Answer:
1
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
let x be the fifth number , then
[tex]\frac{8+10+12+10+x}{5}[/tex] = 8.2 ( multiply both sides by 5 to clear the fraction )
40 + x = 41 ( subtract 40 from both sides )
x = 1
the fifth number is 1
Given that n is an integer and that n>1
Prove algebraically that n²-(n-2)²-2 is always an even number.
The expression can be rewritten as:
2*(n - 3)
This is twice an integer number, so this is an even number
How to prove that the expression gives an even number?Here we know that n is an integer larger than 1, and we have the expression:
n² - (n - 2)² - 2
Now, remember that for any integer m, 2m is always an even number.
Expanding the term in the middle of the expression we get:
n² - (n - 2)² - 2
n² - (n² - 4n + 4) - 2
4n - 4 - 2 = 4n - 6 = 2*(n - 3)
Integer numbers are closed under addition, then n - 3 is an integer, so we have:
2*(n - 3)
This is twice an integer, so this is an even number.
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The temperature of a place was 6°F in the morning. At noon, the
temperature rose by 13°F and dropped by 4°F at night. What was the
temperature recorded at the end of the day?
At the sewing store, Brooke bought a bag of mixed buttons. The bag included 76 buttons, of which 75% were large. How many large buttons did Brooke get?
Answer:
57
Step-by-step explanation:
75/100 *76
5700/100 =57
The four algebra classes at sanchez school are going on a field trip to a museum. each class contains s students. the museum charges $8 per student for admission. there is also a flat fee of $200 for the buses. a. write an expression for the total cost of the buses and the museum admission fees for all four classes. b. write a rational expression for the cost per student. simplify the expression as much as possible. c. use the expression you wrote in part (b) to find the cost per student if each class has 20 students.
a)The expression for the total cost for all four classes can be given as 32s + 200. b) the rational expression for the cost per student is 2(4s+25)/s c) if each class has 20 students then the cost per student is equal to $10.50.
a) Total cost expression can be determined as follows:
total fees of admission + fees of bus = total cost
total cost = (4s × 8) + 200
total cost = 32s + 200
b) A rational expression to determine the cost per student can be calculated as follows:
cost per student = total cost ÷ the total number of students
cost per student = 32s + 200 ÷ 4s
We now factor the numerator by using its GCF;
cost per student = 4 × 2 (4s + 25) / 4×s
cost per student =2 (4s + 25) / s
c) Now using this expression we can find the cost per student if each class has 20 students;
cost per student = 2 (4s + 25) / s
cost per student = 2 ( 4×20 + 25)/ 20
cost per student = 2 ( 80 + 25) / 20
cost per student = 2 (105) / 20
cost per student = 210 / 20 = $10.50
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Grace has a job power washing houses.
She needs to power wash 11 houses to
earn enough money to pay for a new robot
kit. If each house takes the same amount
of time, and she can wash 2 houses in 8
hours, how long will it take her to wash 11
houses?
Which graph matched matches the equation
Y+6=3/(x+4)
Answer: The graph that matches the equation:
I need helppppppppp I d don't know what to do
EXPLANATION
The perimeter Perimeter is given by the sum of the sides as follows:
P = z + 5 + z + 5 + z + z
Substituting P=26 and adding like terms,
26 = 10 + 4z
Subtracting -10 to both sides:
26 - 10 = 10 - 10 + 4z
Simplifying:
16 = 4z
Dividing both sides by 4:
16/4 = z
Switching and simplifying:
z = 4
So,
Equation: 26 = 10 + 4z
z = 4
on a drive, a football team gained 3 yards, lost 11 yards, and gained 15 yards. What was their total yardage for that drive?
Help me :(
By using subtraction, we get that, the total yardage for the drive was that they gained 7 yards.
We are given that:
On a drive,
A football team first gains = 3 yards.
Then it lost = 11 yards.
Then it again gained = 15 yards.
We need to find its total yardage.
For this, we will subtract the yards lost from the yards gained by the team.
So, we get that:
total yardage = 3 + 15 - 11
total yardage = 18 - 11
total yardage = 7 yards.
Therefore, by using subtraction, we get that, the total yardage for the drive was that they gained 7 yards.
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On january 1, 2021, frontier world issues $39.3 million of 7% bonds, due in 10 years, with interest payable semiannually on june 30 and december 31 each year. the proceeds will be used to build a new ride that combines a roller coaster, a water ride, a dark tunnel, and the great smell of outdoor barbeque, all in one ride.
The issue price (present value) of the bonds issued by Frontier World is $42,223,423.81.
