Data:
Cheese: c
People: p
Sarah:
c=2.5 cups
p=10
Arun:
c=1.6 cups
p=8
To find the number of cups of cheese that Arun need to a serving you divide the 1.6 cups into 8 (8 servings):
[tex]\frac{1.6}{8}=0.2[/tex]Then, Arun needs 0.2 cups of cheese for 1 serving.Which of the following are solutions to the inequality 5 < X ?
The inequality:
[tex]\begin{gathered} 55 \end{gathered}[/tex]Basically tells us that the solutions will be the numbers strictly greater than 5, so:
[tex]\begin{gathered} 3>5 \\ False \\ ---- \\ 8>5 \\ True \\ ---- \\ 10>5 \\ True \\ ---- \\ 6>5 \\ True \end{gathered}[/tex]Therefore, the solutions are:
8, 10, 6
Geometry: solve this problem, ASAP!!
The area of an equilateral triangle is 48√3km².
find the length of one side 3√3km.
The area of an equilateral triangle is given as 48√3
We know that area of an equilateral triangle is
[tex] \frac{ \sqrt{3} }{4} {a}^{2} [/tex]
Just put them equally and solve it ---
[tex] \frac{ \sqrt{3} }{4} {a}^{2} = 48 \sqrt{3} \\ {a}^{2} = (48 \sqrt{3} ) \times \frac{4}{ \sqrt{3} } \\ {a }^{2} = 4 \times 48 \\ {a}^{2} =192 \\ a = \sqrt{192 \\ } \\ a = 3 \sqrt{3} [/tex]
So we have a side of the triangle as 3√3km
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Cellular phone services is available for nine dollars per month for 1140 minutes what is the monthly cost per minute round to the nearest 10th of a cent?
Convert $9 to cents
[tex]\$9\times100=900\text{ cents}[/tex]Divide it by 1140 minutes
[tex]900\div1140=0.78947[/tex]Rounding to tenth of a cent, the cost per minute is 0.8 cents per minute.
Perform the operation.
(6x^2+2x)-(-9x^2-10x)
please help
Answer:
15x^2 + 12x
Step-by-step explanation:
Answer:
15x² + 12x
Step-by-step explanation:
Algebraic expression addition:Open the brackets by multiplying each term of (-9x² - 10x) by (-1).Then combine like terms. Like terms have same variable with same exponent.6x² & 9x² are like terms and 2x & 10x are like terms.
6x² + 2x - (-9x² - 10x) = 6x² + 2x + 9x² + 10x
= 6x² + 9x² + 2x + 10x
= 15x² + 12x
Find the value of x and y.
Answer:
x and y are both 45
Step-by-step explanation:
Answer:
x = 3√2 ≈ 4.243y = 3√2 ≈ 4.243Step-by-step explanation:
Given an isosceles right triangle with hypotenuse length 6, you want the lengths of the two legs of the triangle.
Isosceles right triangleThe ratios of side lengths in an isosceles right triangle are ...
1 : 1 : √2 = x : y : 6
Multiplying by 6/√2 = 3√2, the side length ratios are ...
x : y : 6 = 3√2 : 3√2 : 6
The values of x and y are 3√2 ≈ 4.243.
Amy is 8 years older than Ben. The sum of their ages is 28. The system of equations representing their ages is ...Solve the system using inverses. Then select the correct calculation and the ages of Amy and Ben.
So Amy is 18 and Ben is 10.
A chemist mixes 500 milliliters of a solution that is 62% acid with 125 milliliters of a solution that is 27% acid. Do not do any rounding.
Hello there. To solve this question, we'll have to remember some properties about percentages.
Given that a chemist mixes 500 mililiters of a solution that is 62% acid with 125 mililiters of a solution that is 27% acid, we have to determine:
a) How many mililiters of acid are in the resulting mixture?
For this, we find how much is 62% of 500 and 27% of 125, adding the results.
62% of 500 can be calculated by multiplying:
[tex]\frac{62}{100}\cdot500=62\cdot5=310\text{ ml}[/tex]And 27% of 125 is calculated as:
[tex]\frac{27}{100}\cdot125=\frac{27}{4}\cdot5=27\cdot1.25=33.75\text{ ml}[/tex]Adding the results, we have
[tex]343.75\text{ ml}[/tex]worth of acid in the mixture.
b) What percentage of the resulting mixture is acid?
