The sum of -1 (3/4) and 2 (1/2) is the same as the difference between 2 (1/2) and 1 (3/4).
Firstly, we will convert the mixed fractions into improper fractions.
-1 and 3/4 = -7/4
2 and 1/2 = 5/2
Addition of -1 (3/4) and 2 (1/2) = -7/4 + 5/2 = -7/4 + 10/4 = 3/4
Difference between 2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4
As both the values equal to 3/4 , we can say that the addition of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
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Need help with #6 don’t know how to find truth values.
The statement p is: Saturn is a planet.
The statement q is: Hong Kong is a city.
Now the first part of our composite proposition is:
[tex]p\lor\sim q[/tex]This means that we have to negate the statement q, this would be: Hong Kong is not a city.
Now we make the disjunction between the statement p and the negation of q, then we have:
[tex]p\lor\sim q\text{ means: Saturn is a planet or Hong Kong is not a city}[/tex]The second part of our composite porposition is:
[tex]\sim p\wedge q[/tex]This means that we have to negate the statement p, then we have: Saturn is not a planet. Then we make the conjunction between the negation of p and q, then we have:
[tex]\sim p\wedge q\text{ means: Saturn is not a planet and Hong Kong is a city}[/tex]Finally we make the disjunction between the statements discussed so far, hence the statament
[tex](p\lor\sim q)\lor(\sim p\wedge q)[/tex]means:
Saturs is a planet or Hon kong is not a city OR Saturn is not a planet and Hong Kong is not a city.
Now, to determine the truth value of the composite proposition we have to remember that a disjunction is TRUE if one of the statements that make it is true and that the conjunction is TRUE only if both stataments that make it are true.
The first statement is: Saturn is a planet or Hong kong is not a city. Since this is a disjunction and the statement Saturn is a planet is TRUE, then the proposition is true.
The second statement is: Saturn is not a planet and Hong Kong is not a city. Since this is a conjunction and the statement Saturs is not a planet is FALSE, the the second statement is FALSE.
Now since the composite statemtent is made of a TRUE and a FALSE statement and it is a disjunction we conclude that the truth value of the statement given is TRUE.
The coordinates of rhombus abcd are a(-4,-2) b(-2,6) c(6,8) d(4,0). What is the area of the rhombus
First, graph the rhombus:
Area of a rhombus = Product of diagonals / 2
Find the length of the diagonals:
Distance between points:
[tex]\sqrt[\placeholder{⬚}]{(x2-x1)^2+(y2-y1)2^}[/tex]Diagonal AC
[tex]AC=\sqrt[\placeholder{⬚}]{(6-(-4))^2+(8-(-2))^2}[/tex]AC= 10√2
Diagonal BD
[tex]BD=\sqrt[\placeholder{⬚}]{(4-(-2))^2+(0-6)^{^2}}[/tex]BD=6√2
Area= AC x BD / 2
Area = [(10√2) x (6√2)]/2
Area = 60
Ruth is a costume designer for the local children's theater company. Yesterday, she sewed 1 female costume and 5 male costumes, which used 52 yards of fabric. Today, she sewed 5 female costumes and 2 male costumes, which used a total of 76 yards. How many yards of fabric does each type of costume require? yards of fabric, and every male costume requires Each female costume requires yards.
Given:
Yesterday:
1 female and 5 male = 52 yards
Today:
5 female and 2 male = 76 yards
Let's find the number of yards of fabric each type of costume requires.
Let F represent the number if yards for each female customer use.
Let M represent the number of yards each male customer uses.
From this situation, we have the system of equations:
1F + 5M = 52
5F + 2M = 76
Now, let's solve the system of equations simultaneously using substitution method.