What is the present value?The present value refers to the discounted future cash flows of the bonds (including interests and the repayment of the bonds).
The present value represents the current price of the bonds, at which they are issued.
The present value can be computed using the online finance calculator.
N (# of periods) = 20 (10 x 2)
I/Y (Interest per year) = 6% (Market Rate)
PMT (Periodic Payment) = $1,375,500
FV (Future Value) = $39,300,000
Bond Interest Rate = 7%
Semi-Annual Interest Payments:June 30 = $1,375,500 ($39,300,000 x 3.5%)
Dec. 31 = $1,375,500 ($39,300,000 x 3.5%)
Results:
Present Value (PV) = $42,223,423.81
Sum of all periodic payments = $27,510,000 ($1,375,500 x 20)
Total Interest = $24,586,576.19
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Question Completion:Required: 1-a. If the market rate is 6%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1)
A silo containing 800 gallons of grain is emptied at a constant rate of 400 gallons every 1
hour.
Enter an equation in the form y = mx + b that represents the amount of grain y, in gallons,
remaining in the silo after x hours.
The equation of the line is y = -400x + 800
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the equation that represents the amount of grain?The given parameters are
Initial number of gallon, c = 800
Constant rate, m = -400 gallons per hour
This means that
Slope = -400
y-intercept = 800
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = mx + c
So, we have
y = -400x + 800
Hence. the equation of the amount of grain is y = -400x + 800
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Joanne slices a large banana bread into pieces 16 There are 6 adults and 6 children who get a piece of banana bread. The rest of the pieces will be donated to the homeless. What fraction of the banana bread will be donated?
The most appropriate choice for fraction will be given by
Fraction of banana bread will be donated to the homeless is [tex]\frac{1}{4}[/tex]
What is a fraction?
Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
Here,
Total number of banana breads 16
Number of adults who got banana bread = 6
Number of Children who got banana bread = 6
Total number of children and adult who got banana bread = 6 + 6 = 12
Number of banana breads given to the homeless = 16 - 12 = 4
Fraction of banana bread given to the homeless = [tex]\frac{4}{16}[/tex]
= [tex]\frac{1}{4}[/tex]
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Write 9.75 as a mixed number.
Answer:
9 57/ 100
Step-by-step explanation:o convert the decimal 9.57 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
9.57 = 9.57/ 1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,
9.57 / 1
= (9.57 × 100)
(1 × 100)
= 9 57/ 100
.
(This fraction is alread reduced, We can't reduce it any further).
As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 9 57/ 100
is also equal to 9 57/ 100
when expressed as a mixed numbeR
Answer:
9 3/4
Step-by-step explanation:
Convert to a mixed number by placing the numbers to the right of the decimal over 100. Reduce the fraction.
Indicate whether the line on the graph is a function
The line on the graph is a function
How to determine if the line is a function?The given parameter is the graph
From the graph, we can see that the curve or the line is a quadratic function
As a general rule, all lines represented by a quadratic function are functions
This implies that the line is a function
It should be noted that:
Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
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Out of 120 students, 80 passed in Science, 70 in Nepali, 10 failed in both subjects and 7 did not appear in an examination. Find the number of students who passed in both subjects by representing the above information in a Venn-diagram.
Step-by-step explanation:
we can find the number of students passed in both subject by following method.
Solution;
A binomial experiment has independent trials and the outcome of a trial can be classified as either a success or a failure. Which two of the following statements also describe features of a binomial experiment?.
The features of a binomial experiment are
Identical number of trialsEqual probability of successHow to determine the features of a binomial experiment?From the question, we understand that the experiment is a binomial experiment
As a general rule, a binomial experiment is any experiment that has only two possible outcomes
These outcomes are represented as
True FalseThese outcomes can also be represented as
SuccessFailureThe representation of the outcomes are:
Success = pFailure = qThere are other features of a binomial experiment.
One of these features is:
The binomial experiment has a number of n identical or unique trials
Another features of a binomial experiment is
The probability of success on one trial is the same for all other trials
Hence, the two other features of a binomial experiment are
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the number of women graduating from 4-yr colleges in a particular country grew from 1930, when 48780 women earned a bachelor's degree, to 2003, when approximately 756000 women received such a degree. find an exponential function that fits the data, and the exponential growth rate.
The exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).
What is defined as the Growth Function?When we need to start writing a growth function, we use three separate components. The first component is the starting population, the second is the growth rate, and also the third is the time elapsed. By combining all three, we can create a growth equation that will assist us in determining the growth rate if we are provided with the final population as well as the time elapsed.The following equation can be used to calculate an exponential function again for number of women graduating from four-year colleges in t years after 1930:
A(t) = A₀e∧(rt)
In which A₀ is the starting point and r is the exponential growth rate expressed as a decimal.
