The average quantity of juice that is consumed per person in this country is given as 3.84
How to solve for the averageWe have the following data with which to answer this question
The consumption of juice = 1.92 billion
The population of the country = 500 million
The question wants us to calculate the amount of drink that the persons would consume on average in this nation.
we have average = quantity consumed / total number of persons
This would give us
average = 1.92 billion / 500 million
= 1, 920, 000, 000 / 500, 000 ,000
= 3.84
Hence the amount of juice that is consumed per person in this country is given as 3.84
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What is the coordinate of G' if triangle E'F'G' is created by dilating EFG with factor of 4 about the origin?
Answer:
G' (8, - 8 )
Step-by-step explanation:
since the dilatation is centred at the origin then multiply each of the coordinates by the scale factor of 4
G (2, - 2 ) → G' (4(2), 4(- 2)) → G' (8, - 8 )
I have a test coming up, and I think I will have questions like 7a+5a+4b-b etc. please help!
Answer:
12a + 3b = no solution
Step-by-step explanation:
You have to add like terms here!
7a + 5a = 12a
12a + 4b - b
4b - b = 3b
And now you're left with 12a and 3b, you can't go any further because 12 a and 3b are not like terms, you cannot add, or subtract them. Which means there is no solution.
I hope this helped :)
The number of new bicycles must be more than 13 times the number of new treadmills. Each bicycle costs $340 and each treadmill costs $670. He must spend less than $5,650.
Select all of the constraints for this situation.
y>13x
y greater than fraction 1 over 3 end fraction x
x>0
x is greater than 0
340x+670y<5650
340 x plus 670 y less than 5650
x>13y
x greater than fraction 1 over 3 end fraction y
340x+670y≤5650
340 x plus 670 y less than or equal to 5650
y>0
The constraints of the equation will be x > 13 y and 340 x + 670 y < 5650.
Let the number of new bicycles be x
Let the number of new treadmills be y.
Cost of 1 new bicycle = $ 340
Cost of 1 new treadmill = $ 670
Also, he must spend less than $ 56,50
Now, the constraints for this will be:
x > 13 y
x greater than 13 y
340 x + 670 y < 5650
340 x plus 670 y less than or equal to 5650
Therefore, the constraints of the equation will be x > 13 y and 340 x + 670 y < 5650 .
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Let P=(-2,2), Q=(3,4), R=(-2,5) , and S=(2,-8) . What are the component forms of the following vectors? PQ
The components of PQ are given by {5; 2}
The components of a vector in a two-dimensional coordinate system are usually thought of as the x and y components. This can be expressed as V = (vx, vy), where V is a vector. These are part of the vectors generated along the axis.
Suppose an angle θ is formed between the vector V and the x component of the vector. A vector V and its x component (vx) form a right triangle if you draw a line parallel to the y component (vy).
Due to the trigonometric relationship:
cos θ = adjacent side/hypotenuse = vx/V
sin θ = opposite side/hypotenuse = vy/V
where V is the magnitude of vector V.
So, the Component of PQ is Given by
PQ = {Bx - Ax; By - Ay} = {3 - (-2); 4 - 2} = {5; 2}
PQ= {5; 2}
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Use the properties of logarithms to simplify and solve each equation. Round to the nearest thousandth.
ln (x+1)+ln (x-1)=4
The simplified form of the given logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).
What precisely are logarithms?A logarithmic term represents a number in log form. A log term is another name for it.
A quantity can also be the sum of two or so more quantities. As a result, a term can be the product of 2 or more quantities, one of which must be in logarithmic form. In those kind of instances, the terms are recognized as log terms.
A quantity can also be defined as the quotient of two quantities. So, if a term includes a quotient of quantities, or at least each of the quantities could be expressed in log form, this same terms are known as log terms.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, according to the stated condition in question;
ln (x+1)+ln (x-1) = 4
Applying the Product Rule on the left side of the equation;
ln (x+1)/ (x-1) = 4
Convert the obtained expression in the exponent form.
Thus,
e∧[ln (x+1)/ (x-1)] = e⁴
Now, apply the exponent rule.
(x+1)/ (x-1) = 4
Now, simplifying the equation.
(x+1) = 4 (x-1)
x+1 = 4x - 1
4x - x = 1 + 1
3x = 2
x = 2/3
x = 0.666...
x = 0.67 (to the nearest thousandth).
Therefore, the solution for the stated logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).
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Estimate 3 √ 70 to the nearest integer.
