Let's call C to the cups of chocolate chips and S to the cups of sugar. We are told that the cups of sugar are 2 2/3 times the cups of chocolate, then we can formulate the following equation:
[tex]S=2\frac{2}{3}C[/tex]In the case 4 1/3 of sugar is added, we can replace 4 1/3 for S to get:
[tex]4\frac{1}{3}=2\frac{2}{3}C[/tex]By dividing both sides by 2 2/3 we get:
[tex]\begin{gathered} 4\frac{1}{3}\div2\frac{2}{3}=2\frac{2}{3}C\div2\frac{2}{3} \\ 4\frac{1}{3}\div2\frac{2}{3}=C \end{gathered}[/tex]We can rewrite the mixed fractions to get:
[tex]\begin{gathered} \frac{4\times3+1}{3}\div\frac{2\times3+2}{3}=C \\ \frac{12+1}{3}\div\frac{6+2}{3}=C \\ \frac{13}{3}\div\frac{8}{3}=C \end{gathered}[/tex]By changing the division symbol to a multiplication symbol and flipping the 8/3, we get:
[tex]\begin{gathered} \frac{13}{3}\times\frac{3}{8}=C \\ \frac{13}{8}=C \\ \frac{8+5}{8}=C \\ \frac{8}{8}+\frac{5}{8}=C \\ 1+\frac{5}{8}=C \\ 1\frac{5}{8}=C \\ C=1\frac{5}{8} \end{gathered}[/tex]Then, 1 5/8 cups of chocolate chips are needed
What is the value of the expression below when w = 3?3w² - 6w - 4
ANSWER:
5
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]3w^2-6w-4\:[/tex]We substitute the value of w, when it is equal to 3, just like this:
[tex]\begin{gathered} 3\left(3\right)^2-6\left(3\right)-4\: \\ \\ 3\cdot \:9-6\left(3\right)-4 \\ \\ 27-18-4 \\ \\ 5 \end{gathered}[/tex]The value of the expression is equal to 5
Yes or no to tell wether the fact the fraction is equivalent to this decimal __(4.05)_____________________________________Is the following fractions equal to the one decimal listed? 405/99401/9981/33802/198
802/198 is equal to 4.0505
I need help IMMEDIATELY! I'm so confused and this is due in 7 minutes!!
I won't hesitate to give brainliest to whoever answers fastest! Please please please show work
1. Given [tex]f(x)= 2x^2-4x+2[/tex], what is the value of [tex]f(2/3)[/tex]?
2. Given [tex]f(x)= 4x^2+2x-6[/tex], what is the value of [tex]f(1/4)[/tex]?
The values of the functions are:
1. f(2/3) = 2/9
2. f(1/4) = -21/4
How to Find the Value of a Function?If we are given the a function to find the value for which x assumes a given value, substitute the given value of x into the function and solve.
1. To find the value of f(2/3), substitute x = 2/3 into the function f(x) = 2x² - 4x + 2.
f(2/3) = 2(2/3)² - 4(2/3) + 2
f(2/3) = 2(4/9) - 8/3 + 2
f(2/3) = 8/9 - 8/3 + 2
f(2/3) = (8 - 24 + 18)/9
f(2/3) = 2/9
2. To find the value of f(1/4), substitute x = 1/4 into the function f(x) = 4x² + 2x - 6.
f(1/4) = 4(1/4)² + 2(1/4) - 6
f(1/4) = 4(1/16) + 1/2 - 6
f(1/4) = 1/4 + 1/2 - 6
f(1/4) = (1 + 2 - 24)/4
f(1/4) = -21/4
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the diameter of the bagels 4.2 in what is the biggest circumference in inches
Diammeter = 4.2 inch
Radius = diammeter/2 = 4.2/2 =2.1 inch
[tex]\text{Circumference =2}\times\text{ }\pi\times r[/tex][tex]\begin{gathered} \pi\text{ = 3.14} \\ \text{Circumference = 2 }\times3.14\times2.1\text{ =13.188 inches} \end{gathered}[/tex]What’s 1/5 + 1/2 ? Pls help me
We need to calculate 1/5 + 1/2:
H = 1/5 + 1/2
Then: H = 7/10
2. Find the equation ofthe line:through (-5,1) parallel to2y = 2x - 4
Given data:
The given point is (a,b)=(-5,1).
