a 9 in the denominator of 1/3, multiply top and bottom by 3.
This gives us 3/9.
So we have 8/9 - 3/9 which is 5/9.
#7777
You are catering at a ceremony and have a budget of R1 200 to spend on meat. You
want to serve chicken and steak. Chicken costs R30 per kilogram and steak costs R120
per kilogram.
3.1.1 In the problem description in 3.1 above, state what changes and what remains
the same. In other words, mention the variables for the problem.
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Answer:
Step-by-step explanation:
Let h(x) = (fog)(x) = (x - 2)^4. Find f(x) given g(x) = x - 2.
f(x) =
Answers
Answer:
f(x) = x^4
Step-by-step explanation:
h(x) = f(g(x)) = (x - 2)^4
g(x) = x - 2
h(x) = f(g(x)) = (g(x))^4
f(x) = x^4
what is the value of -20 - (-23)?
Answers
Given:
[tex]-2-(-23)=[/tex]When two negetive sign comes together it becomes positive.
[tex]\begin{gathered} -2-(-23)=-2+23 \\ =23-2 \\ =21 \end{gathered}[/tex]Thus, the final answer is 21.
K increased by the product of 5 and 3 what is the expression
Answers
K (5 * 3)
K * 15
15K
The answer is 15K based on the information available. I asked the student twice if he has more details about this exercise but he become unresponsive.
Hope that this is the answer to the actual exercise.
Closing the session.
At Shannon’s hats, 356 out of the 400 hats at the store are baseball caps. What percentage of the hats at the store are baseball caps?
Answers
Answer:
89%
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. -35=5b2. x-6=-263. 130=13b4. 19=16+m5. a+15=116. p-8= -87. -17+x= -248. 4+n=139. -3x=010. 0.6=m-0.811. x-5.3=1.27
Answers
In any equation in math, the most basic thing is the the fact that both expressions on either side of the equality sign are of the same value. This means -35 and 5b (in number 1) are of the same value. Therefore, whatever you do to the one on the left, you must likewise do to the one on the right. That is, if you have to add 10 to the one on the left, you must simultaneously add 10 to the one on the right. Hence, number 1 is solved as follows;
(1) -35 = 5b
To eliminate the 5 and isolate the b variable, divide both sides by 5
-35/5 = 5b/5
- 7 = b
(2) x - 6 = - 26
Add 6 to both sides of the equation;
x - 6 + 6 = - 26 + 6
x = - 20
(3) 130 = 13b
Divide both sides of the equation by 13
130/13 = 13b/13
10 = b
(4) 19 = 16 + m
Subtract 16 from both sides of the equation
19 - 16 = 16 - 16 + m
3 = m
(5) a + 15 = 11
Subtract 15 from both sides of the equation
a + 15 - 15 = 11 - 15
a = - 4
(6) p - 8 = - 8
Add 8 to both sides of the equation
p - 8 + 8 = - 8 + 8
p = 0
(7) - 17 + x = - 24
Add 17 to both sides of the equation
- 17 + 17 + x = - 24 + 17
x = - 7
(8) 4 + n = 13
Subtract 4 from both sides of the equation
4 - 4 + n = 13 - 4
n = 9
(9) - 3x = 0
Divide both sides of the equation by - 3
- 3x/-3 = 0/-3
x = 0
(10) 0.6 = m - 0.8
Add 0.8 to both sides of the equation
0.6 + 0.8 = m - 0.8 + 0.8
1.4 = m
(11) x - 5.3 = 1.27
Add 5.3 to both sides of the equation
x - 5.3 + 5.3 = 1.27 + 5.3
x = 6.57
Let f(x)=(x−7)(x+6)(x−5). Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0.
2. Find the x-intercept(s). List your answers as points in the form (a,b).
Answers
Answer:
ez
Step-by-step explanation:
ezz
The population of a certain city has been increasing exponentially accordingto the functionP (t) = 800, 000e0.051where t is the time in years (with t = 0 corresponding to 2014).a.) What was the population in the year 2014?b.) In what year will the population reach 1,200,000?c. what was the rate of change of the population in the year 2019?