The value of the expression 3√70 to the nearest integer will be 25.10.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ 3√70
We know that the value of √70 will be 8.3666. Then the value of the expression will be given as,
⇒ 3√70
⇒ 3 x 8.3666
⇒ 25.0998 ≈ 25.10
The value of the expression 3√70 to the nearest integer will be 25.10.
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Mr. Lawson needs to borrow 8000 to help pay his son's college tuition. He explored options from several banks. Which option allows Mr. Lawson to pay the smallest amount of interest?
BANK: INTREST RATE: LOAN TERM:
United Bank 4% simple interest. 6 years
Nations First 3.8% simple interest. 7 years
City Credit Union 5.1% simple interest. 4 years
Priority Bank 4.2% simple interest. 5 years.
Mr. Lawson is to pay the smallest amount of interest that is allowed in the City Credit Union which is a simple interest would be 1632.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
To determine the smallest amount of interest.
We have to calculate the simple interest of each bank
United Bank : 4% interest rate and 6 years
S.I. of United Bank = 8000 × 4/100 × 6 = 1920
Nations First :3.8% interest rate and 7 years
S.I. of Nations First = 8000 × 3.8/100 × 7 = 2128
City Credit Union :5.1% interest rate and 4 years
S.I. of City Credit Union = 8000 × 5.1/100 × 4 = 1632
Priority Bank : 4.2%interest rate and 5 years.
S.I. of Priority Bank = 8000 × 4.2/100 × 5 = 1680
So the smallest amount of interest would be City Credit Union which is 1632.
Therefore, Mr. Lawson is to pay the smallest amount of interest that is allowed in the City Credit Union which is a simple interest would be 1632.
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Suppose that (x₁, y₁) and (x₂, y₂) are values from an inverse variation. Show that x₁/x₂=y₂/y₁.
It can be proved using the method of inverse variation.
What is inverse variation?
In mathematics, inverse variation refers to the relationships between variables expressed as y = k/x, where x and y are two variables and k is a constant. According to this statement, if the value of one item rises, the value of the other quantity falls.
Given,
(x₁, y₁) and (x₂, y₂) are values from an inverse variation.
inverse function of x and y will be -
y1 = k. 1 / x1
k = y1 / x1 ....(1)
y2 = k. 1 / x2
k = y2 / x2 ....(2)
from (1) , (2)
we can say that,
y1 / x1 = y2 / x2
⇒ y2 / y1 = x1 / x2
Hence proved.
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A teacher wishes to know whether the males in his/her class have more conservative attitudes than the females. a questionnaire is distributed assessing attitudes.
a. is this a sampling or a census?
b. is this an observational study or an experiment?
c. are there any possible sources of bias in this study?
Descriptive statistics is the correct answer.
Descriptive statistics are numbers that are used to summarize and describe data. The word "data" refers to the information that has been collected from an experiment, a survey, a historical record, etc. (By the way, "data" is plural. One piece of information is called a "datum.") If we are analyzing birth certificates, for example, a descriptive statistic might be the percentage of certificates issued in New York State or the average age of the mother. Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed. Several descriptive statistics are often used at one time to give a full picture of the data.
Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand. Generalizing from our data to another set of cases is the business of inferential statistics, which you'll be studying in another section. Here we focus on (mere) descriptive statistics.
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What is the value of the expression 38x − 17 if x is equal to −5?
Answer:
-207
Step-by-step explanation:
38x - 17
38(-5) - 17
-190 - 17
-207
*Please mark brainliest answer
Answer:-173
Step-by-step explanation:
38x - -17
38 multiplied by -5 equals -190
-190 - -17 equals -173
A family spends ; of their monthly income
on food,
5
14
on clothing and ‡on rent.
What fraction of the family's income is
spent on other things? If in a particular
month, the family spends GH&2,400 on
other things, how much did the family
spend on clothing? What was the family's
income for the month.
They spent 1/70 of their monthly income on other things.
The family spent GH¢60,000 on clothing.
The monthly income of the family is GH¢168,000.
What is Fraction?
The number is expressed as a quotient in which the numerator is divided by the denominator is called fraction.
Since, The family spend;
On food = (3/7)*x
On clothing = (5/14)*x
On rent = (1/5)*x
Let the family's monthly income = x
Now, To find the fraction of the family's income is spent on other things, we can assume that y is spent on other things, then we should have;
(3/7)*x + (5/14)*x + (1/5)*x + y*x = x
We can divide both sides by x, we get:
(3/7) + (5/14) + (1/5) + y = 1
Now, we can solve this for y as;
3/7 + 5/14 + 1/5 + y = 1
6/14 + 5/14 + 1/5 + y = 1
(6 + 5)/14 + 1/5 + y = 1
11/14 + 1/5 + y = 1
The smallest common factor of 14 and 5 = 14*5 = 70
So, we can multiply in the first fraction by 5/5 and the second by 14/14,
(5/5)*(11/14) + (14/14)*(1/5) + y = 1
55/70 + 14/70 + y = 1
69/70 + y = 1
y = 1 - 69/70
y = 1/70
Hence, They spent 1/70 of their monthly income on other things.
