Answer:
20% reduction in price
Step-by-step explanation:
Let the original price of each box be P and original quantity be Q. The unit rate is P/Q
Jack's approach
increase quantity by 25% = 0.25Q
New quantity = Q + 0.25Q = Q(1 +0.25) = 1.25Q
Unit rate = P/1.25Q
Sadia's approach
Reduce price and keep quantity same
Let price reduction be d% = d/100
Let us denote d/100 as r. This will be a decimal value. For example, a reduction of 10% means that the price is reduced by 0.10
Price reduction = P x r = Pr
New price = P - Pr = P(1-r)
Unit rate by this method =P(1-r) /Q
Both unit rates have to be the same if both values are the same
So
[tex]\dfrac{P}{1.25Q} = \dfrac{P(1-r)}{Q}\\\\\dfrac{P}{Q} \cdot \dfrac{1}{1.25} = \dfrac{P}{Q} \cdot (1-r)\\\\[/tex]
Eliminate [tex]\displaystyle {\dfrac{P}{Q}}[/tex] common factor from both sides to get
[tex]\dfrac{1}{1.25} = 1- r[/tex]
[tex]\dfrac{1}{1.25} = 0.8\\\\[/tex]
So we get
[tex]1 - r = 0.8\\\\\implies r = 1 - 0.8 = 0.2\\\\[/tex]
0.2 works out to 0.2 x 100 = 20%
So for Sadia's idea to have the same value as Jack's idea, the price should be reduced by 20%
How would you check values for x and y after solving linear equations in x and y?
Answers:
1. substitute the x and y values into the original equations
2. divide the x and y values into the original equations
3. cross-multiply the x and y values by the original equations
4. subtract the x and y values from the original equations
help me solve this equation
The area of the shaded portion is 6x^2
How to determine this?
The area of the shaded portion = Area of big rectangle - Area of small rectangle.
To get the area of big rectangle = L * B
A = 2x * 4x
A = 8x^2
To get area of small rectangle = L * B
A = 2x * x
A = 2x^2
To get the area of shaded portion ,
= 8x^2 - 2x^2
= 6X^2
Read more about Rectangle
https://brainly.in/question/35168519
#SPJ1
find the value of x . round to the nearest tenth 15° -2- 70°
The value of x, given the triangle, the length of the side and the angle, would be
How to find the value x ?The angle given is 23 degrees and the sides given are 15 and x. These two sides are the hypotenuse and the opposite sides which means that the operation to be used is Sin.
The value of x would therefore be :
Sin ( angle ) = Opposite / Hypotenuse
Sin ( 23 ) = x / 15
x = 15 x Sin ( 23 )
The value of x is:
x = 15 x Sin ( 23 )
x = 5. 86
x = 5. 9 units
Find out more on values at https://brainly.com/question/15823430
#SPJ1
In a normal distribution the mean and the __ are equal
In a normal distribution, the mean and the 'median' are equal.
In a normal distribution, the mean represents the central tendency of the data, while the median represents the middle value. In a perfectly symmetrical normal distribution, the mean and median are exactly the same value. This is because the normal distribution is a bell-shaped curve that is symmetric around the mean. However, in skewed distributions, the mean and median can differ, with the mean being pulled towards the tail of the distribution. Overall, the equality of the mean and median in a normal distribution is a reflection of the symmetry of the data.
You can learn more about median at
https://brainly.com/question/26151333
#SPJ4
Help me please
Choose all that are correct
A.Random samples from the same population will vary from sample to sample
B.Values of a sample statistic of different random samples of the same size from the same population will be the same
C.As the sample size increases, the sample distribution more closely resembles the population distribution.
D.if a random sample is chosen from a population with a large cluster of points at the maximum, the sample is likely to have at least one element near the maximum.
The solution is, Option a
Stratified random sample
What is random sample?In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.
here, we have,
Explanation:
(a) In stratified random sampling, a division of the population occurs in such a way that a population is stratified in different small groups or strata with common traits and same proportion both in population and sample. this type of sample so formed is known as stratified random sample.
