The three consecutive even integers are -2, 0 and 2.
How to calculate the value?Let the three consecutive even integers be x, x+2 and x+4.
Since the product of the first two is taken, the result is four less than the square of the third one. This will be:
x(x + 2) = (x + 4)² - 4
x² + 2x = x² + 8x + 16 - 4
x² + 2x = x² + 8x + 12
Collect like terms
x² - x² + 2x - 8x - 12
-6x - 12 = 0
-6x = 12.
Divide
x = -12/6
x = -2
x + 2 = -2 + 2 = 0
x + 4 = -2 + 4 = 2
They're -2, 0, and 2.
Learn more about integers on:
brainly.com/question/17695139
#SPJ1
Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. How many ways can this be done, if the order of the choices is not taken into consideration
Thus, the number of ways in which to choose 4 letters, without replacement, from 17 distinct letters is 57,120.
Define the term permutation?The term permutation applies to a mathematical computation of a number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something can be organized or arranged.Total distinct letters are 17.
There are 17 alternatives for the initial letter if there are 17 letters.
There are just 16 alternatives left once you remove the letter.
Each time you remove a letter, the bag contains one fewer letter.
Number of ways = 17 x 16 x 15 x 14
Number of ways = 57,120
Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.
To know more about the permutation, here
https://brainly.com/question/1216161
#SPJ4
a 61 mg of a vaccine is given to a patient to prevent measles. the vaccine leaves the body at a rate of 6.1% per hour. define a function g that gives the mass of the vaccine remaining in the body, v, in terms of the number of hours, n since the vaccine was administered. how much of the vaccine remains in the body 24 hours after it was administered? mg use your graphing calculator to determine how many hours passed before there were only 5mg of the vaccine remaining in the body.
The linear equation that represent the amount vaccine that remain is g = 61 - 0.061n. The vaccine remains in the body 24 hours after it was administered 59.536 mg. There were only 5mg of the vaccine remaining in the body after 918.033 hours.
What is rate?
A rate is a unique ratio where the two words are expressed in several units.
Given that the amount of vaccine is 61 mg.
The vaccine leaves the body at a rate of 6.1% per hour.
After 1 hour the body will consume 6.1% = 6.1/100 = 0.061 mg.
After n hour the body will consume 6.1%× n = 0.061n mg.
The remaining amount of vaccine is (61 - 0.061n).
The required linear equation that represent the remaining amount of vaccine is g = 61 - 0.061n.
Putting n =24 in the equation:
g = 61 - 0.061×24
g = 59.536 mg
The vaccine remains in the body 24 hours after it was administered 59.536 mg.
The graph represents that there were only 5mg of the vaccine remaining in the body after 918.033 hours.
To learn more about linear equation, you can visit:
https://brainly.com/question/24085666?
#SPJ4
The variable p represents number of presents. If it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used. If there are 7 presents, how much ribbon is needed? Ribbon is sold in 15 feet packages. How many do you need to buy?
The number of ribbons that is needed for 7 presents is 73 ribbons.
She needs 5 packages.
What is an expression?An expression is simply used to illustrate the relationship between the variables.
In this case, it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used.
The ribbons needed for 7 presents will be:
= 10p + 3
= 10(7) + 3
= 70 + 3
= 73
Since it's sold in 15 feet packages, the number needed will be:
= 73 / 15
= 5
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
If Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.
The time taken to label 750 books if Clare labels books at 15 books per minute is 50 minutes.
How to calculate the time used?In this situation, Clare volunteers at a library during the summer and has to label 750 books and she labels books at 15 books per minute and she takes no breaks.
Let the time taken to label the 750 books be represented by x.
This will be illustrated as:
1/x = 15/750
Cross multiply
(15 × x) = (750 × 1)
15x = 750
Divide
x = 750 / 15
x = 50
The time is 50 minutes.
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
Complete question
Clare volunteers at a library during the summer and has to label 750 books. Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.
