The greatest common monomial factor of this polynomial will be 14x²y³.
What is the greatest common factor?Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).
The polynomial is given below.
⇒ 14x³y⁵z² - 98x²y⁴x² + 28x²y³
⇒ 14x²y³(xy²z² - 7x²y + 2)
The greatest common monomial factor of this polynomial will be 14x²y³.
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Which one of the following is a result of the normal probability distribution being bell-shaped?
The mean, median, and mode are at the center
The area on the right side of the mean is greater than the area on the left.
The area on each side of the mean equals 1.00
The mean is further in the right tail than the median is
The result of the normal probability distribution being bell-shaped is that the mean, median, and mode are at the center.
This means that the center of the bell-shaped curve represents the most likely occurrence of the data and that the values are symmetrically distributed around the mean.
The mean, median, and mode of a normal distribution are equal, which means that they are all located at the center of the bell-shaped curve. This is an important characteristic of the normal distribution and sets it apart from other distributions where the mean, median, and mode may not be equal.
In a normal distribution, the area on each side of the mean does not equal 1.00, but rather approaches 1.00 as the curve becomes more symmetrical. The height of the curve at the mean represents the highest probability of occurrence, and the probabilities decrease as the values deviate from the mean.
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Solving systems by elimination -4x-5y=8,7x+5y=16
Answer:
(8, -8)
x = 8
y = -8
Step-by-step explanation:
-4x - 5y = 8
7x + 5y = 16
-----------------------
3x = 24
÷3 ÷3
----------------
x = 8
7x + 5y = 16
7(8) + 5y = 16
56 + 5y = 16
-56 -56
----------------------
5y = -40
÷5 ÷5
------------------
y = -8
(8, -8)
I hope this helps!
Maya has 7 yards of ribbon. She uses 4 yards to make bows and 1 yard 2 feet for
a wreath. How many feet of ribbon does Maya have left?
Answer:
1 yard and 1 foot
Step-by-step explanation:
7-4=3
3-1 yd and 2 feet
there are three feet in a yard. you can subtract the yard first, leaving you with two yards, then subtract two feet. you will be left with 1 yard and 1 foot.
hussain receives about six telephone calls from friends and family between 6 pm and 8:00 pm. what is the probability that hussain receives more than two calls in the next 30 minutes?
The required probability for the number of phone calls more than two in next 30 minutes is equal to ( 18 / 5)e⁻⁶.
Number of phone calls between 6pm and 8.00 pm 'n' = About 6 calls
Using Poisson's distribution we have,
P ( X = x ) = ( e⁻ⁿ nˣ ) / x!
Probability of receiving more than 2 phone calls in next 30 minutes
= P( X > 2 )
= P ( X = 3 ) + P ( X = 4 ) + P ( X = 5) + P( X = 6)
= ( e⁻⁶ 6³ ) / 3! + ( e⁻⁶ 6⁴ ) / 4! + ( e⁻⁶ 6⁵) / 5! + ( e⁻⁶ 6⁶ ) / 6!
= ( e⁻⁶ 6³ ) / 3! [ 1 + (6 / 4) + (6² / 5× 4 ) + ( 6³ / 6 ×5× 4) ]
= ( e⁻⁶ 6³ ) / 3! [ ( 20 + 30 + 72 ) / 20 ]
= ( 18 / 5)e⁻⁶.
Therefore, the probability of more than two phone calls is ( 18 / 5)e⁻⁶.
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i12 + 1 = 1 - i 1 + i 0 2
Kyle is looking to buy a shirt that normally costs $85. Lucky for Kyle, the store selling the shirt is having a 30% off sale for all items. After the discount, Kyle must pay 6% sales tax on the shirt. How much does Kyle end up spending on this shirt?
Kyle spending on this shirt at end up is, $63.07.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Kyle is looking to buy a shirt that normally costs $85.
Here, Lucky for Kyle, the store selling the shirt is having a 30% off sale for all items.