In 1930, 48780 women received a bachelor's degree.
This implies that;
A₀ = 48780
In 2004, approximately 756000 people
The year 2003 is 73 years after 1930, that also means
Using the equation as an example:
A(t) = A₀e∧(rt)
Put the values;
756000 = 48780 e∧(73r)
e∧(73r) = 756000/ 48780
e∧(73r) = 15.49
Taking log both side;
73r = ㏑ 15.49
r = 2.7/7
r = 0.037
The function becomes;
A(t) = A₀e∧(0.037t)
Thus, the exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).
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Given the polynomial below:
9m5 +3n³2q² + 1 +
State:
Degree:
Number of Terms:
Constant:
This polynomial have 5 degree , 4 terms and one connstant
What is polynomial ?Algebraic expressions called polynomials only have non-negative integer powers for their variables. A polynomial is, for instance, Expressions with one or more terms that have a non-zero coefficient are called polynomials. The terminology include constants, exponents, and variables. The "leading term" refers to the first term of the polynomial in standard form. A standard polynomial is one in which the first term, which has the highest degree, is followed by succeeding terms that are organized in descending order of the exponents or powers of the variables, then by constant values. A "coefficient" is a number that has been multiplied by a variable.
Given that : [tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]
[tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]
This polynomial have 5 degree , 4 terms and one connstant
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Work out √45 - √5
Give your answer as an integer or as a
surd in its simplest form.
Solve for j.
-20j + 6j + 18j – 9j + 17 = −3
j= [
Answer:
-20j+ 6j=-14j
-14j + 18j=4j
4j-9j=-5j
-5j=-3-17
-5j =-20
j =-20÷-5
j =4
There are 14 red marbles and 20 blue marbles in a bag of marbles.
A. What is the ratio of red to blue marbles in simplest form?
B. What is the ratio of blue marbles to total marbles in simplest form?
Answer:
A. 7:10
B. 10:17
Explanation: The ratio of A. would be 14:20, simplified would be 7:10. The ratio of B. would be 20:34, simplified being half of both numbers. Giving you 10:17.
find a value for c so that the polynomial y^2 + 10y + c factors to (y+5)^2
Notice that
[tex]\begin{gathered} (y+5)^2=y^2+10y+25 \\ \text{and} \\ y^2+10y+c=(y+5)^2 \\ \Rightarrow y^2+10y+c=y^2+10y+25 \\ \Rightarrow c=25 \end{gathered}[/tex]Then, the answer is c=25.
need help with this, thanks
Answer:
x = 11°
Step-by-step explanation:
Hello!
These angles are called vertical angles or angles opposite to each other during the intersection of two lines.
Vertical angles are equal to each other, so we can set the expressions equal to each other and solve for x.
Solve for x9x - 4 = 8x + 7 -> Subtract 8xx - 4 = 7 -> Add 4x = 11The value of x is 11°.
Answer:
[tex]x=\boxed{11}[/tex]
Step-by-step explanation:
Vertical Angle Theorem
The opposite vertical angles of two straight intersecting lines are congruent.
Therefore, equate the expressions and solve for x:
[tex]\boxed{\begin{aligned}(9x-4)^{\circ}&=(8x+7)^{\circ}\\9x-4&=8x+7\\9x-4-8x&=8x+7-8x\\x-4&=7\\x-4+4&=7+4\\x&=11\end{aligned}}[/tex]
Therefore:
[tex]x=\boxed{11}[/tex]
2|x+3|+1>3 I need help!!
Answer:
x < -4 or x > -2
Step-by-step explanation:
[tex]2 |x + 3| + 1 > 3[/tex]
[tex]2 |x + 3| > 2[/tex]
[tex] |x + 3| > 1[/tex]
x + 3 > 1 or x + 3 < -1
x > -2 or x < -4
Answer:
Step-by-step explanation:
Anyone know how to prove these are equal to one another? I also need all the steps.
Answer:
Step-by-step explanation:
it can be simplified to [tex]\frac{sec \theta}{cot\theta+tan\theta} =sin\theta[/tex] . if you multiply each side by the denominator, it becomes [tex]sec\theta=\frac{sin^2\theta}{cos\theta} + cos\theta[/tex] since [tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex] and cotan is the reciprocal of that. Because [tex]sec\theta=\frac{1}{cos\theta}[/tex] so multiplying each side gives [tex]1=sin^2\theta+cos^2\theta[/tex], and [tex]sin^2\theta+cos^2\theta[/tex] is equal to 1.
