Chris is using the expression 4x + 2 to represent the number of students in his gym class. There are four times as many students as basketballs, and there are two more students in the locker room. What does x represent? (4 points)
Answers
X represents the number of basketballs in Chris's gym class.
Chris represents the number of students in his gym class with the expression 4x + 2. We know that the number of students is four times the number of basketballs, so we can set up the equation 4x = the number of basketballs.
If we substitute this expression for the number of students in the gym class, we get 4(4x) + 2 = the total number of students in the gym class and locker room. We also know that there are two more students in the locker room, so we can add 2 to this expression to get 4(4x) + 4 = the total number of students in the gym class and locker room.
Now we can set this expression equal to the original expression for the number of students, 4x + 2, and solve for x:
4(4x) + 4 = 4x + 2
16x + 4 = 4x + 2
12x = -2
x = -1/6
However, x cannot represent a negative number of basketballs, so there must be an error in the problem.
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Related Questions
find (9.3x106) + (1.8x104) express your answer in scientific notation
Answers
Answer: here is your answer
Step-by-step explanation:
(9.3 × 10^6) + (1.8 × 10^4) is 93.18E+5.
(9.3 × 106) + (1.8 × 10^4)
(9.3 × 106) + (0.018 × 10^6)
(9.3 + 0.018)× 10^6
(9.318)× 10^6
scientific notation
(93.18E+5)
PLEASE HELP ME OUT!!!
Answers
Answer:
20/3 or 6.67 or 6 \(\frac{2}{3}\) (any of these are correct)
Step-by-step explanation:
Volume of triangular pyramid formula is V = 1/3 * base area * height
V = 1/3 * 5 * 4 = 20/3
20/3 or 6.67 or 6 \(\frac{2}{3}\)
Consider the rectangle.
2x
Which pair of expressions represents the area of the rectangle?
O 2 (2x) +2 (6) and 4x + 8
O 2 (2x) + 2(6) and 42 +12
O 8x and 6 (2x)
O 120 and 6 (2x)
Calculator
Answers
Answer:
8x and 6(2x)
Step-by-step explanation:
this is because when you calculate the area you multiply the length to the high
Answer:
12x and 6(2x)
Step-by-step explanation:
Area = LW
Area = (2x)(6)
Area = 12x
A car travels for 2 hours at an average speed of 60 mph.
Work out the total distance of the journey.
Answers
Answer: 120 Miles
Step-by-step explanation:
2 x 60 = 120
Answer:
Travels 2hours Speed 60mph
it would be 60 + 2 = 62
I hope this helps you!
XoXo Mashayla
Step-by-step explanation:
A music store sold for 10³ CDs and 10² CD players. If each CD costs $12
and each CD player costs $35, what was the store's total earnings?
Answers
The total earning of the store from the formed equation is: 15,500 dollars.
What is equation?
In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.
According to the question, the given parameter states that the music store sold 1000 CDs and 100 CD players. And the cost of each CD is $12 and each CD player is $35.
Now, to calculate the total earning by forming the equation for the given statement and it is as follows:
(1000)(12) + (100)(35) = 12,000 + 3500 = 15,500 dollars
Hence, the total earning of the store from the formed equation is: 15,500 dollars.
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Denise bikes 3 miles to her friend's house, and then she bikes home. The average rate biking to her friend's house is twice the average rate coming home. Write and simplify an expression for the time it takes Denise to make a round-trip in terms of the average rate coming home x. Hint : Use d = rt.
Answers
Using the relation between velocity, distance and time, it is found that the expression for the total time is given by:
\(t = \frac{9}{2x}\)
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
\(v = \frac{d}{t}\).
Denise bikes 3 miles to her friend's house, hence:
\(v_1 = \frac{3}{t_1}\)
\(t_1 = \frac{3}{v_1}\)
The average rate biking to her friend's house is twice the average rate coming home, hence, on the return, \(v_2 = 0.5v_1\):
\(v_2 = \frac{3}{t_2}\)
\(t_2 = \frac{3}{v_2}\)
\(t_2 = \frac{3}{0.5v_1}\)
\(t_2 = \frac{6}{v_1}\)
The total time is given by, considering \(v_1 = 2v_2 = 2v = 2x\), as we want to consider x the rate coming home:
\(t = t_1 + t_2\)
\(t = \frac{3}{2x} + \frac{6}{2x}\)
\(t = \frac{9}{2x}\)
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really need help on these two questions for geometry, please actually answer it instead of just grabbing points and leaving :')
Answers
Answer:
Step-by-step explanation:
E and F are horizontally aligned, so the slope of EF is 0 and its length is 16-10 = 6.