And, On a particular month, the family spends GH¢2,400 on other things, then if the monthly income is x, we have:
(1/70)*x = GH¢2,400
x = 70* GH¢2,400
x = GH¢168,000
So, The monthly income of the family is GH¢168,000
And, we know that they spend (5/14)*x on clothing,
Then this month they spent on clothing,
⇒ (5/14)*GH¢168,000 = GH¢60,000
So, They spent 1/70 of their monthly income on other things.
The family spent GH¢60,000 on clothing.
The monthly income of the family is GH¢168,000.
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The complete question is this,
A family spends 3/7 of their monthly income on food,5/14 on clothing and 1/5 on rent. What fraction of the family's income is spent on other things? If in a particular month, the family spends GH&2,400 on other things, how much did the family spend on clothing? What was the family's income for the month.
2.39 repeating as a mixed number
15 A railway station has two platforms. Trains stop at the northbound platform every 10 minutes. Trains stop at the southbound platform every 18 minutes Two trains stopped together at 1512 (a) Work out the next time two trains stop together at this station.
The answer is 190m.
The faster train is 160 m long and crosses a lamp post in 12 seconds.
The speed of the faster train = 16012 = 403 m/s
Given that, the speed of the other train is 6 km/hr (53 m/s) less than the faster one. [we can convert speeds from km/h to m/s by multiplying with 5/18]
The speed of the slower train = 353 m/s.
Given that, the two trains cross each other in 14 seconds when running in opposite directions along parallel tracks.
tracks.
Relative speed = total length of two trains time taken to cross each other
25m/s = 160+ length of second train 14
Length of the second train = 190m.
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Simplify the expression. Write your answer as a power 6^2/6 • 6^12 / 6^8
The simplified form of the expression is 6^(-3)
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
6^2/6 • 6^12 / 6^8
Simplifying
6^2/6 • 6^12 / 6^8
Applying the division law of indices
6^(2 -1 ) • 6^(12 - 8)
6^(1) • 6^(4)
Applying the multiplication law of indices
6^(1 - 4)
6^(-3)
Hence, the simplified form of the expression is 6^(-3)
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4^3+/(3+1)x2 please solve 15 points dude
If f(x) = 1 -x, which value is equivalent to f(1)|?
The value corresponding to |f(i)| is √2.
The given function is f(x)=1-x.
Given f(x) = 1 - x
To find the value of |f(i)| we have to substitute x=i.
After substituting this, we get
f(i) = 1 - i
As we all know that, this is an imaginary even function in the form a + ib
The modulus of the imaginary function can be represented as √(a²+b²)
Here a = 1 and b = -1
Now, we will substitute this value in the above formula, we get
|f(i)| = √(1² + (-1)²)
|f(i)| = √(1+1)
|f(i)| = √2
Hence, the value of the given function f(x)=1-x which is equivalent to |f(i)| corresponding value is √2.
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Jenna works for the Parks Department and just completed some maintenance work at the baseball fields in Memorial Park. She needs to drive to the playground at Veteran’s Park next. In which general direction will she drive?
a map of a town showing two parks
A.
southwest
B.
northwest
C.
southeast
D.
northeast
Answer:North west, the roads should have stopped this answer but north alone wasn’t an option so just pretend Jenna is a lawless maniac ig♂️
Step-by-step explanation:
Which function will have the steepest graph
The linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines. (Correct choice: D)
How to find the linear equation with the steepest graph?
Linear equations are equations of the form y = m · x + b, where m, b are the slope and the intercept of the equation, respectively. As slopes may be positive, null or negative, then we should use absolute values to determine the grade of steepness of a linear equation, where |m| ≥ 0. A line is steeper than other line when the absolute value of the former is greater than the absolute value of the latter.
According to this criterion, the linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines.
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20 POINTS! Can someone help me? The question is located below!
A. 12cm x 8cm
B. 12cm x 9cm
C. 13cm x 8cm
D. 13cm x 9cm
The dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.
What are Whole Numbers?Whole numbers are numbers that do not have any fractional part and represents a whole quantity.