For this, we find how many ml there are in the solution by adding:
[tex]500+125=625[/tex]Now, we take the ratio between the amount of acid in the mixture we found in the last step and this number
[tex]\frac{343.75}{625}=0.55[/tex]Multiplying by 100%, we get
[tex]0.55\cdot100\%=55\%[/tex]This is the result we were looking for.
Find the value of y for the given value of x.a. y = 10x; x = -3b. y = 6 - 2x; x = 11 c. y = 4x + 5; x = 1/2
Part a
y = 10x
For x=-3
substitute the value of x in the equation and evaluate it
y=10(-3)=-30
Part b
y = 6 - 2x
For x=11
y=6-2(11)=-16
Part c
y = 4x + 5
For x=1/2
y=4(1/2)+5=7
find the solution the of following systemy=3x+2y=-2x -8a (-2,-4)b (-6/5,8/5)c. (-3/5,-34/5)d. (1,-6)
Given the system of equations:
y = 3x + 2
y = -2x - 8
Let's solve the system of equations for the values of x and y.
Take the following steps:
Step 1:
Eliminate the equal sides of both equations and combine
3x + 2 = -2x - 8
Let's solve for x.
Step 2:
Subtract 2 from both sides:
3x + 2 - 2 = -2x - 8 - 2
3x = -2x - 10
Step 3:
Add 2x to both sides
3x + 2x = -2x + 2x - 10
5x = -10
Divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{-10}{5} \\ \\ x=-2 \end{gathered}[/tex]Step 3:
Substitute -2 for x in either of the equations and solve for y.
Let's take equation 1:
y = 3x + 2
y = 3(-2) + 2
y = -6 + 2
y = -4
Thus, we have;
x = -2, y = -4
In point form, the solution for the system of equations is:
(x, y) ==> (-2, -4)
ANSWER:
a. (-2, -4)
Laura is on her way home in her car. She has driven 6 miles so far, which is two-thirds of the way home. What is the total length of her drive?1 milesх5?
Let
x ------> distance way home
we have that
(2/3)x=6
solve for x
x=6*3/2
x=9 miles
therefore
the answer is 9 milesA coral reef grows 0.18m every week. how much does it grow in 9 weeks? write your answer in millimeters
ANSWER
EXPLANATION
The reef grows 0.18m every week
hence,
after 9weeks, it grows:
[tex]undefined[/tex]96 is 60% of what number?
Let be "x" the number that represents 100%.
According to the information given in the exercise, 96 is 60% of the number "x".
Then, you can set up the following proportion:
[tex]\frac{96}{60}=\frac{x}{100}[/tex]Now you need to solve for "x" in order to find its value:
[tex]\begin{gathered} \frac{96}{60}\cdot100=x \\ \\ \frac{9600}{60}=x \\ \\ x=160 \end{gathered}[/tex]Hence, the answer is:
[tex]160[/tex]Select the graph that best describes the following inequalities and system of inequalities.
Given:
[tex]\begin{gathered} x+y\ge4 \\ \\ y\leq2x-5 \end{gathered}[/tex]Find-:
Select the graph that best describes the inequalities and system of inequalities.
Explanation-:
Graph of first inequality is:
[tex]x+y\ge4[/tex]Graph of the second inequality:
[tex]y\leq2x-5[/tex]So the graph of inequality.
A rectangle has a perimeter of 116 centimeters and a length of 26 centimeters. What is the width of the rectangle?A. Find the width of the rectangle and include all of your work.B. In two or more complete sentences, explain your steps in finding the width of the rectangle.
Width= 32 centimeters
Explanation
Step 1
Let
Width=unknown value= W
Length=L=26 centimeters
Perimeter(is the distance around the edge of a shape)= 2L+2W( two purple line+two green line),then
P=2L+2W
Step 2
find w using L= 26 and P=116 in the equation for the perimeter
[tex]\begin{gathered} P=2L+2W \\ 116=2\cdot26+2W \\ 116=52+2W \\ \text{subtract 52 in both sides} \\ 116-52=52+2W-52 \\ 64=2W \\ \text{divide both sides by 2 } \\ \frac{64}{2}=\frac{2W}{2} \\ 32=W \end{gathered}[/tex]so, the width is 32 centimeters.
I hope this helps you.
which type of equation is this 4x-3=y
In linear equation, The graph of the equation is a straight line drawn between the points (0, 3) and (1, 7)
What are instances of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.To graph the equation y = 4x + 3 by hand choose any two values of x. For example x = 1 gives y = 7 and x = 0 gives y = 3.
