Answer: centimeters 3
Samuel is folding his laundry. The table shows the proportional relationship between the number of shirts he folds and the time, in minutes, it takes him to fold them.
Number of Shirts 3 6 ?
Time (minutes) 0.25 0.50 2
How many shirts can Samuel fold in 2 minutes?
8 shirts
9 shirts
24 shirts
25 shirts
The number of shirts Samuel can fold in 2 minutes is 12
How to determine the number of shirts Samuel can fold in 2 minutes?From the question, we have the following parameters that can be used in our computation:
Number of Shirts 3 6 ?
Time (minutes) 0.25 0.50 2
Represent the missing value with x
So, we have the following representation
Number of Shirts 3 6 x
Time (minutes) 0.25 0.50 2
From the above table of values, we have the following equation
6 : x = 0.5 : 2
Multiply the second ratio by 12
So, we have
6 : x = 6 : 12
By comparison, we have
x = 12
Hence, the number of shirts is 12
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Pls help I forgot how to do this
You need at least $220 to do your Christmas shopping. You already have $70. You earn $7.00 dollars per hour at your after-school job. Write and solve an inequality to show how many hours you should work earn your Christmas money.
Let
U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A= {1, 2, 4, 6}
B= {3, 7}
C= {1, 3, 6, 7, 8}
List all the members of the following set. (Enter your answers as a comma-separated list. Enter EMPTY or ∅ for the empty set.)
A ∩ (/B ∪ C)
I'm on my last attempt. I got 2,3,4,7,8 and it's wrong. Ughhhh
Please help me!!!
The set A ∩ (/B ∪ C) is given as { 1, 6 }
How to determine the elements of the setFrom the information given, we have the sets as;
U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A= {1, 2, 4, 6}
B= {3, 7}
C= {1, 3, 6, 7, 8}
Note that;
U is the universal setSets A, B and C are subsets of the universal set∪ represents union of the set∩ represents intersection of setB∪C = { 1, 3, 6, 7, 8}
A ∩ (/B ∪ C) = { 1, 6 }
Hence, the set is { 1, 6 }
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Help ME! i really need help for this
Answer:
#4 is one, and #5 is two.
Step-by-step explanation:
Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys?My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?
Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.
But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.
So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.
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Consider this equation.
1/x + 2/x+10 + 1/3
Complete the statements to make them true.
The least common denominator is a)3x(x+10) b)x c)x+10 d)x(x+10)
The equation will have a)2 b)1 c)0 valid solutions.
For the given equation, 1/x + 2/x+10 = 1/3,
1)The least common denominator is x+10. Option c is correct.
2)The equation will have 2 valid solutions. Option a is correct.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation is,
1/x + 2/x+10 = 1/3
[tex]\frac{1}{x}+\frac{2}{x+10}=\frac{1}{3}[/tex]
Cross-multiply the given equation,
[tex]3\left(x+10\right)+6x=x\left(x+10\right)[/tex]
The obtained value of x after simplifying the equation is,
[tex]\\\ x=5,\:x=-6[/tex]
Thus, for the given equation, 1/x + 2/x+10 = 1/3, the least common denominator is x+10. Option c is correct and the equation will have 2 valid solutions. Option a is correct.
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Suppose that you were trying to use the Putzer method to exponentiate the matrix A which has eigenvalues dı = 4 and A2 = 6, in that order. ao(t) is always the function et. Choose the correct equation for a1(t) da1О (а) 6a1 + e4t a1(0) = 1 O (b) dt da1 : 4a1 + e4t P (g) da1 a1(0) = 1 O (c) dt -4a1 + ett a1(0) = 0 da1 O (d) dt 4a1 + et a1(0) = 0 da1 O (e) : 6a1 + e4t a1(0) = 0 dt da1 O (f) dt — 4а, + e# a,(0) — 1
In that order. ao(t) is always the function is [tex]$$m_1=A-2 I $$[/tex].
What is function ?
A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
given: [tex]$\quad d_1=4 \quad$[/tex] and [tex]$A_2=6$[/tex]
[tex]$$m_0=\Sigma=\left[\begin{array}{cc}1 & 0 \\0 & 1\end{array}\right]$$[/tex]
By putzes method
[tex]$$\text { matrix } m_1=A-N_1 p_0=A-d_1 m_0$$[/tex]
here [tex]$r_1=2, m_0=I$[/tex]
[tex]$$m_1=A-2 I $$[/tex]
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At 5pm, Li rented bikes from Pearl's
Wheels. She returned the bike at 11pm, after
riding 38 miles: Li paid $26.00 for the
rentals
a. What was her average speed in miles per hour?
b. What was her cost per hour, to the nearest cent?
c. What was her cost per mile, to the nearest cent?
