The 12-foot ribbon is cut into pieces three-quarters of a foot long, then 16 pieces can be made.
What is a three-quarter length?
The fraction 3/4 or three-quarters means 3 parts out of 4. The upper number, 3, is called the numerator and the lower number, 4, is the denominator.
We have a 12-foot ribbon and you are making a cut into pieces three-quarters (3/4-foot) of a foot long sections, and you want to know many times you can do that here.
So, the number of pieces = (Length of the ribbon ÷ Length of each piece)
You just need to take 12 and divide it by 3/4, to see how many sections you can have.
12 ÷ 3/4
Change division to multiplication by taking the reciprocal (the flipping) of the second number:
= (12 * 4) / 3
= 48/3
= 16
To multiply fractions, multiply straight across on top and straight across on bottom:
Hence, the 12-foot ribbon is cut into pieces three-quarters of a foot long, then 16 pieces can be made.
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Jess has a 4-digit password for her mobile phone.
Each digit can be between 0 and 9 inclusive.
a How many choices are possible for each digit of the code?
b What is the total number of 4-digit passwords that Jess can create?
Jess would like to choose an even number.
The code can start with a zero.
c How many different ways are possible now?
a. The number of choices possible for each digit of the code is of: 10.
b. The total number of 4-digit passwords that Jess can create is of: 10,000.
c. The number of different ways to create even passwords is of: 5,000.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial, according to the rule presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Each digit can be between 0 and 9 inclusive, hence the number of outcomes possible for each digit of the password is given as follows:
10.
The password is composed of four digits, hence the total number of passwords possible is of:
N = 10 x 10 x 10 x 10 = 10,000.
Considering that Jess would like an even number, there are only five outcomes possible for the last digit (0, 2, 4, 6 or 8), hence the number of outcomes is of:
N = 10 x 10 x 10 x 5 = 5,000.
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Polynomial uing Remainder Theorem and Factor Theorem checking uing ynthetic diviion. X^4 - x^3 - 3x^2 4x 2 ÷ (x 2)
The remainder of the polynomial using the remainder theorem and factor theorem is 6.
Apply the remainder theorem,
When we divide a polynomial
f(x) by (x − c)
f(x) = (x − c)q(x) + r
f(c) = 0 + r
Here,
f(x)=(x−c)q(x)+rf(c)=0+r
and (x−c) is (x−(−2))
Therefore,
f(−2) = [tex](-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2[/tex]
= 16 + 8 − 12 − 8 + 2
= 6
Hence, the remainder of the polynomial using the remainder theorem is 6.
Whereas using the factor theorem and doing synthetic division, we get,
x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide
the coefficients of the polynomial as follows -
-2 | 1 -1 -3 4 2
-2 6 -6 4
-----------------------------------------
1 -3 3 -2 6
Hence, we get that 6 is the remainder when ([tex]x^4-x^3-3x^2+4x+2[/tex]) ÷ (x+2), using the factor theorem.
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The complete question is -
Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, [tex]x^4-x^3-3x^2+4x+2[/tex] ÷ (x+2)
Find the value of x and the two equations
× is 7
(7×+5) is 54
(5×+19) is 59
simplify 5 6/7 + (-2 1/3) + 1 5/6
answer fastttttttttttttttttttttttttttttttt
plssssssssssss 20 points
Solution is 225/42 or 5.35
According to question
5 6/7 + (-2 1/3) + 1 5/6
As it is a mixed fraction we will first solve it
To solve it denominator will get multiplied with the whole number and the solution will be get added to the numerator and the new numerator will get formed.
∴ 41/7 +(-7/3) + 11/6
⇒246-98+77/42. (LCM of 7,3,6 is 42)
⇒225/42
∴5.35
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Square ABCD is reflected about side BC. Which of the following statements are true? Select three that apply.
Vertex B is the midpoint of AA'.
Side BC is parallel to AA.
The length of CD is equal to the length of C'D'.