Rewrite equation 1 for F:
F = 52 - 5M
Substitute 52 - 5M for F in equation 2:
[tex]\begin{gathered} 5F+2M=76 \\ \\ 5(52-5M)+2M=76 \\ \\ 5(52)+5(-5M)+2M=76 \\ \\ 260-25M+2M=76 \\ \\ 260-23M=76 \end{gathered}[/tex]Subtract 260 from both sides:
[tex]\begin{gathered} 260-260-23M=76-260 \\ \\ -23M=-184 \end{gathered}[/tex]Divide both sides by -23:
[tex]\begin{gathered} \frac{-23M}{-23}=\frac{-184}{-23} \\ \\ M=8 \end{gathered}[/tex]Substitute 8 for M in either of the equations:
F = 52 - 5M
F = 52 - 5(8)
F = 52 - 40
F = 12
Therefore, we have the solution:
F = 12, M = 8
Each male customer requires 8 yards while each female customer requires 12 yards.
ANSWER:
• Male customer = 8 yards
,• Female customer = 12 yards
The area of Eh Kri's rectangular backyard, in square feet, can be found using the expression 2(4x + 5y). Use the distributive property to write an equivalent expression for the area of Eh Kri's backyard.
The area of a rectangular backyard = 2(4x - 5y)
The algebraic expression has a equivalent expression as = 2 x 4x + 2 x 5y
= 8x + 10y
“Order these numbers from smallest to largest: 2/3, 7/8, 0.5, 2/5. Justify your answer”
Step 1
Given
[tex]\frac{2}{3},\frac{7}{8},\frac{1}{2}\text{ and }\frac{2}{5}[/tex]Required: To arrange them from smallest to largest.
Note: 0.5 = 1/2
Step 2
Find the lowest common multiple of the numbers in the denominator : 3,8,2 and 5
Hence, the lowest common multiple will be
[tex]2\times2\times2\times3\times5\text{ = 120}[/tex]Step 3
Use the LCM to arrange the numbers as seen below
From the numbers gotten from using the LCM, we can now conclude
Step 4
Arrange them from smallest to largest
[tex]\begin{gathered} \text{From the size of the numbers related to the image above,} \\ 80->\frac{2}{3},\text{ 105}\to\frac{7}{8},\text{ 60}\to\frac{1}{2},\text{ 48}\to\frac{2}{5} \end{gathered}[/tex]We can arrange them as follows
[tex]\frac{2}{5},\frac{1}{2},\frac{2}{3},\frac{7}{8}[/tex]a license plate in a certain state consists of 4 digits, not necessarily distinct, and 2 letters, also not necessarily distinct. these six characters may appear in any order, except that the two letters must appear next to each other. how many distinct license plates are possible?
33,800,000 are total distinct six characters license plates possible such that the two letters must appear next to each other. We can solve it by using combination formula ( ⁿCr ) .
Total number of digits are 10 i.e., 0,1,2,3,4,5,6,7,8,9. We have given the option to select any four digits out of 10 with repetition. So, we use combination formula
ⁿ C r = n!/(r! ×(n-r)! )
For 1ˢᵗ digit, the number ways to choose the 1ˢᵗ digit is ¹⁰C ₁= 10
For 1ˢᵗ letter, the number of ways to choose the 1ˢᵗ letter is ²⁶C ₁= 26
There are 10×10×10×10 = 10⁴ ways to choose four digits . In a similar way, the total number of letters for choice is 26 ; i.e., from A to Z. We were given the task of choosing two letters from a list of 26 , which were not necessarily distinct .
There are 26×26 = 26²ways to choose the two letters . For the letters to be next to each other, they can be the 1ˢᵗ and 2ⁿᵈ, 2ⁿᵈand 3ʳᵈ, 3ʳᵈand 4ᵗʰ, 4ᵗʰand 5ᵗʰ, 5ᵗʰ and 6ᵗʰ characters . So, there are 6-1 = 5 are choices for the positions of the letters .
Therefore, numbers of distinct license plates is 5×10⁴× 26² = 33,800,000
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Complete the flow proof of the converse of the corresponding angles theorem. Fill in the blanks.
When two lines and a transversal form comparable angles that are congruent, the lines are parallel, which is the converse of the corresponding angles theorem's flow proof. Which means that line c ║ to line d.