G and H are horizontally aligned, so the slope of GH is 0 and its length is 16-10 = 6.
F and G are vertically aligned, so FG is vertical and its length is 10-4 = 6.
E and HG are vertically aligned, so EH is vertical and its length is 10-4 = 6.
Quadrilateral EFGH is a square.
You have $50,000 to invest (YAY!). You need $350,000 in the account to retire in 30 years. At what continuously compounded interest rate would you need to invest to reach your goal?
What formula will you be using? Type your answer in the first math box below.
In the following math boxes, make your substitutions and show the ALGEBRAIC steps to your solution.
Answers
Answer:
You need to invest at a continuous compound interest rate of 6.701355026%
Step-by-step explanation:
The formula to use is the compound interest formula:A=P(1+r/100)^t
where A=Total amount at the end of the investment period
P=Principal amount
R=Rate of interest
T=Investment tenor/time
Now,
350,000=50000(1+r/100)^30 is what needs to be simplified to 6.701355026%
A dog was west of his home for a short time and returns home then runs past it in the
other direction (east). The graph shows his position as a function of time.
How long did the dog stop at his home before running again?
O 2 second
O 3 seconds
O 5 seconds
O 11 seconds
Answers
Answer:
maybe 3 seconds.
but I am not sure
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!
Answers
Answer:
-6 =x
Step-by-step explanation:
g(x) = -3x -8
g(x) = 10
10 = -3x-8
Add 8 to each side
10+8 = -3x-8+8
18 = -3x
Divide by -3
18/-3 = -3x/-3
-6 =x
Which of the following statements regarding the expansion of (x + y)^n are correct? A. For any term x^ay^b in the expansion, a + b = n. B. For any term x^a y^b in the expansion, a - b = n. C. The coefficients of x^a y^b and x^b y^a are equal. D. The coefficients of x^n and y^n both equal 1.
Answers
Among the given statements, statement A is correct, which states that for any term x^a * y^b in the expansion of (x + y)^n, the sum of the exponents a and b is equal to n. The other statements, B, C, and D, are incorrect.
In the expansion of (x + y)^n, each term is generated by multiplying x and y with different exponents, ranging from 0 to n. The exponents of x and y in each term must add up to n in order to cover all possible combinations. This is represented by statement A, which correctly states that a + b = n.
Statement B is incorrect because subtracting the exponents of x and y in each term does not equal n. Statement C is also incorrect because the coefficients of x^a * y^b and x^b * y^a are not necessarily equal unless a and b are the same. Statement D is also incorrect because the coefficients of x^n and y^n may not both equal 1 unless n is 0 or 1.
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Given the following formula, solve for y. W = x-y/2 - z
A.) Y= 2(w + z) - x
B.) y = x– (2w + z)
C.) Y = x – (2W + z)
D.) Y= 2w + 2 - z - x
Answers
Answer:
the answer is B. y=x-(2w+z)
Step-by-step explanation:
The solution to the given expression is y = x - 2(W + z).
What is an expression ?An expression is a mathematical expression formed by numbers and mathematical operations.There are many types of expressions like trigonometric expressions,Algebraic expressions, logarithmic expressions and many more.
According to the given question we have to solve for y for the given expression W = (x-y)/2 - z.
W = (x-y)/2 - z.
2W = x - y - 2z.
y = x - 2W - 2z.
y = x -2( W + z).
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What is a Turned triangle?
Please tell me QUICKLY.
Answers
like the place where you are applying TURNED TRIANGLE.
coz literrally it means that if the trianlge has for example angle a on its right side then we turn the triangle as a whole and make the turn such that angle a is anywhere else but not on our right side....
I believe the explanation is clear, if not do contact me
Expand and simplify 2(x + 7) + 3(x + 1)
Answers
Answer:
the answer is in the picture
A scientist isolates 47.593 g of a new, unidentified substance. The scientists also determines the following masses for the elements in the substance: carbon: 43.910 g; hydrogen: 3.683 g.
Finally, the scientist is also able to determine the molecular mass of the substance to be 78.11 u. From these data determine:
a. the percent composition
b. the empirical formula
c. the molecular formula
Answers
the molecular formula is obtained by multiplying the empirical formula (CH) by the molecular formula ratio: Molecular formula = (CH) * 6 = C6H6
To determine the percent composition, empirical formula, and molecular formula of the substance, we need to use the given masses of the elements and the molecular mass.
a. Percent Composition:
The percent composition represents the proportion of each element's mass in the total mass of the substance.