The given line is 2y=2x-4.
The given line can be written as,
2y=2(x-2)
y=x-2
The standard equation of the line is,
y=mx+c
comapre the given line with the standard form.
m=1
The slope of two parallel lines are always equal.
m'=m
=1
The expression of the line which is parallel to the given line is,
y-b=m'(x-a)
Substitue the given values in the expression.
y-1=1(x-(-5))
y-1=x+5
y=x+6.
Thus, the equation of the line parallel to the given line is y=x+6.
Question 2.Draw diagrams to represent the following situations.a. The amount of flour that the bakery used this month was a 50% increase relative to last month.b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.
Given:
a. The amount of flour that the bakery used this month was a 50% increase relative to last month.
So, we will draw a diagram that represents the situation
As shown, for last month, we have drawn a rectangle divided into two equal areas, each one represents 50%
this month was a 50% increase, so, we have drawn 3 areas which represent 50% increase
b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.
As shown, for last month, we have drawn a rectangle with four equal areas
75% decrease, so, we have to remove 3 areas to make the remaining = 25%
So, the difference will give a 75% decrease
Zales sells diamonds for $1,100 that cost $800. What is Zales’s percent markup on selling price? Check the selling price.
Zale's percent mark up is 37.5 percent.
How to find the percent mark-up?Mark up percentage is calculated by dividing the gross profit of a unit by the cost of that unit.
In other words, Mark-up percentage is the difference between a product's selling price and cost as a percentage of the cost.
Therefore, Zale's sells diamonds for $1,100 that cost $800.
Hence,
mark up = 1100 - 800
mark up = $300
percentage mark up = 300 / 800 × 100
percentage mark up = 30000 / 800
Therefore,
percentage mark up = 37.5%
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A COMPUTER OPERATOR MUST SELECT FOUR JOBS AMOUNG 10 AVAILABLE JOB WAITING TO BE COMPLETED. HOW MANY DIFFERENT ARRANGMENTS CAN BE MADE?
This is a problem based on permutations. We must select four jobs among ten jobs and see how many arrangments can be made.
The formula for the number of permutations is:
[tex]P(n,r)=\frac{n!}{(n-r)!}.[/tex]Where:
• n = total number of jobs = 10,
,• r = number of jobs to be selected = 4.
Replacing these data in the formula above, we get:
[tex]P(10,4)=\frac{10!}{(10-4)!}=\frac{10!}{6!}=\frac{10\cdot9\cdot8\cdot7\cdot6!}{6!}=10\cdot9\cdot8\cdot7=5040.[/tex]Answer5040
the running trail in the local park is 3.826 miles long. If the park board were planning to extend the trail by 2.46 miles, what would the new length of the running trail be?
The running trail is 3.826 miles long. If we add 2.46 miles, the new length will be:
[tex]3.826miles+2.46\text{ miles}[/tex]which gives 6.286 miles. Then, the new lenght will be 6.286 miles long.
A triangle can have sides 2,3 and 5. True or false
First, remember that:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this problem, notice that:
2 + 3 is not greater than 5.
3 + 5 is not greater than 2.
2 + 5 is not greater than 3.
So, the statement is false. A triangle can't have sides 2
As the table shows, projections indicate that the percent of adults with diabetes could dramatically increase.Answer parts a. through c.c. In what year does this model predict the percent to be 27.96%(round to the closest year)
b. You have to consider year 2000 as the initial year, i.e. as x=0.