What are perpendicular lines?The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I
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for rayleigh winds with an average wind speed of 8 m/s: a. how many hours per year do the winds blow at less than 13 m/s? (5') b. how many hours per year are wind speeds above 25 m/s? (5')
A. 7658.8 hr/year
B. 4.082 hr/year
C. 99206 kwh
Moreover, The annual average wind speed was calculated directly at 4.56 m/s. Using the Weibull distribution, the annual wind speed is 4.55 m/s, while using the Rayleigh distribution it is 4.523 m/s. The annual wind power density was directly calculated to be 114.54 W/m2.
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the altitude of an airplane is decreasing at a rate of 45 feet per second what si the change in altitude of the airplane over a period of 34 seconds
a -1,530
b 79
c -79
d 1530
Answer:
Step-by-step explanation:
d that the answer pls mark me brianlest
Find the area.
a.1604 ft
b.2600 ft
c.2160 ft
d.2180 ft
Answer:
d.2180
Step-by-step explanation:
add the two sides and subtract that one number on top I believe
3. there are 27 tasks available. you will be randomly assigned 12 of them. there are 10 of them that you want to do. (a) what is the probability that you will be assigned none of the tasks that you want? (b) what is the probability that you will be assigned exactly 7 of the tasks that you want? (c) what is the probability that you will be assigned at least 1 of the tasks that you want? (d) what is the probability that you will be assigned at least 7 of the tasks that you want?
On solving using combinations (C) we get the answers for part a)the probability that you will be assigned none of the tasks that you want = 0.035% b) the Probability that I am assigned exactly 7 of the tasks that I want = 0.0427 c)The probability that I am assigned at least one of the tasks I want = 0.9996 d)Probability that I am assigned at least 7 of the tasks I want = 0.049
a) There are 27 tasks and 10 tasks I want to do. Thus there are 17 tasks I do not want to do. I am randomly assigned 12 tasks. The probability that I will be assigned none of the tasks that I want is p = 17C12 / 27C12 = 3. 55 * 10 ^ (-4) = 0.035 %
b) The probability that I am assigned exactly 7 of the tasks that I want
p = 10C7 * 17C5 / 27C12 = 0.0427 = 4.27%
c) The probability that I am assigned at least one of the tasks I want
p = 1 - 17C12 / 27C12 where 17C12 / 27C12 is the probability that I get assigned 0 tasks I want.
Thus, p = 1 - (7/19665) = 0.9996
d)Probability that I am assigned at least 7 of the tasks I want
p = (10C7*17C5+10C8*17C4 + 10C9*17C3 + 10C10*17C2) / 27C12
⇒ p = 17 / 345 = 0.049 = 4.9%
The usefulness of combinations in finding out probability:
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PLSSSSSSSSS HELP DUE SOON!!!
Answer:
option 4
Step-by-step explanation:
let c represent the old amount , then twice the old amount is 2c.
1.5 less than twice the old amount is 2c - 1.5 , so
2c - 5 = 6
David has a wooden board that is 6 feet long. how many pieces can be cut from the board if the length of each piece is 1/3 of a foot
total length = 6 ft
length of the piece = 1/3
[tex]\text{Number of pieces = 6 / }\frac{1}{3}\text{ = }\frac{\frac{6}{1}}{\frac{1}{3}}\text{ = }\frac{6x\text{ 3}}{1\text{ x 1}}=\text{ }\frac{18}{1}\text{ = 18}[/tex]There will be 18 pieces
Find the missing dimension of the figure shown to the right round to the nearest 10th
Given the right triangle:
The Pythagorean theorem states that:
[tex]a^2+b^2=c^2[/tex]From the problem, we identify:
[tex]\begin{gathered} b=14^{\prime}^{\prime} \\ c=19^{\prime}^{\prime} \end{gathered}[/tex]And a is our missing value. Using the Pythagorean theorem:
[tex]\begin{gathered} a+14^2=19^2 \\ a^2=361-196 \\ a=\sqrt[]{165} \\ a=12.8^{\prime}^{\prime} \end{gathered}[/tex]24, 10:33:13
If f(x) = 4x4 - 3x² + 4, then what is the remainder when f(x) is divided by
x + 3?
