The text mentions a product of two terms and a subtraction. The first term is the number - 13 times the difference of c and d. As a mathematical expression, this would be
[tex](-13)\times(c-d)[/tex]Expanding this expression using the distributive rule, we have
[tex]\begin{gathered} (-13)\times(c-d) \\ =-13c+13d \end{gathered}[/tex]Determine the intervals where the function f(x)=x^3-6x^2 is increasing and decreasing. Also determine the local maximum and minimum values for the function. Sketch a graph of the function showing these maximum and minimum points on your graph.
For the function f(x) = x³ - 6x², we have that:
The function is increasing on these following intervals: (-∞, 0) U (4, ∞).The function is decreasing on the interval (0,4).The local maximum value for the function is at point (0,0).The local minimum value for the function is at point (-4,32).When a function is increasing and when it is decreasing, looking at it's graph?Considering the graph of the function, it is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.Then, it is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when x increases, y decreases.In the context of this function, we have that it is increasing to the left of x = 0 and to the right of x = 4, hence the interval is given by:
(-∞, 0) U (4, ∞).
On the remaining interval, that is, (0,4), the function is decreasing.
The critical points are given as follows:
At x = 0, the function changes from increasing to decreasing, hence there is a local maximum at point (0,0).At x = 4, the function changes from decreasing to increasing, hence there is a local minimum at point (4,32).More can be learned about functions at https://brainly.com/question/24808124
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during spring break a class of 14 children went to walt disney world in florida the price for each child's ticket was &75 while each adult ticket was $85 if the total amount spent on tickets was $1,475 how many adults went on the trip?
hello
cost of the adult tickets = $85
cost of children ticket = $75
let the number of adults be represented by x
let the number of children be represented by y
total number of children that attended = 14
total number of adults that attended = ?
total amount spent on ticket = $1,475
[tex]\begin{gathered} 85x+75y=1475 \\ y\text{ = 14} \\ \text{let's put y into the equation above} \\ 85x+75(14)=1475 \\ 85x+1050=1475 \\ 85x=1475-1050 \\ 85x=425 \\ \text{divide both sides by 85} \\ \frac{85x}{85}=\frac{425}{85} \\ x=5 \end{gathered}[/tex]only 5 adults went on the trip
What would be the annual percentage yield for a savings account that earned $56 in interest on $800 over the past 365 days?
The annual percentage yield (APY) for a savings account that earned $56 in interest on $800 over 365 days is 7%.
The APY (annual percentage yield) is calculated using the formula:
(Interest / Principal)x100
By plugging in the values for interest and principal, we can determine the APY.
Given that,
Principal amount: $800
Interest earned: $56
Time period: 365 days
To calculate the annual percentage yield (APY),
Use the formula:
APY = (Interest / Principal)x100
In this case,
The interest earned = $56
The principal (initial amount) = $800.
Plugging these values into the formula:
APY = (56 / 800)x100
= 0.07x100
= 7%
Hence,
The annual percentage yield for this savings account is 7%.
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all you need is in the photo PLEASE ANSWER FAST
We will investigate the use of Venn diagrams to determine the respective probabilities.
A Algebra 2 class consists of total students ( T ):
[tex]T\text{ = 29 students}[/tex]We will define two sports events ( A ) and ( B ) as follows:
[tex]\begin{gathered} A\text{ : Students who play basketball} \\ B\text{ : Students who play baseball} \end{gathered}[/tex]We will define the respective proportions of students associated with each event using set notations.
[tex]\begin{gathered} A\text{ = 17 , B = 6} \\ p(A)=\frac{17}{29}\text{ , p ( B ) = }\frac{6}{29} \end{gathered}[/tex][tex]A^{\prime}\text{ \& B' = 8 students}[/tex][tex]p\text{ ( A' \& B' ) = }\frac{8}{29}[/tex]We will construct a venn Diagram to grasp the entire distribution of events in the Algebra class:
From the above venn diagram and using the law of probabilities i.e all probabilities concerning a universal set must add up to 1.