For carbon:
Percent composition of carbon = (mass of carbon / total mass of substance) * 100
Percent composition of carbon = (43.910 g / 47.593 g) * 100
Percent composition of carbon ≈ 92.09%
For hydrogen:
Percent composition of hydrogen = (mass of hydrogen / total mass of substance) * 100
Percent composition of hydrogen = (3.683 g / 47.593 g) * 100
Percent composition of hydrogen ≈ 7.74%
Therefore, the percent composition of carbon and hydrogen in the substance is approximately 92.09% and 7.74%, respectively.
b. Empirical Formula:
The empirical formula represents the simplest ratio of the elements in a compound.
To determine the empirical formula, we need to find the mole ratios of the elements. First, we calculate the moles of each element using their masses and molar masses:
Moles of carbon = mass of carbon / molar mass of carbon
Moles of carbon = 43.910 g / 12.01 g/mol
Moles of carbon ≈ 3.659 mol
Moles of hydrogen = mass of hydrogen / molar mass of hydrogen
Moles of hydrogen = 3.683 g / 1.01 g/mol
Moles of hydrogen ≈ 3.649 mol
Next, we divide the number of moles of each element by the smallest number of moles to get the simplest ratio:
Carbon : Hydrogen ≈ 3.659 mol / 3.649 mol ≈ 1:1
The empirical formula of the substance is CH.
c. Molecular Formula:
To determine the molecular formula, we need the molecular mass of the substance.
The molecular mass is given as 78.11 u.
The empirical formula mass can be calculated by adding the molar masses of carbon and hydrogen:
Empirical formula mass = (molar mass of carbon * number of carbon atoms) + (molar mass of hydrogen * number of hydrogen atoms)
Empirical formula mass = (12.01 g/mol * 1) + (1.01 g/mol * 1)
Empirical formula mass = 13.02 g/mol
To find the molecular formula, we divide the molecular mass by the empirical formula mass and determine the whole-number ratio:
Molecular formula ratio = molecular mass / empirical formula mass
Molecular formula ratio = 78.11 g/mol / 13.02 g/mol
Molecular formula ratio ≈ 6
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Pls help me I need the answer
Answers
Answer:
C
Step-by-step explanation:
The quotient of d minus 16 and 3 means that d - 16 is in the numerator and 3 is in the denominator. This equation is equal to 4, so the answer is:
(d - 16) / 3 = 4
I hope this helped and please mark me as brainliest!
Which expression has a greater value: log3 1/3 or logb 1/b? Explain how you know.
Answers
Answer:
They are equalStep-by-step explanation:
Given\(log_3 1/3 \ and\ log_b 1/b\)Compare the expressions\(log_31/3=log_33^{-1}=-1\)\(log_b1/b=log_bb^{-1}=-1\)As we see the two expressions are equal in value
Answer:
log3 1/3 = logb 1/b
(Both expressions are equal)
Step-by-step explanation:
Now we have to,
→ find the expression with greater value.
Then the greatest value is,
→ log3 1/3 = logb 1/b
→ log3 3^(-1) = logb b^(-1)
→ -1 = -1
→ [ LHS = RHS ]
Hence, both have same value.
See question in attached photo.
Answers
Answer:
√-1 or iStep-by-step explanation:
Since A² = 0 we need to get the value of λ when A = 0:
A = λ*λ - 1(-1) = λ² + 1 A = 0λ² + 1 = 0 ⇒ λ² = -1 ⇒ λ = √-1 ⇒ λ = iThe Lewiston Company issues 23-year bonds, but it pays nocoupon. Calculate the price per $1,000 face value of thiszero-coupon bond using an interest rate of 6.7%. Answer to thenearest cent.
Answers
The price per $1,000 face value of the zero-coupon bond issued by the Lewiston Company is approximately $288.12.
To calculate the price of the zero-coupon bond, we can use the present value formula:
Price = Face Value / (1 + Interest Rate)^(Number of Years)
In this case, the face value is $1,000, the interest rate is 6.7%, and the number of years is 23.
Price = 1000 / (1 + 0.067)^23 = 1000 / 2.871 = $348.35
However, this value represents the future value of the bond. To determine the present value, we need to discount it to today's value. To do that, we can divide the future value by (1 + Interest Rate).
Present Value = Price / (1 + Interest Rate) = 348.35 / (1 + 0.067) = $288.12 (rounded to the nearest cent)
The price per $1,000 face value of the zero-coupon bond issued by the Lewiston Company, using an interest rate of 6.7%, is approximately $288.12. Zero-coupon bonds are sold at a discount to their face value because they do not pay any periodic interest payments. The price reflects the present value of the bond, taking into account the time value of money and the specified interest rate.
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What kind of triangle has 105 degress?
Answers
Answer:
obtuse angled triangle
HELP ME! In a complete sentence, describe the relationship between the three angles in the diagram below. Write and solve an equation to find the value of b and the measures of ∠QPS, ∠SPT, and ∠TPR.
