Answer: Tom can come up with 13 different wacky personalities for Mr Potato Head.
Step-by-step explanation:
Tom can come up with 3 different hairstyles for Mr Potato Head, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips. He also has 2 pairs of shoes to choose from. If Mr Potato Head can be bald, Tom can also choose to not include a hairstyle.
In total, Tom can come up with 3+2+1+2+2+2+1=13 different combinations of features for Mr Potato Head. Since each combination represents a different personality, Tom can come up with 13 different wacky personalities for Mr Potato Head.
23
Luke invested £4000 in a savings account for 3 years.
Compound interest was paid at a rate of 1. 8% each year.
Alexa also invested £4000 in a savings account for 3 years.
Simple interest was paid at a rate of 1. 8% each year.
Luke got more interest than Alexa in total over the 3 years.
How much more?
You must show all your working.
The amount luke made more than alexa is $3.91 .
What is simple interest ?
simple interest can be defined as the ratio of product of principal amount , rate and time and 100.
Luke investment,
This is compound interest so the future value formula will be used:
= Amount * ( 1 + rate) ^ no. of years
= 4,000 * ( 1 + 1.8%)³
= $4,219.91
Alexa investment:
Simple interest is calculated with the formula:
= Amount * ( 1 + rate * time)
= 4,000 * ( 1 + 1.8% * 3)
= $4,216
Amount Luke made more than Alexa:
= 4,219.91 - 4,216
= $3.91
Hence , The amount luke made more than alexa is $3.91 .
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help help help help help help help help PLEASE
Gabe and Bridgette are preparing meals to serve at a local homeless shelter. The number of people they will be able to serve depends on the number of meals they prepare.
p = the number of people Gabe and Bridgette will be able to serve
m = the number of meals Gabe and Bridgette prepare
Which of the variables is independent and which is dependent?
Answer:
The independent variable in this scenario is the number of meals Gabe and Bridgette prepare (m), because this is the variable that they can control and manipulate. The dependent variable is the number of people they will be able to serve (p), because this is the variable that depends on the number of meals they prepare.
Step-by-step explanation:
In other words, the number of people they can serve is affected by the number of meals they prepare, but the number of meals they prepare is not affected by the number of people they can serve.
Answer:
independent variable = m
dependent variable = p
Step-by-step explanation:
The number of people they are able to serve depends on the number of meals they prepare.
Ritu had 6 time a number of tamp and Raj took twice the number from Ritu o that he ha a total of 24. Write the algebraic equation and find the root of the equation
The equation to find the root of the statement given in the question is , 12x = 2x - 24.
Let the number of tamp which Ritu have be x
Then the number of tamp which Raj have be 2x = 24
Now as Ritu has 6 times more than Raj , 6( 2x) = 24 x 6
Therefore, the required equation becomes,
12x = 2x - 24
=> 10x = 24
=> x = 2.4 answer.
An equation is a mathematical statement which is made up of constants , variables and operators. There are two parts of an equation which are equated using the equal sign . The right hand and the left hand side of the equation.
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What is the example of zero polynomial?
A polynomial in which the degrees of all the variables is 0 is called a zero degree polynomial .
The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
For example- 6 x 0 , − 9 a 0.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division .
Degree of polynomial
The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial .
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The table lists recommended amounts of food to order for party guests. And are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should and order for a graduation party with drop-in guests?
To calculate the amount of food to order for the graduation party with drop-in guests, you should multiply the number of "full" guests, which is 40 + x/2, by the recommended amounts listed in the table.
To calculate the amount of food to order for the graduation party, you need to take into account the number of guests and the recommended amounts listed on the table. Since the party is for 40 guests and there will also be "drop-in" guests, you need to convert these guests into an equivalent number of "full" guests. To do this, you can divide the number of drop-in guests by 2.
So if there are x drop-in guests, the number of "full" guests will be 40 + x/2.
Now you can use this number of "full" guests to calculate how much of each food item to order. For example, if the table recommends 1/4 lb of meat per guest, you would order (40 + x/2) × 1/4 lb = 10 + x/8 lb of meat.
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How Do You Solve 3 linear equations with 3 variables?
The standard way to solve 3 linear equations with 3 variables is to use elimination or substitution.
-Elimination: To solve the 3 equations using elimination, add or subtract equations together to eliminate one of the variables. Keep repeating this process until you are left with one equation with one variable. Solve the equation and then use the value of the variable to substitute back into the other equations to find the values of the other variables.
-Substitution: To solve the 3 equations using substitution, pick one of the equations and solve it for one of the variables. Then substitute the value of the variable into the other equations. Keep repeating this process with the other equations and variables until you have a system of equations with one variable that you can solve. Once you have the value of the variable, substitute it back into the other equations to find the value of the other variables.
