Answer:
Sarah=x
Lea=3x-4
Rachel=1/2x-3
Amanda=2x+1
Sum=46
x+3x-4+1/2x-3+2x+1=46
6.5x-6=46
6.5x=52
x=52/6.5x
x=8
input x in each sister's age:
Sarah= 8 years
Lea = 3(8)-4=20 years
Rachel = 1/2(8)-3=1 year
Amanda = 2(8)+1=17years
Step-by-step explanation:
wHAT IS THE ANSWER OF THIS? the correct answer will be marked brainliest
six tickets to a movie cost $76.50. What constant of proportionality relates the number of tickets and total cost?
The constant of proportionality is 12.75
The constant of proportionality is the ratio of the constant values of two proportional quantities.
Two changing values are said to be in proportion when either their ratio or product results in a constant. The proportionality constant's value is determined by the Direct Variation and Inverse Variation types of proportions between the two supplied values.The direct proportionality equation, y = kx, shows that when x increases, y increases at the same rate. As an illustration, y x stands for the cost per item(y), which is inversely related to the quantity of items(x) bought.The indirect proportionality equation, y = k/x, shows that when y increases, x decreases, and vice versa.The direct variation is given by y = k x where k is the constant of proportionality.
Now the cost of 6 tickets is $76.50
76.50 = k × 6
or, k = 12.75
Therefore the constant of proportionality is 12.75
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Algebraic Identity help
In the picture, the polynomial equation is (3x-k)². The values of k=4 and p=-24.
Given that,
In the picture, the polynomial equation is (3x-k)²
We have to find the k value and p value if (3x-k)²=9x²+px+16
Polynomial means polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.
We get,
(3x-k)²=9x²+px+16
9x²-6xk+k²=9x²+px+16
We get,
p=-6k and k²=16
k²=16
k=4
Substitute in p=-6k
p=-6×4
p=-24
Therefore, the values of k=4 and p=-24.
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Assume that when human resource managers are randomly selected, % say job applicants should follow up within two weeks. If human resource managers are randomly selected, find the probability that exactly of them say job applicants should follow up within two weeks.
The probability that exactly of them say job applicants should follow up within two weeks is 0.2291
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The binary probability distribution can be used to model the given issue.
Assume that X is a binomial random variable with the values n and p, where n is the total number of human resource managers that were randomly chosen and p is the likelihood that the chosen manager will advise job seekers to follow up within two weeks.
total human resource managers were chosen at random, n = 9
The likelihood that the chosen human resources manager will advise job seekers to follow up within two weeks = 57 (0.57)
As we are aware, the probability of "m" successes for a binomial distribution is calculated as -
[tex]P(X=m) = ^{n}C_{m} (p)^{m}(1-p)^{n-m} = \frac{n!}{m! (n-m)!}(p)^{m}(1-p)^{n-m}[/tex]
Using the aforementioned data, we can now calculate the likelihood that exactly 6 of the 9 applications who were chosen will advise job seekers to follow up within two weeks as follows:
n = 9
p = 0.57
m = 6
[tex]P(X=m) = \frac{n!}{m! (n-m)!}(p)^{m}(1-p)^{n-m}[/tex]
[tex]P(X=6) = \frac{9!}{6! (9-6)!}(0.57)^{6}(1-0.57)^{9-6}[/tex]
[tex]= \frac{9!}{6! 3!} (0.57)^{6} (0.43)^{3}[/tex] = 0.2291 (rounded to 4 decimal places)
Therefore, the probability that exactly of them say job applicants should follow up within two weeks is 0.2291
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Please help me i really need help. you get 49+ pts
Answer:For the first one i only know the answer to the division problem i don't know how to do the box things but the division problem is 2,867 divided by 61=47 with no remainder.
The second one is 3,353 divided by 75 =40 R 4
What is the equation of the line that passes through (-2, 2) and (1,-4)?
Oy=-2x-4
OY=2x-2
Oy=2x+4
Oy=-2 X-2
Answer:
2x-4 ravdhzfjztjt,h,rufhfjfjfjufff,ufhfutitig
Step-by-step explanation:
xbsndnsnfnzndnzanayrURJfjgjgkgjgk gk
Please tell me the answer to this and i will mark you brainliest
Answer:
A = 2x0 = 0
B= 2x2 = 4
Similarity: they both pass the origin
Difference: They have different gradients: y=2x has a gradient of 2 and y=x has a gradient of one
Step-by-step explanation:
A = 2x0 = 0
B= 2x2 = 4
Similarity: they both pass the origin
Difference: They have different gradients: y=2x has a gradient of 2 and y=x has a gradient of one
9 x 87 = (9 x _) + (_ x 7)
The missing numbers here are given by 9×(80+7)=(9×80)+(9×7)
What are missing numbers?