Answers
Answer:
b = 17
∠QPS = 124°
∠SPT = 17°
∠TPR = 39°
Step-by-step explanation:
The sum of the three angles shown is a linear angle, with a measure of 180°.This fact can be used to write an equation:
(8b -12)° +b° +(2b+5)° = 180°
11b -7 = 180
11b = 187
b = 17
8b -12 = 8(17) -12 = 124
2b +5 = 2(17) +5 = 39
The value of b is 17.
The angle measures are ...
∠QPS = 124°
∠SPT = 17°
∠TPR = 39°
Joan shared $120.00 among her 3 siblings, Jane, Sally and Rita. She gave Rita $15.00 more than Jane and Sally. How much money did Rita get?
Answers
Answer:
55
Step-by-step explanation:
120/3 = 40.
40-15= 25.
so it's 10
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Find (g∘k)(1)for g(x)=11x2−4x+6and k(x)=4x−11. (g∘k)(1)=
Answers
The first step you have to follow is to find k(1) by replacing each x in k(x) for 1:
\(k(1)=4(1)-11=4-11=-7\)Now, find g(k(1)), it means, g(-7):
\(g(-7)=11(-7)^2-4(-7)+6=573\)(g°k)(1)=573.
(2,0) (5,6) in slope form
Answers
Slope= change in y / change in x
Slope = 6-0 / 5-2
=6/3
Slope = 2
Answer:
slope intercept form is mx+b=y where the slope is 2 because 6/3=2 so therefore we need to find b which you can subsitute the values to get 2(2)+b=(0) so b=-4 therefore the slope intercept is 2x-4=y
to check my answer we used (2,0) so we use (5,6) to get 2*5-4=6 which is a true statement
give me brainliest :)
Step-by-step explanation:
help plzz
i really need help
Answers
Answer:
f multiplied by 3 divided by 625
Step-by-step explanation:
cant really explain
Use the following prompt to answer the next 6 questions. Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131 Is there evidence to doubt the color distribution claimed by the website? Use ????=0.05
Answers
Answer:
The claim on the M&M’s website is not true.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
\(\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}\)
Here,
\(O_{i}\) = Observed frequencies
\(E_{i}=N\times p_{i}\) = Expected frequency.
The chi-square test statistic value is, 14.433.
The degrees of freedom is:
df = k - 1 = 6 - 1 = 5
Compute the p-value as follows:
\(p-value=P(\chi^{2}_{k-1} >14.433) =P(\chi^{2}_{5} >14.433) =0.013\)
*Use a Chi-square table.
The significance level is, α = 0.05.
p-value = 0.013 < α = 0.05.
So, the null hypothesis will be rejected at 5% significance level.
Thus, concluding that the claim on the M&M’s website is not true.
1. At the end of the trading day on June 5, Traders, Inc. announced that its CEO had a heart attack. This news caused the stock to drop to $48.62, a drop 6.75%. If Steve had 1,000 shares of Traders, Inc., in his portfolio, what was the value of his portfolio before the announcement ?
Answers
The value of Steve's portfolio before the announcement was $52.15.
Let's denote the original value of Steve's portfolio before the announcement as "P".
The drop in the stock price is given as 6.75%, which means the stock price decreased by 6.75% from the original value.
To calculate the original value (P), we can use the following equation:
P - 6.75% of P = $48.62
P - (6.75/100) x P = $48.62
P - 0.0675P = $48.62
0.9325P = $48.62
P = $48.62 / 0.9325
P ≈ $52.15
Therefore, the value of Steve's portfolio before the announcement was $52.15.
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You want to surround the perimeter of a garden with 35 stones. You need to place a certain number of large and small stones and every large stone you want to use 4 small stones. Choose the correct equation to find the number of stones for each size
Answers
Answer:
The answer is "x + 4x = 35; 7 large stones and 28 small stones"
Step-by-step explanation:
Please find the complete question in the attached file.
Let
\(x = \text{big stone number}\\\\y = \text{tiny stone number}\\\\x + y= 35\)
Users want to use four small stones for each big stone:
\(Y = 4x\)
solving the equations system:
\(x + y = 35\\\\y = 4x\)
we find:
\(x = 7 \ \text{for big stones}\\\\y = 28\ \text{for tiny stones}\\\\\)
solve for x in the equation (x-3)³
Answers
Answer:
x=3
Step-by-step explanation:
firstly this equation isn't possible without it equaling to something. I set it equal to zero and got x=3.
EX:
(x-3)^(3)=0
A line passes through the points (1, 9) and (0, 4). What is its equation in slope-intercept