Answer:
(a) 6.33 miles per hour
(b) $4.33 per hour
(c) $0.68 per mile
Step-by-step explanation:
Li drove 6 hours (5pm - 11pm) for a total of 38 miles
[tex]\textrm{(a) Her average speed is determined by the formula}\\\\\dfrac{\textrm{Distance Travelled}}{\textrm{Time taken for travel}}[/tex]
[tex]\textrm{So average speed }=$\dfrac{38}{6} = 6.33$ \;\textrm{miles per hour}}\\\\[/tex]
(b) She paid $26 for 6 hours of usage
[tex]\textrm{So cost per hour } = \dfrac{26}{6} = \$4.33\;\textrm{per hour}\\\\[/tex]
(c) Cost per mile, c, can be computed as follows
[tex]c = \dfrac{\textrm{Total Cost}}{\textrm{Miles Traveled}}[/tex]
[tex]\longrightarrow \dfrac{26}{38} = \$0.68\; \textrm{per mile}[/tex]
A population of beetles are growing according to a linear growth model. The initial population (week 0) is
PO=4
, and the population after 8 weeks is
P8=52
Find an explicit formula for the beetle population after
n weeks
After how many weeks will the beetle population reach 184?
Thus, 18 weeks are needed for the population of beetles to reach 183. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will take place.
How does one determine probability?The number of possible outcomes is divided by the total of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event but by probability that it won't.
How do probability and an example work?For instance, how many heads would appear if you throw a coin 100 times? Assuming a probability of 1/2, we can anticipate 50 heads. However, when we actually attempt it, we might just get 48 heads, 55 heads, or anything else, but most of the time it will be close to 50.
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m/2 = 10x + 7
2
67°
Q. Solve for x.
e for x.
9
If ∠2=10x+7 and one angle is 67 degrees then value of x is 6.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that the triangle has two equal sides which makes the triangle as isosceles.
In an isosceles triangle the two sides will be always equal and the angles will be also equal.
One angle of the triangle is 67 degrees
We need to find the ∠2.
As we know that the equal sides make equal angles.
∠2=67 degrees
and from given ∠2=10x+7
Now equation 67 with the 10x+7 to find the value of x.
So 67=10x+7
subtract 7 from both sides
67-7=10x+7-7
60=10x
Divide both sides by 10
x=60/10
x=6
Hence, the value of x is 6.
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the rate of electricity charge of 20 units is RS 3 per units and rs 6.50 per units from 21 to 30 unit. find the charge of consumption of 28 units with rs 50 service charge
electricity consumed:28 units
charge upto 20 units : 20 * Rs 3 : Rs 60
charge from (21 to 28) : 8 * Rs 6.50 : 52
total charge including service charge : Rs 60 + Rs 52 + Rs 50 : Rs 162
Write an equation of the graph.
The equation of the graph in slope intercept form is y = x + 2
How to find the equation of a graph?The equation of a graph can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptHence, let's find the slope using (1, 3) and (2, 4)
Therefore,
slope = 4 - 3 / 2 - 1
slope = 1 / 1
slope = 1
Let's find the y-intercept using (1, 3)
y = x + b
3 = 1 + b
b = 3 - 1
b = 2
Therefore, the equation is y = x + 2
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The game is played on a square court divided into four smaller squares that meet at the center. If a line is drawn diagonally from one corner to another corner, then a right triangle QTS is formed, where _QTS is 45°. Using a trigonometric function, find the length of the
diagonal for a 15-foot square court.The length of the diagonal is about how many feet. (round to nearest tenth)
The length of the diagonal of the right triangle is 21.2 units.
How to find the side of a right triangle?The game is played on a square court divided into four smaller squares that meet at the centre.
A right triangle QTS is formed, where QTS is 45°. Using trigonometric function, the length of the diagonal can be found as follows:
Therefore,
sin 45 = opposite / hypotenuse
opposite side = 15 feet
hypotenuse side = 15 feet
The hypotenuse side is the diagonal.
Hence,
sin 45° = 15 / h
cross multiply
h = 15 / sin 45
h = 15 / 0.70710678118
h = 21.2132034356
h = 21.2 units
Therefore,
length of diagonal = 21.2 units
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Please Help ASAP!!
100pts + Brainliest if correct!
1. If a polynomial function with rational coefficients has -4 and 8 as roots, it means we can factor this polynomial this way :
What is rational coefficients?
A coefficient is a number that is placed in front of a variable. A variable and a rational number are preceded by a rational coefficient, which may be an integer, decimal, or fraction.
(x - (-4))(x-8) = (x+4)(x-8) = x² - 8x + 4x - 32 = x² - 4x - 32
1x² - 4x - 32 is a polynomial function of least degree with rational coefficients that satisfices the given conditions. The leading coefficient here is 1, we call this a monic polynomial.