[tex]\text{Sum of all probabilities = 1}[/tex][tex]p\text{ ( A ) + p ( B ) - p ( A \& B ) + p ( A' \& B' ) = 1}[/tex]We will use the above universal law of probabilities to determine the probability that a randomly chosen student from the class plays both basketball and baseball ( A & B ):
[tex]\begin{gathered} \frac{17}{29}\text{ + }\frac{6}{29}\text{ + }\frac{8}{29}\text{ - 1 = p ( A \& B )} \\ \\ \text{p ( A \& B ) = }\frac{31}{29}\text{ - 1} \\ \\ \text{p ( A \& B ) = }\frac{31\text{ - 29}}{29}\text{ = }\frac{2}{29} \\ \\ \text{p ( A \& B ) = }\frac{2}{29}\text{ = 0.069 }\ldots\text{ Answer} \end{gathered}[/tex]1/3 - 1/2 (7 - 2/15) + 3/10
You are asked to perform:
[tex]\frac{1}{3}-\frac{1}{2}(7-\frac{2}{15})+\frac{3}{10}[/tex]Wee need to start with the parenthesis.
[tex]7-\frac{2}{15}=\frac{7}{1}-\frac{2}{15}[/tex]We the numerator will be 7 times 15 minus 2 (2x1), and the denominator will be 15 (15x1)
[tex]\frac{105-2}{15}=\frac{103}{15}[/tex]Now, the expression to solve is:
[tex]\frac{1}{3}-\frac{1}{2}\cdot\frac{103}{15}+\frac{3}{10}[/tex]We need to perform the multiplication first (the second term)
[tex]\frac{1}{2}\cdot\frac{103}{15}=\frac{103}{2\cdot15}=\frac{103}{30}[/tex]Now, the expression to solve will be:
[tex]\frac{1}{3}-\frac{103}{30}+\frac{3}{10}[/tex]Now we can solve either the substraction or the sum. Let's go first with the substraction:
[tex]\frac{1}{3}-\frac{103}{30}=\frac{1\cdot30-3\cdot103}{3\cdot30}=\frac{30-309}{90}=\frac{-279}{90}[/tex][tex]\begin{gathered} \frac{-279}{90}\text{ can be simplified since both numerator and denominator are divisible by 3} \\ \end{gathered}[/tex][tex]\frac{-279}{90}=\frac{-93}{30}=\frac{-31}{10}[/tex]Note that it could be simplified twice, dividing both numerator and denominator by 3.
Then, the expression to solve is reduced to:
[tex]-\frac{31}{10}+\frac{3}{10}=\frac{3}{10}-\frac{31}{10}[/tex]We can make that substraction easily since they have the same denominator. 3 - 31 = -28
Then, the first expressions equals to:
[tex]\frac{-28}{10}=\frac{-14}{5}[/tex]Then, the full answer will be:
[tex]\frac{1}{3}-\frac{1}{2}\cdot(7-\frac{2}{15})+\frac{3}{10}=-\frac{14}{5}[/tex]Estimating fractions sums
We are given the following sum of fractions
[tex]\frac{3}{7}-\frac{1}{5}[/tex]We are asked to round off each term to 0, 1/2, or 1.
Notice that the term 3/7 (0.43 in decimal) is closest to 1/5 (0.50 in decimal), so we will round off 3/7 to 1/2
The term 1/5 (0.20 in decimal) is closest to 0, so we will 1/5 to 0.
So, the fractions become
[tex]\frac{1}{2}-0=\frac{1}{2}[/tex]Therefore, the estimated sum of fractions is 1/2
A street built in the city must be 25 feet in width with a tolerance of 0.5 feet. Streets that are not within tolerated widths must be repaired.
Which of the following absolute value inequalities can be used to determine which streets are within tolerance? Let W be the width of the
street.
The absolute value inequalities can be used to determine which streets are within tolerance would be; |W - 32| ≥ 0.5
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.
We have been given that a street built in the city must be 25 feet in width with a tolerance of 0.5 feet.
Let's consider that W is the width of the street.
Then the absolute value inequalities would be;
|W - 32| ≥ 0.5
Hence, absolute value inequalities can be used to determine which streets are within tolerance would be; |W - 32| ≥ 0.5
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Here is the probability model for the blood type of a randomly chosen person in the United States.Blood typeoABABProbability 0.59 0.16 0.1 0.15What is the probability that a randomly chosen American does not have type o blood?% Round to the nearest 0.01%
The complement of an event E, consists of any outcome in an experiment in which event E does not occur.
For the experiment shownin the table, the event is an American chosen at random having blood type O. Therefore the complement of that event in the experiment is that of an American NOT having blood type O.