Answer:Given : f(x)=x
4
−3x
2
+4
f(2)=(2)
4
−3(2)
2
+4
=16−12+4=8
This can also be verified by the actual divison
what is the formula to find the circumference of a circle?
Answer:
C = 2 \pi r
Step-by-step explanation:
write the answer in standard form(-3x^4 + x^6 – 9x^5+ 2x^2– 7) + (-2x^5 + x - 4x^2– x^4 + 12)
Simplify the expression and express in standard form.
[tex]\begin{gathered} (-3x^4+x^6-9x^5+2x^2-7)+(-2x^5+x-4x^2-x^4+12) \\ =-3x^4+x^6-9x^5+2x^2-7-2x^5+x-4x^2-x^4+12 \\ =x^6-11x^5-4x^4-2x^2+x+5 \end{gathered}[/tex]So answer is,
[tex]x^6-11x^5-4x^4-2x^2+x+5[/tex]Paul bought 1 7/8 m of fabric to make a shirt, while Rita bought 1 3/4 m to make her shirt. How much MORE fabric did Paula buy then Rita?
Fabric bought by Paul and Rita to make a shirt was 1 7/8 m and 1 3/4 m respectively , Paul bought 1/8 m more than Rita.
As given in the question,
Length of fabric bought by Paul to make his shirt = 1 7/8 m
Length of fabric bought by Rita to make his shirt = 1 3/4 m
Convert length of fabric into proper fraction
Paul fabric = 1 7/8 m
= 15 /8 m
Rita fabric = 1 3/4 m
= 7 /4 m
Length of Paul fabric more than Rita
Length of more fabric bought by Paul than Rita = (15 /8) - ( 7/4)
= (15/8) - (14/8)
= 1/8 m
Therefore, fabric bought by Paul and Rita to make a shirt was 1 7/8 m and 1 3/4 m respectively , Paul bought 1/8 m more than Rita.
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A boat can travel 228 miles on 19
gallons of gasoline. How much gasoline
will it need to go 48 miles?
Round the answer to two decimal digits
Answer: 4 gallons
Step-by-step explanation:
The boat can travel 228 miles on 19 gallons of gasoline. We can divide 228 by 19 to find out how many miles the boat can travel on 1 gallon of gasoline, which is 12. For the boat to go 48 miles, we can divide 48 by 12 to get the answer, which is 4. The boat can travel 48 miles with 4 gallons of gasoline.
Taylor works on an art project that uses only rectangular pieces of paper. The first rectangle ha length 3/8 and width of 3in. Detriment wether the dimensions of each rectangle described as a proportional to the dimensions of tailors first rectangle
By comparing the dimensions above with the dimensions of Taylor's first rectangle, we have the following:
No, a length of 6 in, width 3/4 in. is not proportional.Yes, a length of 1/2 in, width 4 in. is not proportional.No, a length of 1 1/8 in, width 9 in. is not proportional.No, a length of 3 in, width 5 5/8 in. is not proportional.What is a direct proportion?Mathematically, a direct proportion (direct variation) can be represented the following mathematical expression:
y = kx
Where:
y and x are the variables or dimensions.k represents the constant of proportionality.For the dimensions of the rectangular pieces of paper to be proportional, the length and width must remain in a constant ratio.
Next, we would determine the constant of proportionality (k) as follows:
k = y/x
k = (3/8)/3
k = 3/24
k = 1/8
For dimension 1, we have:
k = y/x
k = (6)/(3/4)
k = 24/3
k = 8 (No).
For dimension 2, we have:
k = y/x
k = (1/2)/4
k = 1/2 × 1/4
k = 1/8 (Yes).
For dimension 3, we have:
k = y/x
k = (1 1/8)/9
k = (9/8)/8
k = 9/8 × 1/8
k = 9/64 (No).
