The shortest side of the triangle measures 17 feet.The second side of the triangle measures 20 feet.The third side of the triangle measures 31 feet.What is the length of the three sides?The perimeter of a triangle is the sum of the length of the three sides of the triangle. Let the shortest side be represented with s.The second side = 3 + s The third side = 2s - 3 2s - 3 + 3 + s + s = 68 4s = 68s = 17The second side = 17 + 3 = 20 The third side = = (2 x 17) - 3 = 31
machine a, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. machine b, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. how many minutes will it take machines a and b, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?
The total time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.
What is the concept of time and work?
Time and work defines the way how the particular work is done in the given time. It gives an exact relationship between the work and the number of days required to complete it.
Calculation of the total time taken by the machines A and B working together
Given that Machine A completes the entire job in 12 minutes.
So, machine A completes 1/12 of the job in one minute.
Machine B takes 18 minutes to complete the entire job.
So, machine B completes 1/18 of the job in one minute
When we combine their work, they will complete (1 / 12 + 1 / 18) job in one minute i.e. (3 + 2) / 36 = 5/36 job in one minute —---- 1
To find the time taketaken by them to produce x amount of peanut butter, we will reciprocate the result obtained in equation 1
i.e. 36 / 5 minutes to complete the entire job
i.e. 7.2 minutes
Hence, the time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.
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The following table presents the time taken to review articles that were submitted for publication to a particular journal during a recent year. A few articles took longer than 6 months to review; these are omitted from the table. Consider the data to be a population.
A) Variance = 10.24
B) Standard Deviation = 3.2
One of the measurements of dispersion is the standard deviation, which is exclusively used for quantitative data. It aids in determining if the data's mean is a suitable measurement to reflect the core value.
TIME FREQUENCY(f) MIDPOINT(x) d d² fd fd²
0 - 0.9 43 0.45 -3 9 -129 387
1.0 - 1.9 17 1.45 -2 4 -34 68
2.0 - 2.9 19 2.45 -1 1 -19 19
3.0 - 3.9 18 3.45 0 0 0 0
4.0 - 4.9 14 4.45 1 1 14 14
5.0 -5.9 16 5.45 2 4 32 64
∑f = 127
∑fd = -136
∑fd² = 552
[tex]d = \frac{x - 3.45}{1}[/tex]
Standard Deviation = [tex]\sqrt \frac{fd^{2} }{N} - \sqrt \frac{(fd)^{2} }{N} * i[/tex]
[tex]\sqrt \frac{552}{127} -\sqrt (\frac{-136}{127})^{2} * 1[/tex]
√4.35 - √1.15
Standard Deviation = 3.2
(SD)² = (3.2)² = 10.24
Variance = 10.24
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consider a clock with an hour hand and a minute hand. what is the measure of the angle the minute hand traces in 36 minutes. your answer should be in radians.
The measure of the angle the minute hand traces in 36 minutes is 3.77 radians
Calculating AngleFrom the question, we are to determine the measure of the angle the minute hand traces in 36 minutes
The minute hand makes a complete rotation after 60 minutes.
Thus,
The angle the minute hand would have traced in 36 minutes is
36/60 × 360°
= 12960/60
= 216°
Now, convert to radians
216° = 216 × π/180 rad
= 3.77 rad
Hence, the measure of the angle the minute hand traces in 36 minutes is 3.77 radians
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A large polymeric molecule that is nonpolar over most of its structure but very polar at one end:_____.
A large polymeric molecule that is nonpolar over most of its structure but very polar at one end DNA and Phospholipid.
DNA and phospholipid were two examples of huge polymeric molecules that would be polar solely on a single end although nonpolar on the majority of their structure, as opposed to the other alternatives, which would be all monomeric compounds. Nucleotides are used to help DNA create its polymeric structure. Phosphodiester linkage aids in the arrangement of the nucleotides.
The polar molecule would only be found in one area of the vast strand-like polymeric structure. At one extremity of the strand, there is a polar phosphate link; with its assistance, some other monomeric units were joined, generating the phosphodiester bonds. Two fatty acids and the first molecule of glycerol work together to generate the structure known as the phosphodiester.
The phosphate group is present in the polar head region of the phosphate group. This help in the polarity of the phospholipid structure making the head region of the polymeric molecule hydrophilic.
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marvin was completing the square, and his work is shown below. identify the line where he made his mistake. (2 points) f(x)
It can be seen that the mistake that was made by Marvin was on line 1.