What are Mixed Numbers?A mixed number consist of an whole number and a proper fraction or fractional part.
How to Convert Mixed Numbers to Improper Fractions?Given the dimensions of the rectangular photo as, 12 11/16 cm by 8 3/4cm, convert each dimension to improper fractions:
12 11/16 would be converted to 203/16
8 3/4 would be converted to 35/4
203/16 = 12.6875 ≈ 13 [nearest whole number of cm]
35/4 = 8.75 ≈ 9 [nearest whole number of cm]
Therefore, the dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.
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In cooking class, the instructor divided 1/2 of an ounce of salt evenly to make 4 servings of a dish. How much salt did he put in each serving? Write your answer as a fraction or as a whole or mixed number.
During the cooking class, the instructor put 1/8 of the salt in each serving
How to calculate the number of salt placed in each serving ?The instructor divided 1/2 of an ounce of salt evenly
The instructor needs to 4 servings in a dish
Therefore the number of salt in each serving can be calculated as follows
= 1/2 ÷ 4
change the expression to multiplication
1/2 × 1/4
= 1/8
Hence 1/8 of the salt was placed in each serving of the dish
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Answer the 2 question in the photo
[easy points]
How many pieces of string each measuring 10cm can be cut from a length measuring 2.5metres
Two thirds equals negative eight times a number
Answer:
Step-by-step explanation:
25/3
Solve the system of equations using elimination: − 2 x − 4 y = − 30 −2x−4y=−30 and − x + y = 6 −x+y=6.
Answer:
(1, 7 )
Step-by-step explanation:
- 2x - 4y = - 30 → (1)
- x + y = 6 → (2)
multiplying (2) by 4 and adding to (1) will eliminate y
- 4x + 4y = 24 → (3)
add (1) and (3) term by term to eliminate y
- 6x + 0 = - 6
- 6x = - 6 ( divide both sides by - 6 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (1)
- 2(1) - 4y = - 30
- 2 - 4y = - 30 ( add 2 to both sides )
- 4y = - 28 ( divide both sides by - 4 )
y = 7
solution is (1, 7 )
Work out the perimeter of a regular octagon with side length 1.7mm.
Answer:
13.6mm
Step-by-step explanation:
1.7mm x 8 sides =
HELP ME PLEASE!!!
I will give brainlist to whoever helps me!!!!
Answer: t=15
Step-by-step explanation:
ST=9. BC=3
ST/BC=
9/3=3 ==> with this information, we can conclude that triangle ABC needs to be stretched by a scale factor of 3 in order to become triangle RST.
t=RS
RS=AB*3
RS=5*3
RS=15
t=15
Solve each equation.
3x =9
Solution of this polynomial equation is x = 3
What are polynomial equations ?In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
3x = 9
=> 3x / 3 = 9 /3
=> x = 3
Thus solution for given equation is x = 3.
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fluctuates
increases
stays the same
decreases
Answer:
d)decreases
Step-by-step explanation:
. You get paid on the first day of each month. You cash your check and pay
all of your essential expenses. You keep the balance in your "discretionary
spending" envelope. A scatter plot shows the number of days that have passed
since you were paid and the amount left in your discretionary spending
envelope. The explanatory x-variable is the number of days that have passed.
The response y-variable is the amount left in your envelope. Is there a positive
or negative correlation? Explain.
From the given scatter plot with x and y variables, we can say that the correlation is; Negative Correlation.
How to interpret scatter plot correlation?We are told that you kept the balance in your "discretionary spending" envelope.
Now, we are further told that a scatter plot shows the number of days that have passed since you were paid and the amount left in your discretionary spending envelope.
Now, In this case, the day of the salary increases the money spent, that is, the amount of money in the envelope decreases. Thus, as the variable increases and the other decreases, it is a negative correlation.
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I need this with overtime pay.
Kerry worked 46 hours last week. His hourly rate is $9.60. He has the following deductions taken from his pay: federal income tax at the rate of 10 percent, Social Security tax at the rate of 6.2 percent, Medicare tax at the rate of 1.45 percent, health insurance premiums of $12.20, and union dues of $9.50. Kerry’s net pay for last week was $. Hide Feedback Incorrect Check My Work Feedback Gross pay includes regular hours times regular pay, plus overtime hours times overtime pay. The overtime pay rate is 1½ times the regular rate of pay. Deductions—both required and voluntary—are subtracted from gross pay to compute net pay. (Round to the nearest cent for all calculations.)
Answer:
here to try to help!
Step-by-step explanation:
346.96 why? Kerry was not payed at the overtime for extra hours hope it helped!