To predict the percent of adults with diabetes in 2014, first, you have to calculate the difference between this year and the initial year to determine which value of x you need to use:
[tex]x=2014-2000=\text{ }14[/tex]The value of x you have to use is x=14
Replace this value into the linear model calculated in item a to predict the percentage of adults with diabetes (y)
[tex]\begin{gathered} y=0.508x+10.692 \\ y=0.508\cdot14+10.692 \\ y=7.112+10.692 \\ y=17.804 \end{gathered}[/tex]In the year 2014, the predicted percentage of adults with diabetes is 17.8%
c. You have to determine the year in which the model predicts the percent to be 27.96%.
To determine this year, you have to equal the linear model to 27.96% and calculate for x:
[tex]\begin{gathered} y=0.508x+10.692 \\ 27.96=0.508x+10.692 \end{gathered}[/tex]-Subtract 10.692 from both sides of the equal sign
[tex]\begin{gathered} 27.96-10.692=0.508x+10.692-10.692 \\ 17.268=0.508x \end{gathered}[/tex]-Divide both sides by 0.508
[tex]\begin{gathered} \frac{17.268}{0.508}=\frac{0.508x}{0.508} \\ 33.99=x \\ x\approx34 \end{gathered}[/tex]Next, add x=34 to the initial year:
[tex]2000+34=2034[/tex]The model predicts the percentage to be 27.96% for the year 2034
Help 20 points (show ur work)
There are 2 questions
The length of the trail is equal to 3mi and the selling price of the item is equal to $120.
RatioIn mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
In this question, we have to use the ratio given to determine the length of the trail.
Given that the ratio is 5in : 2mi, we have to convert the values to uniform units.
[tex]1mi = 63360in\\2mi = x\\x = 126720[/tex]
The ratio is now 5in : 126720in
Given that on the map, the length is 7.5in
[tex]5 = 126720\\7.5 = x\\x = 190080in[/tex]
Let's convert this into mi.
[tex]190080in = 3mi[/tex]
The actual length of the trail is 3in.
b)
To find the selling price of the item, let's use the percentage given to do that.
discount = 40%actual price = $200We can find 40% of 200 and then subtract the value from 200.
[tex]40\% of 200 = 0.4 * 200 = 80[/tex]
The discount price is $80 and we can find the selling price here.
[tex]selling price = actual price - discount price\\selling price = 200 - 80\\selling price = 120[/tex]
The selling price of the item is $120
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Martin Brothers Moving rents moving vans by the hour. The company charges a flat fee of $17.99, plus an additional $19.99 per hour. One customer pays $57.97 for her rental. How long was her rental?
Let h be the number of hours that the customer rented the van, then we can set the following equation:
[tex]19.99h+17.99=57.97.[/tex]Subtracting 17.99 from the above equation we get:
[tex]\begin{gathered} 19.99h+17.99-17.99=57.97-17.99, \\ 19.99h=39.98. \end{gathered}[/tex]Dividing by 19.99 we get:
[tex]\begin{gathered} \frac{19.99h}{19.99}=\frac{39.98}{19.99}, \\ h=2. \end{gathered}[/tex]Answer: 2 hours.
A student takes out 2 loans to pay for college. One loan at 8% interest and the other at 9% interest. The total amount borrowed is $3,500, and the interest after 1 year for both loans is $294. Find the amount of each loan.
The amount of each loan are $2,100 and $1,400.
What is mean by Simple interest?
The simple interest is defined as;
Simple interest = P r t
Where, P is principal amount.
r is rate and t is time period.
Given that;
Student take 2 loans for pay the college.
One loan at 8% interest and the other at 9% interest.
And, The total borrowed amount = $3,500
and, The interest loan = $294
Let The first amount of loan = x
And, The other amount of loan = y
So, We can formulate;
x + y = $3,500 ..... (i)
And, The interest loan = $294
So, We can formulate;
8x/100 + 9y/100 = $294
8x + 9y = 29400 ... (ii)
Solve equation (i) and (ii) , we get;
Multiply by 8 in equation (i) and subtract from (ii), we get;
y = $1400
Hence,
x + y = $3,500
x + 1400 = 3500
x = 3500 - 1400
x = $2,100
Therefore, The amount of each loan are $2,100 and $1,400.