Answers
(b) To determine the year the population will reach 1,200,000, substitute p(t) = 1,200,000 into p(t) above and calculate the value of t
[tex]\begin{gathered} \text{ p(t) = 1,200,000} \\ 1,200,000=800,000e^{0.05t} \\ \text{divide both sides by 800,000} \\ \frac{1200000}{800000}\text{ =}\frac{\text{ 800000}e^{0.05t}}{800000} \\ \\ 1.5=e^{0.05t} \\ \text{take }\ln \text{ of both sides} \\ \ln 1.5\text{ = }\ln e^{0.05t} \\ \ln 1.5=0.05t\ln e \\ \ln 1.5=0.05t(1) \\ \ln 1.5\text{ = 0.05t} \\ \text{divide both sides by 0.05} \\ \frac{\ln 1.5}{0.05}\text{ = t} \\ t=8 \end{gathered}[/tex]The year when t= 8, given that t=0 in 2014 is the year 2022
(c) the rate of change of the population in the year 2019
Firstly, differentiate p(t) with respect to t
[tex]\begin{gathered} p(t)\text{ = }800,000e^{0.05t} \\ \frac{\text{ dp}}{\text{ dt}}\text{ = 0.05(800,000)}e^{0.05t} \\ \frac{dp}{\mathrm{d}t}\text{ = 40,000}e^{0.05t} \\ \text{ This means that the rate of change of the function at any time t is 40,000}e^{0.05t} \\ \end{gathered}[/tex]In the year 2019, t = 5
Substitute t=5 into the rate of change above
[tex]\begin{gathered} \text{ at t= 5, } \\ \text{rate of change = 40,000}e^{0.05(5)} \\ =\text{ 40,000}e^{0.25} \\ =40,000(1.284025) \\ =51361 \end{gathered}[/tex]The length of a rectangle is 5 in. longer than its width and the rectangle has an area of
50in².
What are the dimensions of the rectangle
Answers
The dimensions of the rectangle are L=10in, B=5in
What is rectangle?A rectangle includes everything listed below:
A plane figureA closed formA quadrilateralThe parallelogramYour polygon's four sides must be two congruent pairings in order to have two pairs of parallel sides. The length of the left and right sides, as well as the base and top, will be equal.
let width of rectangle be x, then length will be
B=5+x
given area of rectangle
A=50in²
area = length×width
A=L×B
50 = x×(5+x)
50=5x+x²
x²+5x-50=0
x²+10x-5x-50=0
x(x+10)-5(x+10)=0
x=-10 or x=5
since x=-10 is not possible
therefore, x=5
Length(L)=5+5=10in
Width(B) = 5in
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Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Jim arrive first and Kim Last?
c. Find the probability that Jim will arrive first and Kim last.
Answers
Part a: The people can arrive in 5040 ways
Part b: In 120 ways, Jim can arrive first and Kim last
Part c: The probability that Jim will arrive first and Kim last is 1/42
People invited to the party: Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim
Part a:
Since there are 7 people, the number of ways they can arrive is 7*6*5*4*3*2*1 =.5040 ways
Part b:
For Jim to arrive first and Kim last:
The remaining 5 people can arrive in any order so, the number of ways in which they can arrive is 5*4*3*2*1 = 120 ways
Part c:
The probability that Jim will arrive first and Kim last is given by:
Number of ways Jim can arrive first and Kim last/ Total number of ways in which all the people can arrive at the party
= 120/5040 = 1/42
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8. The length, width, and a height of a box are different integer lengths. If the volume is 125
cubic centimetres, then which of the following could be the length of the height in
centimetres?
(a) 1
(b) 5
(c) 25
(d)125
(e) 50
Answers
The length , width and height of a box with volume 125 cubic centimeters will be
1, 5 and 25.
Explanation:
The volume of a box can be calculated by multiplying its length, width, and height.
here given volume = 125
V = l x w x h
125 = l x w x h
l, w, h is the factors of 125
To find the common factors, we must first list the factors of each of the given numbers.
since 125 is composite number, it will have more than two factors.
125 → 1, 5, 25 and 125.
The factors of 125 is 1, 5, 25,125
here 125 cannot consider as length since volume is 125 other sides cannot be 0.
so the length, width, height can be 1 , 5, 25.
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Put the numbers in order from smallest to largest.
