Answer:
Let's mark Pat's age is x. Then Mattie's age is 2x and Jon's age is 4x.
So (x + 4) + (2x + 4) + (4x + 4) = 61.
7x + 12 = 61 => 7x = 49 => x = 7.
So the answer is
Pat = 7
Mattie = 14
Jon = 28
The ages of Pat, Mattie, and Jon are as follows: 7 years, 14 years & 28 years.
If we take Pat's age as = 'x' years,
so, Mattie's age will be = '2x' years.
and then, Jon would be = 2(2x)
= '4x' years.
Now, the sum of their ages after 4 years =
=> (x+4) + (2x+4) + (4x+4) = 61
=> 7x+12 = 61
=> 7x= 61-12
=> 7x= 49
=> x= 49/7
=> x = 7
Therefore, Pat's age is = 7 years.
Mattie's age is = 14 years (2×7).
Jon's age is = 28 years (4×7).
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Write an explicit formula for a_na
n
, the n^{\text{th}}n
th
term of the sequence 27, 9, 3, ...27,9,3,....
The equation which correctly represents the explicit formula for the nth term of the given sequence is; a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.
Which equation represents the nth term of the given sequence?As evident in the task content; the given sequence is a geometric sequence and the common ratio of the sequence can be determined as;
r = 3 / 9 = 9 / 27 = 1 / 3.
On this note, since the common ratio of the consecutive terms of the sequence is; 1/3 it follows that the required explicit formula which represents the nth term , a (n) is;
a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.
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How many positive two-digit integers are multiples of 5 and of 7?
The number of positive two-digit integers that are multiples of 5 and 7 are 2
What ae multiples?In mathematics, multiples are the results of multiplying an integer by a given number.
The multiples of 5 and 7 within 10 to 100 are
35 and 70
multiples of 5: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
multiples of 7: 7 14 21 28 35 42 49 56 63 70 77 84 91 98
The common numbers are 2 which are 35 and 70
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There are two chords AB and CD in a circle. |AB| = 10 cm, |CD| 10 cm, |CD| = 8 cm and the radius of the circle is 12 cm. What is the distance of each chord from the centre of the circle?
The distance of each chord from the centre of the circle are √119 and √128 respectively .
Given,
Radius of a circle = 12 cm
AB = 10 cm
CD = 8 cm
Now, we get
BG = 10/2 = 5 cm
HD = 8/2 = 4 cm
(A perpendicular coming from the centre, which is not a diameter, bisects the chord.)
Now,
BE = ED = EF = 12 cm (All radii of a circle are equal.)
Now, by Pythagoras Theorem, we get
H² = P² + B²
For GE —
(BE)² = (GE)² + (BG)²
or, (12)² = GE² + (5)²
or, 144 = GE² + 25
or, GE² = 144 — 25
or, GE² = 119
or GE = ±√119
or GE = √119 (Since, length cannot be negative.)
For HE —
(DE)² = (HE)² + (HD)²
or, (12)² = HE² + (4)²
or, 144 = HE² + 16
or, HE² = 144 — 16
or, HE² = 128
or, HE = ± √128
or, HE = √128 or 8√2(Since, length cannot be negative.)
Hence , the distance of each chord from the centre of the circle are √119 and √128 respectively .
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Write an expression to represent the area of the shaded region in simplest from
We know that the area of a square/rectangle is the multiplication of its length by its width. We also know that this specific area does not include the blank region, therefore we need to subtract it from the area of the shaded region!
We can come up with two expressions:
Shaded Area:
[tex](5x + 2)(3x - 1)\\= 15x^2-5x+6x-2\\=15x^2+x-2[/tex]
Blank area:
[tex](x)(x+7)\\x^2+7x[/tex]
Now all we have to do is subtract the blank area's expression from the shaded area's and simplify since the question asks for the simplest form.
[tex](15x^2+x-2)-(x^2+7x)\\15x^2-x^2+x-7x-2\\14x^2-6x-2[/tex]
Therefore, your final answer should be:
14x^2 - 6x - 2
In ΔNOP,
m
∠
N
=
(
9
x
+
8
)
∘
m∠N=(9x+8)
∘
,
m
∠
O
=
(
4
x
+
13
)
∘
m∠O=(4x+13)
∘
, and
m
∠
P
=
(
2
x
−
6
)
∘
m∠P=(2x−6)
∘
. Find
m
∠
N
.
m∠N
Answer: 15
Step-by-step explanation: In ΔNOP,
m
∠
N
=
(
9
x
+
8
)
∘
m∠N=(9x+8)
∘
,
m
∠
O
=
(
4
x
+
13
)
∘
m∠O=(4x+13)
∘
, and
m
∠
P
=
(
2
x
−
6
)
∘
m∠P=(2x−6)
∘
. Find
m
∠
N
.
m∠N
If 7 is an element in the domain of f(x)= 6x-18/2, what is the corresponding element in the range?