Therefore;
[tex]\begin{gathered} P\lbrack blood\text{ type O\rbrack=0.59} \\ P\lbrack\text{not blood type O\rbrack=1-P\lbrack{}blood type O\rbrack} \\ P\lbrack\text{not blood type O\rbrack=1-0.59} \\ P\lbrack\text{not blood type O\rbrack=0.41} \end{gathered}[/tex]Expressed as a percentage, this becomes;
[tex]\begin{gathered} P\lbrack\text{not blood type O\rbrack=0.41 x 100} \\ P\lbrack\text{not blood type O\rbrack=41\%} \end{gathered}[/tex]Write an inequality and solve it. Rebecca bought one goldfish for $32. She spends the rest of her money on guppy fish. She starts with $80. Each guppy costs $6. Write an inequality for the number of guppies she can purchase. Part A: Write an inequality to represent the situation. Use g for the variable.
According to the information given in the statement you have
[tex]32+6g\le80[/tex]Where g is the number of guppy fish that Rebecca can purchase.
Now, solving the inequation you have
[tex]\begin{gathered} 32+6g\le80 \\ \text{ Subtract }32\text{ from both sides of the inequality} \\ 32+6g-32\le80-32 \\ 6g\le48 \\ \text{ Divide }by\text{ 6 on both sides of the inequality} \\ \frac{6g}{6}\le\frac{48}{6} \\ g\le6 \end{gathered}[/tex]Therefore, Rebecca can purchase 6 guppy fish.
25% of _________________________is 6.
Answer:
24
Step-by-step explanation:
25/100 = 6/x
when you use the butterfly method or cross multiply you get: 25x = 600
25x/25 is just x
600/25= 24
so x=24 and it is 24
hope this helps!!!
I need help on the first one it’s confusing for me and it’s geometry
$ 6'282,312.524
Explanation
Step 1
find the length of the street:
we have a rigth triangle, then
Let
[tex]\begin{gathered} \text{side}1=\text{ 6 miles} \\ \text{side}2=\text{ 9 miles} \\ \text{hypotenuse = new str}et=\text{ h} \end{gathered}[/tex]so, we need to find the valur for hypotenuse, to do that, we can use the Pythagorean theorem, it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} (Side1)^2+(Side2)^2=h^2 \\ \text{replace} \\ (6m)^2+(9m)^2=h^2 \\ 36m^2+81m^2=h^2 \\ 117m^2=h^2 \\ \sqrt[]{117m^2}=\sqrt{h^2} \\ \text{hence} \\ h=10.81\text{ mi} \end{gathered}[/tex]Step 2
find the total cost,
a) convert the length from miles to ft,so
[tex]\begin{gathered} 10.81\text{ mi(}\frac{5280\text{ ft}}{1\text{ mi}}\text{)}=5711.9322 \\ 5711.9322\text{ft} \end{gathered}[/tex]b) finally, to know the total cost multiply the length by the rate,so
[tex]\begin{gathered} \text{total cost= ralte}\cdot length\text{ ( ft)} \\ \text{total cost= }110\frac{\text{ \$}}{ft}\cdot5711.9322\text{ ft} \\ \text{total cost= \$ }6^{\prime}282,321.542 \end{gathered}[/tex]therefore, the estimated cost is
$ 6'282,312.524
I hope this helps you
Question: Four times the difference of half a number and 1 is 20.Can someone please help me the answer choices are in the picture
We have the following:
[tex]4\cdot(\frac{1}{2}x-1)=20[/tex]The answer is the first option
A point representing the location of a library is shown on the coordinate grid. A museum is located 3.75 units from the library.
We are going to plot the library located at coordinate (3,4)
Then let's plot the museum which is located at 3.75 units.
Which is the equation of a line in point-slope form containing the points (-3, -5) and (1, -3).