PLEASE HELPP!!!
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The order of the numbers from lowest to highest is 4.68 × 10⁻⁶, 8.34 × 10⁻², 1.2 × 10⁷, 3.24 × 10⁹ and 5.48 × 10⁹
What is the order of the numbers from lowest to highest?The given numbers are expressed in standard form. Standard form is a way of writing numbers as a power 10 e.g 100 = 1 × 10² and 0.01 = 1 × 10⁻².
So converting the numbers back to ordinary numbers will be useful.
To do this, we will multiply or divide the powers of 10 with the decimal numbers.
We will multiply if the power is positive e.g 2.4 x 10² = 2.4 x 100 = 240 and divide if the power is negative 2.4 x 10⁻² = 2.4/100 = 0.024
3.24 × 10⁹ = 3.24 x 1000,000,000 = 3240000000
4.68 × 10⁻⁶ = 4.68 / 1000000 = 0.00000468
5.48 × 10⁹ = 5480000000
8.34 × 10⁻² = 8.34/100 = 0.0834
1.2 × 10⁷ = 12000000
Therefore, arranging from lowest to highest. We have:
4.68 × 10⁻⁶, 8.34 × 10⁻², 1.2 × 10⁷, 3.24 × 10⁹ and 5.48 × 10⁹
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Rewrite the following equation in slope-intercept format.x-11=-3y
Answers
Slope-intercept format is represented by the following expression:
[tex]y=mx+b[/tex]Then to rewrite it, we need to isolate the variable y, using inverse operations to solve equations:
[tex]\begin{gathered} 3y=-x+11 \\ y=-\frac{1}{3}x+\frac{11}{3} \end{gathered}[/tex]Max knows that 1/2 stick of butter is enough for 2 batches of cookies how many cookies can he make with 4 sticks of butter
Answers
Answer:
16 batches of cookies
Step-by-step explanation:
First, I converted the fraction (1/2) to a decimal (.5). Then I divided 4 by .5 and got 8. Next, multiply 8 by 2 and we get 16, which means we can make 16 batches of cookies.
4 ÷ .5 = 8
8 × 2 = 16
The full-time year-round median salary for U.S. men in 2010 was $42,600, and the full-time year-round salary for U.S. women in 2010 was $35,600.
Answers
If the full-time year-round median salary for U.S. men in 2010 was $42,600. The full-time year-round median salary for U.S. men in 2010 was 121% of the full-time year-round median salary for U.S. women in 2010.
Median salary percentageUsing this formula
Median salary percentage = 2010 Median salary in US men / 2010 Median salary in US women
Let plug in the formula
Median salary percentage = $42,500 / $35,000
Median salary percentage = 1.2143 × 100
Median salary percentage = 121.43%
Median salary percentage = 121% (Approximately)
Therefore median salary for men in 2010 was 121% of median salary for women in 2010.
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Geometry help for A and B. Answer B approximate volume?
Answers
The volume of the silo with given height and diameter is 4374π ft or 13734.36 ft. (approximately).
What is volume?
Volume is a measurement of 3-D space that is occupied. Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.
Given in the question,
The diameter of the cylindrical silo is 18 ft,
and its height is 54 ft.
Volume of a cylinder can be calculated using the formula:
[tex]V = \pi r^2 h[/tex]
Here, V = volume, r = radius, h = height,
We know that, radius is half of diameter. So, radius = 18/2 = 9 ft
Putting the given value in the formula:
[tex]V = \pi 9^2 \times 54[/tex]
[tex]V = \pi \times 81 \times 54[/tex]
V = 4374π ft.
Putting the value of π as 3.14 (approximately)
So, volume of the silo becomes 13734.36 ft.
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Could you better explain what the question is asking please ?
Answers
Recall that two figures are similar if their corresponding angles have the same measure.
Therefore, if we reduce or increment the measurement of each angle, the resulting figure will not be similar to the original figure.
Now, notice that increasing the length of the sides of a polygon does not necessarily result in a similar figure, for example:
Now, recall that translations, rotations, reflections, and dilations result in similar figures.
Answer: Third and last options.