For dimension 4, we have:
k = y/x
k = (3)/(5 5/8)
k = 3/(45/8)
k = 3 × 8/45
k = 24/45 (No).
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Complete Question:
Taylor works on an art project that uses only rectangular pieces of paper. The first rectangle has length 3/8 in. and width 3 in. Determine which dimensions below are proportional to the dimensions of Taylor's first rectangle.
Graph the solution to the following system of inequalities. Don’t forget to answer the point in the solution set.
Given the following System of Inequalities:
[tex]\begin{cases}7x+4y<16 \\ -5x+4y\ge12\end{cases}[/tex]You need to remember that the Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
The steps to graph the System of Inequalities are:
1. In this case, you know that the first line is:
[tex]7x+4y=16[/tex]So you need to solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 4y=-7x+16 \\ \\ y=\frac{-7}{4}x+\frac{16}{4} \\ \\ y=-\frac{7}{4}x+4 \end{gathered}[/tex]You can identify that the y-intercept is:
[tex]b_1=4[/tex]2. Since the value of "y" is zero when the line intersects the x-axis, you can substitute that value into the equation and solve for "x", in order to find the x-intercept:
[tex]\begin{gathered} 7x+4y=16 \\ 7x+4(0)=16 \\ 7x=16 \\ \\ x=\frac{16}{7}\approx2.286 \end{gathered}[/tex]3. Now you know that the first line passes through these points:
[tex](0,4);(2.286,0)[/tex]4. The second line is:
[tex]-5x+4y=12[/tex]So you can solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 4y=5x+12 \\ \\ y=\frac{5}{4}x+\frac{12}{4} \\ \\ y=\frac{5}{4}x+3 \end{gathered}[/tex]Notice that the y-intercept is:
[tex]b_2=3[/tex]5. Knowing that "y" is zero when the line intersects the x-axis, you can substitute that value into the equation of the second line and solve for "x" to find the x-intercept:
[tex]\begin{gathered} -5x+4y=12 \\ -5x+4(0)=12 \\ -5x=12 \\ \\ x=\frac{12}{-5} \\ \\ x=-2.4 \end{gathered}[/tex]a $25$ foot ladder is resting against a wall so that the bottom of the ladder is $7$ feet from the wall. the bottom of the ladder starts slipping away from the wall at a rate of $1$ foot per second. how many feet per second is the top of the ladder sliding down the wall when it is $15$ feet above the ground?
The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. When the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.
Given that,
The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. A feet per second of the ladder's bottom begins to slide away from the wall.
We have to find when the ladder is 15 feet above the ground, how many feet per second is the top of the ladder falling down the wall.
Let us take x = height where the ladder hits the building
7 squared + x squared=25 squared
49+x squared=625
x squared=576
x=24 feet
Now,
If it slips 15 feet that 24-15=9 feet
Let x = distance from wall:
x² + 9² = 25²
x² + 81= 625
x² = 544
x = 23.3 feet
Therefore, when the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.
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Solve the unequality
10 is greater than X over six
Answer:
x25 - 24.1x square would be your answer
Step-by-step explanation:
what are the coordinates of the image P for a dilation with center (0,0) and a scale factor 2? answer choices :• (2,0) • (0,6)• (-4, 2)• (0,5)
Rule for a dilation with center (0,0)
[tex](x,y)\rightarrow(kx,ky)[/tex]k is the scale factor.
For point P (0,3):
[tex]\begin{gathered} P(0,3)\rightarrow P^{\prime}(2(0),2(3)) \\ P(0,3)\rightarrow P^{\prime}(0,6) \end{gathered}[/tex]Then the coordiantes of point P after the dilation are (0,6)What is the end behavior of the polynomial function? Drag the choices into the boxes to correctly describe the end behavior of the function. f(x)=6x9−6x4−6 f(x)=−3x4−6x+4x−5
As x→−∞
As x→∞
The end behavior of the polynomial function is as shown in the attached picture.
