Table that represent input & output value would be:
Input Output
44 45
45 46
46 47
To determine which table represents inputs and outputs that follow the same rule as 44+1, 44+2, and 44+3, we can simply evaluate each of the expressions and look for a pattern.
44 + 1 = 45
44 + 2 = 46
44 + 3 = 47
Therefore, the rule appears to be adding 1 to each subsequent number. We can check this by evaluating additional terms:
44 + 4 = 48
44 + 5 = 49
Based on this pattern, the correct table would be:
Input Output
44 45
45 46
46 47
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O a
Ob
● C
Od
For the following boxplot, what are the upper and lower
fences?
2
3
4 5
Lower Fence: 0 Upper Fence: 8
Lower Fence: -1 Upper Fence: 12
Lower Fence: 3 Upper Fence: 5
Lower Fence: 1
Upper Fence: 8
9
Answer:
Therefore, the lower fence is 1.5 and the upper fence is 5.5.
Step-by-step explanation:
To determine the upper and lower fences for a boxplot, we first need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1). Then, we can use the following formulas:
Lower Fence = Q1 - 1.5 * IQR
Upper Fence = Q3 + 1.5 * IQR
In the given boxplot, the box extends from 2 to 5, with the median (Q2) at 3.5. The first quartile (Q1) is 3 and the third quartile (Q3) is 4. Therefore, the IQR is:
IQR = Q3 - Q1 = 4 - 3 = 1
Using the formulas above, we can calculate the lower and upper fences:
Lower Fence = Q1 - 1.5 * IQR = 3 - 1.5 * 1 = 1.5
Upper Fence = Q3 + 1.5 * IQR = 4 + 1.5 * 1 = 5.5
Therefore, the lower fence is 1.5 and the upper fence is 5.5.
PROBABILITY The spinner has two equal sections, blue (B) and red (R). Use the square of a sum to determine the possible combinations of spinning the spinner two times.
There are 4 possible combinations of spinning the spinner two times: BB, BR, RB, and RR.
Since the spinner has two equal sections, blue and red, the probability of spinning either color is the same.
Hence, For the possible combinations of spinning the spinner two times, we can use the square of a sum formula,
⇒ (a + b)² = a² + 2ab + b².
In this case, we can use the formula to calculate the possible outcomes of spinning the spinner twice.
So, if we let B represent spinning blue and R represent spinning red, the possible outcomes of spinning the spinner twice are:
BB (B + B): 2² = 4
BR (B + R): 2 x 2 = 4
RB (R + B): 2 x 2 = 4
RR (R + R): 2² = 4
Therefore, there are 4 possible combinations of spinning the spinner two times: BB, BR, RB, and RR.
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Nick and jake ran a total of 27 miles combined. Nick ran 13 miles. How many did jake run?
Find the value of x.
BP and DP are straight lines
The value of the variable 'x' using the external angle theorem will be 84°.
What is the triangle?The polygonal form of a triangle has a number of flanks and three independent variables. Angles in the triangle add up to 180°.
The exterior angle of a triangle is practically always equivalent to the accumulation of the interior and opposing interior angles. The term "external angle property" refers to this segment.
The graph is completed and given below.
By the external angle theorem, the equation is given as,
x + 180° - 154° + 180° - 110° = 180°
x + 26° + 70° = 180°
x + 96° = 180°
x = 84°
The value of the variable 'x' using the external angle theorem will be 84°.
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18. Determine the exact value of the product: 3 sin(37.5°) cos( 7.5°) 19. Determine the exact value of the sum: cos (phi/12) - cos (5phi/12)
18. The exact value of the product 3 sin(37.5°) cos( 7.5°) can be determined using the double angle formula for sine:
sin(2x) = 2 sin(x) cos(x)
Substituting x = 22.5° into the formula gives:
sin(45°) = 2 sin(22.5°) cos(22.5°)
Dividing both sides by 2 gives:
sin(45°)/2 = sin(22.5°) cos(22.5°)
Substituting the given values into the equation gives:
3 sin(37.5°) cos( 7.5°) = 3 (sin(45°)/2) (cos(45°)/2)
Simplifying gives:
3 sin(37.5°) cos( 7.5°) = 3/4
Therefore, the exact value of the product is 3/4.
