Answer: To find the point on the directed line segment that partitions it into a ratio of 4 to 5, we can use the formula for a point on a line given two endpoints and a ratio. The formula is:
(x, y) = (1 - t) * (x1, y1) + t * (x2, y2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and t is a value between 0 and 1 that determines the location of the point along the line.
In this case, (x1, y1) = (-1, -9) and (x2, y2) = (8, 9), and we want the point that partitions the line segment into a 4 to 5 ratio, so:
t = 4 / (4 + 5) = 4 / 9
Plugging in the values into the formula:
x = (1 - t) * x1 + t * x2 = (1 - 4/9) * (-1) + (4/9) * 8 = (5/9) * 8 - (4/9) * 1 = 44/9 - 4/9 = 40/9
y = (1 - t) * y1 + t * y2 = (1 - 4/9) * (-9) + (4/9) * 9 = (5/9) * 9 - (4/9) * (-9) = 45/9 + 36/9 = 81/9
So the point that partitions the line segment into a 4 to 5 ratio is (40/9, 81/9).
Step-by-step explanation:
At the end of the summer, a store marks down all the outdoor furniture 20%. A family bought 4 chairs that originally cost $100 each. How much was the cost of the 4 chairs?
Answer:
$320
------------------
Original price of 4 chairs:
100*4 = 400Cost after mark down by 20%:
400*(100 - 20)/100 = 400*0.8 = 320
QUIZ 4-2: PARALLEL LINES & TRANSVERSALS
Identify each angle pair, and tell whether each set is congruent or
supplementary.
1. Type:
or
2. Type:
or
3. Type:
supplementary?
supplementary?
or supplementary?
21 and 27
21 and 23
22 and 2
1. <1 and <7 are supplementary.
2. <1 and <3 are supplementary.
3. <2 and <6 are congruent angles.
What are Supplementary Angles and Congruent Angles?Supplementary angles are two angles that add up to 180 degrees. In other words, they are angles that "complete" each other, forming a straight line. If two angles are supplementary, they are said to be "supplementary to each other."
Congruent angles are angles that have the same measure. They are written with the symbol "≅" and are read as "is congruent to." Two angles are congruent if they have the same degree measure.
1. Angles 1 and 7 add up to 180 degrees, therefore, they are supplementary.
2. Also, angles 1 and 3 are supplementary.
3. Angles 2 and 6 are corresponding angles, therefore, they are congruent angles.
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You select a marble without looking and then put it back. If you do this 12 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?
Answer:
the answer is number of orange marble/number of times
which might be 1/12 because you didn't specify
How Many 2 Cups In Pound?
Converting 1 pound to 2 cups is mainly used for cooking and baking. One pound equals two cups.
Pound:
A pound is a unit of mass used to measure the weight of dry ingredients. It is expressed in "pounds" and equals 16 ounces in the traditional American system. On the other hand, there are two types of pounds used in England, the common American pound (avoirdupois pound) and the British imperial pound, which are slightly different from each other. So remember the pounds used in the recipe book you're working on.
Cups:
Cups are an important tool for measuring ingredients in the kitchen. It is mainly used for measuring the volume of liquid ingredients such as water, milk, butter, etc. or for measuring dry grain or powder ingredients such as coffee beans, chocolate chips, flour, sugar, etc.
There are two types of measuring cups:
Dry measuring cups and liquid measuring cups.Measuring cups are normally supplied with a printed weighing scale. We can fill the cup with ingredients according to this scale. Liquid measuring cups are usually made of a transparent material such as glass or plastic. This makes it easier to fill accurately.
According to the Question:
1 cup = ½ lb
To calculate how many pounds are in a given number of cups, you can do it with the following simple formula:
Pounds = Cups × ½
Or, Pounds = Cups × 0.5
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The equation, A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t, represents the amount of money earned on a compound interest savings account. What does the value 0.031 represent?
The value 0.031 represents the interest rate, which means the annual compounded interest rate is 3.1%.
The value 0.031 represents the interest rate, which means the annual compounded interest rate is 0.31%.
The value 0.031 represents the investment period, which means the investment is invested for 0.031 years.
The value 0.031 represents the investment period, which means the investment is invested for 3.1 years
In The equation, A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t, represents the amount of money earned on a compound interest savings account, A. The value 0.031 represents the interest rate, which means the annual compounded interest rate is 3.1%.