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Suppose you want to save $5000 to put towards remodeling your house in 18 months. You found a bank whose interest rate for savings accounts is 4.5% compounded monthly, but you are unsure of how much to invest to have $5000 saved in 18 months.
Using the compound interest formula, how much should you invest in order to have $5000 saved in 18 months?
The required money to be invested in order to save $5000 is $4677.26.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The principal for each interval is the sum of interest And the principal for the previous interval.
Suppose the amount to be invested be P.
The rate of interest for monthly compounding is given as 4.5/12 = 0.375%.
Time is given as 18 months.
This implies number of time period is 18.
Plug n = 18, r = 0.375% and A = 5000 in A = P(1 + r/100)ⁿ as,
⇒ 5000 = P(1 + 0.375/100)¹⁸
⇒ P = 4677.26
Hence, the amount of money that should be invested is obtained as $4677.26.
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If a scuba diver swam from the surface at −12 1/2 feet per minute, for 4 1/2 minutes, what would be the diver’s change in elevation?
The change in elevation would be -225/4 feet
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here, Speed of scuba diver as -12¹/₂=-25/2 and time in minutes 4¹/2=9/2
Thus distance traversed -25/2 × 9/2 = -225/4
Hence, the change in elevation is -225/4 feet
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Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.
Consequently, the solution of the given problem of perimeter comes out to be 24.5 inches will be adequate to build the bird house, which needs 24 inches.
Define perimeter.The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.
Here,
As stated, Hodi is making a birdhouse.
Four walls make up a birdhouse.
There must be 5.5 inches on each wall.
Board = 24.5 inches for Hodi.
Using comparable numbers, we must now estimate.
6 in. is a suitable size for 5.5 in.
The entire amount of wood needed to construct the bird home will be determined first.
The amount of board needed is equal to the number of walls in the house times the length of each wall.
Required total board: 4 x 6 = 24 inches for a wall count multiplied by the length of each wall.
It takes 24 inches of board in total.
His board is 24.5 inches long.
Consequently, the solution of the given problem of perimeter comes out to be 24.5 inches will be adequate to build the bird house, which needs 24 inches.
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Is it a perfect square trinomial X² 10x 25?
Yes, it is a perfect square trinomial.
What is perfect squares?Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."
The equation X² + 10X + 25 can be factored into (X + 5)²,
which is a perfect square trinomial. In general, a perfect square trinomial is any polynomial of the form A² + 2AB + B² where A and B are constants or variables.
This is because such a polynomial can be factored into (A + B)².
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What is vertically opposite angles in maths class 7?
When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles.
A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=35°, then its opposite angle is also equal to 35°. And the adjacent angle to angle X will be equal to 180 – 35 = 145°
In the given figure, ∠QOR and ∠SOP form a pair of vertically opposite angles and similarly ∠SOQ and ∠POR form such a pair. Therefore,
∠QOR = ∠SOP
∠SOQ = ∠POR
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the composite bar chart shows the number of messages jon received each day for five day
Tim received 8 SMS on Monday, 4 emails on Thursday, and 0.52 of the communications were emails, which is the solution to (a), (b), and (c).
what is composite bar chart ?When two sets of data are joined and their frequencies are combined, a composite bar chart is utilized. Two pieces of data—emails and texts—are included in this inquiry, but they both fall under the same heading, "messages." With regard to question (a), it is clear from the diagram that Tim got 8 texts on Monday. In order to answer question (b), we must determine how many emails Tim received on Thursday. To do this, we must look at the bar for Thursday and divide the total number of texts by the total number of messages to determine the number of emails received. 15-11=4, indicating that Tim received 4 emails on Thursday.
given
Tim for five days, total the emails received, and then determine the percentage of emails relative to messages.
Total messages: 14+16+14+15+14=73.
Emails totaled: 6 + 10 + 10 + 4 + 8 = 38
Email to message ratio is equal to 0.52.
Emails made up 0.52 of the messages, therefore.
Tim got 8 texts on Monday, 4 emails on Thursday, and 0.52 of the messages were emails, according to an analysis of the composite bar chart we used to determine the answers to the three questions.
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The complete question is :- The composite bar chart Messages received shows the number of messages Tim received each day for five days.
a) How many texts did Tim receive on Monday?
b) How many emails did Tim receive on Thursday?
c) In total, what fraction of the messages were emails?
Give your answer in its simplest form.
Urgent!
Use synthetic division to find the remainder
Check the picture below.
solve the following question
Put 38200 in standard Form
Answer: Thirty-eight thousand two hundred.
Step-by-step explanation: You'd get Thirty-eight thousand two hundred because the standard form is writing out the number using letters. So, we should break this down:
38,000 + 200 is a good strategy to divide big numbers.
