The sum of the two consecutive numbers is 31.
Let the two consecutive number are n and n+1.
Given the difference between square of two consecutive Numbers is 31.
(n + 1)² - n² = 31n² + 2n + 1 – n² = 312n + 1 = 312n = 30n = 15Then, two consecutive number = n, n+1 = 15, 16
Therefore
( A ): the sum of two consecutive number = 15 + 16 = 31
( B ): Their difference = 16 – 15 = 1
( C ): Subtract their sum by 8 = 31 – 8 = 23
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Admission to a carnival costs $5. Tickets for games at the carnival costs $2 each.
defines a function in this situation. What does the function
1. The equation C = 5 + 2t
represent?
C=5+2t represents the total cost of attending the carnival: you pay an admission fee of $5 and then $2 for a ticket to play games.
C=5+2 T stands for the carnival's overall ticket price: $5 is the entrance cost, and $2 is the game ticket price.
To determine the inverse function of C(t), solve the following equation for "t" (the function and argument are switched in the inverse function):
t =(C - 5)/2
The number of games someone played during the carnival is represented by the inverse function.
[tex]t=\frac{C-2}{5}[/tex]is not the inverse function of C, according to. (t). In 2, the inverse function was discovered.
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11.5% of an amount is 782.
What is the original amount?
Answer:
15640
let me know If I got it!
The prom committee is decorating the venue for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5 feet, EF=39 feet, and m∠GHF=128° , find GE.
GE = 89 feet when using the definition of a rectangle's diagonals.
Explain the term rectangle's diagonals?A rectangle is split into two equal right triangles by a diagonal. A rectangle's diagonals are all the same length.The sides of a rectangle.Two of the diagonals in a rectangle are congruent, meaning they are equivalent to one another.A rectangle's diagonals cut each other down into equal segments.The rectangle room's diagonals are as follows:
DF and GE
So,
DF = GE
DH = 1/2(DF)
Put
44.5 = 1/2(DF)
DF = 2(44.5)
DF = 89
Thus,
DF = GE = 89
GE = 89 ft.
Therefore, GE = 89 feet when using the definition of a rectangle's diagonals.
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What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer?
Answer:
the interest rate required in order for Josiah to end up with $5,400, assuming the interest is compounded daily, is 10.3%
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^nt
Where:
A = the amount of money in the account after the interest has been added
P = the initial investment (principal) of $4,800
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is left in the account
We know that A = $5,400 and t = 6 years, so we can substitute these values into the formula:
5400 = 4800(1 + r/n)^(6n)
To find the interest rate, we need to solve for r.
we know that the interest is compounded daily, so we will use n = 365
5400 = 4800(1 + r/365)^(6*365)
To find the interest rate, we need to solve for r, we can use a calculator to find the value of r.
r ≈ 0.103 or 10.3% to the nearest tenth of a percent
So, the interest rate required in order for Josiah to end up with $5,400, assuming the interest is compounded daily, is 10.3%
Answer:
Step-by-step explanation:So, the interest rate required in order for Josiah to end up with $5,400, assuming the interest is compounded daily, is 10.3%
A NET FOR A TRIANGULAR PRISM IS SHOWN BELOW WHAT IS THE SURFACE AREA OF THE PRISM THE ANSWER ARE 35.1 81 88.8 90
The surface area of the triangular prism is 224 square units.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given;
Surface area = ( S₁ + S₂ + S₃) × Length
Side1 S₁ = 6
Side2 S₂= 8
Side3 S₃ = 2
Length = 14
Surface area = ( 6+8+2)14
Surface area = 16(14)
Surface area = 224
Therefore, the surface area of the triangular prism will be 224 square units;
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Which is the graph of the piecewise function f(x)?
f(x) = StartLayout Enlarged left-brace 1st row 1st column negative x + 1, 2nd column x less-than-or-equal-to 0 2nd row 1st column x + 1, 2nd column x greater-than 0 EndLayout
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (0, 1). The second line goes from (0, 1) up through (4, 5).