The corresponding element in the range when 7 is an element in the domain is f(7)=33
Step-by-step explanation:
Given that the 7 is an element in the domain of f(x)
The function f is defined by f(x)=6x-18/2
To find the corresponding element in the range:
That is put x=7 in the given function f(x)
Therefore f(x) becomes
f(7) = 6(7)-18/2
=42-18/2
=42-9
=33
Therefore corresponding element in the range when 7 is an element in the domain is f(7)=33
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1
5.
grilato 6.
7.
PS).
se
8.
9.
10.
11.
-2619 12.
t-
13.
to
7-
14.
otal deposit for Problems 5 through 19.
Currency
Tens Fives Ones Half Dollars Quarters Dimes Nickels Pennies Checks Total
$96.23 $
6.51
63 874.56
85
123.65
347.98
134.97
0
43.44
5
168.14
31
777.50
154 123.19
12 11
32
9
40
54
75
32
8
7
11
13
10
12
1
16
67
3
133 19
8
15
23
74
0
9
6
7
4
27
11
9
40
15
13
7
0
3
13
34
or
Coins
18
32
56
13
9
5
7
12
11
62
21
86
11
6
8
17
3
319
45
70
27
13
2
13
7
99
0
37
15. Jess Norton stopped at an ATM location to deposit 2 one hundred-dollar
bills and checks for $474.85 and $321.15. He received $50.00 in cash.
16. Olive Baker, Spirit club treasurer, deposits the club's receipts. She has 4
checks for $10.00 each, 12 for $7.50, and cash consisting of six 20-dollar
bills, five 10-dollar bills, and 18 one-dollar bills.
17. Cyndi Winer deposits three checks for $425.22, $883.99, and $57.05. She
also deposits cash of 45 one-dollar bills, 15 five-dollar bills, and 12 ten-
dollar bills. The change deposited includes 28 quarters, 16 dimes, 19
nickels, and 65 pennies. She would like to receive $60.00 in cash.
18. Elias Rubio deposits three checks for $598.20, $2,274.26, and $3,248.79.
His cash consists of 75 one-dollar bills, 78 five-dollar bills, 33 ten-dollar
bills, 80 quarters, 32 dimes, 95 nickels, and 5 pennies. He would like to
receive $40.00 in cash.
The total cost of Jess Norton is $995.85 and the total cost of Olive Baker is $678 .
What is total cost ?
The total cost formula is used to total up the variable and constant expenses associated with providing commodities. Total cost = (Average Fixed Cost x Average Variable Cost) x Units Produced is the formula.
In economics, total cost is the total of all expenses a company incurs to produce a particular level of output.
The average cost, or the typical sum of money required to create a unit, can be determined using the cost function. The average cost function is A(x)=C(x)x, where x > 0 and C is the constant. Calculating the average cost per unit requires dividing the total cost by the quantity of units produced.
For Jees Norton,2 one hundred dollar bills = 2 x $100
= $200
Total deposits = 2 one hundred dollar bills + Checks
= $200 + $474.85 + $321
= $995.85
For Olive Baker,
Checks amount = $100 x 4
= $400
12 for $7.5
= 12 x $7.5
= $90
Six 20-dollar bills = 6 x $20
= $120
Five 10-dollar bills = 5 x $10
= $50
Eighteen 1-dollar bills = 18 x $1
= $18
Total deposits = $400 + $90 + $120 + $50 + $18
= $678
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answer fast need in 10 min
10 equally sized slices of the spinner's 250 results. 25 times were made by Diane's dial. 12 spins are for 208.33333333333334 .
What is the probability of spinner?12 spins are for 208.33333333333334, 5 spins are worth 500, and 8 spins are worth 312.5. There are eight possibilities each time you spin the spinner (1-8). One of these eight options is for you to land on the number 8. In this case, the probability is 18.
If you spin three times and fall on red (or any other colour), the likelihood is 3/30. The likelihood that the spinner will land on an even number is 5/10. The ratio of the number of "1s" to all the other numbers on the spinner determines this probability. The spinner has a total of 8 numbers on it. The spinner has three ones on it.
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what is the common difference for this arithmetic sequence? -6, -2, 2, 6, 10, …
Answer:
The common difference is 4.