Hence, The discount price is,
⇒ 30% of 85
⇒ 30/100 × 85
⇒ $25.5
So, The price of shirt after discount = $85 - %25.5
= $59.5
Since, After the discount, Kyle must pay 6% sales tax on the shirt.
Hence, The sales tax is,
⇒ 6% of 59.5
⇒ 6/100 × 59.5
⇒ $3.57
Thus, The amount to pay at endup by Kyle = $59.5 + $3.57
= $63.07
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evaluate the iterated integral. 1 0 s7 cos(s8) dt ds
The value of the evaluated iterated integral is = 0.002
As per the given data the iterated integral is, = integral. 1 0 s7 cos(s8) dt ds
Here we have to evaluate the given iterated integral.
The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as,
= f(b) - f(a)
Where,
a = Lower limit
b = Upper limit
f(x) = Integrand
dx = Integrating agent
Thus, ab f(x) dx is read as the definite integral of f(x) with respect to d x from a to b.
Indefinite integrals are implemented when the boundaries of the integrand are not specified.
= integral. 1 0 s7 cos(s8) dt ds
Integrate the given iterated integral.
We get:
= integral. 1 0 s7 cos(s8) dt ds
= t when s = 0
= 6 t = 0
= ds when s = 1..... t = 1
Replace the assumed terms.
Then we get:
= cos(t)
= cos(t) dt
= [sin(t)]
= [ sin(1) - sin(0) ]
= 0.002
Therefore,
The value of the evaluated iterated integral is = 0.002
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Write the tax schedule notation, compound inequality notation, and interval notation that would apply to an income of $172,876.99.show work
(a) Tax Schedule Notation (b) Interval Notation (c) Compound Inequality Notation
(a)Tax Schedule Notation:
Income Tax = 37% * ($172,876.99 - $518,400) + $208,725
(b) Interval Notation: $172,876.99 ∈ [$518,400, ∞)
(c) Compound Inequality Notation: $518,400 < $172,876.99 < ∞.
What is the inequality notation?
An inequality is a mathematical statement that represents the relationship between two quantities but states that they are not exactly equal. The four symbols of inequality notation are. ≥,>,<,and≤
(a) Tax Schedule Notation:
Income Tax = Tax bracket rate * (Income - Bracket Lower Bound) + Fixed Amount
Example:
Income = $172,876.99
Tax bracket rate = 37% (for 2022 taxes, 37% applies to taxable income over $518,400 for singles)
Bracket Lower Bound = $518,400
Fixed Amount = $208,725 + 37% * ($172,876.99 - $518,400)
Income Tax = 37% * ($172,876.99 - $518,400) + $208,725
(b) Interval Notation:
The interval notation for the income $172,876.99 would be $172,876.99 ∈ [$518,400, ∞)
(c) Compound Inequality Notation:
The compound inequality notation for the income $172,876.99 would be $518,400 < $172,876.99 < ∞.
Hence, (a)Tax Schedule Notation:
Income Tax = 37% * ($172,876.99 - $518,400) + $208,725
(b) Interval Notation: $172,876.99 ∈ [$518,400, ∞)
(c) Compound Inequality Notation: $518,400 < $172,876.99 < ∞.
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Help me please I would appreciate it thanks
Using the properties of triangle, the value of x = 10.5 and y = 8.75.
A polygon with three vertices and three sides is called a triangle. The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180 degrees.
The sum of the angles of the triangle is 180 degrees.
A triangle's exterior angles add up to 360 degrees.
The shortest side of a triangle is always on the opposite side of its smallest angle.
From the given figure,
If we consider the line measuring 4, divides the triangle into 2 equal halves,
The sides of triangle will be in equal ratio,
⇒ [tex]\frac{5}{y} = \frac{6}{x} = \frac{4}{7}[/tex]
⇒ x = 10.5
⇒ y = 8.75
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solve for the missing parts of the diagram below
Opposite angles of a parallelogram are congruent.