Missing numbers are the numbers that got missed in the given series of numbers with similar differences among them. The process of writing the missing numbers is termed as finding similar changes between those numbers and filling their missing values in their specific series and places.
Here, given 9×87=(9×some number)+(another number×7)
Let x and y be the missing numbers.
9×87=(9×x)+(y×7)
We can write 9×87=9×(80+7)
Using distributive property,
9×87=(9×80)+(9×7)
On comparing, we get x=80,y=9.
Hence, the missing numbers are 80, 9
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A recipe calls for 3/4 of a pound of flour to make 1 batch of cookies. how many batches of cookies can be made with 5 pounds of flour? include parts of the batch in the answer.
Answer:
20/3 batches of cookies can be made with 5 pounds of flour.
Step-by-step explanation:
given-
A recipe calls for 3/4 of a pound of flour to make 1 batch of cookies
asking-how many batches of cookies can be made with 5 pounds of flour
3/4 pound of flour=> 1 batch of cookies
then,
1 pound of flour=> 4/3 batch of cookies
so, required answer---
5 pound of flour=>5*( 4/3) batch of cookies
=>20/3=6.66 batch of cookies
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every tuesday joe has a beer with 2 friends. they each have a unique token and every tuesday, they each put their token in a hat and ask the bartender to draw one token out. the person whose token is drawn pays the tab. over the next 3 weeks, what is the chance that joe has to pay the tab at least once? fill in the answer as a percent carried to one decimal place, but without the percent sign.
0.384 is the chance that joe has to pay the tab at least once by probability.
What is a math illustration of probability?
The likelihood or chance of an event happening is known as probability. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.Every tuesday Joe has beer with 4 friends .
Each have unique token , and the person whose token is drawn pays the tab.
Since , there are Joe and 4 friends , so we have total of 5 persons.
Now, probability that Joe token will be drawn is = 1 / 5 { 1 (Favourable Outcome) \small / 5 (Total Outcome) }
i.e there is 1/5 = 0.20 probability that Joe token will be drawn and he will pay the tab.
Over the next 3 weeks , we need to find the change that Joe pays the tab exactly one time.
Here we have n = 3 ( weeks ) , and probability of success is p = 0.20
i.e probability that Joe will pay tab (Success) is p = 0.20 and probability that Joe will not pay tab ( failure ) is 1-p = 0.80.
So we can model it by binomial distribution , as we have only two outcome which are i) Joe pays the tab , ii) Joe do not pay tab.
X ~ B(n=3 , p =0.20)
We need to find P(X=1) , i.e exactly one time Joe pays the tab .
Since, we have approximate that X follows binomial distribution , so we have
f(x) = P(X=x) = \small \binom{n}{x}p^x(1-p)^{n-x}
Hence
P(X=1) = ( n 1 ) p¹ ( 1 - p)ⁿ⁻¹
= ( 3 1 ) 0.2¹ ( 1 - 0.2)³⁻¹
= 3 * 0.2 * 0.8²
= 0.384
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Round 387.869911589 to 3 decimal places.
\Big(\frac{1}{6}-0.5\Big) \div\frac{5}{11}
(
6
1
−0.5)÷
11
5
387.869911589 to 3 decimal places is 387.870.
What is the number rounded to 3 decimal placesA decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.
In order to round off a number to 3 decimal places, there must be 2 numbers to the right of the decimal point.
In order to round off a number to 3 decimal places, if the ten thousandth figure is equal to five or greater than 5, one is added to the thousandth figure. If the ten thousandth figure is less than 5, there is no change in the thousandth digit.
The ten thousandth is greater than 9, so one is added to the thousandth digit. The number becomes 387. 870
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Evaluate a/b if a=-48 and b = 6
Answer:
-8
Step-by-step explanation:
A= - 48
B= 6
-48/6
= 8
Negative x Negative = Positive
Negative x Positive = Negative
Positive + Positive = Positive
7 231/500 As a decimal
Answer:
7.462
Step-by-step explanation:
Answer:
7 231/500 As a decimal
Step-by-step explanation:
To write 231/500 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 231 by 500 what we write down as 231/500 and we get 0.462
Hope this helps!