Step-by-step explanation:
A restaurant manager believes that a majority of customers who dine at his restaurant would rate the food as excellent. To investigate this belief, he sends an email survey to a random sample of 50 customers from the large list of customers who have signed up for his frequent diner club. To encourage the customers to complete the survey, he offers a $10 gift card upon completion of the survey. He receives 22 responses, of which 20 rated the food as excellent. He would like to know if these data provide convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent. Are the conditions for inference met
The conditions for inference are: The customers who are surveyed are chosen independently at random, so we can assume that the survey results are independent.
What do you mean by normalcy?The amount of grams or mole equivalents of solute present in a solution that contains one liter is what is referred to as normalcy according to the accepted definition. The amount of moles of reactive units in a compound is what we mean when we say it is equal.
Sample size: The manager is surveying 50 customers, which is a moderate-sized sample.Normality: Since the manager is only looking at the proportion of customers who rated the food as excellent, we can assume that the data are approximately normally distributed.Randomness: The manager is using a random sample from the list of customers who have signed up for his frequent diner club, so we can assume that the sample is random.The conditions for inference are met.
However, to conclude that more than 50% of customers who dine at his restaurant would rate the food as excellent, we need to conduct a statistical test such as a one-sample proportion test or a confidence interval. The manager would need to compare the proportion of the customers who rated the food as excellent from the survey with the proportion of customers who would rate the food as excellent. This would allow to see if the data provides convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent.
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How do you find the 3 side of a triangle?
Answer:
by using sine rule and cosine rule.
Math help quick guys where ya at
The required dimensions are solved using linear pair and vertical angle to get the result as
x = 40y = 35Angle AED = angle CEB = 125 degreesAngle DEB = Angle AEC = 55 degreesHow to find the value of x and yThe value of x and y is calculated using linear pair theorem, the theorem implies that
solving for x
(3x + 5) + (x + 15) = 180
3x + x + 5 + 15 = 180
collecting like terms
4x = 180 - 15 - 5
4x = 160
x = 40
solving for y
(y + 20) + (4y - 15) = 180
y + 4y + 20 - 15 = 180
collecting like terms
5y = 180 - 20 + 15
5y = 175
y = 35
Angle AED
= 3x + 5
= 3 * 40 + 5
= 125 degrees
Angle AED = angle CEB = 125 degrees (vertical angles)
Angle DEB
= x + 15
= 40 + 15
= 55 degrees
Angle DEB = Angle AEC = 55 degrees (vertical angles)
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Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
The values are 13 and 1
I hope this is correct
H)
how many five- card hands are possible that contain at least three kings?
==========================================================
Explanation:
We'll break things up into cases. The phrasing "at least 3" means "3 or more".
We either will have 3 kings or 4 kings.
----------------------------------------------
Case A) There are exactly 3 kings.
Use the nCr combination formula. There are n = 4 kings total and we select r = 3 of them. That gives 4C3 = 4 ways to pick the 3 kings.
Put another way: there are 4 ways to leave a certain king out of the hand.
Then we have 52-4 = 48 cards that aren't a king, and we need to fill the remaining r = 2 slots. Through the nCr formula, you should find that 48C2 = 1128
To recap, we found
4 ways to pick the three kings1128 ways to pick the other two cards that aren't kingsThat gives 4*1128 = 4512 ways to have case A happen.
----------------------------------------------
Case B) There are exactly 4 kings
4C4 = 1, so there's only one way to select all the kings. The order doesn't matter. Then we have 48 cards to pick from for the fifth slot.
Overall there are 1*48 = 48 ways to have case B play out.
----------------------------------------------
There were 4512 ways to have case A happen, and 48 ways to have case B happen.
These cases are mutually exclusive to allow us to simply add the counts:
4512+48 = 4560
This is why the final answer is 4560
Select the interval where the graph f is positive
Answer: A
Step-by-step explanation:
Based on the graph, we know that it is positive if it is above the x-axis. It is also indicated by the positive labels.
A: correct
Looking at choice A, it says the interval is from -2<x<-1. This means we have to find x=-2 and x=-1. On the graph, that interval is above the x-axis, so it is positive.
B: incorrect
Looking at choice B, it says the interval is from -1<x<0. This means we have to find x=-1 and x=1. On the graph, that interval is below the x-axis, so it is negative.
C: incorrect
Looking at choice C, it says the interval is from 0<x<1. This means we have to find x=0 and x=1. On the graph, that interval is below the x-axis, so it is negative.
Therefore, A is the correct answer.