The graph of the equation is a straight line drawn between the points (0, 3) and (1, 7)
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The subject of the formula below is y.
y=x+ a-b
Rearrange the formula to make x the subject.
Answer:
x = y − a + b
hope this is correct if not tell me so I can change it!
The heights of women in college follow a Normal distribution with a mean of 65 inches and a standard deviation of 2.5 inches. Determine the percentage of women with a height between 61 and 68 inches
Let X be the height of women in college. We are told that this variable is distributed as a normal distribution with mean 65 and a standard deviation of 2.5. To solve this problem, we will use a standard normal distribution table. So, the first step is to transform X to a variable Z where Z is a standar normal distribution. We do this by subtracting the mean and dividing by the standard deviation.
Recall that the problem is asking the following probability P(61<=X <= 68).
So, now, lets subtract 65 to the inequality, we get
P(-4<=X-65<=3). Now, we divide everything by the standard deviation, so we get
[tex]P(\frac{-4}{2.5}\le\frac{X-65}{2.5}\le\frac{3}{2.5})\text{ =P(}-1.6\le\frac{X-65}{2.5}\le1.2)[/tex]Now, call Z = (X-65)/2.5. With this transformation Z is distributed now with a standard normal distribution. So the question to answer is
P(-1.6<=Z<=1.2)
This translates to calculating the area under the curve as follows
We can picture two areas
So the area we want to calculate is the sames as the red area minus the blue area. Then, we have the following
[tex]P(-1.6\le Z\le1.2)=P(Z\le1.2)-P(Z\le-1.6)[/tex]Using a standard deviation table, we have that P(Z<=1.2) = 0.8849 and P(Z<=-1.6) = 0.1446
Then
[tex]P(-1.6\le Z\le1.2)=0.8849-0.1446\text{ = }0.7403[/tex]which means that 74.03% of women in college have a height between 61 and 68 inches
(1, -3/4) and (4, -3)
Slope of line passing through two points (1, -3/4) and (4, -3) is -27/4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (1, -3/4) and (4, -3)
x₁=1, y₁=-3/4, x₂=4, y₂=-3
m=-3-(-3/4)/4-1
=-3+3/4/3
=((-12+3)/4)/3
=(-9/4)/3=-27/4
Hence slope of line passing through two points (1, -3/4) and (4, -3) is -27/4
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From 2010 to 2013, the numberof full-time workers in theUnited States increased byapproximately 5%. In 2010, thenumber of full-time workerswas 110 million. (Source: U.S.Bureau of Labor Statistics)Find the increase in the number of full-time workers from 2010 to 2013 Find the total amount number of full time workers in 2013
We have:
In 2010 --> 110 million
Increase in 2013 is 5% = 0.05
So, for the increase in the number of full-time workers from 2010 to 2013 is:
[tex]110\times0.05=5.5[/tex]Answer: 5.5 million
And the total amount number of full time workers in 2013 is:
[tex]110+5.5=115.5[/tex]Answer: 115.5 million
Compute the monthly payments for an add-on interest loan of $840, with an annual interest rate of 9% and a term of 3 years.
To determine the monthly payment for add -on -interest:
[tex]\begin{gathered} \text{ principal= \$840} \\ \text{ annual interest rate = 9\%} \\ \text{time = 3 years} \end{gathered}[/tex][tex]\begin{gathered} \text{Interest = }\frac{P\text{ X R X T}}{100} \\ \text{Interest = }\frac{\text{ \$ 840 x 9 x 3}}{100} \\ \text{Interest = \$226.8} \end{gathered}[/tex]Payment Amount = $840 + $226.8 = $1066.8
Term of 3 years = 3 x 12 = 36months
[tex]\begin{gathered} \text{Add on Interest = }\frac{\text{ \$ 1066.8}}{36} \\ \text{Add on interest = \$29.6333} \\ \text{Add on interest = \$29.63} \end{gathered}[/tex]Therefore the monthly payment for add on interest loan = $29.63
Jane's school is due west of her house and due south of her friend Norma's house. The distance between the school and Norma's house is 8 kilometers and the straight-line distance between Jane's house and Norma's house is 9 kilometers. How far is Jane's house from school? If necessary, round to the nearest tenth.
