Given: Mitchell's dog is 1/3 as old as Katie's cat. The sum of their ages is 12 years.
Required: To find out how old is Mitchell's dog.
Explanation: Let Mitchell's dog be x years old. Then Katie's cat is 3x. Now according to the question-
[tex]\begin{gathered} x+3x=12 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]Hence Mitchell's dog is 3 years old.
Final Answer: Mitchell's dog is 3 years old.
maddie is determind to finish some extra credit math homework by completeing 4 math puzzles each day. Create a table of values to represent the relationship between the number of days and the number of puzzles she has completed determine if it is proportional and show your reasoning Brainliest will possibly be a prize :)
The table of values to represent the relationship between the number of days and the number of puzzles she has completed will be:
Days Puzzle completed
1. 4
2. 8
3. 12
4. 16
5. 20
How to illustrate the information?From the information, Maddie is determind to finish some extra credit math homework by completeing 4 math puzzles each day.
Therefore, the first day, she will do 4 puzzles. The second day will be:
= 2 × 4 = 8 puzzles
Third day = 3 × 4 = 12 puzzles.
In this case, the method that was used is simply to multiply the number of days by 4 since he does 4 puzzles everyday.
It should be noted that this illustrates a proportional relationship
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if x is the number of years since 2000 and y is the percent of people using travel services the following equations represent the percent of people using travel agents and the percent of people using the internet to plan travel. y=-2x+30 y=6x+41 Find the year travel agents and the Internet were used equally
We need to solve a system of two variables with two equations, using elimination method.
y=-2x+30 (1)
y=6x+41 (2)
We are going to multiply first equation by 3, doing so the equation (1) can be written as:
3y = -6x + 90 (1)
Then, we are going to add the last equation to the second equation
3y = -6x + 90 (1)
+ y= 6x + 41 (2)
-----------------------------
4y = 131
y = 131 / 4 Isolating y
y= 131/ 4
Then, we replace y= 131/4 in the first equation and solve for x
[tex]\begin{gathered} \frac{131}{4}=-2x+30 \\ \frac{131}{4}-30=-2x\text{ Transposing 30 to the other side of the equation} \\ \frac{131}{4}-\frac{120}{4}=-2x\text{ Converting 30 to an improper fraction} \\ \frac{11}{4}=-2x\text{ Operating homogeneous fractions} \\ \frac{\frac{11}{4}}{-2}=-\frac{2}{-2}x\text{ Dividing by -2 on both sides of the equation} \\ -\frac{11}{8}=x \end{gathered}[/tex]Since -11/8 is equal to -1.4 and x represents the number of years since 2000, then the year travel agents and the Internet were used equally was 1998.
A company prints designs on T-shirts. They charge $40 for set-up costs plus $12 per shirt. Write the equation for the situation.
The equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.
According to the situation,
We have the following information:
The company charges $40 for set-up costs plus $12 per shirt.
So, the basic charge is added to every t-shirt.
Now, let's take the number of T-shirts on which the company prints designs on shirts to be x.
So, we have the charge for x number of t-shirts is:
$(40+12x)
Hence, the equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.
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Which is a better value for money, $5.99 for a package of 8 cold remedy
capsules or $2.85 for 2 capsules?
Answer:
the 8 pack
Step-by-step explanation:
So to start we should find how much an individual capsule in each is
Well start off by 5.99/8 which will give us 0.74875 per capsule and well round in to 0.75 each to put it in terms of money.
Now we will do 2.85/2 which then gives you 1.425 and well say that's about 1.43 per capsule
Write a quadratic function in standard form whose graph has the given characteristics.
The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
The standard form of a quadratic equation in vertex form is given as,
y = a(x-h)² + 8
Where (h,k) is the coordinate of the vertex and a is constant.
Given the vertex (h,k) = (-1,8)
Substitute, vertex, and (0,2)
2 = a(0 + 1)² + 8
a = -6
Therefore, the equation converts as,
y = -6(x+1)²+8
Hence "The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8".
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Simplify: - 1x - 11 - 16x - 22 =
The given expression is
[tex]-x-11-16x-22[/tex]To simplify it add the like terms
[tex]\begin{gathered} (-x-16x)+(-11-22)= \\ \\ -17x+(-33)= \\ \\ -17x-33 \end{gathered}[/tex]Then the simplest form is
-17x - 33
Alice is saving to buy a house and currently has$2,000 in her savings account. She's planning tocontribute $150 to the account each month,Identify the function that describes therelationship between the number of monthsthat pass (n) and the balance of her savingsaccount,f(n).
Alice plans to buy a house. She has $2,000 in her savings account.
She plans to contribute $150 to the account each month.
We know that with each month, n, she deposits $150 and so, each month, her savings account balance increases by $150.