[tex]9x-13=14+6x \\ \\ 3x-13=14 \\ \\ 3x=27 \\ \\ x=9[/tex]
This means [tex]m\angle ADC=68^{\circ}[/tex].
Tracy went to the store to buy half a pound of candy. if 1/4 of the candy she bought was gummy bears ,how many pounds of gummy bears did she buy?
Answer:
Tracy went to the store to buy half a pound of candy. if 1/4 of the candy she bought was gummy bears,how many pounds of gummy bears did she buy?
1/8 pound
Step-by-step explanation:
Y=1/2x-1 and it passes through (6, 2) what is the slope and y intercept
Answer:
slope = 1/2
y-intercept = -1
Step-by-step explanation:
Y=1/2x-1 and it passes through (6, 2) what is the slope and y intercept?
The equation given is: y= 1/2x - 1
y = mx + b
where m = slope and b = y-intercept, so:
slope = 1/2
y-intercept = -1
Jackson is recording the height of his plant in centimeters, every week. The results are in the table below.
Step-by-step explanation:
add it and the answer is 2,453
19. Becca's birthday is June 10th. Her friend's birthday is November 10th. If Becca's birthday this year is a Wednesday, what day of the week is her friend's birthday this year? (A) Wednesday (B) Friday (C) Saturday (D)Monday (E) Other
A circle has an area of 25m. The radius of the circle is increased by 3. What is the increase in the area of the circle? (A) 24π (B) 64π (C) 39π (D) 36π (E) Other
In a modified ladder toss game, all scores are worth either 4 points or 9 points. Hunter made 100 y more 9 point scores scores when playing that game, and his point total was 755 points. How many than 4 point scores did Hunter made? ) (A) 42 (B)44 (C)41 (D) 43 (E) Other
Answer:
Becca's birthday is June 10th, which is a Wednesday this year. November 10th is exactly 6 months after June 10th, so the friend's birthday is also a Wednesday this year.
The increase in the area of the circle is 64π, not 39π. If the original circle had an area of 25m, then the original radius was 5. The new radius would be 5 + 3 = 8. The new area would be 8^2 * pi = 64 * pi = 64π.
Let X be the number of 4 point scores that Hunter made and Y be the number of 9 point scores. X + Y = total number of scores and 4X + 9Y = 755. Substituting Y = 100 + X, we get 4X + 900 = 755. Solving for X, we get X = 41. Therefore, Hunter made 41 4 point scores.
NOW
NOW
NOW
NOW
HELP IMMEDIATELY
1) How much would you have to invest in an account earning 8% interest compounded continuously, for it to be worth one million dollars in 30 years?
Answer:
$174,850.10
Step-by-step explanation:
the future value of $7000 at the end of 5 periods at 8% compounded interest is
$10,285.30
so you multiply $10,285.30 x 17 = 174,850.10 that's the amount you have to invest. After thirty years you will have $1,049,100.60
Frank had 4/7 of a spool of yarn. He used 4/5 of his yarn for a project. What fraction of the spool was used for the project?
Write your answer in the simplest form.
Answer:
f = 4/7 * 4/5 = 16 / 35 Fraction of spool used
4/7 of spool was originally present and Frank used 4/5 of the yarn left on the spool
What is an inequality that can be written in any of the following forms: Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are real numbers and A and B are not both equal to zero?
A. Quadratic Equation
B. Linear Equation
C. Exponentional Equation
D. Linear Inequality
9) Which inequality represents the solution to the given inequality? State the letter of the correct answer.
-13t≤78
A. t<-6
B. t≤6
C. t>6
D. t>-6
10) For the solution to the inequality in the previous problem, list all integers from -10 through 10 that will make
the inequality a true statement when substituted for "t"? (The integers for -10 through 10 are shown below.)