Answer
Distance = 4.1 km
Explanation
Let the distance between Jane's house from school be x
The distance can be calculated using pythagora's theorem
[tex]\begin{gathered} \text{Hypotenus}^2=opposite^2+adjacent^2 \\ \text{Hypotenus = 9km, opposite = 8km and adjacent = x km} \\ 9^2=8^2+x^2 \\ \text{Isolate x}^2 \\ 81=64+x^2 \\ \text{Collect the like terms} \\ 81-64=x^2 \\ 17=x^2 \\ \text{Take the square roots of both sides} \\ \text{x = }\sqrt[]{17} \\ \text{x = 4.1 km} \end{gathered}[/tex]Therefore, the distance between Jane's house from school is 4.1 km
4/35 x 5/16 in simplest form
Answer:
4/35x5/16=1/7x1/4=1/28 the final answer is1/28
List all the numbers that are a distance from 6 away from the number 7
Let x be a number such that
[tex]|x-7|=6.[/tex]Solving the above equation for x we get:
[tex]\begin{gathered} x-7=\pm6, \\ x=7\pm6, \\ x=1\text{ or x=13.} \end{gathered}[/tex]Answer: The numbers that are a distance of 6 away from the number 7 are:
1, and 13.
A lottery offers one $1000 prize, one $400 prize, and 10 $100 prizes. One thousand tickets are sold at $2 each. Find the expectation (expected value) if a person buys one ticket.(The answer will be in dollars, but just type the amount, not the dollar sign. Be sure to indicate whether it is positive or negative.)
Total number of tickets is one thousand.
Formula for probability is given below as,
[tex]\text{Prob}=\frac{required\text{ outcome}}{total\text{ outcome}}[/tex]Probability of one $1000 prize is given below as,
[tex]P(\text{\$1000)=}\frac{1}{1000}[/tex]Probability of one $400 prize is given below as,
[tex]P(\text{\$400)=}\frac{1}{1000}[/tex]Probability of ten $100 prize is given below as,
[tex]P(\text{\$100)=}\frac{10}{1000}=\frac{1}{100}[/tex]For the expected value if each person buys one ticket,
[tex]\begin{gathered} Expected\text{ value=}(\frac{1}{1000}\times1000)+(\frac{1}{1000}\times1000)+(\frac{1}{100}\times1000) \\ \text{Expected value=}(1+1+10)=\text{\$12} \end{gathered}[/tex]Expected value is $12
The price of a condominium is $73,000. The bank requires a 5% down payment and one point at the time of closing. The cost of the condominium is financed with a 30-year fixed-rate mortgage at 6.5%. Use the following formula to determine the regular payment amount. Complete parts (a) through (c) below. a. Find the required down payment.(b) Find the amount of the mortgage.(c) How much must b paid for the one point at closing?
a) The required down payment
Down payment = Percentage of down payment x Condominium price
5% = 0.05
[tex]73000\times0.05=3650[/tex]Answer: $3650
b) The amount of the mortgage
Loan amount = Condominium price - Down payment
[tex]73000-3650=69350[/tex]Answer: $69350
c) The cost of one point
One point mean 1% of amount financed has to be paid at closing, so:
Cost of one point = Loan amount x 1%
And we have 1% = 0.01
[tex]69350\times0.01=693.5[/tex]Answer: $693.5
Hey! Been stuck on this problem, if anyone could helpThe officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 70 students, requires 6 chaperones, and costs $1300 to rent. Each van can transport 10 students, requires 1 chaperone, and costs $80 to rent. Since there are 630 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 630 students. Since only 60 parents have volunteered to serve as chaperones, the officers must plan to use at most 60 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?The officers should rent how many buses and how many vans to minimize the transportation costs
hello
to solve this question, we need to write down details we have first in order to take some key facts into consideration.
1 bus (70 students + 6 chaperones) = $1300
1 van (10 students +1 chaperone) = $80
we have to take into consideration that the trip can only accomodate only 60 chaperone and also find the least expensive options to take.
the total number of students in senior class = 630 students
the best option would be to pick 7 buses and 15 vans
7 buses would be
[tex]\begin{gathered} 7\text{ buses} \\ 70\times7=490\text{ students} \end{gathered}[/tex]7 buses would accomodate 490 students and will require
[tex]7(\text{buses)}\times6\text{ chaperones }=42[/tex]7 buses will accomodate 490 students and would require 42 chaperones.
now we would need at least 14 vans to accomodate the remaining students.