This simply means that after n months, her savings account balance would have increased by:
150 * n = 150n
Her initial balance was $2000, therefore, her balance after n months will be the sum of 150n and the amount that was initially there.
That is:
f(n) = 2000 + 150n
This is the function that describes the relationship between the number of months and her balance.
Marcus has an aquarium with three different types of fish. 1/9 of the fish are goldfish. 5/9of the fish are angelfish. • The rest of the fish are guppies. What fraction of the fish are guppies?
The fraction of fishes which are guppies in Marcus's aquarium is 2/3
Number of gold fishes in the aquarium = 1/9
Number of angelfish in the aquarium = 5/9
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Let x be the total number of fishes in Marcus's aquarium:
Number of guppies = Total fishes - Number of gold fishes - Number of angelfishes
= x - 1/9 - 5/9
= x - 6/9
x = 6/9 or 2/3
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Solve the inequality for x
(x+8)(x-3)^2(x-7)^3<0
The solution for the given inequality is −8<x<3 or 3<x<7.
The given inequality is (x+8)(x-3)²(x-7)³<0.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality can be solved as follows
Solve for x by simplifying both sides of the inequality, then isolating the variable.
Inequality Form: x+8<0
x<-8 (Subtract 8 on both the sides of the inequality)
(x-3)²<0
⇒ x-3<0
⇒ x<3 (Add 3 on both the sides of the inequality)
(x-7)³<0
⇒ x-7<0
⇒ x<7 (Add 7 on both the sides of the inequality)
Solution is −8<x<3 or 3<x<7
Therefore, the solution for the given inequality is −8<x<3 or 3<x<7.
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Marshall's Theater Company claims that of its 2,937 costumes in inventory, 972 are just old used clothes, while the rest are collector's items. What percent of total inventory is collector's items?
In order to calculate the percent of items that are collector's items, let's first find the amount of collector's items by subtracting the total number of items by the number of old used clothes:
[tex]2937-972=1965[/tex]Now, to find the percent from the total, let's divide this amount we calculated by the total number of items:
[tex]\frac{1965}{2937}=0.669=66.9\text{\%}[/tex]Therefore the percent of items that are collector's items is 66.9%.
a new ipad costs $101.99 in the store. what would your total cost be if the sales tax is 7.5% round your answer to the nearest cent, if necessary
ANSWER:
$109.64
STEP-BY-STEP EXPLANATION:
The price after applying the tax would be the sum between the original value and the value equivalent to the established percentage, just like this:
[tex]\begin{gathered} p=101.99+101.99\cdot\frac{7.5}{100} \\ p=101.99+7.65 \\ p=109.64\cong\text{ \$109.6}4 \end{gathered}[/tex]⚠⚠⚠⚠⚠⚠⚠⚠⚠ Pleases Help ME!!!!!!!
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.20). What is the slope of the graph? What is the unit rate? Complete the explanation.
The slope is _____. The unit rate is $_____/min. If the graph of a proportional relationship passes through the point (_____, r), then r equals the slope and unit rate.
The complete statement is:
The slope is 3.20. The unit rate is $3.20/min. If the graph of a proportional relationship passes through the point (1, r), then r equals the slope and unit rate.How to complete the statement?The slope
From the question, we have the following parameters
Point = (1, 3.20)
The point is a proportional relationship
So, the slope of the proportional relationship is
Slope = y/x
Where
(x, y) = (1, 3.20)
Substitute the known values in the above equation
So, we have the following equation
Slope = 3.20/1
Evaluate
Slope = 3.20
The unit rate
Here, we have
Point = (1, 3.20)
Also, we have
The point is a proportional relationship
The unit rate is
Rate = y/x
Where
(x, y) = (1, 3.20)
Substitute the known values in the above equation
So, we have the following equation
Rate = 3.20/1
Evaluate
Rate = 3.20
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what number is 90% of 20
Let's begin by listing out the given information:
[tex]\begin{gathered} 90\text{\%}\cdot20\Rightarrow\frac{90}{100}\cdot20 \\ \Rightarrow0.9\cdot20=18 \\ \Rightarrow18 \end{gathered}[/tex]Therefore, 90% of 20 is equal to 18
Please help I am stuck
Compute the given function
[tex]f(x)=- 3x^{2}-7x-3[/tex]
How the given function is computed?
Let us consider f (-3)
f(-3)= -3(9)- 7(-3) -3
=-27+21-3
= -9
Let us consider f (4)
f(4) = -3(16)-7(4)-3
=-48-28-3
= - 79
A) f(-3) * f (4)
= (-9) * (-79)
= 711
B) f(-3) / f (4)
= (-9) / (-79)
= 9/79 (or 0.11)
What are functions?
The core of calculus in mathematics is the concept of functions. The unique types of relations are the ones with functions. Mathematical functions are represented as a rule that, for each input x, produces a distinct result.Mathematicians refer to a function as being mapped or transformed.To learn more about functions, refer:
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What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?