(b) Simple random Sample:
This sample is formed by the random and unbiased selection of individual that represents the population.
(c) Population:
The entire set of individuals with certain specific characteristics represents a population whereas a sample is drawn out of the population and can be referred to as the subset of the population.
(d) Cluster Sample:
In this, separate sample groups are formed known as clusters, here sampling of random clusters take place.
To learn more on random sample click:
https://brainly.com/question/13934398
#SPJ9
Which expression is NOT equal to 125?
5(5^3/2/5)^2
(5^3/5^4)^-3
5^-2/5^-5
5(5^5/5^3)
One hundred people were asked about their favorite sport.
The statement that best describes the two - way frequency table is b. More females like soccer.
How to find the correct statement ?The number of females who like soccer are 31 females out of a total of fifty females who were interviewed.
This means that the number of females who like basketball are :
= 50 - 31 females for soccer
= 19 females
31 females like soccer while 19 females like basketball which shows that more females prefer soccer to basketball.
Find out more on frequency tables at https://brainly.com/question/16148316
#SPJ1
For nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F. Which equation can be used to find the maximum and minimum temperatures at which nitrogen is a liquid, x?
The equation that can be used to find the maximum and minimum temperatures is
|x +
| =
.
Answer:
its b
Step-by-step explanation:
help with question 24 please
Answer:
Midpoint M (2,5)
S (3,2)
R (x,y) {we will find values for x and y}
(x + 3) / 2 = 2 and (y + 2) /2 = 5
x + 3 = 4 and y + 2 = 10
x = 4-3 and y = 10-2
x = 1 and y = 8
Therefore, coordinates of R (1,8)
what do i do if there is a word problem with x but there isnt a number for x
You might need to utilise algebra to answer for the variable x in a word problem if there isn't a particular number provided for it.
Create an equation involving x using the information provided.
For instance, if the question is, "What is the value of x if x is 5 more than twice y and y is 3?" you may write up an equation like this:
x = 5 + 2y
x = 5 + 2(3) (3) (Replace y = 3)
x = 11
By changing the supplied value of y, you can answer for x in this situation by first solving the ensuing equation.
You might need to utilise many equations and algebraic techniques like substitution, elimination, or graphing to solve for x if the issue is more complicated. It could be beneficial to divide the problem into smaller steps and work through each step methodically if you are unclear of how to proceed.
To know more about word problem with x refer to:
brainly.com/question/21405634
#SPJ4
The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.
a. 10.6%
b. 89.4%
c. 39.4%
d. 78.8%
e. 68.27%
write the equations from word form.
The transformed functions is
a) The absolute value function reflected across the x axis and shifted up 2 units is y₁ = -| x₁ | + 2
b) The absolute value function that is shifted left 3 units and is compressed by a third is y₂ = ( 1/3 ) | x₂ + 3 |
c) The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃ = -5 | x₃ + 4 | + 6
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
a) The absolute value function reflected across the x axis and shifted up 2 units is y₁
The absolute value function is y₁ = | x₁ |
when reflected over x axis , the new function is
y₁ = - | x |
when shifted up 2 units ,
y₁ = -| x₁ | + 2
b)The absolute value function that is shifted left 3 units and is compressed by a third is y₂
The absolute value function is y₂ = | x₂ |
when shifted left 3 units ,
y₂ = | x₂ + 3 |
when compressed by a third , the new function is
y₂ = ( 1/3 ) | x₂ + 3 |
c)The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃
The absolute value function is y₃ = | x₃ |
when reflected across the x axis ,
y₃ = - | x₃ |
when stretched vertically by 5 units ,
y₃ = - 5 | x₃ |
when shifted 4 units left ,
y₃ = - 5 | x₃ + 4 |
when shifted 6 units up ,
y₃ = -5 | x₃ + 4 | + 6
Hence , the transformation of functions are solved
To learn more about transformation of functions click :
https://brainly.com/question/26896273
#SPJ1
In the country of Enigmia the postage charge for sending a letter is calculated according to the
following formula:
20 cents per 50 square centimetres of envelope area plus 32 cents per 40 grams of weight.