Greta offers to buy a team photo for 15 of her teammates, but 6 of them don't want one. If a team photo costs $2, how much will Greta spend on her teammates? Choose the correct expression and solution to this problem. O A. The expression is 2(15 + 6). Greta will spend $42. OB. The expression is 2(15 - 6). Greta will spend $18. C. The expression is 15(6 - 2). PREVIOUS
Answers
The teammates are 15 but 6 of them do not want the photo, so the number of the teammates who wants the photo is 15 - 6.
Now, each photo cost $2 adn the number of photo is equal to the number of teammates who wants the photo which is (15-6), so the expression for the total cost is:
[tex]2\cdot(15-6)_{}[/tex]We have to multiply the cost of each photo for the number of photo Greta will buy.
Bro help pls I need this done by tmr or else they take point if I turn it late
Answers
Answer:
180
Step-by-step explanation:
So, in the first 4 games, they score 10 points. If this continues to happen in the remaining 18 games, it would be 180.
10 x 18 = 180.
I need help I’m not sure I did this right and need help on the graphing!! And table next to it please :( !
Answers
The solution for the given system of equations, y = [tex]\frac{-1}{2}[/tex]x + 5 and y = 3x - 2 is (2,4) and the graph is attached below
What is the system of equations?The system of equations is a set of equations consist the same variables. If the given equation are all linear then, it is the system of linear equation.
To solve such system, it is required to figure out the variable values that can solve all the equations involved in the system.
For the given system of equation the variable value is x.
So, [tex]\frac{-1}{2}[/tex]x + 5 = 3x - 2
2 + 5 = 3x + [tex]\frac{x}{2}[/tex]
7 = x ([tex]\frac{6+1}{2}[/tex]) = [tex]\frac{7x}{2}[/tex]
x = 2
Now apply the obtained value of x in either of the equations:
y = 3x - 2
y = 6 - 2
y = 4
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Find the volume of the following right rectangular prism. Round answers to the hundredth.3.6 m21 m1.5 mthe height is 3.6m the base side is 2.1m and the base is 1.5m
Answers
Answer:
11.34 m³
Explanation:
The volume of a right rectangular prism can be calculated as:
[tex]\text{Volume}=\text{Height}\times\text{ Length}\times\text{ Width}[/tex]So, replacing the height by 3.6 m, the length by 2.1 m, and the width by 1.5m, we get:
[tex]\begin{gathered} \text{Volume}=3.6\text{ m }\times2.1\text{ m }\times1.5\text{ m } \\ \text{Volume = 11.34 m}^3 \end{gathered}[/tex]Therefore, the volume of the prism is 11.34 m³
1. When a number is divided by 5, the result is 50 less than if the number had been divided by 6. What is the number?
2. I have two turtles. Today, the older turtle's age is 11 times that of the younger turtle. In 24 years, the older turtle's age will only be 7 times that of the younger turtle. If both turtles survive until then, how many years from today will the older turtle's age be 3 times that of the younger turtle?
Answers
1) A number that is divided by 5, with the result as 50 less than if the number had been divided by 6 is; -1500
2) If both turtles survive until then, the number of years from today that the older turtle's age would be 3 times that of the younger turtle is; 146 years
How to solve Algebra Word Problems?1) Let the number be x. We are told that it is divided by 5, and the result is 50 less than if the number had been divided by 6. Thus, we have;
(x/6) - (x/5) = 50
Multiply through by 30 to get;
5x - 6x = 1500
-x = 1500
x = -1500
2) Let the older turtle be x and the younger one be y.
Today, the older turtle's age is 11 times that of the younger turtle. Thus;
Todays age;
Older turtle = 11y years
Younger turtle = y years
In 24 years, the older turtle's age will only be 7 times that of the younger turtle. Thus;
11y + 24 = 7(y + 24)
11y + 24 = 7y + 168
11y - 7y = 168 - 24
4y = 144
y = 144/4
y = 36
Thus;
Age of older turtle today = 11 * 36 = 396 years
Age of younger turtle today = 36 years
Thus, for older turtle to be thrice the age of younger turtle, then;
3(36 + t) = 396 + t
108 + 3t = 396 + t
2t = 292
t = 292/2
t = 146 years
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Ahmed is 144 miles away from Blake. They are traveling towards each other. If Blake travels 8 mph fasterthan Ahmed and they meet after 4 hours, how fast was each traveling?