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What is the area of a rectangle with length of 6.5 feet (ft) and width of 2.5 ft?
The area of a rectangle is given by the formula
[tex]\begin{gathered} A=l\cdot w \\ \text{ Where l is the length and} \\ w\text{ is the width of the rectangle} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} l=6.5\text{ ft} \\ w=2.5\text{ ft} \\ A=l\cdot w \\ A=6.5\text{ ft }\cdot2.5\text{ ft} \\ A=16.25\text{ ft}^2 \end{gathered}[/tex]Therefore, the area of this rectangle is 16.25 square feet.
I need to use my work and I don’t know what to put please help me !!!
We are given the information that Bailey reads 2 and a half books in 3 and a third weeks.
2 and a half books can be seen as 5/2 books, just as follows
[tex]2\frac{1}{2}\text{ = }\frac{4}{2}+\frac{1}{2}\text{ = }\frac{5}{2}[/tex]On the other hand, 3 and a third weeks can be seen as 10/ weeks, just as follows:
[tex]3\frac{1}{3}\text{ = }\frac{9}{3}+\frac{1}{3}=\text{ }\frac{10}{3}[/tex]Next, we just have to use a rule of three, its as follows: "if Bailey read 5/ books in 10/3 weeks, how many books does she reads per week?"
[tex]\begin{gathered} 10/3\text{ --> 5/2} \\ 1\text{ --> x} \end{gathered}[/tex]With that, we proceed with the division:
[tex]\frac{\frac{5}{2}}{\frac{10}{3}}\text{ = }\frac{15}{20}\text{ = }\frac{3}{4}[/tex]That means that Bailey reads 3/4 books per week
simplest form , 7/6 ÷ 4
[tex]\text{ }\frac{7}{6}\text{ / 4 = }\frac{\frac{7}{6}}{\frac{4}{1}}\text{ = }\frac{7}{24}[/tex]
The answer is 7/24
n is equal to 30% of 600
Given:
[tex]n=\frac{30}{100}\times600[/tex]Solve the expression,
[tex]\begin{gathered} n=\frac{30}{100}\times600 \\ n=30\times6 \\ n=180 \end{gathered}[/tex]Answer: n = 180
Someone please help me with this
Polynomial equations are those created using exponents, coefficients, and variables. It may have several exponents, with the higher one being referred to as the equation's degree.
How are polynomial equations solved?Polynomial equation illustration
Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.
6h²(5 + 9h)(5 - 9h)
6h²(9h + 5)(5 - 9h)
6h²(9h + 5)(-9h + 5)
Distribute6h²(9h + 5)(-9h + 5)
54(-9h +5)h³ + 30(-9h + 5)h²
(-486h)4 + 270h³+30(-9h+5)h²
(-486h)4 + 270h³-270h³+150h²
(-486h)4 + 150h²
Solution(-486h)4 + 150h²
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What is the solution to the equation below? √x+9 = 11 O A. x= 2 O B. X= √ O C. x = 42 D. x = 4
answer: D. x = 4
How do you solve the system of equations by graphing? y=-3x/2 + 6y=5x - 7
The given system of equations are
y=-3x/2 + 6
y=5x - 7
We would substitute values for x into the equations and find the corresponding y values. These values would be plotted on a graph. Where the lines of both equations meet would represent the solution of the system of equations.
For the first equation,
y = - 3x/2 + 6
if x = 0, y = 3 * 0/2 + 6 = 6
If x = 1, y = - 3 * 1/2 + 6 = 4.5
if x = 2, y = - 3 * 2/2 + 6 = 3
We would plot these values on the graph
For the second equation,
y = 5x - 7
if x = 0, y = 5 * 0 - 7 = - 7
If x = 1, y = 5 * 1 - 7 = - 2
if x = 2, y = 5 * 2 - 7 = 3
We would plot these values on the graph
The diagram of the graph is shown below
Looking at the graph, at the point where both lines meet,
x = 2, y = 3
Thus, the solution is (2,3)
how to solve 4(a+1)=12how to solve 13+2k=5+4khow to solve -4e+28=10ehow to solve -6(4+c)=-66
In this problem, we must solve some linear equations.