19. The exact value of the sum cos (phi/12) - cos (5phi/12) can be determined using the sum-to-product formula for cosine:
cos(x) - cos(y) = -2 sin((x+y)/2) sin((y-x)/2)
Substituting x = phi/12 and y = 5phi/12 into the formula gives:
cos (phi/12) - cos (5phi/12) = -2 sin((phi/12 + 5phi/12)/2) sin((5phi/12 - phi/12)/2)
Simplifying gives:
cos (phi/12) - cos (5phi/12) = -2 sin(3phi/12) sin(2phi/12)
Therefore, the exact value of the sum is -2 sin(3phi/12) sin(2phi/12).
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Working alone, it takes Stephanie seven hours to clean an attic. Shayna can clean the same attic in 12 hours. Find how long it would take them if they worked together.
The answer would take Stephanie and Shayna approximately 4.42 hours to clean the attic if they worked together.
Working alone, it takes Stephanie seven hours to clean an attic. Shayna can clean the same attic in 12 hours. To find how long it would take them if they worked together,
we can use the formula:
1/T = 1/t1 + 1/t2
Where T is the time it takes for both to complete the task together, t1 is the time it takes for the first person to complete the task alone, and t2 is the time it takes for the second person to complete the task alone.
Plugging in the given values, we get:
1/T = 1/7 + 1/12
1/T = 12/84 + 7/84
1/T = 19/84
T = 84/19
T = 4.42 hours
Therefore, it would take Stephanie and Shayna approximately 4.42 hours to clean the attic if they worked together.
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The surface area of a rectangular prism is 250 cm 2. If its height is 10 centimeters, and its width is 5 centimeters, what is its volume?
The volume of the rectangular prism whose surface area is 250 cm square is 250cubic centimeters.
The surface area of a rectanular prism is calculates by the formula
= 2( length*width + length*height + width*height ) square units
Let the length of the given prism be l centimeters.
Given, width is 5 centimeters and height is 10 centimeters of the rectangular prism.
The surface area of the rectangular prism is 250 cm square.
Thus by the above formula,
250 = 2 ( l*5 + l*10 +10*5)
⇒250 = 2 (15*l +50)
⇒ 250= 30*l + 100
⇒ 150 = 30*l
⇒l = 150/30 = 5 (centimeters)
Thus the volume of the given rectangular prism is calculated as
= ( length*width*height) cubic units
= (5*5*10) cubic centimeters
= 250 cubic centimeters
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1. Ben joins a book club. He pays $12 for each book and $5 for shipping and handling
charges for each order.
a.Name the quantities that change in this problem situation and the quantities that
remain constant. Determine which quantity is independent and which quantity
is dependent.
B. Create a table of values to represent the total cost if Ben orders 1 or 2 books or
spends $41, $65, or $125.
Answer:
A. The quantities that change in this problem situation are the number of books Ben orders and the total cost. The quantities that remain constant are the cost per book ($12) and the shipping and handling charge per order ($5).
The independent variable is the number of books Ben orders, as this is the variable that Ben has control over and chooses to change. The dependent variable is the total cost, as it depends on the number of books Ben orders.
B.
(imagine this as a chart)
Number of books Total cost
1 $17
2 $29
3 $41
5 $65
10 $125
----------------------------------------------------------------------------------------------------------
To create this table, we used the formula:
Total cost = (Cost per book x Number of books) + Shipping and handling charge
For example, when Ben orders 3 books, the total cost is:
Total cost = ($12 x 3) + $5 = $41
Similarly, when Ben spends $65, the number of books he can order is:
Number of books = (Total cost - Shipping and handling charge) / Cost per book
Number of books = ($65 - $5) / $12 = 5
And so on for the other values in the table.
Answer:
See below
Step-by-step explanation:
Let x be he cost per book and y be the total cost including shipping and handling.