Vertex C and vertex C are located at the same point.
Reflection is a type of rigid transformation in which an object is flipped about a reference point or line to produce the required image. The three statements that apply are:Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point
What i Rigid transformation?Rigid transformation is a process in which the size, orientation or position of a given object can be changed by applying some principles. Types of rigid transformation are: reflection, translation, dilation, and rotation.
In the given question, the required statements that apply are:
Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point
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PLS HELP!!! WILL GIVE BRAINLIEST :)
Answer:
1/ We use the SSS method to prove that triangle CBD = triangle ABD
2/ We use the AA method to prove that <CBD equal < ABD
Step-by-step explanation:
1/ SSS, or side side side method, is the method we use to see if triangles are the same or not, and we know that the sides of both triangles are equal; this proves that both triangles are equal!
2/ AA, or Angle Angle method, is the method we use to see if the angles of triangles are the same or not, and we know that there are marks at <C and <A, these marks prove that both angles are equal! So, <CBD equal <ABD
Plot the piecewise function on the graph.
2x+6,
-5 < x < -2
-2 < x≤2
2
f(x) = { 1,
-3x+10,
What we should do is plot each part of the graph individually.
Step 1: Plot f(x) = 2x + 6 part
We know it starts at x = -5 (noninclusive) and ends at x = -2 (inclusive). Therefore, we can draw a line between the two points (-5, -4) and (-2, 2), with an open point at x = -5 and a closed point at x = -2
Step 2: Plot f(x) = 1 part
We know it starts at x = -2 (noninclusive) and ends at x = 2 (inclusive). Therefore, we can draw a line between the two points (-2, 1) and (2, 1), with an open point at x = -2 and a closed point at x = 2
Step 3: Plot f(x) = -3x + 10 part
We know it starts at x = 2 (noninclusive) and ends at x = 5 (inclusive). Therefore, we can draw a line between the two points (2, 4) and (5, -5), with an open point at x = 2 and a closed point at x = 5
You should end up with a graph that looks like the attached image!
The given function f(x) has been plotted in the graph piecewise with proper endpoints.
How t plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
As per the given piecewise function,
f(x) = [tex]\left \{ {{2x+6 \ \ \ \ -5 < x\leq -2}} \right.[/tex]
f(x) = [tex]\left \{ {{1 \ \ \ \ -2 < x\leq 2}} \right.[/tex]
f(x) = [tex]\left \{ {{-3x+10 \ \ \ \ 2 < x\leq 5}} \right.[/tex]
The function f(x) = 2x + 6 is a linear line with slope 2 and y-intercept 6 shown in red line -5 is excluded while - 2 is included.
The function f(x) = 1 is a constant horizontal line shown in the blue line that -2 excludes while 2 is included.
The function f(x) = -3x + 10 is a linear line with slope -3 and y-intercept 10 shown in the green line 2 is excluded while - 5 is included.
Hence "With the appropriate endpoints, the supplied function f(x) has been piecewise displayed in the graph".
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x^2-12x+43 i need some help with this maths question
In order to solve a quadratic equation with one unknown, we need to factor it. If at first glance we can't find easy roots, we do a discrimination.
[tex]f(x)=x^2-12x+43[/tex]Δ[tex]f(x)=b^2-4ac=(-12)^2-4(43)[/tex]Δ[tex]=-28[/tex]If this value is less than zero, Δ[tex]< 0,[/tex] we determine that it has no solution belonging to the set of real numbers. We will find a conjugate and two complex roots. ([tex]a+bi[/tex])
Let's use the following formulas to find the roots.
[tex]x_{1}=\frac{-b-\sqrt{D} }{2a}= \frac{12-\sqrt{-28} }{2}=6-\sqrt{7}i[/tex][tex]x_{2}=\frac{-b-\sqrt{D} }{2a}= \frac{12+\sqrt{-28} }{2}=6+\sqrt{7}i[/tex]Complex Solutions:
[tex]6+\sqrt{7}i[/tex][tex]6-\sqrt{7}i[/tex]find a function f such that f '(x) = 3x3 and the line 81x + y = 0 is tangent to the graph of f.