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (1, 0). The second line goes from (1, 0) up through (4, 3).
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (negative 5, negative 4) up to (0, 1). The second line goes from (0, 1) down through (4, negative 3).
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (negative 4, negative 5) up to (1, 0). The second line goes from (1, 0) down through (4, negative 3).
The graph of the piece-wise function for this problem is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The two definitions for the function in this problem are given as follows:
Left of x = 0: y = - x + 1 -> decreasing line.Right of x = 0: y = x + 1 -> increasing line.Both of the lines will meet at the y-intercept of y = 1, as shown in the image presented at the end of the answer.
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Answer: The first one
Step-by-step explanation:
On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (0, 1). The second line goes from (0, 1) up through (4, 5).
Basically it should look like a wide V staring at point 1 on the y axis facing upwards.
-3x +4y = -5
-6x +8y = -10
Answer:
1. The equation you've provided is a linear equation in the form of y = mx + b, where m is the slope, x is the variable and b is the y-intercept.
The slope (m) of the line represented by this equation is -3/4, the y-intercept is -5/4 and x is a variable.
It is a representation of a straight line in the coordinate plane, where x and y are the coordinates. The line passes through the point (-5/4, 0) and the slope of the line is -3/4.
2.The equation you've provided is a linear equation in the form of y = mx + b, where m is the slope, x is the variable and b is the y-intercept.
The slope (m) of the line represented by this equation is -3/4, the y-intercept is -5/4 and x is a variable.
It is a representation of a straight line in the coordinate plane, where x and y are the coordinates. The line passes through the point (-5/4, 0) and the slope of the line is -3/4.
Please note that in the equation you provided -6x +8y = -10 the slope is -3/4 and y-intercept is -5/4.
What does this simplify down to? PLEASE show me how you got your answer!
Answer:
2/3
Step-by-step explanation:
the answer is explain up in the link or photo show up
an organization will give a prize to a local artist. the artist will be randomly chosen from among 7 painters, 4 sculptors, and photographers. what is the probability that the artist chosen will be a painter or a 5 photographer? write your answer as a fraction.
The probability that the artist chosen will be a painter or a photographer is 3/4
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
To solve this exercise the formula and the procedure that we have to use for probability is:
probability= (achieving success / possible outcomes)
Achieving success = 7 painters + 5 photographer = 12
Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16
Applying the formula to calculate the probability we get:
probability= (achieving success / possible outcomes)
probability= 12/16
Simplifying:
probability= 3/4
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Find an expression to represent the volume of the rectangular prism below
Answer: [tex]volume =[/tex] [tex](\frac{x2+11x+30}{x2+7x+6})[/tex] X [tex](\frac{x^{2}-1}{6x^{3} +30x^{2} })[/tex] X [tex]\frac{3x}{8}[/tex]
Step-by-step explanation:
Volume= b x h x l
= [tex](\frac{x2+11x+30}{x2+7x+6})[/tex] X [tex](\frac{x^{2}-1}{6x^{3} +30x^{2} })[/tex] X [tex]\frac{3x}{8}[/tex]
Write 7.67 times 10 -² in standard notation.
7.67 times 10^-² in standard notation can be written as 0.0767.
To convert scientific notation to standard notation, you can simply move the decimal point to the left or right as many times as indicated by the exponent of the power of 10. In this case, the exponent is -2, so you move the decimal point 2 places to the left. The result is 0.0767.
whats the answer!! please asap
Answer:1/90
Step-by-step explanation:
a recent medical study reported that people who own pets have lower blood pressure than people who do not own pets. this led some doctors to believe that pet ownership has positive health benefits. however, more careful analysis of the data showed that the pet owners in the study exercised more and smoked less than those who did not own pets. this is an example of
confounding variables; the medical study did not control for other factors that could have caused the lower blood pressure in pet owners.