So, 38,000 = Thirty-eight thousand
And 200 = two hundred
So, combine it and you get Thirty-eight thousand two hundred or Thirty-eight thousand and two hundred. (it's the same thing)
what is x if 2/6+x=11/18
Answer:
multiply top and bottom of 2/6 to get 6/18, then subtract the answer by 6/18 , you get 5/18
Step-by-step explanation:
Answer:
x = 5/18
Step-by-step explanation:
what is x if 2/6+x=11/18
2/6 + x = 11/18
x = 11/18 - 2/6
x = 5/18
----------------------------
check2/6 + 5/18 = 11/18
11/18 = 11/18
The answer is good
Identifying Characteristics of an Exponential Function
Consider the function f(x) = (6). What is the value of the growth factor of the function?
02
06
O 18
The function be f(x) = (6) then growth factor for the given equation (b) = 6.
What is meant by exponential growth function?Quantity grows exponentially over time. It happens when a quantity's instantaneous rate of change with regard to time is proportional to the quantity itself.
A function called exponential growth illustrates an expansion within a population that happens at the same pace across time. When a population's per capita growth rate remains constant across time, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.
The general exponential growth function is given by :-
[tex]$f(t)=A b^t$[/tex] , where A is the initial amount , b is the growth factor and t is the time period.
The given function : [tex]$f(x)=(6)^x$[/tex]
When we compare it to the general exponential equation , we get
The growth factor for the given equation (b) = 6.
The complete question is:
Consider the function f(x) = (6)x. What is the value of the growth factor of the function?
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The function be f(x) = (6) then growth factor for the given equation (b) = 6.
What is meant by exponential growth function?Quantity grows exponentially over time. It happens when a quantity's instantaneous rate of change with regard to time is proportional to the quantity itself.
A function called exponential growth illustrates an expansion within a population that happens at the same pace across time. When a population's per capita growth rate remains constant across time, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.
The general exponential growth function is given by :-
F(t) = AB^t, where A is the initial amount , b is the growth factor and t is the time period.
The given function : f(t) = (6)^x
When we compare it to the general exponential equation , we get
The growth factor for the given equation (b) = 6.
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The complete question is:
Consider the function f(x) = (6)x. What is the value of the growth factor of the function?
Jill and beth are sisters. Jill is 1/3 of beth's age. Let b represent beth's age.Write an algebraic expression to show jill's age.
The algebraic expression to show Jill's age will be;
Jill = 1/3 x b
What is an Algebraic Expression?Algebraic expressions are the mathematical statements that are derived when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.
There are different parts of an algebraic expression and they are; Variables - a symbol that doesn't have a fixed value is called a variable. It can take any value assigned to it.
Constants - a symbol that has a fixed numerical value is called a constant. All numbers are constants.
Terms - A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants and the operation of multiplication or division with it.
Coefficients - the numbers that are multiplying the variables are called coefficients.
Beth's age = b
Jill's age = 1/3 of Beth's age
Jill's age = 1/3 x b
Jill's age = 1/3b
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someone helpp me plsss
Answer: 2i+5
Step-by-step explanation: so (-2+14i)-(-7+12i)
Multiply (-1) to 7 and -12
Then: -2+14i+7-12i
Common numbers: (7-2) and 14i-12i
Then you get 2i+5
Is (3,6) a solution to this system of equations?
y=2x+1
y=4x+6
Step-by-step explanation:
y = 2x + 1 -------- (I)
y = 4x + 6 --------(ii)
from eqn (I)
y = 2x + 1
sub y = 2x + 1 in eqn (ii)
2x + 1 = 4x + 6
2x - 4x = 6 - 1
-2x = 5
x = -5/2
sub x = -5/2 in eqn (I)
y = 2(-5/2) + 1
y = -5 + 1
y = -4
Therefore, (x, y) = (-5/2, -4)
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)
How to determine the correct representationsFrom the question, we have the following expression that can be used in our computation:
–3(2x – 5) < 5(2 – x)
Divide bot sides of the inequality by -1
So, we have the following representation
3(2x – 5) > -5(2 – x)
Next, we open the brackets
This gives
6x – 15 > -10 + 5x
Hence, the representation is 6x – 15 > -10 + 5x
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Complete question
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
(a) 6x – 15 > -10 + 5x
(b) 6x – 15 < -10 + 5x
(c) 3(2x – 5) > -5(2 – x)
(d) 3(2x – 5) < -5(2 – x)
How do you solve 9x 7 =- 7?