Responses
y+3=2(x−1)y plus 3 is equal to 2 times open paren x minus 1 close paren
y−1=2(x−3)y minus 1 is equal to 2 times open paren x minus 3 close paren
y+3=2(x+1)y plus 3 is equal to 2 times open paren x plus 1 close paren
y−1=12(x+3)y minus 1 is equal to 1 half times open paren x plus 3 close paren
The equation of the line in point-slope form containing the points (-3, -5) and (1, -3) is (y + 5) = 1/2(x + 3)
How to determine equation of the line in point slope formEquation of line in point-slope form is the equation of the form
(y - y') = m(x - x')
where y' and x' are points on the y and x coordinate respectively
m = slope
slope, m of points (-3, -5) and (1, -3) is
m = (-3 - -5) / (1 - -3)
m = (-3 + 5 )) / (1 + 3)
m = 2 / 4
m = 1/2
Using point (-3, -5) the equation of the line is
(y - y') = m(x - x')
(y - -5) = 1/2(x - -3)
(y + 5) = 1/2(x + 3)
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PLEASE HELP DUE IN 30 MINS and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
x = 19
Step-by-step explanation:
(4x - 4) and (6x - 6) are a linear pair and sum to 180° , that is
4x - 4 + 6x - 6 = 180
10x - 10 = 180 ( add 10 to both sides )
10x = 190 ( divide both sides by 10 )
x = 19
A student solved a system of equations by elimination. The answer is not correct. Describe the error in the solution.Original Problem:3−2=8+=2Student Work:3−2=82+2=25=10=2
Let:
[tex]\begin{gathered} 3x-2y=8_{\text{ }}(1) \\ x+y=2_{\text{ }}(2) \end{gathered}[/tex]Multiply (2) by 2:
[tex]2x+2y=4_{\text{ }}(3)[/tex]Add (1) and (3):
[tex]\begin{gathered} 3x+2x-2y+2y=8+4 \\ 5x=12 \\ x=\frac{12}{5} \end{gathered}[/tex]The error is: when the student multiply the equation (2) by 2, he only multiplied the left side of the equation by 2, but he needed to multiply the right side as well.
What is the image of the point (-7,-6) after a rotation of 270° counterclockwise about the origin?
Take into account that a rotation of 270° counterclockwise around the origin can be defined as follow:
T(x,y) => T'(y,-x)
Then, for the point (-7,-6) you have:
(-7,-6) => (-6,7)
Hence, the image of the point is (-6 , 7)
I need some help to tell whether a table is a linear or non linear function
A linear equation has the form:
[tex]y=mx+b[/tex]Let's find a linear equation using the table, and let's check if it satisfy all the points:
[tex]\begin{gathered} x=0,y=-1 \\ -1=b \\ ------ \\ x=1,y=1 \\ 1=m+b \\ 1=m-1 \\ m=2 \end{gathered}[/tex]so:
[tex]y=2x-1[/tex]Let's check the other points:
[tex]\begin{gathered} x=-3 \\ y=2(-3)-1=-6-1=-7_{\text{ }}True \\ ------ \\ x=-2 \\ y=2(-2)-1=-4-1=-5_{\text{ }}True \\ ------ \\ x=-1 \\ y=2(-1)-1=-2-1=-3_{\text{ }}True \end{gathered}[/tex]Therefore, we can conclude it is a linear function.
Hello hope you can help me with 6,11,and 22 please
For 6,
The unknown number is x
Then, 3 more than the number will be
[tex]x+3[/tex]The answer is labelled G
For 11,
Just as it clearly stated "5 minus a number"
Then that is
[tex]5-x[/tex]The answer is labelled S
For 22,
3 fewer than a number can be re-translated 3 is less than a number.
Then it is
[tex]3-x[/tex]The answer is labelled G on the left hand side
A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 90% per year. Estimate the population after one year? After two years?
The amount of deer has to be calculated by this equation:
[tex]A=P(1+r)^y[/tex]Where P is the population of deers, r is the growth percentage, and y is the number of years.
[tex]A_{1year}=50(1+0.9)^1=95\text{ deers.}[/tex][tex]A_{2years}=50(1+0.9)^2=180.5\text{ deers.}[/tex]Which statement is true about the values x=1.5 and y=-1.5?
GIVEN:
We are told that two equations were plotted on the coordinate grid, and these are;
[tex]\begin{gathered} -2y+6x=12---(1) \\ \\ 4x+12y=-12---(2) \end{gathered}[/tex]The graphs intersect at the point;
[tex](1.5,-1.5)[/tex]Required;
Select which statement is true about the values of x and y.
Step-by-step solution;
We will begin by plotting both lines on a graph page as follows;
The graph above clearly shows that the point of intersection (1.5, -1.5) is the ONLY solution that satisfies both linear equations.
Therefore,
ANSWER:
They are the only values that make both equations true.
The correct answer is option A.
Manuel's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Manuel $5.80 per pound, and type B coffee costs $4.55 per pound. This month, Manuel made 115 pounds of the blend, for a total cost of $585.75. How many pounds of type A coffee did he use?
92.75 pounds of type A are used and 22.25 pounds of type B coffee are used.
It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Let "a" denote the quantity of type A utilized in pounds, and "115-a" denote the quantity of type B used. Hence, the equation is:
$585.75 = 5.80 a + 5.9(115-a)
-92.75 = 5.80 a - 5.90 a
0.1a = 92.75
a = 92.75
solving for the number of pounds of type A
So type B coffee is obtained as,
= 115 - 92.75
= 22.25
Thus,92.75 pounds of type A are used and 22.25 pounds of type B are used.