A confounding variable is an extraneous factor that can influence the results of a study. In this case, the medical study reported that people who owned pets had lower blood pressure than those who did not own pets. This led some doctors to believe that pet ownership had positive health benefits. However, further analysis of the data revealed that the pet owners in the study also exercised more and smoked less than those who did not own pets. This means that the pet ownership was not necessarily responsible for the lower blood pressure, but rather these other factors could have contributed to the results. Thus, the study lacked control for these confounding variables, which could have invalidated the results.
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PLEASE HELP! THIS IS DUE TODAY!!
How do you find the base of a trapezoid? The trapezoid is labeled as MNOP, the median being QR. PO is 13 (top base), and QR is 18. How do I find MN?
To find the base of a trapezoid, you need to know the length of at least one of the bases and the height (or the length of the median). Since you know that PO is 13 (top base) and QR is 18 (median), you can use the following formula to find the length of the bottom base (MN):
Height x ((base1 + base2) / 2) = Area
Where the height is the length of the median (QR) and base1 and base2 are the lengths of the two bases (PO and MN).
So, in this case, you would have:
QR x ((PO + MN) / 2) = Area
18 x ((13 + MN) / 2) = Area
Solving for MN:
MN = (2 * Area) / QR - PO
So you can fill the area of trapezoid and substitute the values in the above formula.
===============================================
Explanation:
x = length of MN
A trapezoid has exactly one pair of parallel sides. The median is parallel to those mentioned sides. Think of it like the median to a highway.
A useful property is the median is the average of the parallel sides. We add up the outer sides, then divide by 2, and it gets us the median.
So,
QR = (MN + PO)/2
18 = (x + 13)/2
18*2 = x+13
36 = x+13
x = 36-13
x = 23
Side MN is 23 units long.
The diagram is below.
Scientists want to investigate the effects caffeine on short term memory by randomly assigning 200 volunteers to intake 86mg of caffeine. remaining 200 volunteers to intake 86mg of a placebo. In context, what was the control used in this study?
A placebo is a medication or procedure that is given to a patient for psychological rather than physiological reasons.
The most typical sources of caffeine in nature are the cocoa, tea, and coffee plants. It functions by activating the central nervous system and brain, keeping you alert and delaying the development of fatigue.
Coffee has a maximum of 86 mg of caffeine per serving.
The highest daily dose of caffeine recommended by health authorities, excluding those who are pregnant or breastfeeding, is 400 mg for healthy individuals. Additionally, it is advised to consume no more than 200 mg of caffeine daily from all sources while pregnant or nursing.
Unwanted adverse effects might arise from placebos. Negative placebo effects, often referred to as nocebo effects, have been documented as nausea, drowsiness, and allergic reactions, including skin rashes.
Considering everything, it's clear that placebos aren't used in studies all that frequently. Therefore, the 86mg of placebo is employed in a regulated manner in the study.
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choose the correct answer below. a. false. the method for selecting a cluster sample is to order a population in some way and then select members of the population at regular intervals. b. false. the method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals. c. true.
The researcher could also use a random number generator to select the members of the sample, instead of selecting them at regular intervals.
The formula for calculating a systematic sample is p = (n/N) x 100, where p is the percentage of the population to be sampled, n is the sample size, and N is the total population size. For example, if a researcher wanted to sample 100 people from a population of 500, the formula would be p = (100/500) x 100 = 20%. This means that the researcher would select every fifth person in the population to be included in the sample. The researcher could also use a random number generator to select the members of the sample, instead of selecting them at regular intervals.
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find the interior angle of each regular polygon. Round your answer to the nearest tenth.
The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
What is interior angle of polygon and how to find?Interior Angle of a polygon = 180° – Exterior angle of a polygon. Method 3: If we know the sum of all the interior angles of a regular polygon, we can obtain the interior angle by dividing the sum by the number of sides. Interior Angle = Sum of the interior angles of a polygon / n.
To solve the given problem, it is necessary to know about the polygon. A polygon is a closed curve that consist a set of line segments connected together, such that there is a no intersection between the segments.
A regular polygon refers to a multi-sided convex figure where all the sides are equal in length and all the angles have equal degree measures.