X (3x + 5)°
(4x)
Y
(8x - 14)°
B
N
Answer:2
Step-by-step explanation:
1+1 es 2
Christian buys 18 bottles of grapefruit juice at the corner store for a total cost of $15.66. If each bottle costs the same amount, how much is 3 bottles of juice?
Answer:$2.61
Step-by-step explanation:
18=$15.66
÷6 ÷6
3=$2.61
The cost of 3 bottles of juice based on the given ratio will be $2.61.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
18 bottles cost = $15.66
1 bottle cost = $15.66/18 = $0.87/ bottle
For 3 bottles = 3 × $0.87 = $2.61
Hence "The cost of 3 bottles of juice based on the given ratio will be $2.61".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ2
please help!!
the function shown in the graph is f(x)= ???
Answer:
The answer is x^{3}-2x^{2}-5x+6
Step-by-step explanation:
This is because only a Cubic Function would have such a shape. That leaves x^3 functions from there just substitute points and check
Solve for a side in right triangles
Really need help with this one!!
The value of side AC is AC = 3.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
The given triangle ΔABC is a right angled triangle.
So, to find the side AC we can use the cosine ratio,
[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]
AC ≈ 3.
Hence, the length of side AC is 3.
To know more about the right triangle, click on the link
https://brainly.com/question/2437195
#SPJ1
David picked 15 pears. Jenna picked p fewer pears than David. Write an expression that shows how many pears Jenna picked.
Answer:
15-p
Step-by-step explanation:
15-p
To paint a house, a painting company charges
a flat rate of $500 for
supplies, plus $50 for each hour of labor.
a.
How much would the painting company charge to paint
a house that
needs 20 hours of labor? A house that needs 50 hours?
Call the number of hours of labor x.
A flat rate of $500 -> just $500.
$50 for each hour of labor -> 50x (for x hours)
Therefore, we can represent the amount needed for x hours of labor as the function : 500 + 50x.
We substitute :
20 hours of labor = 500 + 50 x 20 = $1500
50 hours of labor = 500 + 50 x 50 = $3000
Jayce is a taxi driver.
M(n) models Jayce's fee (in dollars) for his nth drive on a certain day.
What does the statement M(10) = K mean?
Choose 1 answer:
A
Jayce's fee for his Kth drive is equal to $10.
(B)
Jayce's fee for his 10th drive is equal to K dollars.
The correct answer is C. Jayce's fee for his 10th drive is equal to K dollars.
Based on the mentioned statements, n refers to the number of drives in a certain day. Additionally, it is mentioned that M(n) models the fee in dollars. As is seen in the equation, M(n) is equal to K. Thus, the fee in dollars is K dollars.
Now, as n is ten, thus the drive is tenth. And the fees for tenth drive is K dollars. So, the third option is correct, which states that Jayce's fee for his tenth drive is equal to K dollars.
Learn more about equations -
https://brainly.com/question/21405634
#SPJ4
the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds. the heaviest 2.5% of the bags packaged by the flour company are labeled as overweight. what is the probability that of 10 randomly chosen bags of flour at least 2 are overweight?
The probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68.
Given, that the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds.
As, we know that
P(X) = (1/s√2π)exp(-1/2((X-m)/s)^2)
where, m is the expected value
and s is the standard deviation.
Now, we have Expected value 10 pounds
and Standard Deviation 0.2 pounds
So, the probability that of 10 randomly chosen bags of flour at least 2 are overweight be
P(X=0) + P(X=1) = (1/0.2√2π)exp(-1/2((0-10)/0.2)^2) + (1/0.2√2π)exp(-1/2((1-10)/0.2)^2)
P(X=0) + P(X=1) = 0.32
So, Required Probability be 0.68.
Now, the probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68
Learn more about Probability here https://brainly.com/question/13604758
#SPJ4
Find the total area for the shape!!
Answer:
56cm²
Step-by-step explanation:
Because this is an irregular shape, you have to split it into two shapes and find the area of each one. Then you can add those two areas together to find the total area of the figure. There are many ways you can split it but the way I did it left me with the equation (12·3)+(4·5). Then all you have to do is multiply and add which will give you a total of 56cm².