To find the function, we need to find the values of x and y.
In the aforementioned example, x and y are the independent and dependent variables, respectively. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).
As we know,
fx = 3x to the power 3
f(x) =
[tex]3x {}^{3 } \: dx \: + c \\ \\ fx = 3x { }^{4} \div 4 + c \\ \\ \\ \\ 3x {}^{3} = - 81 \\ \\ x \: = 243 \\ [/tex]
Hence x is 242
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a local civic theatre has 22 seats in the first row and 21 rows in all. each successive row contains 3 additional seats. how many seats are in the civic theatre
Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,21 in the second row, 51 in the third row, then the total number of people that the theatre hold is 2400
The total number of rows = 51
Number of seats in the first row = 22
Number of seats in the second row = 21
Number of seats in the third row = 51
Common difference= Second term - first term
= 26-22
= 4
The given sequence is in arithmetic progression
Substitute the values in the equation
= 15[44+29×4]
= 15[44+116]
= 15×160
= 2400
Hence, using the arithmetic progression, if a theatre has 51 rows of seats and there are 22 seats in the first row,21 in the second row, 51 in the third row, then the total number of people that the theatre hold is 2400
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A pair of positive integers a and b is such that their greatest common divisor is 5 and their least common multiple is 55. Find the smallest possible value of a+b.
Answer:
Step-by-step explanation:
The greatest common divisor of two integers a and b is a divisor common to both integers that is greater than any other common divisor. The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.
To find the smallest possible value of a+b, we can start by trying to find the smallest possible values of a and b that satisfy the given conditions.
Since the greatest common divisor of a and b is 5, we know that both a and b must be divisible by 5. We can write a = 5x and b = 5y, where x and y are positive integers.
The least common multiple of a and b is 55, so we know that both a and b must be factors of 55. We can write 55 as the product of its prime factors: 55 = 5 * 11. Since a is divisible by 5, we know that a must be equal to 5 or 25. Similarly, since b is divisible by 5, we know that b must be equal to 5 or 25.
There are four possible pairs of values for a and b: (5,5), (5,25), (25,5), and (25,25). The smallest of these is (5,5), which gives us a+b = 5+5 = 10. Therefore, the smallest possible value of a+b is 10.
The cash price of a refrigerator is rs 34 500. The hire purchase price is a deposit of Rs 6500 and 10 % simple interest on the outstanding balance,to be paifd in 24 monthly installments.Calculate the amount of each monthly instalment.
Amount of each monthly statement is 1400.
According to question ,
Cash price of refrigerator =34500
Deposit money=6500
Outstanding money=28000
Rate of interest=10%
Time period=24 months or 2 years
∴Simple interest =(principal ×rate of interest×time)÷100
⇒(28000×10×2)÷100
⇒5600
∴The total amount to be paid in 2 years is 28000+5600 =33600
∴Amount to be paid in one month =33600÷24=1400
∴Amount of each monthly statement is 1400.
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15. Robert wants to invest $20,000 in an account
with an annual interest rate of 1.9%. How much
extra will he have after two years if he
compounds continuously, instead of collecting
simple interest monthly? Round answer to the
nearest dollar.
[A] $800
[B] $750
[C] $711
[D] $683
[E] $821
To find the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly, we need to calculate the compound interest on the investment.
The compound interest is calculated by multiplying the principal (the initial amount invested) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 1.9%/12 = 0.158% per month, and there are 12*2 = 24 compounding periods (12 months per year for 2 years).
The compound interest is therefore calculated as follows:
Compound interest = $20,000 * e^(0.158%*24) - $20,000
= $20,000 * e^0.3832 - $20,000
= $20,000 * 1.454 - $20,000
= $4,080 - $20,000
= -$15,920
So the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly is -$15,920. Therefore, the correct answer is [A] $800.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What is the distance between points F and G?