For example: -
The triangle is a polygon that has 3 interior angles.The square is a polygon that has 4 interior angles.The pentagon is a polygon that has 5 interior angles.The formula for the interior angle of a regular polygon is given by,
= (n-2)*180/n
Here, n is the number of sides.
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how do you write 2.2616161… using bar notation
Answer:2.261 repeating sign on top
Step-by-step explanation:
2.261 repeating sign on top
Answer: 2.261 with the bar notation line over 61. Since I can't actually type it.
Step-by-step explanation: I hope this helps!
need help with a question, thanks
Answer:
Step-by-step explanation:
a football tadium can eat 62,005 people. if there were 58,319 people in the attendance at the game, how many eat were empty?
3,686 seats were empty. This number indicates that the stadium was not full to capacity.
1. Subtract the number of people in from the number of people the stadium can hold:
62,005 - 58,319 = 3,686
2. The answer is 3,686 seats were empty.
The football stadium was able to accommodate up to 62,005 people, but only 58,319 were in attendance at the game. This means that 3,686 seats were left empty. To calculate this, subtract the number of people in attendance from the number of people the stadium can hold. 62,005 - 58,319 = 3,686. Therefore, 3,686 seats were empty. This number indicates that the stadium was not full to capacity.
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40 4. MP.3 Explain James and Amy play 3 more games. They have played the same number of games as last week. Fill in the blanks to make the equation true. Use +, -, or=. 12 72 Explain how you chose the symbols. 3 How do you know the equation is true?
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I need help! ……………….
Answer:
x = 140 degrees
Step-by-step explanation:
this polygon has 6 sides
to find the number of degrees of the six interior angles you can use this formula:
(n-2)*180 where 'n' equals the number of sides
(6-2)*180 = 4(180) = 720 degrees
starting with the 'x' angle and going clockwise, we have the following:
x + 90 + 104 + 123 + 155 + 108 = 720
x + 580 = 720
x = 720 - 580
x = 140
What is the value of x in this triangle?
Answer:
83 degrees
Step-by-step explanation:
Angles inside a triangle is what we called interior angles, which its sum should be equal to 180. Thus, the equation would be like this:
44 + 53 + x = 180
We simply re-arrange the equation to get the value of x.
x = 180 - (44 + 53)
x = 180 - 97
x = 83
olivia runs 52 meters diagonally across a rectangular field that has a length of 48 meters. what is the width of field?
The width of a rectangular field is 20 meters
Let l represents the length of a rectangular field, w represents the width of a rectangular field and d represents the diagonal of a rectangular field
We know that all the four angles of rectangle are right angle.
A diagonal of rectangle divides a rectangle into two equal right triangles.
Consider a right triangle with hypotenuse = diagonal (d) and the sides of the right triangle are nothing but the length and width of recangle.
Using Pythagoras theorem,
d² = l² + w²
52² = 48² + w²
w² = 52² - 48²
w² = 400
w = ±20
But the width can not be -20
So, w = 20
Thus , the width is 20 meters
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five cards were randomly drawn from a standard deck of cards. a) (two pairs) what is the probability that two cards are of the same rank, two are of an
If three cards are drawn from a standard deck of 52 cards , then the probability that all the cards are of same rank is 1/425 .
The number of cards in the standard deck is = 52 cards ;
thee cards are drawn from the deck ,
we have to find the probability that they all are of the same rank , that means ( e.g. all 3 are queens ) ;
we have to draw 3 cards from 4 suits. which means 1 card is taken from the 13 numbers.
the number of favorable outcomes (all from same rank) = ⁴C₃×13
= 52 ;
total number of outcomes is = ⁵²C₃ = 22100 ;
the required probability is = 52/22100 ;
= 1/425 .
Therefore , the probability that all 3 cards are of same rank is 1/425 .
The given question is incomplete , the complete question is
The three cards were randomly drawn from a standard deck of 52 cards.
What is the probability they are all the same rank ?
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The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project. After 3 months, it reaches 42% of its goal. How much was raised during the first 3 months?
