Multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d.
The impact of multiplying all values in a normally distributed random sample and population by 2 on Cohen's d is an increase in effect size. Cohen's d measures the degree of difference between two sets of scores, calculated by dividing the difference between the two means by the pooled standard deviation. Therefore, when values are multiplied by 2, the means increase, leading to an increase in effect size as measured by Cohen's d.
In addition, multiplying values by 2 also increases the magnitude of the standard deviation, which is a measure of spread. When the standard deviation is larger, it requires a larger mean difference for Cohen's d to register a significant effect. Therefore, by increasing the standard deviation, the effect size measure will increase.
To summarize, multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d. This is because multiplying values by 2 increases both the mean and the standard deviation, which results in a larger mean difference and a larger standard deviation, respectively. Consequently, the effect size measure increases.
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Brooke played her flute for 3/4 hour each day for 5 days and for 1/2 hour each day for 2 days how many hours did she play it in all
⇒To be able to answer this question to find how many hours Brooke played his flute for 5 days we ought to first convert the 5 days to hours.
⇒There are 24 hours in a day this means that in 5 days we have =24×5
=120 hours.
⇒We have 120 hours in 5 days , it is said that Brooke played her flute [tex]\frac{3}{4}[/tex],
Meaning she played the flute [tex]\frac{3}{4}[/tex] hours of 120 hours which is equal
[tex]\frac{3}{4} *\frac{120}{1}\\=90[/tex]
For 5 days Brooke played her flute 90 hours
⇒The next step is to convert the 2 days to hours which is equivalent to 24×2
=48 hours are in 2 days, it is said Brooke played the flute [tex]\frac{1}{2}[/tex] hours of 2 days. This simply is equivalent to
[tex]\frac{1}{2} *\frac{48}{1} \\=24[/tex]
⇒For 2 days Brooke played the flute 24 hours,
The total number of hours she played it all is =Number of hours she played it in 5 days+ Number of hours she played it in 2 days.
=90+24
=114
⇒In total of these 7 days she played the flute for 114 hours
The price of a new car is $28,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent. )
(a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 60 months?
36 months=$
60 months=$
(b) What will the interest charges be if she elects the 36-month plan? The 60-month plan?
36-month plan =$
60-month plan=$
(a) The monthly payment for a 36-month plan is $704.41, and for a 60-month plan is $488.08.
(b) The interest charges for the 36-month plan are $1,459.07, and for the 60-month plan are $3,369.10.
For a)
To calculate the monthly payment for a car loan, we need to use the formula for monthly payments:
M = [tex]P[r(1+r)^n / ((1+r)^n - 1)][/tex]
where M is the monthly payment, P is the principal (the loan amount), r is the monthly interest rate (the annual interest rate divided by 12), and n is the number of months over which the loan is to be repaid.
For the 36-month plan, the principal is 75% of $28,000, or $21,000. The monthly interest rate is 6% / 12, or 0.005. The number of months is 36. Plugging in these values, we get:
M = $[tex]21,000[0.005(1+0.005)^{36} / ((1+0.005)^{36} - 1)][/tex] = $704.41
For the 60-month plan, the principal, monthly interest rate, and a number of months are the same, but we change the number of months to 60:
M = $21,000[0.005[tex](1+0.005)^{60[/tex] / ([tex](1+0.005)^{60[/tex] - 1)] = $488.08
Therefore, the monthly payment for a 36-month plan is $704.41, and for a 60-month program is $488.08.
For b)
To calculate the total interest charges for the loan, we need to subtract the principal (the amount of the loan) from the total amount paid and round to the nearest cent:
For the 36-month plan, the total amount paid is $25,459.07 (36 x $704.41), so the interest charges are:
$25,459.07 - $21,000 = $4,459.07, rounded to $1,459.07
For the 60-month plan, the total amount paid is $29,284.80 (60 x $488.08), so the interest charges are:
$29,284.80 - $21,000 = $8,284.80, rounded to $3,369.10
Therefore, the interest charges for the 36-month plan are $1,459.07, and the 60-month plan are $3,369.10.
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the quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is .
The quantity (in pounds) of gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q(p) = 1000 - 40p.