2. There may be something missing in the question here
3. We can use the factoring techniques to find the roots :
x^3 - 5x² + 9x - 45 let us group x^3 with -5x² and 9x with -45 :
(x^3 - 5x²) + (9x - 45) = x²(x - 5) + 9(x - 5)
We can notice now that there is a common factor : (x-5) this allows us to factor again by (x-5) :
Y = (x-5)(x²+9)
This is the maximum we can do on R, but on C the set of complex we can still factor again.
x² + 9 has a negative discriminant : Δ = b² - 4ac where b = 0 , a = 1, c = 9
Δ < 0, Δ = - 36
Applying the formulas for the roots x1 and x2 we get x1 = -3i, and x2 = + 3i
Y = (x-5)(x-3i)(x+3i)
So the solution is S = {5, 3i, -3i} the three roots of the function.
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compare the two methods that you learned for finding the approximate solutions go polynomials equations. what are the pros and or the cons explain
The pros and cons regarding the methods of the polynomial include:
Graphing the related system eliminates the need to rewrite the equation in order to set it equal to 0. It is simpler because you can graph each side of the equation separately.
It can be difficult to locate the system's intersection point at times. You may need to zoom in or learn how to resize the window. Using the related function allows you to find the points by focusing on the x-axis.
What is a polynomial?A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations such as addition, subtraction, multiplication, and division.
The formula is ax² + bx + c = 0, where a and b are coefficients, c is a constant, and the polynomial degree is 2. A trinomial equation is a polynomial with three variable terms. It is also known as a cubic equation. To be a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on variables, and no variables in the denominators of any fractions.
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Vhich postulate or theorem proves A MNQ~A PNQ?
O AAS Congruence Theorem
O SAS Congruence Postulate
O SSS Congruence Postulate
ASA Congruence Postulate
Answer:
Rhs
Step-by-step explanation:
angle N (R)
pq=mq ( h)
Nq (s)
1. Consider the system described by the differential equation: d3y(t)/dt3 + 4d2y(t)/dt2 + 6dy(t)/dt + 8y(t) = 20u(t)
(i) Find the transfer function of the system.
(ii) Derive a state space representation for the system
2. A single input, single output system has the matrix equations:
x.(t)= [0 1 -3 -4] x(t) +[0 1]u(t) and y(t) = [3 0]x(t)
Determine the transfer function G(s) = Y(s)/U(s)
20 is the system's transfer function. A differential equation is a mathematical formula that includes one or more terms
What is a differential equation's formula?A differential equation is a mathematical formula that includes one or more terms as well as the derivatives of one variable (the dependant variable) with respect to another variable (i.e., independent variable) dy/dx = f (x) In this case, "x" is an independent variable and "y" is a dependent variable. For instance, dy/dx = 5x.The Laplace transform of the input variable divided by the Laplace transform of the output variable, with initial conditions of zero, is the definition of transfer functions.Explanation:
4 +2 + 6 + 8 = 20.
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8 a What percentage of $680 is $490 ?
b A price is reduced from $680 to $490. What is the percentage decrease?
a) The percentage of $680 which is $490 is 72.06%.
b) When a price is reduced from $680 to $490, the percentage decrease is 27.94%.
What is the percentage?The percentage is the ratio of a value to another.
Percentages are depicted as fractional values expressed over 100.
To determine percentages, the smaller value is expressed as the numerator, while the more considerable value is described as the denominator.
The result is then multiplied by 100.
For instance:
$490 of $680 is 72.06% ($490/$680 x 100)
Price reduction from $680 to $490, the percentage decrease is computed as the difference between $680 and $490 divided by $680, multiplied by 100.
Thus, the percentage decrease in price from $680 to $490 is 27.94%, showing that the original price of the good or service has been reduced from 100% to 72.06%.
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Which expressions are equivalent to 8(-10x+ 3.5y - 7)? Select two options.
-80x+ 24.5y-56
-80x+28y-56
80x+28y+56
4(-20x+7y-14)
-4(-20x+ 7y-14
Answer:
-80x + 28y -56
4(-20x + 7y -14)
Step-by-step explanation:
The first answer is distributing the 8 through the whole expression. The second answer is when you factor out a 4.
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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Find the slope of the line that passes
through
The slopes of the linear equations are:
a) -1
b) 0
c) undefined, it is a vertical line.
How to find the slopes of the lines?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
1) The points are (3, 5) and (2, 6), so the first slope is:
a = (6 - 5)/(2 - 3) =1/-1 = -1
2) The points are (-3, 2) and (7, 2)
Notice that this is a horizontal line of the form y = 2, so the slope is zero.