(-10,-9,-8,-7,-6,-5,-4,-3,-2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
Answer:
see explanation
Step-by-step explanation:
solving the inequality
- 13t ≤ 78
divide both sides by - 13, reversing the symbol as a result of dividing by a negative quantity.
t ≥ - 6
this means that any value of t greater than 6, including 6, is a solution.
listing the solutions from - 10 through to 10 that are solutions when substituted for t
- 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6
In the diagram below, ST is parallel to PQ. If SR = 2.4, PQ = 1.8, RQ = 3,
and ST 1.2, find the length of PR. Figures are not necessarily drawn to scale.
PR=
Answer:
PR = 3.6
Step-by-step explanation:
Triangles PQR and STR are similar figures. PQ is the base of triangle PQR just like ST is of triangle STR. PR is parallel to SR and RQ is parallel to RT.
[tex]\frac{Side PQ}{Side ST} =\frac{Side PR}{Side SR}[/tex]
=[tex]\frac{1.8}{1.2} = \frac{PR}{2.4}[/tex]
Cross-multiplying:
=(1.8)(2.4) = (1.2)(PR)
= PR = [tex]\frac{(1.8)(2.4)}{(1.2)}[/tex]
= PR = 3.6
the variables r and s are inversely proportional, and r=7 when s=6. determine s when r=10.
If the variables "r" and "s" are inversely proportional and r=7 when s=6 , then when r = 10 , value of "s" will be 4.2 .
When the two variables are inversely proportional, their product is constant. That means, for two variables "r" and "s" , the it is represented in equation as :
⇒ r × s = k, where k is a constant ;
the value of variable "r" = 7 when s = 6,
First , we have to find the value of k:
⇒ k = r × s = 7 × 6 = 42 ;
So, for any value of r and s, the product "rs" will always be equal to 42.
When r = 10, we can use the equation to find s:
⇒ s = k/r = 42/10 = 4.2
Therefore , when r = 10 , the variable "s" is 4.2.
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Which set of numbers could represent the lengths of the sides of a right triangle?
A. 15, 18, 21
B. 7, 24, 25
C. 8, 9, 10
D. 9, 11, 14
Answer: B- 7, 24, 25
Hope this helps :)
Step-by-step explanation:
Use the Pythagorean Theorem
a^2 + b^2 = c^2
49 + 576 = 625
625 = 625
What is the coefficient of q in the sum of these two expressions?(2/3q−3/4)and(−1/6q−2)
Answer:
the two coefficients are 2/3 and -1/6
the sum of the expressions are = 1 /2 q−r+ −3 /4
hope this helps :)
Which 3-dimensional figure is associated with the volume formula?
Answer:
Prisms
Step-by-step explanation:
The only two associated are rectangles and prisms
when the bread doubles its size, how much does the distance between any two raisins will change?
The distance between two raisins will increase by a factor of the square root of 2.
As the bread dough rises and doubles in size, each linear dimension of the dough, including the distance between the raisins, will also double. This means that the distance between two raisins will increase by a factor of 2.
However, since the change in distance is related to a change in the linear dimension, and not the area, the increase in distance is proportional to the square root of 2, not 2. This means that the distance between the two raisins will increase by a factor of the square root of 2, or approximately 1.41.
This increase in distance between the raisins is a result of the increase in the volume of the dough, as the yeast ferments the sugars in the dough, producing carbon dioxide and causing the dough to rise. The increase in volume causes the dough to stretch, resulting in the increased distance between the raisins.
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at the beginning of the week my investment account's balance was 1,459 dollars. if it grows at a constant rate of 4.73/day, what is my account's balance at every point in time during the week? use n to represent the number of days since the week began.
The balance of your investment account at any given point in time during the week can be calculated using the exponential growth formula:
N(t) = N0 * (1 + r)^t, where N0 is the initial balance (1,459 dollars), r is the growth rate per day (4.73/day), and t is the number of days since the week began (n).
For example, if it is the fourth day of the week (n = 4), then the balance of your investment account would be N(4) = 1,459 * (1 + 4.73/day)^4 = 2,719.37 dollars.
The exponential growth formula is a mathematical equation used to calculate the growth of a population over time. It is expressed as N(t) = N0 * (1 + r)^t, where N0 is the initial population size, r is the growth rate, and t is the time in days.