In science and engineering, a quantity is something that has a magnitude or size that may be expressed in numerical terms and that is associated with a unit of measurement. For example, a distance is a quantity with a size expressed in units of length.
A physical quantity that has a directional aspect is referred to as a vector. A quantity is any measurable amount or property of something, typically consisting of a value and a unit of measurement, such as length, weight, volume, or time.
it's also used to refer to a particular sum or amount of something that is counted or measured, such as a number of things or the total amount of a substance.
Therefore, The formula for finding the quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q(p) = 1000 - 40p.
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PLEASE HELP ASAP!!!!!!
Answer:
The greatest common factor (GCF) of -16x^2 - 6x^4 is 2x^2.
To find the GCF, we can factor out the common factors of the two terms. In this case, both terms have a factor of 2 and a factor of x^2.
-16x^2 - 6x^4 = 2x^2(-8 - 3x^2)
So the GCF is 2x^2.
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 10. There are two dots above 6, 7, and 9. There are three dots above 8.
Which of the following is the best measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 8.
The median is the best measure of center, and it equals 7.3.
The mean is the best measure of center, and it equals 7.3.
The median is the best measure of center, and it equals 8.
The best measure of center for the data is Option D: The median, and it equals 8.
What is median?
In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.
The best measure of center for this data is the median because the data is skewed and has outliers.
The median is the middle value when the data is arranged in order, which is less sensitive to outliers than the mean.
To find the median, we need to count the number of data points and find the middle value -
1, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9
We have 11 data points, so the median is the 6th value -
Median = 8
Therefore, the best measure of center for the data is the median, and its value is 8.
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math help needed detailed explanation
The percentage of 8th graders who send more than 50 texts is 56.15%
How to find the percentage?Here we want to find the percentage of eight grades who send more than 50 texts, and to get that we need to use the values in the table.
The formula for that percentage is:
P = 100%*(number that send more than 50 texts)/(total number)
On the table we can see that the total number of 8th gradesr is 130, and the number that send more than 50 messages is 73, then the percentage is:
P = 100%*(73/130)
P = 56.15%
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Which equations can be used to solve for y, the length of the room? Select three options.
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
Which equation has the same solution as x ^2 −12x−16=−2?
Please help!!!
Question below!!
1. Dilation is the process of enlarging or shrinking a figure or shape by a scale factor.
2. Reflection is the process of flipping a figure or shape over an axis. In this example, A'B'C' is reflected over the x-axis.
3. A pair of triangles that are congruent are triangles with the same size and shape.
4. A pair of triangles that are similar are triangles with the same shape but different sizes.
What is dilation?Dilation is a mathematical operation used to expand or contract a shape. It involves multiplying every point in the shape by a given scale factor. The scale factor determines how much the shape is changed. The result is a line segment twice the length of the original.
1. In this example, triangle ABC is dilated by a factor of 2 about the point (-1,4). This means that all points on the triangle ABC will be multiplied by the scale factor 2. So the coordinates of point A will become (N-1,6) x 2 = (-2,12), point B will become (-4,5) x 2 = (-8,10) and point C will become (-4,0) x 2 = (-8,0). The new triangle created by the dilation is A'B'C'.
2. This means that the x-coordinates of the points remain the same, but the y-coordinates are multiplied by -1. So the coordinates of point A' will become (-2,12) x -1 = (-2,-12), point B' will become (-8,10) x -1 = (-8,-10) and point C' will become (-8,0) x -1 = (-8,0). The new triangle created by the reflection is ABC'.
3. A pair of triangles that are congruent are triangles with the same size and shape. In other words, the sides and angles of the two triangles are all equal.
4. A pair of triangles that are similar are triangles with the same shape but different sizes. In other words, the angles of the two triangles are equal, but the sides are not necessarily the same length.
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if 80% of all marketing personnel are extroverted, then what is the probability that 10 or more are extroverts at a party of 15 marketing personnel
The probability that 10 or more of 15 marketing personnel are extroverts is 0.719.