The value of x is 0
Now, According to the question:
Let's know:
How to find the value of 'x'
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
The given equation is:
9x - 7 = -7
To solve the value of 'x'
9x - 7 = -7
Add 7 on both sides:
9x - 7 + 7 = -7 + 7
9x = 0
x = 0/9
x = 0
Hence, The value of x = 0
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The complete question is this:
How do you solve 9x - 7 = -7
whats the awnser i need help
answer:10
Step-by-step explanation:
the graph show it is 1 hour and shows 10 miles and it continues
Answer:
it should be that the miles are 10 times the amount of hours
Step-by-step explanation:
Considering that to bike 10 miles it took 1 hour and to bike 20 miles it took 2 hours it will continue going like that so the miles will always be 10 times the amount of hours
normally distributed with a mean of 5 days and a standard deviation of 4 days. What is the probability that the product has a shelf life of at least 1 week and at most 2 weeks
The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability is a concept in mathematics that helps predict the likelihood of certain events. Probability generally refers to the degree to which something is likely to occur.
A standard normal variable with a mean of 0 and a variance of 1 can be created from a normally distributed random variable with a defined mean and variance.
Thus, The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.
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Express the length a, b, c, and d in the figure in terms of the trigonometric ratios of θ.
a = b = c = d =
The lengths of a,b,c, and d have been derived and expressed in terms of trigonometric ratios below.
As we can see from the figure itself, the value of a = sin θ
This can be written as such because = sin θ = Perpendicular / Hypotenuse
Here, the perpendicular = a and hypotenuse = radius = 1
= sin θ = a
The value of b = tan θ
This is because tan θ = perpendicular/base
Here, the base = radius = 1
= tan θ = b
The value of c = sec θ
This is because sec θ = Hypotenuse / Base
= sec θ = c
The value of d = cos θ
This is because cos θ = Base / Hypotenuse
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I want the answer please
The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
⇒ lim θ → 0 ( sin θ / θ ) = 1
Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.
⇒ lim θ → 0 ( sin θ / θ ) = 1
Take LHS;
⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )
⇒ lim θ → 0 ( cos θ / 1 )
⇒ ( cos 0 )
⇒ 1
⇒ RHS
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Is 9x² 30x 25 a perfect square trinomial?
Yes, [tex]9x^2-30x +25[/tex] is a perfect square trinomial.
How can you tell if a trinomial is a perfect square?A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial of the form [tex]ax^2 + bx + c[/tex] meets the requirement [tex]b^2 = 4ac[/tex], it is said to be a perfect square.
What trinomial has a perfect square?Two of your terms will be perfect squares in a perfect square trinomial. This trinomial is not a perfect square trinomial if it lacks two perfect square terms. The square root of each perfect square word should now be determined, combine the two square roots, then multiply the result by two.
This trinomial is a perfect square. The only thing left to determine is whether the middle term matches when you square (3x-5) because both [tex]9x^2=(3x)^2\ and\ 25=52[/tex] are perfect squares. The minus sign was used to at least produce a negative coefficient for the middle term.
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The function f is defined by f(x) = sqrt 25 - x2 for -5\leq x\leq 5. a) Determine the average rate of change of f over the interval --4\leq x\leq 3 b) Find f (prime) (x). c) Write an equation for the line tangent to the graph of f at x= -3. d) Let g be the function defined by g(x) = f(x) for -5\leq x\leq -3 and x+7 for-3\leq x\leq 5. Is g continuous at x= -3? Use the defintion of continuity to explain your answer.
a) The average rate of change of a function over an interval is the change in the function's output (f(b) - f(a)) divided by the change in the function's input (b - a). So, to find the average rate of change of f over the interval -4 <= x <= 3, we can use the formula:
(f(3) - f(-4)) / (3 - (-4)) = (sqrt(25 - 9) - sqrt(25 - 16)) / (3 - (-4)) = (-2sqrt(7) + 4sqrt(3)) / 7
b) To find the derivative of f(x), we need to use the power rule and the chain rule. The power rule states that the derivative of x^n is nx^(n-1), and the chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x).
So, the derivative of f(x) = sqrt 25 - x^2 is:
-2x
c) To find the equation of the line tangent to the graph of f at x = -3, we need to use the point-slope form of a line, which is:
y - y1 = m(x - x1)
where m is the slope of the line (which is f'(-3) = -6), (x1, y1) is the point on the graph where the line touches (which is (-3, f(-3)) = (-3, sqrt(25 - 9) = 2sqrt(7))
so we have: y - 2sqrt(7) = -6(x + 3)
d) To check if g(x) is continuous at x = -3, we need to check if the limit of g(x) as x approaches -3 exists and is equal to g(-3).
Since g(x) = f(x) for -5 <= x <= -3 and g(x) = x + 7 for -3 <= x <= 5, we have:
g(-3) = f(-3) = sqrt(25 - 9) = 2sqrt(7)
and the limit of g(x) as x approaches -3 is:
lim x->-3 g(x) = lim x->-3 (x + 7) = -3 + 7 = 4
Since g(-3) = 2sqrt(7) and lim x->-3 g(x) = 4, g(x) is not continuous at x = -3.
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HELP!!! Find the value of..
Answer:
The answer to your question is C, 15
Step-by-step explanation:
Answer is 15, C