$174
$942
$1,042
$1,680
PLSSS HELPPP
The amount of money raised during the first 3 months will be $1,680. Then the correct option is D.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project. After 3 months, it reaches 42% of its goal.
Then the amount of money raised is given as,
⇒ 42% of $4,000
⇒ 0.42 x $4,000
⇒ $1,680
The amount of money raised will be $1,680. Then the correct option is D.
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at Freddy's, three steak burgers zzz and two orders of fries cost $18. Two steak burgers and three orders of fries cost $15.75. What is the cost for one steak burger? What is the cost of one order of feries
The cost of one steak burger is $4.5 and the cost of one order of fries is $2.25.
How to find a cost using equation?To find a cost using an equation, you need to first identify the variables involved in the equation.
Variables are values that can change, such as the price of an item or the quantity of an item. Next, you must determine the value of each variable.
Once you have all the values, plug them into the equation and solve for the cost. For example, if you have an equation where x is the cost, y is the quantity, and z is the price per item, you would plug in the values of y and z and solve for x.
The answer you get would be the cost of the item. Additionally, you can use the equation to find the cost of multiple items by changing the value of the variable y to represent the amount of items you need.
After plugging in the new values into the equation, you can solve for the cost of all the items.
Let x be the fries and y be the steak burgers.
From the following information, the equation are as follows:
2x + 3y = 18 ---------equation 1
3x + 2y = 15.75 -------equation 2
To find cost of one steak burger and cost of one order of fries,
Multiply by 3 in equation 1 and 2 in equation 2,
6x + 9y = 54 -------3
6x + 4y = 31.5 -----4
Subtracting the equation 3 and 4, we get
5y = 22.5
y = 22.5/5
y = 4.5
Substitute y=4.5 in eq 1,
2x + 3(4.5) = 18
2x = 4.5
x = 2.25
∴ The cost of one steak burger is $4.5
∴The cost of one order of fries is $2.25.
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at a dance, there are 20 girls and 20 boys. how many ways are there to form 20 pairs consisting of 1 boy and 1 girl?
There are 400 different ways possible to form 20 pairs consisting of 1 boy and 1 girl
What is a combination?In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.
To solve this problem the formula and the combination procedure we must use is:
C(n/r) = n! / [(n-r)! *r!]
Where:
C(n/r) = combination
n = total number of objects
r = number of selected objects
! = factorial of the number
Information about the problem:
n(girl) = 20n(girl) = 1n(boy) = 20n(boy) =1Applying the combination formula we have:
C(n/r) = n! / [(n-r)! *r!]
C(20/1) = 20! / [(20-1)! *1!]
C(20/1) = 20! / [(19)! *1!]
C(20/1) = 20*19! / [(19)! *1!]
C(20/1) = 20/1!
C(20/1) = 20
Cgirl(20/1) * Cboy(20/1) = 20*20
Cgirl(20/1) * Cboy(20/1) = 400
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Martina made 3 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 3 necklaces was $11.10 . If the beads cost $1.80 for each necklace, how much did each pendant cost?
Answer:
1.9
Step-by-step explanation:
11.1 /3 =3.7 for beads + pendants per necklace
pendant =3.7-1.8 =1.9
Companies A and B provide housekeeping services. The charges are shown in the table. After how many hours will Company A be cheaper than Company B?
After the first 3 hours, Company A will be cheaper than Company B, based on a system of equations.
What is a system of equations?A system of equations or simultaneous equations refers to two or more equations whose solutions are computed concurrently or simultaneously.
Company A Company B
First-hour charge $28 $20
Subsequent half hour $10 $12
Subsequent one-hour $20 $24 ($12 x 2)
Let one hour of housekeeping service after the first-hour charge = x
Company A's total charge for x hours = 28 + 20x ... Equation 1
Company B's total charge for x hours = 20 + 24x ... Equation 2
For the costs to become equal:
28 + 20x = 20 + 24x
-4x = -8
x = 2
For the first 3 hours (2 + 1) of housekeeping service, the costs for both companies are equal.
Thus, after the first 3 hours of service, Company A's charges become cheaper than Company B's.
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