The relevant equation is
y = 12x + 5
A. Variables are number of books ordered(x) and total cost(y)
The constant is the shipping and handling cost
Since the total cost depends on the number of books ordered, the independent variable x = number of books
The total cost y is the dependent variable
--------------------------------------------------------------------------------------
B. Cost of 1 or 2 books can be found by plugging in x = 1 and x =2 into the equations and solving for y
Total Cost of 1 book = 12(1) + 5 = $17
Total cost of 2 books = 12(2) + 5 = 24 + 5 = $29
To compute the number of books that can be ordered for different total cost amounts is obtained by substituting for y and solving for x
For $41:
41 = 12x + 5
41 - 5 = 12x
36 = 12z
x = 36/12 = 3 books
For $65:
65 = 12x + 5
65 - 5 = 12x
60 = 12x
x = 60/12 = 5 books
For $125:
125 = 12x + 5
125 - 5 = 12x
120 = 12x
x = 120/12 = 10 books
Here is the table
Number Total Cost(y)
of books (x)
1 $17
2 $29
3 $41
5 $65
10 $125
Marco bought a pair of jeans on sale for 30% off the regular price of $54.00. What was the discount he
received at the cash register and what was the sale price (not including tax)?
Answer:
Step-by-step explanation:
He received $16.20
because 30% of $54.00 is $16.20
2. [45 marks] Consider the following linear system \[ \left[\begin{array}{rrr} 6 & 2 & -3 \\ -5 & 3 & 9 \\ 2 & -7 & -1 \end{array}\right]\left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\righ
To solve the given linear system, we can use the Gaussian elimination method. This method involves reducing the given matrix to a row echelon form and then solving for the variables using back substitution.
Step 1: Reduce the given matrix to a row echelon form by performing elementary row operations.
\[ \left[\begin{array}{rrr|r} 6 & 2 & -3 & 0 \\ -5 & 3 & 9 & 0 \\ 2 & -7 & -1 & 0 \end{array}\right] \]
We can start by dividing the first row by 6 to get a leading 1:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ -5 & 3 & 9 & 0 \\ 2 & -7 & -1 & 0 \end{array}\right] \]
Next, we can add 5 times the first row to the second row and subtract 2 times the first row from the third row:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ 0 & \frac{16}{3} & \frac{17}{2} & 0 \\ 0 & -\frac{23}{3} & 0 & 0 \end{array}\right] \]
Finally, we can multiply the second row by $\frac{3}{16}$ and the third row by $-\frac{3}{23}$ to get a leading 1 in each row:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ 0 & 1 & \frac{51}{32} & 0 \\ 0 & 1 & 0 & 0 \end{array}\right] \]
Step 2: Use back substitution to solve for the variables.
From the third row, we have:
$x_2 = 0$
Substituting this into the second row gives us:
$x_3 = 0$
And substituting these values into the first row gives us:
$x_1 = 0$
Therefore, the solution to the given linear system is:
$x_1 = 0$, $x_2 = 0$, and $x_3 = 0$
This means that the given linear system has a unique solution at the origin.
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Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2400 what was the rate charged per hour by each mechanic if the sum of the two rates was $195 per hour? Note that the ALEKS.graphing calculator can be used to make computations easier. First mechanie: s1 per hour Second mechanic: $ per hour ?
The rate charged per hour by the first mechanic and the second mechanic.
The total number of hours worked by the two mechanics is 10 hours + 15 hours = <<10+15=25>>25 hours. The total amount charged by the two mechanics is $2400. If we let x be the rate charged per hour by the first mechanic, and y be the rate charged per hour by the second mechanic, we can write the following equations:
x + y = 195 (the sum of the two rates is $195 per hour)
10x + 15y = 2400 (the total amount charged is $2400)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:
y = 195 - x
We can then substitute this expression for y into the second equation:
10x + 15(195 - x) = 2400
Simplifying this equation gives us:
10x + 2925 - 15x = 2400
-5x = -525
x = 105
We can then substitute this value of x back into the first equation to find the value of y:
105 + y = 195
y = 90
Therefore, the rate charged per hour by the first mechanic is $105 per hour, and the rate charged per hour by the second mechanic is $90 per hour.
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16. Arden surveyed the 6th grade to see what there favorite colors were.
If 48
students chose yellow, how many students
were surveyed in all?"
How
students chose blue?
many
red?
How many chose purple, green& other?
a. 240 students were surveyed in all. b. 60 students chose blue. c. The number of students who chose purple is 7, green is 10, others is 7 students.