How many dogs could Roscoe groom if he worked for 40 hours?
90
120
220
200
There are 200 dogs Roscoe groom if he worked for 40 hours.
What is working time?
A person's working time is the time they are engaged in paid work. Personal housework, childcare, and pet care are examples of unpaid work that is not included in the definition of the working week.
In most cases, when someone inquires about your working hours, you should first provide the start time before providing the time you leave for home.
From the given graph we can see that for each three hours the number of dogs are increased by 15.
So, for each one hour the number of dogs increased by 5.
For 18 hours the the number of dogs are 90.
After 18 hours to complete 40 hours we need 22 hours.
So, for 22 hours the number of dogs are
22 x 5 = 110.
Therefore, the total number of dogs worked for 40 hours are,
90 + 110 = 220.
Hence, there are 200 dogs Roscoe groom if he worked for 40 hours.
To know more about the working time, click on the link
https://brainly.com/question/25748643
#SPJ1
I really need help on this one.The amount of milk needed for each of 5 recipes is shown on the line plot.What is the total amount of milk needed for the recipes?
The total amount of milk needed for the recipes, considering the line plot, is of:
5.25 cups.
How to obtain the total amount of milk needed for the recipes?The total amount of milk needed for the recipes is obtained adding all the measures of the line plots.
The measures of the line plot given by the image at the end of the answer are given as follows:
Two measures of 1/4 cups = 0.25 cups, which is half the distance between 0 and 1/2.One measure of 1.25 cups, which is the value at the midpoint between 1 and 1.5.One measure of 1.5 cups.One measure of 2 cups.The total amount is given by the sum of all these measures, hence:
2 x 0.25 + 1.25 + 1.5 + 2 = 5.25 cups.
Missing InformationThe line plot is given by the image at the end of the answer.
More can be learned about line plots at https://brainly.com/question/24644930
#SPJ1
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of function is positive so the function have maximum value at x=3.
In the given question we have to find the maximum or the minimum value of a function.
The given function is
f(x) = -3x^2+18x+3
To find the maximum or minimum value we firstly find the value of f'(x).
f'(x) = -6x+18
Now put f'(x)=0
-6x+18=0
Subtract 18 on both side we get
-6x=-18
Divide by -6 on both side we get
x = 3
Now finding the value of function at x=3
f(3)= -3*(3)^2+18*3+3
f(3)= -3*9+54+3
f(3)= -27+54+3
f(3)= 30
Since the value of function is positive so the function have maximum value at x=3.
To learn more about maximim and minimum value of quadratic equation link is here
brainly.com/question/28769828
#SPJ1
work out the minimum number of hikers who could have walked between 6 miles and 17 miles work out the maximum number of hikers who could have walked between 6 miles and 17 miles
The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
We need to find the maximum number of hikers who could have walked between 6 miles and 17 miles.
What is meant by minimum and maximum value?When the derivative equals 0, rearrange the function using elementary algebraic principles to find the value for x. The x-coordinate of the function's vertex, which is where the maximum or lowest will occur, is provided in this answer. the solution back into the original function to determine the minimum or maximum.
From the table, we can see
Between intervals 5≤x<10 there are 2 hikers
Between intervals 10≤x<15 there are 9 hikers
Between intervals 15≤x<20 there are 8 hikers
So, total number of hikers = 2+9+8
= 19
Hence, the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
Learn more about minimum and maximum value here:
brainly.com/question/14993153.
#SPJ1
what is 56/60 as a percentage
Answer:
93.33%
Step-by-step explanation:
56/60 as a percentage:
56/60 = 0.93333
0.93333 as a percent:
0.93333 * 100 = 93.33%
The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
We have to given that,
To change a number 56/60 into a percentage.
Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Hence, We can write as,
⇒ 56/60 × 100%
⇒ 5600/60
⇒ 93.33%
Therefore, The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ6
PLEASE HELP
In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems. In March's Math Meet, they solved $\frac23$ of the problems. (There might be different numbers of problems asked in November and March.)
In total, the Little Monsters solved $13$ of $30$ problems over both Math Meets. How many problems were asked at March's Math Meet?
The number problems solved by the little Monsters of Beast Academy in March's meet is 15.
How to determine the number of problems solved in March meetThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
let the number of questions solved by little Monsters of Beast Academy in
March's meet be xNovember's meet be yIn November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems = y/5
In March's Math Meet, they solved $\frac23$ of the problems = 2x/3
Hence:
y/5 + 2x/3 = 12
x + y = 30
solving the equation gives
x = y = 15
Learn more on simultaneous equation here:
https://brainly.com/question/15165519
#SPJ1
Which equation represents a line that is parallel to the line y = -2/3x + 5? Pls Hurry :/
The equation of the line parallel to the equation y = - 2 / 3 x + 5 is 2x - 3y = 21
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Lines are parallel when they have the same slope.
Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = - 2 / 3 x + 5.
The slope of the equation is - 2 / 3.
Hence, let's find the equation that has the same slope as - 2 / 3. First, we will have to represent the equation in slope intercept form.
2x - 3y = 21
add 2x to both sides of the equation
2x + 2x - 3y = 21 + 2x
- 3y = 2x + 21
divide both ides by - 3
- 3y / - 3 = 2x / -3 + 21 / - 3
y = - 2 / 3 x - 7
Therefore, the slope is - 2 / 3 , the equation is 2x - 3y = 21
learn more on equation here: https://brainly.com/question/24394330
#SPJ1
which contours are usually drawn darker than the other contours? group of answer choices index contours largest (max) value contour contour interval smallest (min) value contour
Index contours are usually drawn darker than the other contours.
Index Contours are darker and wider than the other regular contour lines for ease of identification. They are labeled with elevation and also have their altitude value mentioned on the dark lines and these values represent the altitudes of the particular contours. Index contours appears after every fifth contours. If the number with contours will increase then its elevation will also increase and similarly if the number associated with contours starts to decrease then its elevation also decreases.
For more information regarding contours and Index Contours:
https://brainly.com/question/15942208
#SPJ4
Pls pls pls help it has to be turned in today!
Using the compound amount formula, the amount after 40 years is 2000(107/100)^40.
In the given question,
Esther got a summer job and decided to set aside $2000 to prepare for retirement without making monthly contribution.
She invests in the US stock market through as index fund that averages a 7% return compounded annually over this 40 year period.
We have to find the total balance in the account after 40 years.
We have to find total balance compounded annually.
The formula of the compound amount is
A = P(1+r/100)^n
where A = Amount
P = Principal Amount
r = interest rate
n = time
From the question we know that
P = $2000, r = 7%, n = 40
Now putting the value in formula
A = 2000(1+7/100)^40
Simplifying
A = 2000(1×100/100+7/100)^40
A = 2000(100/100+7/100)^40
A = 2000((100+7)/100)^40
A = 2000(107/100)^40
You can find the amount after simplifying the amount.
Hence, the amount after 40 years is 2000(107/100)^40.
To learn more about compound amount link is here
brainly.com/question/16588348
#SPJ1
The graphing calculator screen below represents time on the horizontal axis and the speed of an object on the vertical axis.
The data graphed on the screen indicates which of the following about an object?
The object was at rest, then began moving, and then stopped.
O The object moved at a constant speed, then sped up, and then stopped.
O The object was at rest, then began moving, and then slowed down.
O The object moved at a constant speed, then sped up, and then moved at a constant speed again.
Check the picture below.
2x + 3x equals to 20x find the value of x.
Answer:
Here,
2x+3x=20x
or,5x=20x
or,5x-20x=0
or,15x=0(divide both sides by -15)
hence,x=0
2x+y=4 1x-y=11 adding subtracting equations to solve systems.
By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
What is meant by an equation?An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.