All measurements of area and weight are rounded up to the next multiples of 50 square
centimetres and 40 grams before calculation.
Jennifer has a letter weighing 125 grams in a 20 cm by 12 cm rectangular envelope that she
wants to send.
What will the postage charge be for Jennifer's letter?
I
Answer:
$2.12
Step-by-step explanation:
First, let's find the area of Jennifer's envelope: 20 cm x 12 cm = 240 square cm.
Since the area needs to be rounded up to the next multiple of 50 square cm, we will round up 240 square cm to 250 square cm.
Next, let's round up the weight of the letter to the next multiple of 40 grams: 125 grams rounded up to 140 grams.
Now that we have the rounded up values for both weight and area, we can use the formula to find the postage charge:
20 cents per 50 square cm x (250 square cm ÷ 50) = 100 cents
32 cents per 40 grams x (140 grams ÷ 40) = 112 cents
So the total postage charge will be 100 cents + 112 cents = 212 cents = $2.12.
Therefore, the postage charge for Jennifer's letter will be $2.12.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
solve the systems of equations using elimination
2x-7y=-13
8x-7y=11
Answer:
( [tex]-\frac{1}{3}[/tex] , [tex]-\frac{41}{21}[/tex] )
Step-by-step explanation:
Determine if events A and B are independent.
P(A)=1/5, P(B)=7/20, P(A and B)= 7/100. The events A and B are independent.
What is independent probability?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).
1) P(A)=1/5, P(B)=7/20, P(A and B)= 7/100
Here, P(A and B)= P(A)×P(B)
= 1/5 × 7/20
= 7/100
So, the events A and B are independent.
2) P(A)=13/20, P(B)=13/20, P(A and B)= 169/400
Here, P(A and B)= P(A)×P(B)
= 13/20 × 13/20
= 169/400
So, the events A and B are independent.
3) P(A)=7/10, P(B)=2/5, P(A and B)= 21/100
Here, P(A and B)= P(A)×P(B)
= 7/10 × 2/5
= 14/50
So, the events A and B are not independent.
2) P(A)=1/5, P(B)=1/5, P(A and B)= 1/25
Here, P(A and B)= P(A)×P(B)
= 1/5 × 1/5
= 1/25
So, the events A and B are independent.
Therefore, options 1, 2 and 4 are correct answers.
Learn more about the independent probability here:
https://brainly.com/question/27987662.
#SPJ1
The Martinez family just bought 6 crates of eggs, and each crate had 12 eggs. The family already had 9eggs in their refrigerator. How many eggs do they have now?
The Martinez family just bought 6 crates of eggs, and each crate had 12 eggs. The family already had 9 eggs in their refrigerator. Total number of eggs they have now is 81.
The problem states that the Martinez family bought 6 crates of eggs, and each crate had 12 eggs. So, we can start by multiplying the number of crates by the number of eggs per crate to find out how many eggs they bought in total:
6 crates x 12 eggs/crate = 72 eggs
This tells us that the family now has 72 eggs. However, the problem also states that the family already had 9 eggs in their refrigerator. To find out how many eggs they have now in total, we need to add the number of eggs they bought to the number of eggs they already had:
72 eggs + 9 eggs = 81 eggs
So the answer is that the Martinez family now has a total of 81 eggs.
To learn more about arithmetics click on,
https://brainly.com/question/14856472
#SPJ4
A.seqn T5 = 20, T₂² = T₁ T4 Find the order of the 1st term whose value is greater than 106.
The order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].
How did we get the value?Using the given information, we can find the common ratio of the geometric sequence A.
First, we can use the equation T₂² = T₁ T4 to find T4. Substituting n = 4, we get:
T₂² = T₁ T4
20² = T₁ T4
T4 = 400/T₁
Next, we can use the equation T5 = 20 to find T₁r⁴:
T5 = T₁r⁴
20 = T₁r⁴
We can now substitute T4 in terms of T₁ in the equation above:
20 = T₁r⁴
20 = T₁(400/T₁)r⁴
20 = 400r⁴
r⁴ = 1/20
Therefore, the common ratio r = (1/20)^(1/4) = 0.5.