Describe Proportion?In mathematics, a proportion is a statement that two ratios or fractions are equal. A proportion can be expressed as an equation of the form:
a/b = c/d
where a, b, c, and d are numbers, and b and d are not equal to zero. This equation can also be written in the form of a cross product:
ad = bc
This equation means that the product of the numerator of one fraction and the denominator of the other fraction is equal to the product of the denominator of the first fraction and the numerator of the second fraction.
a. If 20% of the students surveyed chose yellow and 48 students chose yellow, we can set up the following proportion to find the total number of students surveyed (let "x" be the total number of students):
20/100 = 48/x
Solving for x, we get:
x = 240
Therefore, 240 students were surveyed in all.
b. 25% of the students surveyed chose blue, so the number of students who chose blue is:
25/100 x 240 = 60
Therefore, 60 students chose blue.
c. We are given that 3% of the students surveyed chose purple, and 4% chose green. To find the number of students who chose purple or green, we can add the two percentages and find the corresponding portion of the total number of students:
3/100 + 4/100 = 7/100
So 7% of the students surveyed chose purple or green. The number of students who chose purple is:
3/100 x 240 = 7.2 (rounded to the nearest whole number, this is 7)
Similarly, the number of students who chose green is:
4/100 x 240 = 9.6 (rounded to the nearest whole number, this is 10)
We are also given that 3% of the students surveyed chose "other". Therefore, the number of students who chose "other" is:
3/100 x 240 = 7.2 (rounded to the nearest whole number, this is 7)
So 7 students chose "other".
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The sum of 7 of the angles of a nonagon is 1000° the other two angles are equal to each other. Calculate the size of the other angles
By answering the above question, we may state that Hence, the equation nonagon's last seven angles are all around 140.57 degrees.
What is equation?When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.
S = (n - 2) × 180°
where n is the total number of sides, which in this instance is 9.
The internal angles of a nonagon's sum are as follows:
S = (9 - 2) × 180° = 1260°
Let x represent the dimensions of the nonagon's two equal angles. The nonagon's total angles may therefore be represented as follows:
1000° + 5x + 5x + 180° = 1260°
When we simplify the previous equation, we get:
10x = 80°
x = 8°
Each of the nonagon's two equal angles is 8°, and the total of the remaining seven angles is as follows:
1000° - 2x = 1000° - 2(8°) = 984°
984° ÷ 7 = 140.57° (rounded to two decimal places) (rounded to two decimal places)
Hence, the nonagon's last seven angles are all around 140.57 degrees.
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Given a Markov chain with probability transition matrix
P = [0.4 0.6]
[0.7 0.3]
Verify that this is an irreducible ergodic Markov chain.
Compute the two step transition probability matrix P(2) .
Find the limiting probability π0 and π1.
The limiting probabilities are π0 = 7/12 and π1 = 5/12.
Verify that this is an irreducible ergodic Markov chain.
An irreducible Markov chain is one in which it is possible to move from any state to any other state in a finite number of steps. In this case, the probability transition matrix P is:
P = [0.4 0.6]
[0.7 0.3]
Since there are non-zero probabilities in every row and column, it is possible to move from any state to any other state in a finite number of steps. Therefore, this is an irreducible Markov chain.
An ergodic Markov chain is one in which every state is positive recurrent and aperiodic. Since this is an irreducible Markov chain, every state is positive recurrent. Additionally, there are no cycles in the transition matrix, so every state is aperiodic. Therefore, this is an ergodic Markov chain.
Compute the two step transition probability matrix P(2).
The two step transition probability matrix P(2) is obtained by multiplying the matrix P by itself:
P(2) = P * P = [0.4 0.6] * [0.4 0.6]
[0.7 0.3] [0.7 0.3]
= [0.4*0.4 + 0.6*0.7 0.4*0.6 + 0.6*0.3]
[0.7*0.4 + 0.3*0.7 0.7*0.6 + 0.3*0.3]
= [0.58 0.42]
[0.49 0.51]
Find the limiting probability π0 and π1.
The limiting probabilities are the stationary probabilities of the Markov chain, which are obtained by solving the following system of equations:
π0 = 0.4*π0 + 0.7*π1
π1 = 0.6*π0 + 0.3*π1
π0 + π1 = 1
Solving this system of equations gives:
π0 = 7/12
π1 = 5/12
Therefore, the limiting probabilities are π0 = 7/12 and π1 = 5/12.