Since 80% of all marketing personnel are extroverts, the probability of any single marketing personnel being an extrovert is 0.8. The probability that 10 or more marketing personnel at the party of 15 are extroverts can be calculated using the Binomial Distribution formula:
P(X>=10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]
P(X>=10) = 1 - [15C0*0.80*0.215 + 15C1*0.81*0.214 + 15C2*0.82*0.213 + 15C3*0.83*0.212 + 15C4*0.84*0.211 + 15C5*0.85*0.210 + 15C6*0.86*0.29 + 15C7*0.87*0.28 + 15C8*0.88*0.27 + 15C9*0.89*0.26]
P(X>=10) = 0.719
Therefore, 0.79 is the probability that 10 or more of the 15 marketing personnel at the party are extroverts.
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Solve for z.
z² = 16
Enter your answer in the box.
Answer: 4
Step-by-step explanation:
z^2 = 16
Since z is squared and we know that it equals 16. Take the square root of 16 which is 4.
4 x 4 = 16
Answer:
Step-by-step explanation:
16
I need the answer to this please hurry
Answer: 240 is your answer for 100% of the e-book
Step-by-step explanation: so if we look at the given facts, 180 is 75% of the e-book, now take this and divide 180 by 3, and you get 25% of the e-book (60 is 25%) so if we factor that back into the 180 75%, we now get 240 at 100% of the e-book read
A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
Red
Blue
Green
Yellow
Purple
14
6
12
4
16
Based on these results, express the probability that the next spin will land on purple
as a fraction in simplest form.
Answer:
4/13
Step-by-step explanation:
total = 14 + 6 + 12 + 4 + 16 = 52
purple = 16
p(purple) = 16/52 = 4/13
i thought of a number. four times the number increased by 30 equals 70 decreased by the number. what was my number?
Answer:
number is 8
Step-by-step explanation:
let n be the number then 4 times the number is 4n and increased by 30 means adding 30 to it , that is 4n + 30
70 decreased by the number means subtracting n fro 70 , 70 - n
then
4n + 30 = 70 - n ( add n to both sides )
5n + 30 = 70 ( subtract 30 from both sides )
5n = 40 ( divide both sides by 5 )
n = 8
Write the integers in order from least to greatest. -6, -2, 3, -9, 2, -4
Answer:
-9, -6, -4, -2, 2, 3
Step-by-step explanation:
the higher the negative the lower it is
Pls how do I solve
b) log₂ (7y-1)=3+log₂ (y-1).
Step-by-step explanation:
Put the logs on the same side.
[tex] log_{2}(7y - 1) - log_{2}(y - 1) = 3[/tex]
Using log rules, whenever you separate two logs using subtraction and they have the same base, we can write them as one log where they are a rational function
[tex] log_{2}( \frac{7y - 1}{y - 1} ) = 3[/tex]
Let both of these expression be the power of a exponent with base 2.
[tex]2 {}^{ log_{2}( \frac{7y - 1}{y - 1} ) } = 2 {}^{3} [/tex]
The base 2 and log base 2 cancel out
[tex] \frac{7y - 1}{y - 1} = 8[/tex]
When y =1, we will get undefined so y cannot be 1
However, multiply both sides by y-1
[tex]7y - 1 = 8(y - 1)[/tex]
[tex]7y - 1 = 8y - 8[/tex]
[tex]7 = y[/tex]
I need help with question 1
Hy bro in which class you are?
suppose that you have 9 green cards and 5 yellow cards. the cards are well shuffled. you randomly draw two cards without replacement. what is the probability of at least one being green
The probability of at least one card being green is 0.807. Here's how to calculate it: Let's define the event G as getting a green card and the event Y as getting a yellow card.
The probability of getting a green card on the first draw is: P(G1) = 9/14
The probability of getting a yellow card on the first draw is: P(Y1) = 5/14
The probability of getting a green card on the second draw, given that the first card was yellow, is: P(G2 | Y1) = 9/13
The probability of getting a green card on the second draw, given that the first card was green, is: P(G2 | G1) = 8/13
The probability of getting a yellow card on the second draw, given that the first card was green, is: P(Y2 | G1) = 5/13
The probability of getting a yellow card on the second draw, given that the first card was yellow, is: P(Y2 | Y1) = 4/13
To calculate the probability of at least one card being green, we need to add up the probabilities of getting a green card on the first draw and a yellow card on the second draw, and the probabilities of getting a green card on the second draw given that the first card was yellow, and getting a green card on the second draw given that the first card was green:
P(at least one green card) = P(G1 and Y2) + P(G2 | Y1)
P(Y1 and G2 | G1) + P(G1 and G2) = 9/14 * 5/13 + 5/14 * 9/13 + 8/14 * 5/13 + 9/14 * 8/13 = 45/182 + 45/182 + 40/182 + 72/182 = 0.807
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the mean test score is 80, and the standard deviation is 5. what is the percentage of students scoring 83 or more in the exam?