EU Migration Study
Discussion Question: In the EU migration study, 257 of the 583 immigrants
sampled were male. Let's assume the Trump/Farage claim is true: 60% of all
immigrants are male (p = 0. 60). What is the probability of obtaining 257 or fewer
males in a sample of 583 immigrants? Does this probability make you doubt the
Trump/Farage claim? Why or why not?
P
Normal(up= 0. 6, Op=. 020)
ộ ô
Ô P
ppp
PPPP
ppppppp
Skew The
Scrint
This probability does not support the Trump/Farage claim that 60% of all immigrants are male.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes, and how likely they are.
The probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found using the binomial probability formula, which calculates the probability of a specific number of successes (male immigrants) in a fixed number of trials (sample size) with a fixed probability of success (p = 0.60).
Using the binomial formula, the probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found by summing the probabilities of obtaining 257 males, 256 males, 255 males, etc. up to 0 males.
Using a binomial calculator, we can find that the probability of obtaining 257 or fewer males in a sample of 583 immigrants is about 0.04.
This probability is quite low, which suggests that it is unlikely to obtain 257 or fewer males in a sample of 583 immigrants if the proportion of male immigrants is actually 60%.
Therefore, this probability does not support the Trump/Farage claim that 60% of all immigrants are male.
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Express √75 in basic form
Answer:
[tex]5 \sqrt{3} [/tex]
Step-by-step explanation:
Frist find which perfect square goes into 75. In this case its 25 * 3. You then find out what is the square root of 25. Which is 5. you put that number outside the radical and the other number inside the radical. resulting in 5 square roots of 3.
Answer: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form:
5√3
Decimal Form:
8.66025403…
Help ASAP!!!!
Which of the following statements is NOT true?
I need help, please
and can someone explain so I can stop posting so many of these?
it's infinitely many bc the equations have the same line
Answer:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Here a1, b1, c1, a2, b2, c2 are all real numbers.
Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0
Step-by-step explanation:
How many solutions does the following system have?
y = -2x – 4
y = 3x + 3
Solution:
Given y = -2x – 4
y = 3x + 3
Rewriting to the general form
-2x – y – 4 = 0
3x – y + 3 = 0
Comparing the coefficients,
(a1/a2) = -⅔
(b1/b2) = -1/-1 = 1
(a1/a2) ≠ (b1/b2)
Hence, this system of equations will have only one
please help asap. i need help.
The slope of the linear equation that passes through the two given points is 1/7.
How to find the slope of the line?A general linear equation can be written in the slope-intercept form as:
y = a*x + b
Where the coefficients are:
a: the slope.
b: the y-intercept.
If a line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope is equal to:
a = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that the line passes through (-10, -9) and (-3, -8), then the slope of this linear equation will be:
a = (-8 + 9)/(-3 + 10) = 1/7
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bonjour svp aide moi
Exercice 7: mon et nop sont deux angles adjacents supplémentaires tel que mOn = 60°.
1°) Calculer nOp.
Answer:
n0p = 120°
Step-by-step explanation:
m0n + n0p = 180°
60° + n0p = 180°
n0p = 120°
What are the three types of algorithms?
The three types of algorithms are Brute Force algorithm, Greedy algorithm and Recursive algorithm.
What is Brute Force algorithm?As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search entails iteratively listing all potential candidates for the solution and determining if each one satisfies the problem's statement.
In order to find the divisors of a natural number n, a brute-force algorithm would count all integers from 1 to n & determine whether each one divides n without leaving a remainder.
A brute-force method might look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece may engage in mutually exclusive attacks for each configuration for the eight queens puzzle.
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Wenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:
# of movies Frequency
0 4
1 9
2 5
3 6
4 1
a) Find the sample standard deviation, s. (Round your answer to two decimal places. )
b) Find the sample mean x^-
Answer: 35
Step-by-step explanation:
: i took this quiz before :)
PLEASE HELPP
If A and B are supplementary angles and
m/B = 54, find m/A.
Answer:
m∠A=126°
Step-by-step explanation:
Supplementary means that they add up to 180°.
Therefore we can do 180-54 to get 126° for the m∠A.
Hope this helped! :)
a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 8feet from the base of the building. How high up does the ladder reach?
The ladder would reach a distance of 6 feet up the wall.
The Pythagorean theorem.This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:
/hyp/^2 = /opp/^2 + /adj/^2
In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.
So that, let the height of the ladder on the wall be represented by t. Then;
10^2 = t^2 + 8^2
100 = t^2 + 64
t^2 = 100 -64
= 36
t = (36)^1/2
t = 6 feet
Thus the ladder is placed 6 feet up the vertical wall.