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a car has a circular turning radius of 16.1 ft. the distance between the two front tires is 4.7 ft. how much further does a tire on the outside of the turn travel than a tire on the inside.
Answer:
When a car turns, the tire on the outside of the turn has to travel a greater distance than the tire on the inside of the turn. The difference in the distance traveled by the two tires is equal to the circumference of the circle that the car makes during the turn.
The radius of the circle is given as 16.1 ft, which means the diameter is 2 * 16.1 = 32.2 ft. The distance between the two front tires is given as 4.7 ft, which means that the radius of the circle traced by the inner tire is 16.1 - 2.35 = 13.75 ft, where 2.35 ft is half of the distance between the two front tires.
The circumference of the circle traced by the outer tire is 2 * π * 16.1 = 101.366 ft (rounded to three decimal places). The circumference of the circle traced by the inner tire is 2 * π * 13.75 = 86.415 ft (rounded to three decimal places).
The difference in the distance traveled by the two tires is:
101.366 - 86.415 = 14.951 ft (rounded to three decimal places)
Therefore, the tire on the outside of the turn travels about 14.951 ft further than the tire on the inside.
Solving a rational equation that simplifies to linear: Denominat Solve for v. 6=(5)/(v-8)
The value of v is 8.83.
What is rational equation?A rational equation is an equation that includes one or more fractions with polynomials. It can be solved by cancelling common factors between the numerator and the denominator, and then solving the resulting equation. It is important to note that when cancelling common factors, one must always check that the original equation is still satisfied.
To solve this rational equation that simplifies to linear, you need to solve for v. To do this, first multiply both sides by the denominator:
6(v-8) = 5
Then add 8 to both sides to get rid of the variable in the denominator:
6v - 48 = 5
Finally, add 48 to both sides to isolate the variable v:
6v = 53
Finally, divide both sides by 6 to solve for v:
v = 53/6 = 8.83
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Which point has coordinates (4.9, 3.9)?
Answer:
C
Step-by-step explanation:
Suppose you deposit $800 in an account with an annual interest rate of 10 % compounded quarterly.
Use the nt formula A = P(1+ -) and round each answer to 2 decimal places, if necessary.
a. Find an equation that gives the amount of money in the account after t years. A(t) =
b. Find the amount of money in the account after 5 years. After 5 years, there will be $ in the account.
c. How many years will it take for the account to contain $1600? It will take years for there to be $1600 in the account. d. If the same account and interest were compounded continuously, how much money would the account contain after 5 years? With continuous compounding interest, there would be $ in the account after 5 years.
So, with continuous compounding interest, there would be $1324.46 in the account after 5 years.
A(t) = P(1 + r/n)^(nt)
a. To find an equation that gives the amount of money in the account after t years, we can plug in the given values for P, r, and n into the formula. P is the initial deposit, r is the annual interest rate, and n is the number of times the interest is compounded per year. So, the equation will be:
A(t) = 800(1 + 0.10/4)^(4t)
b. To find the amount of money in the account after 5 years, we can plug in t = 5 into the equation and solve for A(t):
A(5) = 800(1 + 0.10/4)^(4*5)
A(5) = 800(1.025)^20
A(5) = 1303.04
So, after 5 years, there will be $1303.04 in the account.
c. To find how many years it will take for the account to contain $1600, we can set A(t) = 1600 and solve for t:
1600 = 800(1 + 0.10/4)^(4t)
2 = (1.025)^4t
log(2) = 4t*log(1.025)
t = log(2)/(4*log(1.025))
t = 7.22
So, it will take 7.22 years for there to be $1600 in the account.
d. If the same account and interest were compounded continuously, we can use the formula A(t) = Pe^(rt) to find how much money would be in the account after 5 years:
A(5) = 800e^(0.10*5)
A(5) = 800e^0.5
A(5) = 1324.46
So, with continuous compounding interest, there would be $1324.46 in the account after 5 years.
Learn more about Compounding
(a) The equation that gives the amount of money in the account after t years is A(t) = 800(1.025)^4t.
(b) After 5 years, there will be $1304.56 in the account.