The area of the triangle bounded by the x-axis, the y-axis, and the line y = −4x + 4 is 2 square units
How to find the area of the trianglegiven data
y = −4x + 4
Area of a triangle is equal to 1/2 * base * height
Assuming the y direction to be the height and the base is x direction
Point on the y direction is the y intercept since the line bounds the area
y intercept = −4( 0 ) + 4
y intercept = 0 + 4
y intercept = 4
Point on the x direction is the x intercept since the line bounds the area
y = −4x + 4
4x = 4 - y
4x = 4 - 0
x = 1
Area of a triangle = 1/2 * 1 * 4
= 2 square units
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please help I've been trying to solve this for over an hour
24x +8y ≥ 20
3x - 6y > 24
First, express both equations in slope-intercept form
y= mx+b
Where:
m= slope ( rise (y) / run (x))
b= y-intercept (where the line crosses the y axis)
Solve for y:
24x +8y ≥ 20
8y ≥ -24x +20
y ≥ (-24x +20 ) / 8
y ≥ -3x + 2.5
3x - 6y > 24
-6y > 24- 3x
y < (24 -3x) / -6
y < 1/2x -4
System:
y ≥ -3x + 2.5
y < 1/2x -4
Solution = the area where the 2 solutions overlap (blue+ red)
Steve scores in a card game is five points away from zero zinnias score is the opposite of an of Steve's score positive value what is the score
Problem
Steve scores in a card game is five points away from zero zinnias score is the opposite of an of Steve's score positive value what is the score
Solution
Let x the score for Steve and y the score for Denia.
We know that the score of Denia is the opposite of Steve
So then the scores needs to be:
Steve =-5
Denia =5
And with this we satisfy all the requirements
If x
2 = 25 , where x ε z then x =
After thoroughly calculation, we have come to find that, If equation x² = 25, where x ε z then x = √25 = 5, thus x is 5.
What is equation?Equation, also known as a statement of equality between two expressions with variable- and/or number-based components. Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics.
From straightforward algebraic equations that only require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity. Numerous physics laws are expressed using them.
Simultaneously occurring equations, or system of equations Algebra requires the simultaneous solution of two or more equations (i.e., the solution must satisfy all the equations in the system). The quantity of equations must match the quantity of unknowns for a system to have a distinct solution.
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write in standard form the equation of the line through each pair of points
9. (0,1) and (3,0)
10. (1/2,2/3) and (-3/2,5/3)
11. (-3,-2) and (1,6)
The equation of the line 3y + x = 3 through pair of points (0,1) and (3,0), the equation of the line 6y = 2x +3 through pair of points (1/2,2/3) and (-3/2,5/3) and the equation of the line y = 2x + 4 through pair of points (-3,-2) and (1,6)
The equation of the line through pair of points (0,1) and (3,0)
⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )
Here x₁ = 0 and y₁ = 1
x₂ = 3 and y₂ = 0
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 1 = [(0-1)/(3-0)](x -0)
⇒ y - 1 = (-1/3)x
⇒ 3y - 3 = x
⇒ 3y + x = 3
The equation of the line through pair of points (1/2,2/3) and (-3/2,5/3)
⇒ y - 2/3 = [(5/3 -2/3)/(-3/2-1/2)](x -1/2)
⇒ y - 2/3 = [(3/3)/(-4/2)](x -1/2)
⇒ y - 2/3 = (1/3)(x -1/2)
Multiply by 6 both sides of the equation,
⇒ 6y - 4 = 2(x -1/2)
⇒ 6y = 2x -1 + 4
⇒ 6y = 2x +3
The equation of the line through pair of points (-3,-2) and (1,6)
⇒ y - (-2) = [(6-(-2))/(1-(-3))](x -(-3))
⇒ y + 2= (8/4)(x + 3)
⇒ y = 2x + 6 -2
⇒ y = 2x + 4
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Which statement allows the line q and p are parallel ?
According to the converse of corresponding angles theorem, the statement that allows Carmen to conclude that lines p and q are parallel is: ∠2 ≅ ∠6.
What is a Transversal?A transversal is a line that crosses two straight lines. For example, line t is a transversal that crosses the lines p and q in the given diagram above.
What are Parallel Lines?Parallel lines are lines that do not meet each other at any point and are of equal distant to each other.
When a transversal intersects two parallel lines, they form angle pairs. One of such angle pairs is, corresponding angles, which are always congruent to each other.
Thus, if corresponding angles are formed and are equal to each other, then the lines they lie on must be parallel lines based on the corresponding angles converse theorem.
Angles 2 and 6 are corresponding angles that are formed by the transversal that intersects lines q and p. If they are congruent angles, then the lines are parallel.