Answer:
27.43% of the students scored 83 or more in the exam.
Step-by-step explanation:
We can use the Z-score formula to find the percentage of students scoring 83 or more:
Z = (X - μ) / σ
where X is the test score, μ is the mean test score, and σ is the standard deviation.
Substituting the given values, we get:
Z = (83 - 80) / 5 = 0.6
Using a Z-score table or calculator, we can find the percentage of students scoring 83 or more:
P(Z > 0.6) = 1 - P(Z < 0.6) = 1 - 0.7257 ≈ 0.274
27.43% of the students scored 83 or more in the exam.
OR. USING PROPERTIES OF NORMAL DISTRIBUTION
convert the raw score of 83 into a standardized score, also known as a z-score.
The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
x = raw score
μ = mean
σ = standard deviation
Substituting the values given in the question, we get:
z = (83 - 80) / 5
z = 0.6
This means that a student who scored 83 on the exam has a z-score of 0.6.
Next, we need to find the area under the normal distribution curve to the right of this z-score. We can use a standard normal distribution table or calculator for this purpose.
Using a standard normal distribution table, we find that the area to the right of z = 0.6 is approximately 0.2743.
Therefore, the percentage of students scoring 83 or more in the exam is approximately:
0.2743 x 100% = 27.43%
So, about 27.43% of students scored 83 or higher on the exam.
What is i 48 equal to? Show steps how you get your answer please.
Answer: Bro Didnt give any context dont report if wrong
Step-by-step explanation:
i is the imaginary unit, which is defined as the square root of -1.
To find the value of i^48, we can use the fact that i^2 = -1, and simplify the expression as follows:
i^48 = (i^2)^24
Since i^2 = -1, we can substitute -1 in the above expression:
(i^2)^24 = (-1)^24
Any non-zero number raised to an even power is positive, so (-1)^24 = 1. Therefore:
i^48 = 1
Hence, i^48 is equal to 1.
A box contains 4 rows of eggs with 12 eggs in each row .if these eggs are arranged in 6 rows ,how many eggs will be in each row?
Answer:
8
Step-by-step explanation:
The box contains a total of 4 x 12 = 48 eggs.
If we arrange these eggs in 6 rows, we need to divide the total number of eggs by 6:
48 ÷ 6 = 8
Therefore, there will be 8 eggs in each row.
8 2.2 Trigonometric Functions of Non-Acute Angles
Find exact values of the six trigonometric functions for each angle. Rationalize
denominators when applicable.
1. 135°
3.-690°
5. 225°
7. 1380°
sin 135°=-√2/2, cos 135° = -√2/2, tan 135° = -1, csc 135°= -√2, sec 135°= -√2, cot 135° = -1; sin (-690°) = -1/2, cos (-690°) =√3/2, tan (-690°) = -√3/3, csc (-690°) = -2, sec (-690°) = 2/√3, cot (-690°) = -√3; sin 225° = -√2/2, cos 225° = -√2/2, tan 225° = 1, csc 225° =-√2, sec 225° = -√2, cot 225° =-1; sin 1380° = -√3/2, cos 1380° = 1/2, tan 1380° = -√3, csc 1380° = -2/√3, sec 1380° = 2, cot 1380° =-1/√3.
Describe Trigonometric Ratios?Trigonometric ratios are mathematical functions used to relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.
To use these ratios, we typically label the sides of the right triangle relative to the angle we are interested in. The hypotenuse is always the side opposite the right angle and is labeled with the letter "c." The two other sides are labeled relative to the angle we are interested in: the side adjacent to the angle is labeled with the letter "a," and the side opposite the angle is labeled with the letter "b."
The sine of an angle is defined as the ratio of the length of the side opposite the angle (b) to the length of the hypotenuse (c): sin(angle) = b/c.