How to illustrate the information?2x² - 8x + 5.... move the 5 to the other side
2x² - 8x = -5
Now divide by 2
x² - 4x = -5/2
x² - 4x + 4 = -5/2 + 4
(x - 2)² = -5/2 + 8/2
(x - 2)² = 3/2
x - 2 = (+-)sqrt 3/2
x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2
Therefore, he made his mistake on line 1.
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Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27
Write the following solution in interval notation:
x≥-3
Answer:
[-3,∞)
Step-by-step explanation:
Since x is on the left side and is greater than -3, we will use a bracket in front of the -3. Since we do not know when the interval ends, we finish it with a positive infinity because we know that x is GREATER than (or equal) to -3. If it were less than -3, it would be negative infinity. Similarly, we use a rounded bracket because infinity is a positive value greater than -3.
Two pounds of grapes cost `\$5`. jordan says that's `2.5` pounds per dollar. emika says it's `0.4` pounds per dollar. which rate is correct?
The rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.
We know that the rate is nothing but the ratio of two different quantities which have different units.
In this question, we have been given two pounds of grapes cost $5
First we find the rate in pounds per dollar.
2 pounds of grapes = $5
As rate is the ratio of two different quantities, we find the ratio (pounds per dollar).
= 2 pounds /5 dollars
= (2/5) pounds per dollar
= 0.4 pounds per dollar .......(1)
This means the rate of grapes is 0.4 pounds per dollar.
In this question, we have been given Jordan says that's 2.5 pounds per dollar and Emika says it's 0.4 pounds per dollar.
From (1), we can clearly say that Emika is correct.
Therefore, the rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.
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State the domain and range of the sin, cos, tan, functions. State the domain
and range of the inverse sin, cos, and tangent functions.
The domain and range of trigonometric functions are as follows;
Function Domain Range
sin(x). All real numbers [-1, 1]
cos(x). All real numbers [-1, 1]
tan(x). {x| x ≠ -3•π/2, -π/2, π/2, } R
The domain and range of the inverse sine, cosine, and tangent are;
Function Domain Range
arcsin(x). (-1, 1) [-π/2, π/2]
arccos(x). (-1, 1) [0, π]
arctan(x) (-∞, ∞). [-π/2, π/2]
What are the domains and ranges of the trigonometric functions?sin(x)
The domain of sin(x) is the set of possible values for x, for which sin(x) is defined, which is;
All real numbers.The range of sin(x) is the set of possible values output values of sin(x) is, which is; -1 ≤ sin(x) ≤ 1
The range is therefore; [-1, 1]cos(x)
Similarly;
The domain of cos(x) is the set of all real numbersThe range of cos(x) is; -1 ≤ cos(x) ≤ 1tan(x)
tan(x) = sin(x)/cos(x), however, cos(x) = 0, when x = -3•π/2, -π/2, π/2, 3•π/2...
The domain of tan(x) is therefore;
{x| x ≠ -3•π/2, -π/2, π/2, 3•π/2...}sin(x) increases as cos(x) decreases, therefore;
The range of tan(x) = sin(x)/cos(x) is therefore;
-∞ < tan(x) < ∞ which is {-∞, ∞}arcsin(x)
The input of arcsin(x) is sin(x)
sin(x) = opposite/hypotenuse
Given that the magnitude of hypotenuse > opposite, the ratio, opposite/hypotenuse is < 1 in magnitude
The domain of arcsin(x) is therefore;
-1 < sin(x) < 1, which is (-1, 1)The range is the set of possible outputs, which is [-π/2, π/2], given that sin(x) is positive and negative from -π/2, π/2
The range is [-π/2, π/2]arccos(x)
Similarly;
The domain of arccos (x) is (-1, 1) The range is [0, π]arctan(x)
The input of arctan(x) is tan(x)
tan(x) = sin(x)/cos(x)
The domain of arctan(x) is therefore;
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Here is the histogram of a data distribution.
What is the shape of this distribution?
O A. Unimodal skewed
• B. Bimodal symmetric
• C. Unimodal symmetric
• D. Bimodal skewed
O E. Uniform
Answer: your answer would be unimodal skewed. This graph only has one maxima, thus it can't be bimodal. However, it's not symmetric, meaning that it is skewed
Hope this helps you
Step-by-step explanation:
The histogram is solved and it is uni-modal skewed
What is Histogram?A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable.
A histogram displays the frequency distribution of a set of continuous data. It is useful for visualizing the shape of the data distribution, such as whether it is symmetrical or skewed, and identifying any outliers or gaps in the data.