Therefore, Carmen can use the statement, ∠2 ≅ ∠6 to show that lines q and p are parallel.
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A poll showed that 62.4% of Americans say they believe that some people see the future in their dreams. What is the probability (in percent form) of randomly selecting someone who does not believe that some people see the future in their dreams.Probability = % (Please round your answer to one decimal place.)
Let
A
be the event of selecting an American that believes that some people see the future in their dreams. From the problem,
P(A)=62.4%=0.624
Let
A' be the event of selecting an American who does not believe that some people see the future in their dreams
Remember that
P(A')=1-P(A)
substitute given value
P(A')=1-0.624=0.376=37.6%
Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 37.6%
The sum of three consecutive even integers
is –78. What are the integers?
Describe how you would use the strategy of writing an equation to solve the given problem.
Answer:
- 28, - 26 and - 24Step-by-step explanation:
The difference between two consecutive even integers is 2.
Let the first of the three integers is x, then the following ones are:
x + 2 and x + 4.
The sum of the three is - 78. Express it as equation and solve for x:
x + x + 2 + x + 4 = - 783x + 6 = - 783x = - 84x = - 84/3x = - 28The integers are - 28, - 26 and - 24
Introduction to the probability of an eventA spinner with 8 equally sized slices has 8 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellowslice?write your answer as a fraction in simplest form.
Step 1:
[tex]Probability\text{ of any event = }\frac{Number\text{ of required outcomes}}{\text{Number of possible outcomes}}[/tex]Step 2:
There are 8 slices, hence the possible outcomes = 8
All the slices are color yellow. hence the required outcomes = 8
Step 3:
[tex]\text{The probability that the dial stops on yellow slice = }\frac{8}{8}\text{ = 1}[/tex]The probability that the dial stops on yellow slice = 1
Final answer
What is the number of terms in the polynomial -y4 + 7y³
4n+1=25Please help with an explanation as well
Question:
Solve
4n + 1 = 25
Solution:
Consider the following formula:
[tex]4n+1\text{ = 25}[/tex]this is equivalent to:
[tex]4n\text{ = 25 -1}[/tex]this is equivalent to:
[tex]4n\text{ = 24}[/tex]solving for n, we get
[tex]n\text{ = }\frac{24}{4}=\text{ 6}[/tex]Then, we can conclude that the correct answer is:
[tex]n\text{ = 6}[/tex]Math
-2-(-7) = ?
Bookmark
Answer:
5
Step-by-step explanation:
We know that - (-7) = +7, so
-2 - (-7) = -2 + 7 = 5
Leonard Desmond founded his traveling circus many years ago, and since that time he has featured 32 high-wire unicyclists and 24 ball-balancing seals. What is the ratio of high-wire unicyclists to ball-balancing seals?
Answer:
The ratio of the high-wire unicyclists to ball-balancing seals is;
[tex]4\colon3[/tex]Explanation:
Given that;
He has featured 32 high-wire unicyclists and 24 ball-balancing seals.
The ratio of the high-wire unicyclists to ball-balancing seals can be written as;
[tex]32\colon24[/tex]Reducing toits lowest form, we have;
divide both sides by 8;
[tex]\begin{gathered} \frac{32}{8}\colon\frac{24}{8} \\ 4\colon3 \end{gathered}[/tex]Therefore, the ratio of the high-wire unicyclists to ball-balancing seals is;
[tex]4\colon3[/tex]4. What is the mean of the following data? (Show your work){5, 6, 8, 4, 5, 7, 4, 3, 2, 6)
The mean of the data values is their average.
To obtain the average, find the sum of the data values and then divide the sum by total number of data.
In the given, we have 10 data values. Thus, the mean is as follows.
[tex]\begin{gathered} \overline{x}=\frac{5+6+8+4+5+7+4+3+2+6}{10} \\ =\frac{50}{10} \\ =5 \end{gathered}[/tex]Therefore, the mean is 5.
The part 1 picture of the same question the part 2Because is a little long.
The answer would be B.
The relationship is proportional. The constant of proportionality is 5.
Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Shirley, and Matthew are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.
The probability that you, Shirley, and Matthew are chosen is 0.0001
Probability:
Probability refers the measure of the likelihood of an event to occur.
The formula of Probability is
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Given,
Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat.
Here we need to find the probability that you, Shirley, and Matthew are chosen.
Here we have assuming that the selection process is fair;
We know that, the total number of employees is 28
Therefore, the probability of selecting each employee is,
=> 1/28
So, the probability of selecting yourself, Shirley, and Matthew is calculated as,
=> 1/28 x 1/27 x 1/26
=> 1/19656
=> 0.00005
When we round off it into four decimal place then we get,
=> 0.0001
Therefore, the probability that you, Shirley, and Matthew are chosen 0.0001.
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