The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle (a) to the length of the hypotenuse (c): cos(angle) = a/c.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle (b) to the length of the side adjacent to the angle (a): tan(angle) = b/a.
To find the exact values of the six trigonometric functions for each angle, we need to first determine the reference angle, which is the acute angle formed between the terminal side of the angle and the x-axis. Then, we can use the properties of the trigonometric functions in each quadrant to determine the sign and value of each function.
135°
Reference angle = 45° (since 135° is in the second quadrant)
sin 135° = -sin 45° = -√2/2
cos 135° = -cos 45° = -√2/2
tan 135° = -tan 45° = -1
csc 135° = -csc 45° = -√2
sec 135° = -sec 45° = -√2
cot 135° = -cot 45° = -1
-690°
Reference angle = 30° (since -690° is in the fourth quadrant)
sin (-690°) = -sin 30° = -1/2
cos (-690°) = cos 30° = √3/2
tan (-690°) = -tan 30° = -√3/3
csc (-690°) = -csc 30° = -2
sec (-690°) = sec 30° = 2/√3
cot (-690°) = -cot 30° = -√3
225°
Reference angle = 45° (since 225° is in the third quadrant)
sin 225° = -sin 45° = -√2/2
cos 225° = -cos 45° = -√2/2
tan 225° = -tan 45° = 1
csc 225° = -csc 45° = -√2
sec 225° = -sec 45° = -√2
cot 225° = -cot 45° = -1
1380°
Reference angle = 60° (since 1380° is in the second quadrant)
sin 1380° = -sin 60° = -√3/2
cos 1380° = cos 60° = 1/2
tan 1380° = -tan 60° = -√3
csc 1380° = -csc 60° = -2/√3
sec 1380° = sec 60° = 2
cot 1380° = -cot 60° = -1/√3
Note: In the calculations above, we rationalized denominators whenever applicable to obtain exact values.
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7(g−10h+4) please helpppppppppppp
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{7(g - 10h + 4)}[/tex]
[tex]\large\text{\underline{Distribute} \boxed{\text{7}} \underline{within the parentheses}:}[/tex]
[tex]\mathsf{= 7(g - 10h + 4)}[/tex]
[tex]\mathsf{= 7(g) + 7(-10h) + 7(4)}[/tex]
[tex]\mathsf{= 7g - 70h + 28}[/tex]
[tex]\large\text{We \boxed{\text{cannot}} do anything further because we do NOT have any \underline{like}}\\\large\text{\underline{terms}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\mathsf{7g - 70h + 28}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
HELP I’m struggling and it’s due today :,)) please help.
Will give brainliest :,,))))
Answer:
Step-by-step explanation:
4. a
x cannot be 0 because 2/0 cannot be calculated - we say that it is undefined.
b. x cannot be 1 as that would mke the denominator x - 1 = 0 which is undefined.
5 a. (9x - 5)(9x + 5)
b. (2x + 1)(x - 3).
6.
C. (x + 7)/3
7.
a. (-5, ∝)
b. (-∝, 2]
c.(-3, 7].
8.
y = kx
24 = 16k
k = 1.5
So, y = 1.5x
When x = 50
y = 1.5*50 = 75.
jenelle draws one from a standard deck of 52 cards. determine the probability of drawing either a two or a king? write your answer as a reduced fraction. answer
Answer:
2/13
Step-by-step explanation:
A standard deck of cards has four suits
Therefore there are four twos, one from each suit
There are also 4 kings, one from each suit
P(two) = 4 twos/52 cards = 4/ 52 = 1/13
PKing) = 4 kings/52 cards = 1/13
P(two or king) = P(two) + P(king)
= 1/13 + 1/3
= 2/13
a). A woman bought a bag of oranges at the cost of 50gp. She sold them at 60 gp each and made a profit of GHC 3. 05. all the oranges bought were sold, calculate: a)the number of oranges of in the bag. b) the cost price of the bag of oranges. c)the selling price of all the oranges d)percentage profit she made
Therefore , the solution of the given problem of percentage comes out to be earned 6.1% from the selling of the oranges.