To find the order of the first term whose value is greater than 106, we can use the formula for the nth term of a geometric sequence:
Tn = T₁r^(n-1)
We want to find the smallest value of n such that Tn > 106. Substituting r = 0.5 and rearranging, we get:
T₁(0.5)^(n-1) > 106
T₁ > 212(0.5)^(1-n)
Since T₁ > 0, we can take the logarithm base 0.5 of both sides:
log(0.5)(T₁) < log(0.5)(212) + (n-1)
Solving for n, we get:
n > 1 + [log(0.5)(T₁) - log(0.5)(212)]
Therefore, the order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].
Note that the exact value of this order depends on the value of T₁, which was not given in the original problem statement.
learn more about geometric sequence:
https://brainly.com/question/1509142
#SPJ1
the flashlight batteries produced by one of the northern manufacturers are known to have an average life of 60 hours with a standard deviation of 4 hours. assuming that the this phenomenon is not normally distributed (ie not symmetric) please answer the following questions: a. at least what percentage of flashlights will have a life of 54 to 66 hours? b. at least what percentage of the batteries will have a life of 52 to 68 hours? c. determine an interval for the batteries' lives that will be true for at least 80% of the batteries.
a) The percentage of flashlights that have a life of 55 to 65 is about 36%
b) The percentage of the batteries that have a life of 52 to 68 hours is about 75%.
Probability Under Normal Distribution:Standard normal distribution is a type of continuous distribution with a mean of zero and standard deviation of one. The random variables are standardized into z scores using z score formula.
a) The Chebyshev's theorem states that; for sample or population, percentage (p) of values are contained within two, three or more standard deviations within the mean, provided that the values of k is greater than 1:
P(%) = [tex]1-\frac{1}{k^2}[/tex]
Calculate the value of k:
[tex]k =\frac{65-60}{4}=1.25[/tex]
The percentage is calculated as;
p(%) = [tex]1-\frac{1}{1.25^2}[/tex] = 36%
The percentage of flashlights that have a life of 55 to 65 is about 36%
b) k = [tex]\frac{68-60}{4}=2[/tex]
p(%) = [tex]1-\frac{1}{2^2}[/tex] = 75%
The percentage of the batteries that have a life of 52 to 68 hours is about 75%.
Learn more about Chebyshev's theorem at:
https://brainly.com/question/30584845
#SPJ4
Gina Wilson unit 5 : homework 6: Slope-Intercept Form
The slope-intercept form of the equation of the line is y = x + 6.
What is an equation of the line?A linear equation with a degree of one is referred to as an equation of the line. Two variables, x, and y, are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.
The equation of the line's general form is:
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The formula for calculating the line's slope is
Slope = ( 6 - 4) / ( 2 - 0)
Slope = 1
The y-intercept will be calculated as:-
y = mx + c
y = x +c
6 = c
The equation of the line can be written as:-
y = x + 6
To know more about an equation of the line follow
https://brainly.com/question/18831322
#SPJ9
Three times the quantity of a number increased by 4 is -9. Write the equation and solve
The value of the number is -13/3
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of arithmetic operations such as subtraction, multiplication, division, addition, bracket and parentheses.
These expressions are also made up of variables, terms, coefficients, constants and factors.
From the information given, we have that;
The number = x
3x + 4 = -9
collect like terms
3x = -9 - 4
subtract the like terms
3x = -13
Make 'x' the subject
x = -13/3
Hence, the value is -13/3
Learn about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
Please help i’ll give brainliest
Answer: 4.5
Step-by-step explanation:
2/3 thrids subtract 1/4
Answer: 5/12
Step-by-step explanation:
2/3 - 1/4 = 5/12
Answer:
1.75
Step-by-step explanation:
Pls help i’m desperate
Answer: 5/13
Step-by-step explanation: cos is adj/hyp giving us a 12 for adj and 13 for hyp. Tan is Opp/Adj confirming 12 is the adj and 5 being the Opp. Sin is Opp/Hyp giving us 5/13. Hope it helps
If 3 garbage trucks can collect the trash of 24 homes in a day, how many trucks are needed to collect in 72 houses?