1)
[tex]\begin{gathered} 4\cdot(a+1)=12, \\ a+1=\frac{12}{4}, \\ a+1=3, \\ a=3-1, \\ a=2. \end{gathered}[/tex]2)
[tex]\begin{gathered} 13+2k=5+4k, \\ 13-5+2k=4k, \\ 8+2k=4k, \\ 4k-2k=8 \\ 2k=8, \\ k=\frac{8}{2}, \\ k=4. \end{gathered}[/tex]3)
[tex]\begin{gathered} -4e+28=10e, \\ 28=10e+4e, \\ 28=14e, \\ e=\frac{28}{14}, \\ e=2. \end{gathered}[/tex]4)
[tex]\begin{gathered} -6(4+c)=-66, \\ 4+c=\frac{-66}{-6}, \\ 4+c=11, \\ c=11-4, \\ c=7. \end{gathered}[/tex]Answers
• a = 2
,• k = 4
,• e = 2
,• c = 7
II
Finding simple interest without a calculator
Lella deposits $600 into an account that pays simple interest at a rate of 2% per year. How much interest will she be paid in the first 3 years?
The Solution:
Given:
Lella deposited $600 into an account that pays 2% simple interest per year.
Required:
To find the interest Lella will get in the first 3 years.
To find the interest, we shall use the formula below:
[tex]I=\frac{PRT}{100}[/tex]In this case,
[tex]\begin{gathered} P=\text{amount deposited=\$600} \\ T=\text{time in years =3 years} \\ R=\text{rate in percent=2\%} \\ I=\text{simple interest paid=?} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]I=\frac{600\times2\times3}{100}=6\times2\times3=\text{ \$36}[/tex]Thus, the interest she will be paid in 3 years is $36.00
Therefore, the correct answer is $36.00
Use the sequence below to complete each task. 34, 25, 16, 7, ... a. Identify the common difference (a). b. Write an equation to represent the sequence. c. Find the 20th term (azo)
Problem
Solution
We have the following sequence of terms 34,25,16,7,....
Part a
The common difference for this case would be:
25-34= -9
16-25=-9
7-16= -9
Then the answer for part a would be -9
Part b
We want to write the following form:
an = a1 + (n-1) d
For this case d=-9, a1= 34
And then we can write the genral expression like this:
an = 34 + (n-1 ) (-9)
With n = 1,2,3,4....
Part c
In order to find the 20 th term we can replace n =20 and we got:
a20= 34 + (20-1) (-9) = 34-171= -137
a rectangular rug has dimensions of 9'×12'find area of the rug
Explanation:
Area of the rectangular rug = length × width
dimension of rug = 9'×12'
length = 12', width = 9'
Area = 12 × 9
Area = 18
helpppppppppppppppppppppppppppppp
Step-by-step explanation:
im still working on the 2nd part
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
√52
Step-by-step explanation:
[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]
For each value of y, determine whether it is a solution to y÷2 = 6.
y
6
16
10
14
Is it a solution?
Answer:
None are solutions.
Step-by-step explanation:
Divide each value of y by 2 and see if it equals 6. If it does, then it is a solution. If it doesn't then it isn't a solution.
6 ÷ 2 = 6
3 ≠ 6
not a solution
16 ÷ 2 = 6
8 ≠ 6
not a solution
10 ÷ 2 = 6
5 ≠ 6
not a solution
14 ÷ 2 = 6
7 ≠ 6
not a solution
A triangle has vertices P (4.1), Q (4, 5) and R (7,5) What is the area of ∆PQR? (Area= 1/12 basexheight)
First, plot the points on a graph and form the triangle:
By looking at the triangle we can see that:
Base: 2
Height: 4
Area : 1/2 x 2 x 4 = 4 units2