What is polynomial function?Polynomial functions refers to equation that consists of variables that have non negative exponents or powers. The when there is only one term in the equation it is referred to as monomial
What is end behavior of polynomial function?The end behavior refers to the behavior of the function at the extremes of the x direction.
The end behavior of a polynomial function is controlled by the term that has the leading terms
In the given question,
The first question has 6x^9 as the term that controls the end behavior hence substituting the -∞ and +∞ gives the end behavior as attachedSimilarly, the second function has -3x^4 as the leading term substituting the -∞ and +∞ gives the end behavior as attachedLearn more on end behavior at: https://brainly.com/question/1365136
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I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Using the information of the factors f ( x ) are
( x + 1 ) ⇒ f ( -1 )( x - 4 ) ⇒ f ( 4 )( 2x - 3 ) ⇒ f ( 3/2 )What is a function in math?The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include
The dependent variableThe independent variableThe given function is substituted in the several equations given but the equations that yielded the desirable result of f ( x ) = 0 are:
option 4option 5option 6Therefore they are the correct choice
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A test is worth 100 pts. Each problem is worth either 2 or 5 pts. The number of 5 pt problems is 22 less than 2pt problems. How many problems of each type are on the test
The number of two pt problems are 30 and 5 pt problems are 8.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x= one type of question
Let x-22= the other type of questions
100=2x+5(x-22) Distribute
100=2x+5x-110
100=7x-110
100+110=7x
210=7x
Divide both sides by 7
one type 30=x
second type 30-22=8
Hence the number of two pt problems are 30 and 5 pt problems are 8.
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two functions are given below: f(x) and h(x). state the axis of symmetry for each function and explain how to find it
HELP ME PLEASE
The axis of symmetry for function
f(x) is x = 8 and for h(x) is x = 3.
We know that the quadratic equation in vertex form is, y = a (x - m)² + n
where (m, n) is the vertex of the parabola.
And, the axis of symmetry is x = m.
Consider function f(x)
f(x) = -4(x - 8)² + 3
This function represents a quadratic equation in vertex form with vertex (8, 3)
So, the axis of symmetry for function f(x) would be x = 8
We know that the axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetrical.
Consider the function h(x)
We can observe that the vertex of parabola is (3, 2)
So, the axis of symmetry would be x = 3.
Therefore, the axis of symmetry for function
f(x) is x = 8 and for h(x) is x = 3.
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kid had 10 apples and he gic
Answer:
The meal cost $14.51 per person.
Step by step explanation:
Meal cost: 46.72
Sales tax: 8%
Then.
then we take out 8% of the value
[tex]46.72\text{ x 0.08 =3.74}[/tex][tex]46.72+3.74\text{ = 50.46}[/tex]Tip : 15% (meal and sales tax)
[tex]50.46\text{ x 0.15 = 7.57}[/tex][tex]50.46\text{ + 7.57 = 58.03}[/tex]There are 4 people.
[tex]\frac{58.03}{4}=14.51[/tex]Here are the scores that Jenna has received on her seven quizzes: 16, 11, 20, 16, 12, 17, 18 What is the lower quartile?
Based on the scores that Jenna received on her quizzes, the lower quartile can be found to be 12
How to find the lower quartile?To find the lower quartile, use the formula:
= (Number of scores + 1) x 1/4
But before that, you need to arrange the scores that Jenna received, from ascending order:
11, 12, 16, 16, 17, 18, 20
Then use the formula to find the position of the lower quartile:
= (7 + 1) x 1/4
= 8 x 1/4
= 2
It is in the second position. The lower quartile score is therefore 12.
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Based on the scores that Jenna received on her quizzes, the lower quartile would be; 12
What is quartile?Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
To determine the lower quartile, use the formula as;
= (Number of scores + 1) x 1/4
But before that, we need to arrange the scores that Jenna received, from ascending order which is;
11, 12, 16, 16, 17, 18, 20
Thus, use the formula for the position of the lower quartile:
= (7 + 1) x 1/4
= 8 x 1/4
= 2
Hence, It's in the second position. The lower quartile score is; 12.
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