[tex]\begin{gathered} 14\text{ buses} \\ 10(\text{students)}\times14=140\text{ students} \end{gathered}[/tex]14 vans would require a total of 14 chaperones
[tex]\begin{gathered} 7\text{ buses}=490\text{ students and 42 chaperones} \\ 14\text{ vans}=140\text{ students and 14 chaperones} \\ \text{total number of students = 630 students} \\ \text{total number of chaperones required = 42 + 14 =56} \end{gathered}[/tex]now we can calculate the cost of the journey
[tex]\begin{gathered} 1\text{ bus costs =\$1300} \\ 7\text{ buses = 7}\times\text{ \$1300}=\text{ \$9,100} \\ 1\text{ van costs =\$80} \\ 14\text{ vans will cost = 14}\times\text{ \$80}=\text{ \$1,120} \\ \text{total costs = \$9,100 + \$1,120}=\text{ \$10,220} \end{gathered}[/tex]from the calculations above, the minimal cost of the journey is $10,220 and
15.In AABC, AB = 3, BC = 4 and
AC = 6. Name the largest angle.
The largest angle of triangle ABC is angle B.
In this question, we have been given the side length of triangle ABC.
In ΔABC, AB = 3, BC = 4 and AC = 6.
We need to name the largest angle.
We know that the largest angle of triangle is always opposite to the longest side of the triangle.
We can observe that the longest side of ΔABC is AC = 6 units
The angle opposite to side AC is angle B.
Therefore, the largest angle of triangle ABC is angle B.
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Lamar, Sang and Ester are all baking desserts for the school bake sale. Lamar baked 12 more copkies than Sang, and Ester baked half as many cookies as Lamar. All together they baked 63 cookies. How many cookies did they each bake? Write an expression that represents how many cookies each person baked Use your expressions to write the equation that can be used to determine how many cookies each person baked. Label each part of your equation with the person that it represents.
Let L be the number of cookies of Lamar, S the number of cookies of Sang and E the number of cookes of Ester.
Since Lamar baked 12 more cookes than Sang, we can write the following equation:
[tex]L=S+12[/tex]Next, we have that Ester baked half as many cookies as Lamar, then we can write:
[tex]E=\frac{1}{2}L=\frac{1}{2}(S+12)[/tex]finally, we have that they baked 63 cookes altogether, then we have:
[tex]L+S+E=63[/tex]Using the values L = S + 12 and E = 1/2(S+12), we can find an equation and solve for S:
[tex]\begin{gathered} S+12+S+\frac{1}{2}(S+12)=63 \\ \Rightarrow2S+12+\frac{1}{2}S+6=63 \\ \Rightarrow\frac{5}{2}S+18=63 \\ \Rightarrow\frac{5}{2}S=63-18=45 \\ \Rightarrow S=45(\frac{2}{5})=\frac{90}{5}=18 \\ S=18 \end{gathered}[/tex]We have that Sang baked 18 cookies, then we can use this value to find how many cookies baked Lamar and Ester:
[tex]\begin{gathered} L=12+18=30 \\ E=\frac{1}{2}(12+18)=\frac{1}{2}(30)=15 \end{gathered}[/tex]therefore, Lamar baked 30 cookes, Sang baked 18 cookies and Ester baked 15 cookies
Tim takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is 10 inches long and the width of the paper is 9 inches. What is the paper's length?
In a diagram, this is the information we have
Notice that, after cutting the sheet of paper, we get 2 right triangles.
We can use the Pythagorean theorem to find the length of the paper as follows:
[tex]\begin{gathered} (10in)^2=(9in)^2+(length)^2 \\ \Rightarrow\text{length}=\sqrt[]{(10in)^2-(9in)^2}^{} \\ \Rightarrow\text{length}=\sqrt[]{19in^2} \\ \Rightarrow\text{length}=\sqrt[]{19}in \end{gathered}[/tex]The answer is sqrt(19) in, which is, approximately, 4.36 in
I dont understand this problem can someone hlp me understand
The town will have a population of 20683 after 5 years
Explanations:Let the initial population be P₀
P₀ = 17000
Growth rate, R = 4% = 4/100 = 0.04
Time, T = 5
The population after 5 years will be given by the formula:
[tex]\begin{gathered} P=P_0(1+R)^T \\ P\text{ = 17000(1 + 0.04})^5 \\ P=17000(1.04)^5 \\ P\text{ = }20683.09 \\ P\text{ = 20683 (to the nearest whole number)} \end{gathered}[/tex]The town will have a population of 20683 after 5 years