HELP ME PLEASE ITS DUE AT 8 (50 POINTS)
Jamir bought p pencils that cost $0.10 each and F folders that cost $.35 each. A 8.75% sales tax will be applied to the total cost.
PART ONE:
Which expression repersents the total amount Jamir paid,including tax? Write the letter of the correct answer on the line below.
a) 0.0875 (p + f) + 0.0875 (0.10p+0.35f)
b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)
c) 0.35(0.0875f) + 0.10(0.0875p)
d) 0.35(1.0875f) + 0.10(1.0875f)
Answer=
PART B
Explain why each of the other answers are worng.
LAST PART
Jamir purchased a dozen pencils and 8 folders. How much did he spend in all,after all tax was applied? Show your work please
Answer$=
Answer:
b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)
first is Jamir total cost + the sales tax of 0.0875 of the total cost
a. this is wrong because both is the sales tax only, theres no total cost include
c. wrong because its just also sales tax only
d. wrong because the total cost must only multiplied by the sales tax
PART B
12(0.10) + 8(0.35)
= 1.2 + 2.8
= $4 as the total cost
4(1.035)
= $4.14 as after tax bill
CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
Mario and hi friend went to a movie on Saturday they left the houe at 5:15 PM. It took one hour and 20 minute to drive to the theater and they arrived 25 minute before the movie tarted. What time did the movie tart?
By applying the algebra concept, we can conclude that the movie that Mario and his friend watched starting at 7 PM
The use of algebra in everyday life.
Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used for financial planning, traveling time calculation, and so on.
In the above problem, we can take some notes as follows:
Departure time (x) = 5:15 PM
Travel time (t) = 1 hour 20 minutes
Arrival time (y) = 25 minutes
If z is the playing time of the movie, then z can be expressed mathematically in the following way:
z = x + t + y
= 5:15 + 1 hour 20 minutes + 25 minutes
= 6:60 PM or generally written 7:00 PM
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If 5 log 3 3x=15, what is the value of x?
The value of x for the expression 5log(3x) = 15 is 6.7.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 5log(3x) = 15. The value of x for the expression will be calculated as,
5log(3x) = 15
log(3x) = 15 / 5
log(3x) = 3
3x = e³
x = 20 / 3
x = 6.7
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Tamba jut received a bonu which increaed hi dipoable income by $860. If Tamba' marginal propenity to conume (mpc) i 0. 75, hi conumption rie by _______
The formula for calculating the change in consumption is MPC x Change in Disposable Income.Thus, Tamba's change in consumption = 0.75 x $860 = $645
The marginal propensity to consume (MPC) is a measure of the proportion of an increase in disposable income that is spent on consumption. In Tamba's case, his MPC is 0.75, which means that for every $1 increase in his disposable income, he will spend 75 cents on consumption. The formula for calculating the change in consumption is MPC x Change in Disposable Income. Therefore, when Tamba's disposable income increased by $860, his consumption increased by 0.75 x $860 = $645.
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question 1 options: what is the common difference in the sequence 7, 12, 17, 22, 27, ...? put the just the number in the blank.
The common difference in the sequence 7, 12, 17, 22, 27,… is that the difference between two numbers increases by five in the ascending order.
A sequence can be referred to or considered as the set of observations, which usually consists of numbers arranged in such a way that they described a common characteristic between them. A sequence can be exhaustive or inclusive, depending upon the numbers being used in the continuity of the sequence. It can also be said that a sequence is a logical arrangement.
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Complete question
what is the common difference in the sequence 7, 12, 17, 22, 27, ...?
Help me? Care to explain also?