What is the compound interest equation?The general compound interest equation is given as:
Formula:
A = P(1 + r/n)^nt
A = final amount or future value
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Compounding interest involves computing interest on both the principal and the accumulated interest.
On the other hand, the simple interest method does not compute interest on accumulated interest.
Thus, the correct representation of the value 0.031 is the compound interest rate as 3.1%.
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In a lab, a substance was cooled by 18 °C over a period of 3 hours at a constant rate. What
was the change in temperature each hour?
The change in temperature each hour is 6 °C.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
In other words it compares 1 unit of some quantity with different amount of another quantity
Given that,
In a lab, a substance was cooled by 18 °C over a period of 3 hours at a constant rate.
Since the rate at which the substance is cooling down is constant,
Amount by which substance cooled down in 3 hours = 18 °C
Amount by which substance cooled down in 1 hour = 18 °C / 3 = 6 °C, which is the unit rate.
Hence the unit rate of the change in temperature is 6 °C per hour.
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Jacinta notices a pattern when she multiplies fractions. Her pattern is
written below.
When you multiply with
fractions, the product is less
than each of the two factors.
Is Jacinta's pattern correct for the fractions you worked with in Questions A
and B? Explain your reasoning.
When two positive fractions are multiplied the product is always less than the factors.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole. In mathematics, fraction is a number that is expressed as a proportion, as 1/2 or 2/3. The number on the bottom represents the total number of parts of one unit, while the number on the top is the portion of the unit being considered.
here,
Let's assume an example,
1 / 8 × 1 / 9 = 1 / 72
So as we see in the above example,
1 / 8 and 1/ 9 is a positive fractions and their product is less than their own factors.
Thus, when two positive fractions are multiplied the product is always less than the factors.
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Jacinta's pattern is correct for question A.
Jacinta's pattern is not correct for question B.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
Jacinta's:
Fractions are 1/3 and 1/5 (say).
Product.
= 1/3 x 1/5
= 1/15
Now,
1/15 < 1/3
1/15 < 1.5
For Question A:
We can assume that,
The fractions are 1/3 and 3/4.
Their product.
= (1/3) x (3/4)
= 3/12
= 1/4
1/4 < 1/3
1/4 < 3/4.
So,
Jacinta's pattern is correct.
For Question B.
The fractions are 2/5 and 4/7.
Their product.
= (2/5) x (4/7)
= 8/35
We see that,
8/35 < 2/5
8/35 > 4/7
So,
Jacinta's pattern is not correct.
Thus,
Jacinta's pattern is correct for question A.
Jacinta's pattern is not correct for question B.
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The complete question.
A) The two fractions are 1/3 and 3/4
B The two fractions are 2/5 and 5/7
I need some help please - The box plot shows the test scores of students in Mr. Lenard’s class. What is the most appropriate measure of center?
The most appropriate measure of center is median.
option B.
Which parameter is the most appropriate for the measure of center?
The choice of measure of center (i.e., the most appropriate way to summarize the "typical" value of a dataset) depends on the distribution of the data and the research question being addressed. In general, the most commonly used measures of center are the mean and the median.
The mean is the arithmetic average of a dataset, and is often used as the measure of center for datasets that follow a normal or symmetrical distribution, where the data are roughly evenly distributed around a central value.
The median, on the other hand, is the middle value of a dataset when the values are arranged in order from smallest to largest.
For the given data, it is not evenly distributed but it is arranged from the smallest to the largest, so we can use median as the most appropriate measure of center.
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x-intercepts: (-2, 0), (3, 0)
y-intercept: (0, 4)
Answer: The x-intercepts of the line are points where the y-coordinate is equal to 0. The x-intercepts of this line are (-2, 0) and (3, 0). The y-intercept is the point where the x-coordinate is equal to 0, which in this case is (0, 4).
Step-by-step explanation:
Solve the problem pls
Answer:
x = 2
Step-by-step explanation:
7 [tex]\frac{1}{3}[/tex] x - 5 [tex]\frac{1}{2}[/tex] = 4x + 1 [tex]\frac{1}{6}[/tex] ( change mixed numbers to improper fractions )
[tex]\frac{22}{3}[/tex] x - [tex]\frac{11}{2}[/tex] = 4x + [tex]\frac{7}{6}[/tex]
multiply through by 6 ( the LCM of 3, 2, 6 ) to clear the fractions
44x - 33 = 24x + 7 ( subtract 24x from both sides )
20x - 33 = 7 ( add 33 to both sides )
20x = 40 ( divide both sides by 20 )
x = 2
regroup the like terms?