Answers
Data:
• Distance ( ,D ,)= 144 miles
,• Time ( ,t ,) = 4 hours
,• Speed of Ahmed (,A,): unknown
,• Speed of Blake (,B,): unknown
,• Formula of speed:
[tex]D=\frac{speed}{t}[/tex]Procedure:
• As Blake travels 8 mph faster than Ahmed
[tex]B=8+A[/tex]Since they are traveling towards each other, we can add up their speeds as follows:
[tex]B+A=(8+A)+A=2A+8[/tex]Using the distance formula, we can find the speed:
[tex]D=\frac{2A+8}{t}[/tex][tex]2A+8=D\cdot t[/tex][tex]2A=D\cdot t-8[/tex][tex]A=\frac{D\cdot t-8}{2}=\frac{144\cdot4-8}{2}=284[/tex]To know the speed of Blake:
[tex]B=284+8=292[/tex]Answer:
• Blake = 292 mph
,• Ahmed = 284 mph
look at step by step solution shown below and fill in the missing stepthe solution is the missing step
Answers
Solving an Equation
We are given the equation:
[tex]3(2x+5)=4(5-x)[/tex]The first step is to multiply the constants by the binomials in parentheses:
[tex]6x+15=20-4x[/tex]This step was correctly done by Jose.
The second step is to 'pass' the 4x from the right side of the equation to the left by adding 4x on both sides:
[tex]10x+15=20[/tex]This step was also correct.
Now we must 'pass' 15 to the right by subtracting 15:
[tex]10x=5[/tex]And here we find the first error. Jose subtracted 15-20 instead of 20-15 and erroneously got -5.
Answer: First error in step 3
There were 18,652 geese on a lake. What is this number rounded to the tenthousands place?A20,000B19.600C19.000D18.600car mechanic rounds a car's weight to the nearest thousand. He says theweight is 4,000 pounds. What is the least and the greatest amounts the carcould actually weigh? Explain.
Answers
Step 1
There are 18,652 geese on a lake
Required: To round this off to the ten thousand place
Step 2
Hence, we will approximate the thousands and add its value to the ten thousand.
[tex]=\text{ 20,000}[/tex]Step 3
The mechanic rounds the weight of the car to the nearest thousand and gets 4000 lb.
Using the rule below;
[tex]\begin{gathered} (4000\text{ - 500)lb - least} \\ or \\ (4000\text{ + 49}9)lb-\text{ greatest} \\ \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{If we subtract 500 from 4000 we get 3500lb} \\ 3500lb\text{ is the least weight of the car} \\ \text{Notice that 3500 rounded off to the nearest thousand = 4000} \\ \text{Any number less than that say 3499 rounded off to the nearest thousand}=3000 \end{gathered}[/tex][tex]\begin{gathered} \text{If we add 499 to 4000, we get 4499 pounds} \\ 4499\text{ pounds is the greatest weight of the car} \\ \text{Notice if you round off 4499 to the nearest thousand = 4000} \\ \text{Any number more than this say 4500 rounded to the nearest thousand=5}000lb \\ \text{Hence the greatest weight of the car= 4499} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Least weight of the car = 3500}lb \\ \text{Greatest weight of the car = }4499lb \end{gathered}[/tex]PLEASE HELP I HAVE BEEN STUCK FOR 2 DAYS
A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies, you pick one candy at random, find the probability that it is green or yellow
Answers
Answer: i believe its 0.46 im not for sure though
Step-by-step explanation:
whats 1 plus 1 in mathmaticals
Answers
Answer:
2
Step-by-step explanation:
If you have 1 cookie and someone gives you another cookie you now have 2.
how do I do this. . I don't know ho2
Answers
A linear equation has a constant slope.
For every step increase in x, there needs to be another step increase in y.
From the table,
x decreases by 2 units
y doesn't decrease by the same unit
So, this cannot be linear relationship.
To see whether it is quadratic or exponential, we graph the (x,y) points and see the general shape of the curve by connecting the points in a smooth curve.
The graph is shown below:
From seeing the graph, it is quite evident that the tabular relationship represents a quadratic function.
Thus, the correct answer is:
B