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(pesos and Php are philippine coins and money so just imagine pesos as coins if u arent filipino)
It has been Cheri's habit to collect 5 peso and 10 peso coins starting january of every year, to save up for her family's annual outreach to a local community at the end of the year. At the end of the year, she has saved a total of Php 2285 . If she has 11 more 10 pesos than 5 peso coins, how many coins of each does she have
Cheri collected 145 number of 5 peso coin and 156 number of 10 peso coin during her family's annual outreach
What is an equation?An equation is used to show the relationship between numbers and variables.
Let x represent the number of 5 peso coins and y represent the number of 10 peso coin
At the end of the year, she has saved a total of Php 2285, hence:
5x + 10y = 2285 (1)
Also, she has 11 more 10 pesos than 5 peso coins, hence:
y = x + 11 (2)
Solving both equations using elimination method gives:
x = 145, y = 156
Cheri had 145 number of 5 peso coin and 156 number of 10 peso coin.
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If A=(7,9) and B=(3,12) what is the length of AB
The distance between two points A and B is 5 units.
(1 point) | Question Attempt: 1 of Unlimited
Suppose that the functions h and g are defined as follows.
h(x)=x-2
g(x)=(x-4)(x+2)
h
(²)(-1).
(a) Find
h
(b) Find all values that are NOT in the domain of
9
If there is more than one value, separate them with commas.
All values that are NOT in the domain of 9 are 5 /11 at x=9, where function h=7.
How can I determine a rational function's domain?All real numbers x, with the exception of those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.
h(x)=x-2\sg(x)=(x-4)(x+2)
Suppose x = 9 and h(9) = 9-2 and g(9) = (9-4) (9+2) =5 /11
Because it is impossible to divide by zero while h is in the denominator, there will always be an issue anytime h = 7. After solving them, we discover that x cannot be either -2 or 5. So, the answer to part B would be x-5/11.or 5/11 are examples of x values that are beyond the domain.
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What are the top 5 formulas in math?
According to the use and the fundamental knowledge behind these formulas, The top 5 formulas in mathematics are quadratic, Pythagorean , slope-intercept , exponential and Euler's Formula.
What is mathematics?Mathematics is the study of numbers, shapes, and patterns. It is the science of studying the properties and relationships of quantities and shapes using logic, symbols and mathematical operations. It is a way of understanding the world and solving problems using quantitative reasoning.
What do you mean by formula?A mathematical formula is a set of symbols, numbers and mathematical operations that express a relationship or equation. These formulas are used to model, describe and explain phenomena in the natural and physical world, as well as in abstract mathematical theories. Formulas can take many forms, including equations, identities, and inequalities. They allow us to make predictions and calculations, and can be used in various fields of science, engineering and other fields to solve problems.
1. root of [tex]ax^2+bx+c[/tex] is [tex]x= \frac {-b+- \sqrt{b^2-4ac}}{2a}[/tex].
2.[tex]h^2 = p^2 +b^2[/tex]
3. [tex]y =mx+c[/tex]
4.[tex]e^x[/tex]
5.[tex]e^{ix} = cosx+isinx[/tex]
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Which function is shown on the graph?
of(x) = 1/2cos x
of(x) = -1/2cos x
Of(x) = -1/2sin x
Of(x) = 1/2sin x
The reasons and responses to the graphs in the question are as follows:
Graph 1.
The amplitude of the first graph is (1/2) which is the height from the midline to the peak
The value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine function
The period of the graph is 2·π, which is the period of the parent cosine function
Therefore, the correct option is
Graph 2: Please find attached the graph of the function g(x) = 2×cos(x)
Graph 3: The frequency of a sinusoidal function is given as follows;
The period of the graph = π
Therefore;
The frequency of the sinusoidal graph is 2
Graph 4. Required:
To find the equation that represents the function of the graph
Solution;
The period of the function, T = π
The graph of the function has a maximum at x = 0, therefore, the graph is similar to a cosine function, y = cos(B·x)
Where;
B = 2·π/T
Therefore;
B = 2·π/π = 2
Therefore;
The equation that represent the function in the graph is f(x) = cos(2·x)
Question 5. The given function is f(x) = cos(2·x)
The frequency factor in the given function, B = 2
The period, T = 2·π/B
Therefore, T = 2·π/2 = π
The period of the function, f(x) = cos(2·x), is 2
To learn more about sinusoidal function refer to:
https://brainly.com/question/9133917
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