(c) It will take 7.24 years for there to be $1600 in the account.
(d) With continuous compounding interest, there would be $1340.95 in the account after 5 years.
a. The equation for the amount of money in the account after t years is A(t) = 800(1 + 0.10/4)^(4t) = 800(1.025)^4t. This is derived from the formula A = P(1+ r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
b. To find the amount of money in the account after 5 years, we can plug in the values into the equation from part a. A(5) = 800(1 + 0.10/4)^(4)(5) = 800(1.025)^20 = $1304.56. Therefore, after 5 years, there will be $1304.56 in the account.
c. To find how many years it will take for the account to contain $1600, we can set the equation from part a equal to 1600 and solve for t. 1600 = 800(1 + 0.10/4)^(4t) => 2 = (1.025)^4t => 4t = log(2)/log(1.025) => t = 7.24 years. Therefore, it will take 7.24 years for there to be $1600 in the account.
d. If the same account and interest were compounded continuously, the formula for the amount of money in the account after t years would be A(t) = 800e^(0.10t). To find how much money the account would contain after 5 years, we can plug in the values into this equation. A(5) = 800e^(0.10)(5) = $1340.95. Therefore, with continuous compounding interest, there would be $1340.95 in the account after 5 years.
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Which is greater, 3 miles or 1,000 yards? How much greater? Explain. (15pts)
Answer:
1 mile is equal to 1,760 yards. Therefore, 3 miles is equal to 3 x 1,760 = 5,280 yards.
Comparing 5,280 yards to 1,000 yards, we can see that 5,280 yards is greater than 1,000 yards.
To determine how much greater, we can subtract 1,000 from 5,280:
5,280 - 1,000 = 4,280
Therefore, 3 miles is 4,280 yards greater than 1,000 yards.
How would you modify the statement of the limit of a rational function?
This would give us a modified statement of the limit, which would be "the limit of the rational function as x approaches 4".
What is rational function?A rational function is a type of mathematical function that can be expressed as the ratio of two polynomials. It can be written in the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials with q(x) not equal to zero. Rational functions are used to model many real-world phenomena, such as the rate of change of a quantity with respect to another. They can also be used to solve complex equations and to analyze the behavior of a system.
The statement of the limit of a rational function can be modified by substituting different values for the variable and determining the resulting limit. For example, if the limit of the rational function is as x approaches 3, then we can substitute x = 4 and determine the resulting limit. This would give us a modified statement of the limit, which would be "the limit of the rational function as x approaches 4".
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thank you if you help with this
The ratio of amount of flour to amount of water is 8 : 3. 5 cups of flour require 15/8 cups of water
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
From the recipe, 2 cups of flour require 3/4 cups of water
a) The ratio of amount of flour to amount of water = 2 cups of flour / (3/4) cups of water = 8/3 = 8 : 3
b) 2 cups of flour require 3/4 cups of water
5 cups of flour = 5 cups of flour * 3/4 cups of water per 2 cups of flour = 5 * (3/4)÷2 = 5 * 3/8 = 15/8 cups of water
5 cups of flour require 15/8 cups of water
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What fraction of each 100 chart is shaded?
The fraction when a 100-square grid has 70 shaded squares will be 7/10.
How to calculate the FractionA fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, a 100-square grid has 70 shaded squares.
The fraction will be:
= Number it shaded square / Total square
= 70 / 100
= 7 / 10
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A 100-square grid has 70 shaded squares. Explain how you could express this model as a fraction.
Answer:
The fraction when a 100-square grid has 70 shaded squares will be 7/10.
what order do these go in?
For [tex]4x + 2x^2(3x-5)[/tex] : degree = 3, number of terms = 3, so the answer is 3 and 3.
For [tex](-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6)[/tex]: degree = 5, number of terms = 4, so the answer is 5 and 4.
For [tex](3x^2 - 3)(3x^2 + 3)[/tex] : degree = 4, number of terms = 1, so the answer is 4 and 1.
What is expression ?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, ×, ÷, etc.) that represents a mathematical relationship or quantity.
Expressions can be simple, such as 2 + 3, or more complex, such as [tex](4x^2 - 2x + 5)/(x - 1).[/tex] They can also include variables, which are symbols that represent unknown or changing values.