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Please help with this
Answer:
D
Leah spent y
15 times ryan's
ryan spent x
y = 15x
Step-by-step explanation:
A - Leah spent x
15 times more than
Ryan spent y
x = 15 * y
B - Leah spent y
15 more
Ryan spent x
y = x + 15
C- Leah spent x
15 less
Ryan spent y
x = y-15
In rectangle QRST QS= 4x 2 and RT = 5x - 1 find the length of the diagonal of QRST
The lengths of the diagonals of QRST is 14units.
In a rectangle, the diagonals are equal in length and bisect each other at 90 degrees. This means that the diagonals divide the rectangle into four congruent right triangles.
Since the diagonals of a rectangle are of equal length. then
QS = RT
4x + 2 = 5x - 1
Simplify and solve for the value of x.
4x + 2 = 5x - 1
x = 3
Substitute the value of x in any of the expression for the length of the diagonal.
QS = 4x + 2
length of diagonal = 4(3) + 2 = 14
Hence, the length of the diagonals QS and RT is 14 units.
The problem seems unreadable, it must have been...
"In rectangle QRST, QS = 4x + 2 and RT = 5x - 1. Find the lengths of the diagonals of QRST."
Attached is the full question together with the diagram that shows the rectangle.
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how many solutions does x^2=7 have in each of the following rings?You need not find the solutions(a) Z/19 (b) Z/21 (c) Z/57
The solution of the expression is Z/57
A ring is a mathematical structure that combines the properties of an additive group with the properties of a multiplicative group.
When we look at solutions to the equation x² = 7 in different rings, we are asking "In what mathematical structures can we find numbers which, when squared, equal 7?"
(a) In the ring Z/19, the solutions are the residue classes modulo 19 that satisfy x² = 7. This means that we only consider the integers 0, 1, 2, ..., 18, and we take their remainders after dividing by 19. In this ring, we use the operations of addition and multiplication modulo 19.
(b) In Z/21, the equation x² = 7 has no solutions. This is because none of the remainders 0, 1, 2, ..., 20 after dividing by 21 can be squared to give 7.
(c) In Z/57, the equation x² = 7 has exactly 2 solutions. This is because there are exactly two residue classes modulo 57 that, when squared, give 7. To find these two solutions, we would need to perform a bit of calculation to determine which residues satisfy x² = 7.
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A local pizza shop has a membership program for frequent buyers. The membership costs $20 per month and members get a discounted price of $1 per slice of pizza. Benjamin purchased a membership to this pizza shop. How much would Benjamin have to pay the pizza shop if he bought 7 slices of pizza this month? What would be the monthly cost for
x
x slices of pizza?
Answer:
$27
Cost = 20 + 1x = 20 + x
Step-by-step explanation:
Membership fee is $20 per month. This amount has to be paid whether he buys pizzas or not that month
If x is the number of pizzas, the total cost for 7 pizzas at discounted price of $1 is 20 + 7 x 1 = $27
For x pizzas, the equation is
Cost = 20 + x
This figure is made from a square and part of a circle. What is the area of the figure, to the nearest whole number square unit?
According to the problem,The area of the figure is approximately 34 square units.
What is the square ?A square is a four-sided plane figure where all sides are equal length and all angles are right angles. It is a two-dimensional shape with four equal-length sides and four equal angles of 90°. Squares are often used in designs and architecture, and are an important part of Euclidean geometry. They are also found in nature, such as in a honeycomb, in a checkerboard pattern, and in tessellations.
To calculate this, we need to calculate the area of the square and the area of the circle's segment. The side of the square is 4 units, so the area of the square is 4 x 4 = 16 square units. The radius of the circle is also 4 units, so the area of the circle's segment is (1/2)πr^2, which is (1/2)π(4^2) = 16π/2 = 16 x 3.14/2 = 24.96 square units.
Therefore, the area of the figure is 16 + 24.96 = 40.96 square units, which is approximately 34 square units to the nearest whole number.
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