Given data ,
Let the histogram be represented as A
Now , the value of A is plotted on the graph
A. Unimodal skewed: This distribution has one peak (mode) and the tail of the distribution extends to one side. Depending on which side the tail is longer, it can be either positively skewed (tail extends to the right) or negatively skewed (tail extends to the left).
B. Bimodal symmetric: This distribution has two distinct peaks (modes) and is symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.
C. Unimodal symmetric: This distribution has one peak (mode) and is roughly symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.
D. Bimodal skewed: This distribution has two distinct peaks (modes) and the tail of the distribution extends to one side for each peak. Depending on which side each tail is longer, it can be either positively skewed (tail of one peak extends to the right and the other to the left) or negatively skewed (tail of one peak extends to the left and the other to the right).
E. Uniform: This distribution is flat and has roughly equal frequency for all values in the range of the dataset.
Hence , the histogram is unimodal skewed
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What is the appropriate analysis to use when there are two independent variables that are measured and one dependent variable that is measured?
If there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use
Given,
The conditions
There are two independent variablesThe two independent variables are measured and one dependent variable that is measuredWe know
In multiple regression method the dependent variables are predicted by using the known independent variables. This method is usually used to analyze the relationship between multiple independent variables and one independent variables,
So here multiple regression method is using.
Hence, if there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use
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b. a quality control randomly selects two of five parts to test for defects. in a group of five parts, how many combinations of two parts can be selected?
10 combinations of two parts can be selected.
Combination is defined as the number of arrangements in a collection of items where the order of selection does not matter.
denoted by C(n,x)= ⁿcₓ=[tex]\frac{n!}{(x!)(n-x)!}[/tex] ,
where n is the total number of elements in the set.
x is the number of selected objects.
According to the Question
Total number of elements = 5 = n
Number of objects to be selected = 2 = x
Substituting the values in the above formula
C(5,2)=[tex]\frac{5!}{2!*3!}[/tex]
[tex]=\frac{5*4*3!}{2*3!} \\ \\ =\frac{20}{2} \\ \\ =10[/tex]
Therefore , 10 combinations of two parts can be selected.
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Todd wants to make a cheesecake for a birthday party. The recipe calls for a 9-inch diameter round pan. Todd only has square pans. He has an 8 -inch square pan, a 9-inch square pan, and a 10 -inch square pan. Which pan comes closest in area to the one that the recipe suggests?
The pan that comes closest in area is the 8-inch square pan.
What pan comes closest?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 22/7
R = radius = diameter / 2 = 9/2 = 4.5 inches
22/7 x 4.5² = 63.64 in²
A square is a quadrilateral with four equal sides.
Area of a square = length²
8² = 64 in²
9² = 81 in²
10² = 100 in²
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I need help with 18 and 22. With a full explanation please.
The answer of 18 is y = 0.5x + 0
The answer of 22 is y = -0.4x + 0
Step-by-step explanation:
c is constant, m is gradient
18. m = 1/2
m = 0.5
1 = 0.5(2) + c
1 = 1 + c
c = 0
y = 0.5x + 0
22. m = 2/-5
m = -0.4
2 = -0.4(-5) + c
2 = 2 + c
c = 0
y = -0.4x + 0
\Which set does not contain –3?
the set of all real numbers
the set of all integers
the set of all whole numbers
the set of all rational numbers
Answer:
The set of all whole numbers
Step-by-step explanation:
Real numbers, integers, and rational numbers can all contain negative numbers. Whole numbers include numbers from 0 and up.
Hope this helps!
Have a nice day
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Triangle DEF has vertices D(-2, -1), E(0, 1), and F(1, -3). Graph the
triangle and its image after a dilation with a scale factor of 3.
The image after a dilation with a scale factor of 3 is A(-6, -3), B(0, 3), and C(3, -9) of triangle ABC.
Here, the coordinates are,
D = (-2, -1)
E = (0 , 1)
F = (1, -3)
After dilating triangle DEF using a scale factor of 3 and a center of dilation at the origin to form triangle ABC.
A = (-2 x 3, -1 x 3) = (-6, -3)
B = (0 x 3, 1 x 3) = (0, 3)
C = (1 x 3, -3 x 3) = (3, -9)
Line segments,
AB = 8.48
BC = 12.36
CD = 10.81
Therefore, after dilation by using a scale factor of 3 is A(-6, -3), B(0, 3), and C(3, -9).