For the expression [tex]4x + 2x^2(3x-5):[/tex]
Simplified form:[tex]6x^3 - 10x^2 + 4x[/tex]
Degree: 3
Number of terms: 3
For the expression [tex](-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6):[/tex]
Simplified form: [tex]-x^5 - 3x^4 + 12x^3 - 6[/tex]
Degree: 5
Number of terms: 4
For the expression[tex](3x^2 - 3)(3x^2 + 3):[/tex]
Simplified form: [tex]9x^4 - 9[/tex]
Degree: 4
Number of terms: 1
Therefore, the correct options are:
For [tex]4x + 2x^2(3x-5)[/tex] : degree = 3, number of terms = 3, so the answer is 3 and 3.
For [tex](-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6)[/tex] : degree = 5, number of terms = 4, so the answer is 5 and 4.
For [tex](3x^2 - 3)(3x^2 + 3):[/tex] degree = 4, number of terms = 1, so the answer is 4 and 1.
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Peter and Dan shared some beads. After Peter gave away 1/4 of his beads and Dan gave away 1/5 of his beads, both had the same number of beads left. If Peter had 7 beads more than Dan at first, how many beads did each of them have at the end?
Peter ended up with 31 beads, and Dan ended up with 28 beads.
What is the fraction?
A fraction is a mathematical expression that represents a part of a whole. It is written in the form of a ratio between two numbers, with the top number called the numerator and the bottom number called the denominator.
Let's represent the number of beads that Peter and Dan had at the start by P and D, respectively. Then we can set up an equation based on the information given in the problem:
After giving away 1/4 of his beads, Peter had 3/4 of his original number of beads, which is (3/4)P.
After giving away 1/5 of his beads, Dan had 4/5 of his original number of beads, which is (4/5)D.
According to the problem, both had the same number of beads left after giving away some of their beads:
(3/4)P = (4/5)D
We also know that Peter had 7 more beads than Dan at the start:
P = D + 7
We can use substitution to solve for D:
(3/4)(D+7) = (4/5)D
9D/20 + 21/20 = 4D/5
D = 35
So Dan had 35 beads at the start. Using the equation P = D + 7, we can find that Peter had:
P = D + 7 = 35 + 7 = 42
After giving away 1/4 of his beads, Peter had (3/4)P = (3/4)*42 = 31.5 beads, which we can round down to 31 beads since we're dealing with whole numbers of beads. After giving away 1/5 of his beads, Dan had (4/5)D = (4/5)*35 = 28 beads.
Therefore, Peter ended up with 31 beads, and Dan ended up with 28 beads.
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() Which expression is equivalent to (x^2/x^-4)^5
The expression that is equivalent to [tex](\frac{x^2}{x^-4})^5[/tex] is x³⁰
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
[tex](\frac{x^2}{x^-4})^5[/tex]
An equivalent expression is a different way of writing the same mathematical statement using equivalent mathematical operations or properties.
Evaluate the quotients using the law of indices
So, we have the following representation
(x⁶)⁵
Remove the bracket using the law of indices
So, we have the following representation
x³⁰
Hence, the solution to the expression is x³⁰
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How do you graph y=1/2x and y=x+2
Answer:
To graph y = 1/2x and y = x + 2, follow these steps:
Make a table of values for each equation. Choose several values of x, plug them into the equation, and solve for y. For y = 1/2x, you might choose x = -2, -1, 0, 1, and 2. For y = x + 2, you might choose the same values of x.
For y = 1/2x:
x | y
-2 | -1
-1 | -1/2
0 | 0
1 | 1/2
2 | 1
For y = x + 2:
x | y
-2 | 0
-1 | 1
0 | 2
1 | 3
2 | 4
Plot the points from each table on a graph. For y = 1/2x, plot the points (-2, -1), (-1, -1/2), (0, 0), (1, 1/2), and (2, 1). For y = x + 2, plot the points (-2, 0), (-1, 1), (0, 2), (1, 3), and (2, 4).
Draw a line through each set of points. The line for y = 1/2x should have a slope of 1/2 and pass through the point (0, 0). The line for y = x + 2 should have a slope of 1 and pass through the point (0, 2).