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I need to find the point of intersection Y=.5x+3 & Y=2x-9
SOLUTION:
Step 1:
In this question, we are meant to find the point of intersection of the two lines:
[tex]\begin{gathered} \text{y = 0. 5 x + 3 -- equation 1} \\ \text{and } \\ \text{y = 2x -9 -- equation 2} \end{gathered}[/tex]Step 2:
The details of the solution are as follows:
From the graph, we can see the point of intersection of the two lines
is at:
[tex]\begin{gathered} \text{ x= 8} \\ y=\text{ 7} \end{gathered}[/tex]
What is the y-intercept of f(x) =
100-(3) * ?
5
A. (1,0)
B. (0,0)
(¹3)
D. (0, 1)
C.
Answer:
X intercepts: (100/3,0)
Y intercepts: (0,100)
Write out step by step what needs to be done in order to get the answer to the expressio
To get the answer for this expression, we can follow the next steps:
1. Obtain the product of each of the multiplications inside the square bracket:
[tex]5\lbrack9(2)-2(8)\rbrack=5\cdot\lbrack9\cdot(2)-2\cdot(8)\rbrack=5\cdot\lbrack18-16\rbrack[/tex]2.Now, subtract what is inside the right brackets, and then multiply the resulting numbers:
[tex]5\cdot\lbrack2\rbrack=5\cdot2=10[/tex]Therefore, the resulting answer is equal to 10.
The following scatterplot represents the number of negative consumer reviews for a given model of cell phone and the total number of that same cell phone model that were sold. Is it reasonable to predict that if there are 75 negative reviews the number of cell phones sold of that same model will be close to 850,000? Why or why not
According to the plotted line, we can see that for 75 negative reviews, an approximate number of phones sold is 600,000, that is not close to 850,000. Therefore, it is not reasonable to predict that if there are 75 negative reviews, the number of cell phones sold will be close to 850,000
A student argued that a pizza cut into 12 pieces was more than a pizza cut into 6 pieces. How would you respond?
I would respond with a vehement disagreement because using the division operation, the more the divisor, the less the quotient.
What is a division operation?A division operation is one of the four basic mathematical operations.
The division operation breaks a number or object into many parts. The number to be divided is known as the dividend.
The dividing number or parts are called the divisor while the quotient is the result of the division operation.
For instance, when 144 is divided by 12, the result is 12. When the same number is divided by 6, the result is 24. From this, we can determine the division operation that yields more value.
Thus, a pizza cut into 12 pieces does not yield more than a pizza cut into (divided) 6 pieces.
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Gymnosperms and angiosperms are both vascular plants within the Kingdom Plantae.
Step 1
Angiosperms and gymnosperms are both seed-bearing plants with a few similarities.
Step 2:
The vascular system is common for the both of them, consisting of conjoint and vascular bundles (open and collateral). The ovules of both angiosperms and gymnosperms develop into seeds.
Step 3
a) Angiosperms are flowering plants, and include grasses, herbs, shrubs and most deciduous trees, while (b) gymnosperms are conifers. Both produce seeds but have different reproductive strategies.
Final answer
seeds
A tractor trailer contains a cab for the driver and the trailer for the cargo. Suppose the weight of the cab is 7,600 pounds, and the weight of the trailer is 10,800 pounds. The trailer is carrying palettes for a shipment where each palette is 1,200 pounds. What is the total weight of the tractor trailer when there are 31 palettes in the trailer?
The total weight of the trailer is 55,600 pounds including the cab, trailer and the palettes
Weight of the cab = 7600 pounds
Weight of the trailer = 10,800 pounds
Weight of each palette carried by trailer = 1200 pounds
Weight: Weight is the result of multiplying the mass by the acceleration that is acting on it. Usually, it's the mass of the object times the acceleration brought on by gravity.
So, total weight of 31 palettes = 1200*31 = 37200 pounds
Total weight of the tractor = Weight of the cab + Weight of the trailer + Weight of 31 palettes
= 7600 + 10,800 + 37,200
= 55,600 pounds
So, total weight = 55,600
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What is f(6) for the quadratic function graphed shown below?
In order to find the value of f(6) we look in the graph for the point of the curve in the position of x = 6, then we see with wich value of the y axis its correspond. We see that the value of y is y = 6.
So the answer is: f(6) = 4