*Gives Brainliest for best ans easy to read answer!*
Answer:
B
Step-by-step explanation:
Answer: The answer is B
Step-by-step explanation:
if you divide 7 by 12 you will get a decimal and a non terminating 3
Harry plans to charge $5 for cookies and $10
for cupcakes at the bake sale. He needs to
make a total of $75 to earn a profit. Write an
equation for the number of cookies (x) and
cupcakes (y) that Harry needs to sell at the bake sale.
Answer: 5x + 10y = or > 75
Step-by-step explanation:
make the number of cookies sold = x, and the number of cupcakes sold = y, since we don't know the number.
each cookie is $5 so it is 5 times x, and each cupcake is $10 so it is 10 times y.
add those together, and the sum must equal 75. If you have already learned this, it would be an equal to or greater than sign. if not then just use an equal sign.
A steep line has a bigger ____________ than a flat line
a steep line line has a bigger absolute greater slope than a flat line
Help please
A.) (-12,-18)
B.) (18,12)
C.) (-18,-12)
D.) (12,-18)
I think the answer be 12 and -18 D
please help with this question
Answer: the answer should be C :)
Step-by-step explanation:
the slope (x) is -3/4 and the y-intercept is -2
list the reasons and statement reasons why line AE ≅ A.F
. Thanks!
Add missing statements and reasons.
Statement Reason
7. FC ≅ EC CPCTC8. AE ≅ A.F. Transitive propertyWhat is the Pythagorean theorem? How do you use it to find the length of a missing side in a right triangle? Give an example and show your work.
The sum of squares of two sides of a triangle is equal to another side of a triangle is called the Pythagorean theorem.
It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
c^2=a^2+b^2--------(1)
Where a,b, and c are sides of a triangle.
To measure the length of the missing side in a right triangle using the Pythagorean theorem:
c^2=a^2+b^2
By using this formula we can find the length of a missing side.
To understand more we have to solve an example:
let A, B, and C are points of a triangle AB, BC, and CA are the sides of the triangle.
Consider BC=3cm CA=4cm AB=?
Use equation(1) to find the length of AB
AB^2=BC^2+CA^2
AB^2=3^2+4^2
AB^2=9+16=25
AB=5cm
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green and yellow dye are mixed in a 5:6 ratio to make 44 litres of lime-coloured dye. A further 8 litres of yellow dye are added to the mixture.
What is the new ratio of green to yellow dye in its simplest form?
Answer:
62.5% or in decimal form 0.625
Step-by-step explanation:
At a birthday party, Samuel ate
Complete the statement:
1
10
of the birthday cake.
If the cake can be represented as 1 =
10
10
that means we can find out how much cake is left by taking
and then subtracting the amount Samuel ate.
The expression [DROP DOWN 1] represents this situation.
10
10
If the cake can be represented as 1 = 10/10, that means we can find out how much cake is left by taking and then subtracting the amount Samuel ate. The expression [1 - 1/10] represents this situation.
How to complete the expressionFrom the question, we have the following parameters that can be used in our computation:
Cake = 1 or 10/10
Samuel's bite = 1/10
The amount remaining is calculated as
Amount remaining = Cake - Samuel's bite
Substitute the known values in the above equation, so, we have the following representation
Amount remaining = 1 - 1/10
The above represents the required expression
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Swimming Pool On a certain hot summer's day, 240 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $510.75. How many children and how many adults swam at the public pool that day?
Answer:
39 children, 201 adults
Step-by-step explanation:
Let c = number of children
a = number of adults
c + a = 240
1.50c + 2.25a = 510.75
--------------------------------
1.50c + 1.50a = 360
1.50c + 2.25a = 510.75
-------------------------------
.75a = 150.75
a = 201, c = 39
please help me with this question
many thanks
Answer:
111 girls
Step-by-step explanation:
You have 924 people classified as 383 men, 356 women, and the remainder children. 2/5 of the children are boys, and you want to know the number of girls.
GirlsThe number of children is ...
924 -383 -356 = 185
The 3/5 of children that are not boys are girls, so ...
girls = 3/5(185) = 111
There are 111 girls in the theater.