The arrangement and simplification of like term gives 1/4 x + 3/4 x - 1/2 x + 1 - 2/3.
What are like terms?The term "like terms" in algebra refers to terms that have the same variable raised to the same power. Only the numerical coefficients can vary in terms that are similar to algebra.
Given:
Expression: 1/4 x + 1 + 3/4 x -2/3 - 1/2 x
As, like terms have variables then
1/4 x + 3/4 x - 1/2 x + 1 - 2/3
Now, applying the operation as
= x(1/4 + 3/4- 1/2) + 1 - 2/3
= x(4/4 - 2/4) + 3/3 - 2/3
= 2/4 x + 1/3
= 1/2 x + 1/3
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PLS HELP ME THIS IS HARD
Answer: The first answer
Step-by-step explanation:
x commision/15,000 = $360 comission/4500
If a sphere has a volume of 100in^3 what is the length of the radius
Answer:
Step-by-step explanation:
v=(4/3)*pi*r^3
100=(4/3)*pi*r^3
r=2.879
A pair of parallel lines divide a parallelogram as shown in the diagram into three regions with the same area. If one of the three regions is an equilateral triangle with perimeter $1$, then what is the perimeter of the original parallelogram?
The perimeter of the original parallelogram is 22/9 * √3
What is the perimeter of the original parallelogram?The vertices of the parallelogram are A, B, C, and D, with AB parallel to CD and AD parallel to BC.
The parallel lines intersect the sides of the parallelogram at E, F, G, and H.
The side length of the equilateral triangle is s.
The three regions have the same area, hence, the area of each region is 1/3 of the total area of the parallelogram.
Let's the area of the parallelogram as A.
The area of the equilateral triangle is (s²√3)/4
This area is one-third of A
(s²√3)/4 = A/3
s² = 4A/(3√3)
Considering the whole parallelogram;
AB is parallel to CD, hence, triangle AEF is similar to triangle BGF
Also, AD is parallel to BC, hence, triangle ADE is similar to triangle BCF.
AE/EB = BF/FG AD/DE
AE/EB = BC/CF
Expressing AE, BF, AD, and BC in terms of s:
AE = s/3 (perimeter of the equilateral triangle is 1)
EB = 2s/3
BF = 2s/3
FG = s/3
AD = (2s + 2EB)/3
AD = (2s + 4s/3)/3
AD = 10s/9
DE = (2s + 2AE)/3
DE = (2s + 2s/3)/3
DE = 8s/9
BC = (2s + 2FG)/3
BC = (2s + s/3)/3
BC = 7s/9
CF = (2s + 2BF)/3
CF = (2s + 4s/3)/3
CF = 10s/9
Now we can find the perimeter of the parallelogram:
Perimeter = 2(AB + AD)
Perimeter = 2(EB + BC)
Perimeter = 2(2s/3 + 7s/9)
Perimeter = 4s/3 + 14s/9
Perimeter = (22s/9)
Substituting s² = 4A/(3√3) from the earlier equation, we get:
Perimeter = (22/9)√3
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Nicholas is driving his car at a constant rate of 55 miles per hour.
Select whether Nicholas could achieve the distances listed in the
given times.
165 miles in 3 hours
240 miles in 4 hours
330 miles in 6 hours
504 miles in 9 hours
Using the distance, time, and speed formulas, Nicholas could only achieve the distances listed in the given times for:
A) 165 miles in 3 hoursC) 330 miles in 6 hours.What are the distance, time, and speed formulas?The distance, time, and speed formulas show that:
Speed = distance ÷ time.Distance = speed × timeTime = Distance ÷ speed.Constant driving rate (Speed) = 55 mph
Distance Time Speed
165 miles 3 hours 55 mph (165/3)
240 miles 4 hours 60 mph (240/4)
330 miles 6 hours 55 mph (330/6)
504 miles 9 hours 56 mph (504/9)
Thus, using the distance, time, and speed formulas, we can conclude that Nicholas could not achieve the distances in B and D but only in A and C.