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Do the two functions below appear to be inverses of each other
Answer:
yes
Step-by-step explanation:
if (a,b) is on the graph of f(x) then (-a,-b) is on the graph of f^-1(x)
Mobius, incorporated, has a total debt ratio of .48. a.what is its debt-equity ratio?
debt-equity ratio is 0.92.
What is debt equity ratio?A firm's total liabilities and shareholder equity are compared using the debt-to-equity (D/E) ratio, which may be used to determine how heavily reliant a company is on debt. D/E ratios vary by sector and are most useful for comparing a firm to its closest rivals or tracking changes in its reliance on debt over time. When comparing similar organizations, a larger D/E ratio denotes greater risk, whereas a very low one can signify that a company is not utilizing debt funding to grow. Since long-term debt entails greater risk than short-term commitments, investors frequently change the D/E ratio to simply take it into account.
Debt-equity ratio is computed as follows:
= total debt ratio / (1 - total debt ratio)
= 0.48 / (1 - 0.48)
= 0.48 / 0.52
= 0.92
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Which of the following numbers are irrational?
Answer:
π/2 and ³√4
also -4.8237 and π/2
Step-by-step explanation:
number 2 and 4 are automatically out since every integer is a rational number.
√25 = 5 and 5 + 4 = 9, 9 can be expressed as 9/1 which falls under rational numbers.
π/2 on the other hand is not rational same goes for -4.8237 and ³√4 because these numbers cannot be written as a fraction with integers.
for the above numbers π/4 and ³√9 are irrational.
Jarome is making pizza. He uses 2 1/2 cups of cheese for
every 2 3/4 pizzas. He has 6 1/4 cups of cheese left in the
bag. How many pizza pies can he make with the leftover
cheese?
Jarome can make 6 whole pizzas with the leftover cheese.
Given that Jarome uses 2 1/2 cups of cheese for every 2 3/4 pizzas. He has 6 1/4 cups of cheese left in the bag.
We need to determine the number of pizza pies can he make with the leftover cheese.
To find out how many pizza pies Jarome can make with the leftover cheese, we need to determine how many sets of 2 3/4 pizzas can be made using 6 1/4 cups of cheese.
Let's start by finding the number of sets of 2 3/4 pizzas that can be made from 6 1/4 cups of cheese:
Number of sets = Total cheese available / Cheese per set
Number of sets = 6 1/4 cups / 2 1/2 cups per set
To make the calculation easier, let's convert all the mixed numbers to improper fractions:
6 1/4 cups = (4 x 6 + 1) / 4 = 25/4 cups
2 1/2 cups = (2 x 2 + 1) / 2 = 5/2 cups
Number of sets = (25/4) / (5/2)
Now, to divide fractions, we invert the divisor (5/2) and multiply:
Number of sets = (25/4) x (2/5)
= (25 x 2) / (4 x 5)
= 50/20
= 5/2
So, Jarome can make 5/2 sets of 2 3/4 pizzas with 6 1/4 cups of cheese.
Now, let's see how many pizzas he can make with the leftover cheese:
To calculate the number of pizzas in 5/2 sets, we multiply it by the number of pizzas per set (2 3/4 pizzas):
Number of pizzas = (5/2) x (2 3/4)
Again, let's convert all the mixed numbers to improper fractions:
2 3/4 pizzas = (4 x 2 + 3) / 4 = 11/4 pizzas
Number of pizzas = (5/2) x (11/4)
Now, when multiplying fractions, we simply multiply the numerators together and the denominators together:
Number of pizzas = (5 x 11) / (2 x 4) = 55/8
So, Jarome can make 55/8 pizzas with the leftover 6 1/4 cups of cheese.
Now, let's simplify the fraction:
55/8 = 6 7/8
Therefore, Jarome can make 6 7/8 pizzas with the leftover 6 1/4 cups of cheese.
Since we can't make a fraction of a pizza, he can make 6 whole pizzas with some cheese left over.
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question what is an expression equivalent to 6(24) using the distributive property? drag and drop the appropriate number into each box.
The following can be used to rewrite the provided expression: 6(24) = 6(20 + 4).
What in mathematics is a distributive property?The distributive Property states in that it is necessary to multiply every one of the two numbers by the factor before performing the addition operation when a factor is multiplied by that of the sum or addition of two terms. The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive principle of binary operations.