Answer:
9
Step-by-step explanation:
72/24 = 3
72 is 3 times 24, so you need 3 times as many garbage trucks.
Answer: 9
Use the Pythagorean Theorem to find the distance between points F and C.
A. 2 √3
B. √41
C. 4 √3
D. 3 √5
Joshua invested $97,000 in an account paying an interest rate of 6% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 8 years?
The required after 8 years, the investment will be worth approximately $156,753.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Amount = principal[1 + r/n]ⁿᵃ
Principal = P rate= r Time =a , n = compounding frequency
Here,
To calculate the future value of Joshua's investment after 8 years with an interest rate of 6% compounded daily, we can use the formula:
In this case, P = $97,000, r = 6% = 0.06, n = 365 (since the interest is compounded daily), and t = 8.
So, we have:
[tex]A = $97,000 \times (1 + 0.06/365)^{365 * 8}[/tex]
A = $195,239.00
Therefore, after 8 years, the investment will be worth approximately $156,753.
Learn more about compound interest here:
https://brainly.com/question/14295570
#SPJ9
a Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
y = 2/5x +24/5, is the equation which represents a line that passes through (-2, 4) and has a slope of 2/5.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = 2/5 x +b
Substitute the point (-2,4) into the equation and solve for b
4 = 2/5(-2)+b
4 = -4/5 +b
Add 4/5 to each side
20/5 +4/5 = b
24/5 = b
Hence, y = 2/5x +24/5, is the equation which represents a line that passes through (-2, 4) and has a slope of 2/5.
To learn more on Equation 0f Straight-Line click:
https://brainly.com/question/30216543
#SPJ9
For some value of b, the expression 3(5x - 1) + b(2x - 7) is a constant. What is the constant?
The expression is constant for b = -7.5, and the constant is 49.5.
What is a mathematical Expression?A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that, The expression 3(5x - 1) + b(2x - 7) is constant
It means the expression doesn't consist of a variable. So, we need to find the 'b' such that the variable 'x' need to be eliminated.
The co-efficient of the 'x' should be '0'.
3(5x - 1) + b(2x - 7)
= 15x - 3 + 2bx - 7b
= (15 + 2b)x - 3 - 7b
Now, 15 + 2b = 0
2b = -15
b = -7.5
On substituting the value of 'b' in the expression,
= -3 - 7 * (-7.5)
= 52.5 - 3
= 49.5
Therefore, The expression is constant for b = -7.5, and the constant is 49.5
To learn more about Mathematical Expressions, refer to the link below:
brainly.com/question/1859113
#SPJ1
what is the probability of picking a red ball from the bag and getting heads upon flipping a fair coin? a.) 3 over 16 b.) 7 over 8 c.) 3 over 4 d.) 1 over 8
the probability of picking a red ball from the bag and getting heads upon flipping a fair coin is 1/2 * 1/2 = 1/8.
There are two independent events, and therefore the probability of both occurring is calculated by multiplying the probability of each event. The probability of picking a red ball from the bag is 1/2, and the probability of getting heads upon flipping a fair coin is also 1/2. Therefore, the probability of picking a red ball from the bag and getting heads upon flipping a fair coin is 1/2 * 1/2 = 1/8.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
#5
CONNECTING CONCEPTS You use 94 inches of plastic to frame the perimeter of a kite. One side of the kite has a
length of 18 inches. Find the length of each of the three remaining sides in order from least to greatest.
Length: in.,in., in
The length of the tree remaining sides are 18 inches, 29 inches and 29 inches.
What are the lengths of the remaining sides?A kite is an object with four sides. It length of the two adjacent sides are of equal length. No pair of sides in a kite are parallel. The perimeter of a kite is the sum of the length of the four sides of the kite.
Perimeter of a kite = 2( a + b)
94 = 2(18 + b)
94 / 2 = 18 + b
47 = 18 + b
b = 47 - 18
b = 29 inches
To learn more about kites, please check: https://brainly.com/question/29070896
#SPJ1