3) The points are (6, 8) and (6, -2)
This is a vertical line of the form x = 6, so the slope is undefined.
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[tex]\large\boldsymbol{\rm{Slope}}[/tex]
[tex]\bf{Intro}[/tex]
To find the slope of a line, given that it passes through two points, use the slope formula:
[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Substitute the known values and simplify:
[tex]\bf{m=\dfrac{6-5}{2-3}}[/tex]
[tex]\bf{m=\dfrac{1}{-1}}[/tex]
[tex]\bf{m=-1}[/tex] {slope}
[tex]\rule{250}{1}[/tex]
Substitute the known values and simplify:
[tex]\bf{m=\dfrac{2-2}{7-(-3)}}[/tex]
[tex]\bf{m=\dfrac{0}{7+3}}[/tex]
[tex]\bf{m=\dfrac{0}{10}}[/tex]
[tex]\bf{m=0}[/tex] {slope}
[tex]\rule{250}{1}[/tex]
Substitute the known values and simplify:
[tex]\bf{m=\dfrac{-2-8}{6-6}}[/tex]
[tex]\bf{m=\dfrac{-10}{0}}[/tex]
[tex]\bf{m=not\:de fined}[/tex]
✦ Therefore, the slopes are: -1, 0, not defined.
factor -2x-8x+20 pls
Answer:
10(-x + 1)
Step-by-step explanation:
-2x - 8x + 20
-10x + 20
10(-x + 1)
Find an equation of a line with slope m = −25 that contains the point (10,−5). Write your answer in slope-intercept form
Answer:
-25
Step-by-step explanation:
Kyle owns a movie theater and is figuring out how much money a large box of popcorn should be. Each box has a volume of 132 cubic inches. The height of of the box is 12 inches and length is 4 inches. What is the width of the box? If Kyle needs to pay 5 cents per cubic inch of popcorn how much money will the popcorn in each box cost him?
Answer:
width is 2.75 and $6.60
Step-by-step explanation:
first divided by 132 by 12 which gives you 11 then divided 11 by 4 and you get 2.75.
Dubble Check: to chock multiply 12 x 4 x 2.75 which gives you 132.
Cost: Multiply 132 times 5 and you get 660 then place a decimal point between 6 and 6 to get $6.60
Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=(x²-64)^{1/11} on the domain [-8,9]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum is , which occurs at x= (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)
B. There is no absolute maximum.
The absolute maximum is 1.29, which occurs at x= 9
What is absolute extrema?
An absolute extremum of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.
Main body:
Given =
f(x) = [tex](x^{2} -64)^{1/11[/tex]
f' (x) = derivative of function f(x)
f'(x) = 1/11 . 2x[tex](x^{2} -64)^{-10/11[/tex]
= 2x/11[tex](x^{2} -64)^{-10/11[/tex]
putting f'(x) = 0
2x/11[tex](x^{2} -64)^{-10/11[/tex] = 0
[tex](x^{2} -64)^{-10/11[/tex] = 0
[tex]x^{2} -64[/tex] = 0
x² = 64
x = ±8
We are given interval [-8,9].
Hence, calculating f(x) at -8, 8, 9.
f(-8) = 0
f(8) = 0
f(9) = [tex]17^{1/11[/tex]
= 1.29
Hence, absolute maximum value is 1.29 at x=9.
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Evaluating a regression model: A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y = − 0.693 ⋅ x + 28.802 , with an R-squared value of 0.571536. Assume the model indicates a significant relationship between hours of TV watched and the number of situps a person can do. Use the model to predict the number of situps a person who watches 6 hours of TV can do (to one decimal place).
The predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.
The given results of regression:
y = –0.693x + 28.802
The formula for regression equation is:
y = ax + b
So, given that:
a = –0.693
b = 28.802
r2 = 0.571536
r = 0.756
Back to the given results of regression:
y = –0.693x + 28.802
In this case, y represents the number of sit-ups a person can do, and x represents the hours of TV watched per day.
Thus, the predicted number of sit-ups for a person who watches x = 6 hours of TV is:
y = –0.693x + 28.802
y = –0.693 * 6 + 28.802
y = –4.158 + 28.802
y = 24.644
Hence, the predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.
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Please help me, I beg of you..!
Answer:
Equation in terms of k about the average age is:
(2k + 61) / 5 = 17
After solving the equation, k = 12 years
Step-by-step explanation:
Age of Roxanne = k years
Age of the sister = (k + 8) years
Age of brothers = 21, 18 and 14 years
Total number of siblings = 5
Average age of siblings = [k + (k + 8) + 21 + 18 + 14] / 5
or, 17 = [2k + 61] / 5
or, 85 = 2k + 61
or, 24 = 2k
or, 12 = k
So, k = 12 years
Is a click and drag and.
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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