According to the given data:The following generic form can be used to specify the distribution property:
a(b+c) = ab + bc
the following expression:
6(24)
We can observe the following by contrasting this to the general form:
a = 6
b + c = 24
Consequently, we must identify two integers from the options whose sum is 24.
These numbers, out of the options provided, are 20 and 4.
The following can be used to rewrite the provided expression: 6(24) = 6(20 + 4).
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the expression 14x 3 represents the perimeter of the triangle. what is the length of the third side
609+283+97 pls help help helpp
Answer:
989
Step-by-step explanation:
Answer:
986
DO NOT HAVE A GOOD DAYHAVE A GREAT DAY11. The circlex²+y² = 26 and the line y = x + 4 meet at two points P and Q
a) show that the x co-ordinates of P and Q satisfy the equation x² + 4x-5=0
b) hence find the co-ordinates of P and Q
a)The x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.
b)The co-ordinates of P and Q are (-5, -1) and Q = (1, 5).
What is defined as the equation of the circle?(x-h)² + (y-k)² = r² is the equation for a circle with (h, k) center and r radius. This is the equation's standard form. Thereby, if we recognise the coordinates of the circle's center and radius, we can usually find its equation.The given equation of the circle is;
x² + y² = 26.
Th circle satisfies the line y = x + 4.
Thus, Put the value of y in the main equation.
x² + (x + 4)² = 26.
Simplify the equation;
x² + x² + 16 + 8x = 26
2x² + 8x - 10 = 0
Divide the equation by 2.
x² + 4x - 5 = 0
Part a: This shows that x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.
Part b: Now, do the factorization of x² + 4x - 5 = 0.
(x + 5)(x - 1) = 0
x = -5 and 1.
For x = -5; y = -1
Point P = (-5, -1)
For x = 1; y = 5
Point Q = (1, 5)
Thus, the requires points P and Q are obtained.
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PLSSS HELP IF YOU TURLY KNOW THISS
On simplifying the given expression the no. that goes in green box is -7
The rule of addition of two numbers
(+) (+) = (+)adding two positive integers result in positive integer.
(-)(-) = (+)adding two negative integers results in the sum with a negative sign.
(+)(-) = (-) (-)(+) = (-)addition of two different signed Integer will result in subtraction only and the sign of the result is same as the larger number sign.
so
2 + 16x - 9 - 10x
6x + [-7] HERE [ 2 + (-9) = -7 ]
On simplifying the given expression the no. that goes in green box is -7
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A bike rental fee is $15 plus $0.25 per hour how many hours can Kristen rent a bike if she has $20?
Answer:
Kristen can ride the bike for 20 hours
Step-by-step explanation:
20 - 15 = 5
The rate is 0.25 an hour.
0.25 x 4 = 1 - Currently $4
0.25 x 4 = 1 - Currently $3
0.25 x 4 = 1 - Currently $2
0.25 x 4 = 1 - Currently $1
0.25 x 4 = 1 - No more
Add up all the 4's
She can ride the bike for 20 hours.
Part 1 of 2 Question content area top Part 1 A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 13 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 15 minutes. a. What equation can you use to find the distance of the flowerbed from the hive? b. How far is the flowerbed from the hive?
-4b+5=-27 is what because i have no idea
Answer:
b=8
Step-by-step explanation:
-4b + 5 = -27
Move the 5 to the right side by subtraction, subtract five from the right side as well.
Now you should have:
-4b = -32
Now divide by -4 to get ‘b’ isolated, do this on both sides.
You should be left with:
b=8
A train car is carrying 500 TV's.
If each set weighs 12.85 pounds, what is the
weight of the entire load?
Answer:
6425
Step-by-step explanation:
12.85x500=6425
which of the following values is not a soliution to -4x - 6.8<34
A. X=-9
B. X=-10.2
C. X=-11
D. X=-10
The value not in the solution is x = -10.2
How to determine the value not in the solution?The inequality expression is given as:
-4x - 6.8<34
Add 6.8 to both sides of the inequality
So, we have:
-4x < 40.8
Divide both sides by -4
x > -10.2
This means that only values greater than -10.2 are in the solution set
Hence, the value not in the solution is x = -10.2
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from a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for at least a week.
Option D is the correct answer (We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%)
Since the confidence interval is calculated for population proportion (parameter) based on sample data.
What is a confidence interval?Because the figure is based on a sample of the population you are investigating; there is always uncertainty when you generate an estimate in statistics, whether it be a summary statistic or a test statistic. The confidence interval is the range of values. If you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time. The alpha value determines the confidence level, the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.
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