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What is the standard form of this number?
Answer:
450.092
Step-by-step explanation:
4 × 100 = 400
5 × 10 = 50
9 × 1/100 = 0.09
2 × 1/1000 = 0.002
400 + 50 + 0.09 + 0.002 = 450.092
How to calculate the volume of water in your pool?
Answer:
Step-by-step explanation:
The volume of water in a pool can be calculated using the following formula:
Volume (in gallons) = Length (in feet) x Width (in feet) x Average Depth (in feet) x 7.5
For example, if your pool is 20 feet long, 15 feet wide, and has an average depth of 5 feet, the volume of water in your pool would be:
20 x 15 x 5 x 7.5 = 5625 gallons
Note: If you prefer metric units, the formula for volume in liters would be:
Volume (in liters) = Length (in meters) x Width (in meters) x Average Depth (in meters) x 1000
It's important to note that this formula assumes a standard rectangular or square pool shape. If your pool has a more complex shape, you may need to measure the volume in smaller sections and add the volumes together to get the total volume.
The graph of the rational function f(z) is shown. Which of the following statements are true?
Select all that apply.
Of(x) has end behavior as z → ∞, y → 0
O f(x) has a domain of all real numbers
□ f(x) > 0 on the intervals (-∞, -2) and (2, ∞)
Of(x) has an end behavior as zoo, y → 00
Of(x) <0 on the intervals [-2, 2]
Of(x) has vertical asymptotes x = -2 and x = 2
Of(x) has a horizontal asymptote y=-1
Answer:
x{27}=69+420
Step-by-step explanation:
Find the percent change from the first value to the second.
48;60
The change is (select)
V
by. %
The percent change from the first value to the second is 20%.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
The first number= 48
The second number= 60
Now, difference=60-48=12
Here,
=(60-48) x 100/48
=1200/48
=20
Therefore, the percentage change will be 20%.
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Use the information to answer the question.
Akeem, Diego, and Lily are each making banana bread. Lily uses
3½ cups
cups of flour more than Akeem. She uses 1 cups of flour less than Diego.
How many more cups of flour does Diego use than Akeem? Move numbers to the boxes to show the answer. If there is no whole number,
place a 0 in the first box.
The number of cups of flour that Diego uses more than Akeem will be 4 ½.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
Akeem, Diego, and Lily are each making banana bread. Lily uses 3 ½ cups of flour more than Akeem. She uses 1 cup of flour less than Diego.
L = 3 ½ + A ...1
L = D - 1 ...2
From equations 1 and 2, then we have
D - 1 = 3 ½ + A
D = 4 ½ + A
The number of cups of flour that Diego uses more than Akeem will be 4 ½.
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Please help me solve this and tell me the steps.
The solution to the given fraction polynomial is expressed as; (x - 4)/(x + 4)
How to solve Fraction Polynomials?The polynomial fraction expression is;
[(6x² - x - 1)/(3x² + 25x + 8)] * [(x² + 4x - 32)/(2x² + 7x - 4)]
Let us reduce each of the terms to their factors;
6x² - x - 1 = (3x + 1)(2x - 1)
3x² + 25x + 8 = (3x + 1)(x + 8)
x² + 4x - 32 = (x - 4)(x + 8)
2x² + 7x - 4 = (2x - 1)(x + 4)
Thus, we now have;
[(3x + 1)(2x - 1)/((3x + 1)(x + 8))] * [((x - 4)(x + 8))/(2x - 1)(x + 4))]
Common terms will cancel out to get;
(x - 4)/(x + 4)
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find the surface area of the cylinder use 3.14 for n
The surface area of the cylinders are 565.2 square yards and 395.64 square cm
Calculating the surface area of a cylinderThe formula for calculating the surface area of a cylinder is expressed as:
S = 2πr(r+h)
where
r is the radius
h is the height
1) Given that r = 6yd and h = 9yd
S = 2(3.14)6(6+9)
S = 565.2 square yd
Hence the surface area of the cylinder is 565.2 square yards
2) Given that r = 3cm and h = 18cm
S = 2(3.14)3(3+18)
S = 395.64 square cm
Hence the surface area of the cylinder is 395.64 square cm
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How do you double integrate in polar coordinates?
Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. This is done by setting up a double integral in terms of r and θ, and integrating first with respect to r and then with respect to θ.
Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. The steps to double integrate a function in polar coordinates are as follows:
1. Determine the limits of integration for r and θ. These limits define the region over which the function will be integrated. Typically, the limits are determined by the boundaries of the region in the xy plane.
2. Write the function to be integrated in terms of r and θ. The function must be expressed in polar coordinates for integration in polar coordinates.
3. Set up the double integral by writing the function in polar coordinates, multiplying by the appropriate factors of r and integrating with respect to r first and then θ.
4. Integrate the function with respect to r, using the limits of integration for r determined in step 1.
5. Integrate the result from step 4 with respect to θ, using the limits of integration for θ determined in step 1.
The general form of a double integral in polar coordinates is:
∫∫f(r, θ)r dr dθ
where f(r, θ) is the function to be integrated, and r and θ are the polar coordinates.
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a smoothie is made of 60% fruit and 40% water. if 4 cups of smoothie is to be made, how many cups of smoothie mixture should be fruit?
The cups of smoothie mixture should be fruit is 2.4
How many cups of smoothie mixture should be fruit?To find how many cups of the smoothie mixture should be fruit when 4 cups of smoothie are to be made, we can use proportions.
Let's call the number of cups of fruit needed x.
So, we have
x = percentage of fruit * number of cups
Substitute the known values in the above equation, so, we have the following representation
x = 60% * 4
Evaluate
x = 2.4
Hence, 2.4 cups of the smoothie mixture should be fruit to make 4 cups of smoothie with a 60% fruit and 40% water ratio.
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A is the point with (2,9) and B is the point with coordinates (10,1) calculate the length of the line segment AB
Using the distance formula we can conclude that the measure of line AB is 64 units.
What is the distance formula?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.
The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.
The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.
So, the formula is:
d = √(x2-x1)² + (y2-y1)²
Now, insert values as follows:
d = √(x2-x1)² + (y2-y1)²
d = √(10-2)² + (1-9)²
d = √(8)² + (-8)²
d = √64+64
d = √128
d = 64 units
Therefore, using the distance formula we can conclude that the measure of line AB is 64 units.
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Use the IQR to determine how many outliers there are in the data set with this
Five Number Summary: 1, 2, 8, 20, 21.
a. 2
b. 3
c. 0
d. 1
===================================================
Explanation:
The five number summary is
MinQ1MedianQ3Maxin that exact order.
A five number summary of 1,2,8,20,21 means:
Min = 1Q1 = 2Median = 8Q3 = 20Max = 21The IQR (interquartile range) is the distance from Q1 to Q3
IQR = Q3-Q1
IQR = 20-2
IQR = 18
The lower fence (L) is then calculated like so
L = Q1 - 1.5*IQR
L = 2 - 1.5*18
L = -25
If any values are smaller than this lower fence of -25, then they are considered small outliers. But we know that min = 1 is the smallest value. This means we do not have small outliers.
Now onto the upper fence (U)
U = Q3 + 1.5*IQR
U = 20 + 1.5*18
U = 47
If any values are larger than 47, then they are considered large outliers. But we know that max = 21 is the largest value. This means we do not have large outliers.
In summary, all of the data values are between min = 1 and max = 21, which guarantees they are definitely in the interval between L = -25 and U = 47.
This is why there are no outliers in this data set.
Is t-test better than ANOVA?
Answer:
t-test is less likely to commit an error. ANOVA has more error risks. Sample from class A and B students have given a mathematics course may have different mean and standard deviation.
Step-by-step explanation:
have a nice day
what number is greater than 7/2
Answer:
A) √(13)
Step-by-step explanation:
We can more clearly see the difference in the values of the numbers if we convert/approximate them all to a decimal form.
7/2 = 3.5
A) √(13) ≈ 3.6 > 3.5
B) ∛(27) = 3 < 3.5
C) 3.4 < 3.5
D) π ≈ 3.1 < 3.5
From these approximations, we can see that A) √(13) is the only answer choice that evaluates to greater than 7/2.
(66-6)divided by 12+ 5with exponent of 2
Answer:30
Step-by-step explanation:
use the word Pemdas
P-parenthesis
e-exponent
m-Multiplication
d-divide
a-Add.
s-Subtract.
figure out what’s wrong with it