Label the axes and the lines. You can label the x-axis "x" and the y-axis "y". Label the line for y = 1/2x "y = 1/2x" and the line for y = x + 2 "y = x + 2".
Check your graph. Make sure each point is plotted correctly and the lines are drawn accurately. You can also check your graph by plugging in other values of x and making sure the corresponding points are on the lines.
Use simultaneously equation to eliminate one value and find the other then you find the value of the other one by substituting the value that u find from the other one eg: eliminate X find the value of y and then substitute y in one of your equation to find the value of X.
I need help with this question can anyone tell me ?
Step-by-step explanation:
21
Please answer number 10. Please answer both parts. Show work. Thank you
The volume of the triangular prism is 3x³ + 16x² + 3x - 10. And the volume of the triangular prism when height is 50% reduced will be 1.5x³ + 8x² + 1.5x - 5.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.
The dimensions of the triangular prism are (2x + 2), (x + 5), and (3x - 2). Then the volume is given as,
V = (1/2) · (2x + 2) · (x + 5) · (3x - 2)
V = (x + 1) · (x + 5) · (3x - 2)
V = (x² + 6x + 5) · (3x - 2)
V = 3x³ + 16x² + 3x - 10
If the height is reduced by 50%, then the volume is given as,
V = (1/2) · [0.50 × (2x + 2)] · (x + 5) · (3x - 2)
V = (1/2) · (x + 1) · (x + 5) · (3x - 2)
V = (1/2) · (x² + 6x + 5) · (3x - 2)
V = (1/2) · (3x³ + 16x² + 3x - 10)
V = 1.5x³ + 8x² + 1.5x - 5
The volume of the triangular prism is 3x³ + 16x² + 3x - 10. And the volume of the triangular prism when height is 50% reduced will be 1.5x³ + 8x² + 1.5x - 5.
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Suppose you deposit $1100 in an account with an annual interest rate of 8 % compounded quarterly: Use the formula 4 = P(1+#)" and round each answer to 2 decimal places, if necessary: Find an equation that gives the amount of money in the account after t years: A(t) Preview Find the amount of money in the account after 8 years After 8 years_ there will be $ in the account: c How many years will it take for the account to contain $2200? It will take years for there to be S2200 in the account: d. If the same account and interest were compounded continuously, how much money would the account contain after 8 years? With continuous compounding interest; there would be in the account after 8 years
a) A(t) = 1100(1 + 0.08/4)^(4t)
b) After 8 years, there will be $2203.99 in the account.
c) It will take approximately 8.03 years for there to be $2200 in the account.
d) With continuous compounding interest, there would be $2219.54 in the account after 8 years.
A(t) = P(1 + r/n)^(nt)
Where:
A(t) = the amount of money in the account after t years
P = the initial deposit
r = the annual interest rate
n = the number of times interest is compounded per year
t = the number of years
Find an equation that gives the amount of money in the account after t years:
A(t) = 1100(1 + 0.08/4)^(4t)
Find the amount of money in the account after 8 years:
A(8) = 1100(1 + 0.08/4)^(4*8)
A(8) = 1100(1.02)^32
A(8) = 2203.99
After 8 years, there will be $2203.99 in the account.
How many years will it take for the account to contain $2200?
2200 = 1100(1 + 0.08/4)^(4t)
2 = (1.02)^4t
log(2) = 4t*log(1.02)
t = log(2)/(4*log(1.02))
t = 8.03
It will take approximately 8.03 years for there to be $2200 in the account.
If the same account and interest were compounded continuously, how much money would the account contain after 8 years?
A(t) = Pe^(rt)
A(8) = 1100*e^(0.08*8)
A(8) = 1100*e^0.64
A(8) = 2219.54
With continuous compounding interest, there would be $2219.54 in the account after 8 years.
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Hi due today pls help! Ty! question attached
Snails to Newts iz
There are 36 Snails present in the pond.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Ratio of Snail to Newts = 3:4
So, Number of Snail= 3x and number of Newts = 4x
If 12 more newts added then the ratio is 3:5
So, 3x/ 4x+ 12 = 3/5
15 x = 3(4x+ 12)
15x = 12x + 36
15x - 12x = 36
3x = 36
x= 12
So, the number of Snails in pond are 3x = 3(12)= 36.
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