What is percentage, exactly?In statistics, "a%" refers to a figure or a statistic that is expression as a percentage of 100. The letters "pct," "pct," and "pc" are also rare abbreviations. It is typically represented by the symbol "%," though. There are no indicators and a flat ratio to the overall amount. In reality, percentages are numbers because their sum almost always equals 100.
Here,
Let's suppose that the lady purchased x oranges.
She charged 60gp for each orange she sold, for a total of 60x gp.
She earned a profit of 3.05 GHC, making her overall profit
=> 3.05 GHC = 305p.
Her cost price (50gp) plus her profit (305p) would equal her total income (selling price), which would be 355gp.
=> 60x = 355
=> x = 355/60
=> x = 5.9167
She consequently purchased six bananas.
b) Since she paid 50gp for the container of oranges, their cost would be 50gp.
c) The total sale price of the oranges would be 360gp, or 60gp for each orange multiplied by 6.
d) She would have earned a profit of (profit/cost price) x 100%.
She made 305p, or 3.05 GHC, in earnings.
Her cost was 50gp, so
=> 6.1% = (3.05/50) * 100%.
She thus earned 6.1% from the selling of the oranges.
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a coffee distributor needs to mix a(n) kenya coffee blend that normally sells for $8.20 per pound with a breakfast coffee blend that normally sells for $14.00 per pound to create 10 pounds of a coffee that can sell for $9.36 per pound. how many pounds of each kind of coffee should they mix?
The coffee distributor should mix 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend to make 10 pounds of a coffee blend that can sell for $9.36 per pound.
We can use the idea of weighted averages to overcome this issue. Assume that 10 pounds of the desired blend require x pounds of Kenya coffee blend and y pounds of morning coffee blend.
The price of the Kenya coffee mix per pound is $8.20, while the price of the morning coffee blend per pound is $14.00. The required combination costs $9.36 per pound. On the basis of the weighted average, we can construct the following equation:
8.20x + 14.00y = 9.36(10) (10)
When we simplify this equation, we obtain:
8.20x + 14.00y = 93.60
Given that we are producing 10 pounds of the ideal blend, we also know that x + y = 10. To get the values of x and y, we can use substitution or elimination to solve this system of equations.
Use substitute now. We can find x from the second equation by solving in terms of y:
x = 10 - y
Substitute this into first equation, we get:
8.20(10 - y) + 14.00y = 93.60
82 - 8.20y + 14.00y = 93.60
5.80y = 11.60
y = 2
We obtain x = 8 by substituting y = 2 into x = 10 - y. Hence, to manufacture 10 pounds of a coffee mix that can be sold for $9.36 per pound, we'll need 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend.
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how long did it take lu chao to recite 67,890 digits of pi ?
Lu Chao recited 67,890 digits of pi in 24 hours and 4 minutes using the memory palace technique
Lu Chao, a Chinese engineer, set a new world record by reciting 67,890 digits of pi in 24 hours and 4 minutes on November 20, 2005. This achievement required an incredible amount of focus, memory, and mental discipline. Chao utilized a technique called the "memory palace," in which he associated each digit with a specific image and placed those images in a familiar location in his mind.
This allowed him to recall the digits in order with remarkable accuracy. Chao's achievement demonstrates the incredible potential of the human mind and the power of memory techniques to accomplish seemingly impossible feats.
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 33
and DC = 13, what is the length of BD in simplest radical form?
Answer:
The length of BD in its simplest radical form is [tex]\sf \sqrt{429}[/tex].
Step-by-step explanation:
Geometric Mean Theorem - Altitude RuleThe altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.
[tex]\boxed{\sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}}[/tex]
Given values (see attached diagram):
Altitude = BD = xSegment 1 = AD = 33Segment 2 = DC = 13To find the length of the altitude BD, substitute the values into the formula and solve for x:
[tex]\implies \sf \dfrac{BD}{AD}=\dfrac{DC}{BD}[/tex]
[tex]\implies \sf \dfrac{x}{33}=\dfrac{13}{x}[/tex]
[tex]\implies \sf x^2=429[/tex]
[tex]\implies \sf x=\sqrt{429}[/tex]
As the square root of 429 cannot be simplified any further, the length of BD in its simplest radical form is [tex]\sf \sqrt{429}[/tex].
If x represents the number of balls then write an expression for 4 less than 18 divided by the number of balls.