An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.
Given,
2x+y=4
x-y=1
By solving above two equations we get,
2x+y=4
x-y=1
3x=5
x=5/3
y=-1+x
y=(5/3)-1
y=2/3
Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
To know more about equation, visit:
https://brainly.com/question/10413253
#SPJ1
Write a unit rate for the situation.
Situation: 87 students in 3 classrooms
Unit rate:
students per classroom
The unit rate for the given situation is 29 students per classroom.
What is the unit rate?
A unit rate is described as a ratio comparing the first quantity to one unit of the second quantity.
Given situation is 87 students in 3 classrooms.
So, the unit rate [tex]= \frac{87}{3}[/tex] students/classroom
[tex]= 29[/tex] students per classroom
Hence, the unit rate for the given situation is 29 students per classroom.
To learn more about unit rate
https://brainly.com/question/25416752
#SPJ1
PLS ANSWER THIS Solve the following system of equations for all three variables.
The values of x, y and z are 4, 1 and - 6 respectively.
What is the general equation of a Straight line? What is a system of equations in two or three variable.The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied
We have the following equations -
8x + y + 4z = 9
4x - 3y + z = 7
8x - 4y + 5z = - 2
We have -
4x - 3y + z = 7
z = 7 - 4x + 3y
We can write -
8x + y + 4z = 9
as -
8x + y + 4(7 - 4x + 3y) = 9
8x + y + 28 - 16x + 12y = 9 ...Eq[1]
and we can write -
8x - 4y + 5z = - 2
8x - 4y + 5(7 - 4x + 3y) = -2
8x - 4y + 35 - 20x + 15y = - 2 ...Eq[2]
Plot the graph of equation [1] and [2]. We will will get -
x = 4
y = 1
Now -
z = 7 - 4x + 3y
z = 7 - 16 + 3
z = - 6
Therefore, the values of x, y and z are 4, 1 and - 6 respectively.
To solve more questions on system of equations, visit the link below-
https://brainly.com/question/21620502
#SPJ1
Help with this please (ASAP)
Given the following information about the arithmetic sequence an, find a10. A5=24 a8=39
The 10th term of an arithmetic sequence is found as the 49.
Define the term arithmetic sequence?An ordered group of numbers with a shared difference with each consecutive word is referred as an arithmetic sequence. For particular, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression would be another name for an arithmetic sequence.As per the stated values in question.
Fifth term a5 = 24
8th term a8 = 39.
Let the first term be 'a' and the common difference be 'd'.
Then,
a5 = a + 4d
24 = a + 4d .....eq 1
a8 = a + 7d
39 = a + 7d .....eq 2
Solving eq 1 and 2.
3d = 15
d = 5
a = 4
Now,
a10 = a + 9d
a10 = 4 + (9 x 5)
a10 = 4 + 45
a10 = 49
Thus, the 10th term of an arithmetic sequence is found as the 49.
To know more about the arithmetic sequence, here
https://brainly.com/question/6561461
#SPJ4
Jane was asked to solve the equation `2-4=2(-5+1)`. she believes the solution to the equation is `x=\frac{1}{2}` . explain how jane could confirm that her solution is correct
the solution for the given equation is x= 1/2
an equation could be a formula that communicates the balance of two expressions, by interfacing them with the equals sign. Understanding an equation containing factors comprises deciding which values of the factors make the equality true. The factors for which the equation must be fathomed are moreover called unknowns, and the values of the unknowns that fulfill the balance are called solutions of the condition. There are two sorts of equations such as conditional and identities equations. An identity is genuine for all values of the factors. A conditional equation is as it were genuine for specific values of the factors
since the given expression is :
`(2-4)=2(-5+1)x²
so solving for the simple arithmetic expression on both sides :
=>-2 =2(-4)x²
=> -2 = -8x²
=>2/8=x²
=>1/4= x²
=>x= 1/2
to know more about algebraic equations refer to the link https://brainly.com/question/953809?referrer=searchResults.
#SPJ4