Of which type of equation are there the greatest number:
A )Equations with no solutions
B) Equations with infinitely many solutions
C) Equations with exacly one solution
EXPLAIN YOUR REASONING
The greatest number of equations are available in all the types specified in option A), option B) and option C). So 'all of the above' is the correct choice.
As given in the question,
Let us discuss
option A) Equations with no solutions
examples are:
x+ y = 0
x+ y = 1
Many such pairs of simultaneous linear equations can be formulated and number of such equations possible is infinite.
Let us discuss
option B) Equations with infinitely many solutions
example:
x+ y = 0
Number of such equations possible is infinite.
Let us discuss
option C) Equations with exactly one solution
example:
x=4
Number of such equations possible is infinite.
Therefore, the greatest number of equations are available in all the types specified in option A), option B) and option C). So 'all of the above' is the correct choice.
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which of the following expressions is equivalent to (2x-2)(x+5)
the following data represent the number of grams of fat in breakfast meals offered at a local fast food restaurant. (a) construct an ordered stem-and-leaf plot and (b) describe the shape of the distribution.
An ordered stem-and-leaf plot has the following results:
0=4 counts
1=7 counts
2=6 counts
3=4 counts
4=1 count
The shape of the distribution is skewed to the right
Part 1
An ordered stem-and-leaf plot:
Total Counts
0 | 3 4 5 7 | 4
1 | 2 2 4 4 5 7 7 | 7
2 | 0 3 4 4 5 8 | 6
3 | 3 4 7 9 | 4
4 | 1 | 1
Part 2
Shape of distribution
When the data in the stem-and-leaf plot given above is plotted in graph, the tail of the plot will be on the right. Hence, the shape of the distribution is skewed to the right
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Triangle abc is congruent to triangle a'b'c'. Describe a sequence of rigid motions that takes a to a, b to b', and c to c'
To transform A to A', B to B' and C to C' rotate the triangle ABC clock- wise 90° about the A.
What is a Triangle ?Simple polygons with three sides and three internal angles make up triangles.
It is one of the fundamental geometric shapes in which the three vertices are connected to one another.
Triangles come in 4 different varieties.
1. Equilateral: Equilateral triangles have three equal sides and three identical 60-degree angles.
2. Isosceles: Isosceles triangles have equal sides and angles on both of their two sides.
3. Right-angled: In right-angled triangles, one of the angles is a right angle (90°).
4. Scalene: Triangles with this property do not have equal sides or angles.
To transform A to A', B to B' and C to C' rotate the Triangle ABC 90° clock- wise about the A.
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Mayerlin is deciding between two different movie streaming sites to subscribe to. Plan A costs $34 per month plus $2 per movie watched. Plan B costs $8 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Mayerlin watches xx per month, and let BB represent the monthly cost of Plan B if Mayerlin watches xx movies per month. Write an equation for each situation, in terms of x,x, and determine the number of monthly movies watched, x,x, that would make the two plans have an equal monthly cost.
Considering the definition of an equation and the way to solve it, the number of monthly movies watched that would make the two plans have an equal monthly cost is 26.
Definition of equationAn equation is an algebraic equality in which there are unknowns with unknown value. The unknown represents the number, if any, that makes the equality true. This unknown number is the solution of the equation.
This is, the solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Number of monthly movies watchedBeing "x" the number of monthly movies watched, you know that:
Plan A costs $34 per month plus $2 per movie watched. → A= 34 + 2xPlan B costs $8 per month plus $3 per movie watched. → B= 8 + 3xIf the two plans have an equal monthly cost, the equation in this case is:
A= B
34 + 2x= 8 + 3x
Solving:
34 - 8= 3x - 2x
26= x
Finally, 26 monthly movies watched would make the two plans have an equal monthly cost.
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Eli loads identical crates onto a truck with a load limit of 2000 pounds. Each crate weighs 125 pounds.
A function modeling this situation, where y represents the total weight of the crates in pounds, has a range described by which inequality?
0 < y < 16
0 ≤ y ≤ 125
0 ≤ y ≤ 2,000
0 < y < 2,000
The function modeling given situation, where y represents the total weight of the crates in pounds, has a range described by the inequality 0 ≤ y ≤ 2000. The correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The set that includes all the output values that the function expects is the range of a function.
The following information is provided regarding the input and output for this problem
The number of containers placed inside the vehicle as input.
Total weight of the crates loaded into the truck or output.
The range of this problem is represented by the following inequality:
0 ≤ y ≤ 2000.
The weight of an amount will never assume a negative value, and the maximum weight is 2,000 pounds, as stated in the problem.
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