A penny is dropped from the top of a new building. Its height in feet can be modeled by the equation y = 256 - 16^{2} , where x is the time in seconds since the penny was dropped. How long does it take for the penny to reach the ground?
I would greatly appreciate help with this word problem, thanks!
≧◠ᴥ◠≦✊
Answer:
4 seconds
Step-by-step explanation:
Given equation:
[tex]y=256-16x^2[/tex]
where:
y = The height of the penny (in feet).x = The time since the penny was dropped (in seconds).The penny reaches the ground when the height is zero, so when y = 0.
Substitute y = 0 into the given equation and solve for x:
[tex]\begin{aligned}y&=256-16x^2\\y=0 \implies 0&=256-16x^2\\0+16x^2&=256-16x^2+16x^2\\16x^2&=256\\\dfrac{16x^2}{16}&=\dfrac{256}{16}\\x^2&=16\\\sqrt{x^2}&=\sqrt{16}\\x&=\pm4\end{aligned}[/tex]
As time is positive, x = 4 only.
Therefore, it takes 4 seconds for the penny to reach the ground.
If i=1, what is the value of /³?
Answer:
-1Step-by-step explanation:
using the real question in the comments
If i = -1, what is the value of i^3?
i³
replace values
-1³ =
(-1)x(-1)x(-1)
-1
-----------
The necklace is priced $85. You have a 15% discount and tax is 6%. What
will your final price be?
Mary lives between points (3,-1) and (7,5) on Duval street. Val lives between points (2,15) and (-6,3) on Braxton lane. Are duval st and Braxton lane parallel or perpendicular
Duval Street between latitudes (3,1) and (7,5). Val resides between coordinates (2, 15) and (-6, 3). Braxton Lane and Duval Street are not parallel or perpendicular.
Given that,
Mary resides on Duval Street between latitudes (3,1) and (7,5). On Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3).
We have to find is Braxton Lane and Duval Street parallel or perpendicular.
To find the lines are parallel or perpendicular we have to find the slope of those points.
If slopes are equal then the lines are parallel.
If slopes are negative reciprocal then the lines are perpendicular.
We find the slope of Mary resides on Duval Street between latitudes (3,1) and (7,5).
m₁=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m₁=[tex]\frac{5 -1 }{7-3 }[/tex]
m₁=4/4
m₁=1
The slope of the Mary resides on Duval Street between latitudes (3,1) and (7,5) is 1.
We find the slope of Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3).
m₂=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m₂=[tex]\frac{3 -15 }{-6-2 }[/tex]
m₂=-12/-8
m₂=3/2
The slope of the Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3) is 3/2.
m₁≠m₂
Therefore, Braxton Lane and Duval Street are not parallel or perpendicular.
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In the given triangle, prove that
[tex] \frac{1}{ {ab}^{2} } + \frac{1}{ {ac}^{2} } = \frac{1}{ {ad}^{2} } [/tex]
Answer:
. .........................
3. What is the next term in the sequence?
243, 81, 27,9,...
O
O
-3
O
-9
O`
3
The next term would be 3 then 1 in the sequence 243, 81, 27, 9,... by the term of sequence and series through mathematical sequencing.
What are a series and a sequence?A grouping of numbers in a kind of a specific order is known as a sequence. On the other hand, a series can also be described as the accumulation of a kind of a sequence’s constituent parts.
Basically, the sequence proceeds with a dividing term of 3. The sequence will go on with the square root of the previous number. Basically, from backward, the sequence is an exponential multiple of 3.
What do the terms sequence and series mean?Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of elements in a sequence, which is a group of arranged elements that follow a pattern.
The formulas for the nth term and the sum are typically included in the sequence and series formulas.
What distinguishes serial from sequential data?A series is made up of all the elements in a sequence, while a sequence is a certain arrangement of elements in a specific order.
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Nathan and his brother Zach love to play video games. Right now, Nathan's score is 11 less than 2 times Zach's score.-example, if Zach has 80 points, then Nathan has 149 points. Find four more possibilities for the brothers' scores and fir he table below. Then write a rule relating Nathan's score, N, to Zach's score, Z.
Zach's score, Z, and Nathan's score, N, are related by the formula
2Z-11=N.
This is further explained below.
What are algebraic expressions?Generally, Assume Nathan has a score of N and Zach has a score of Z.
Zach's score is 11 points higher than Nathan's.
It implies,
N equals twice of Z minus 11.
We may format it as follows:
2Z - 11 = N
There are now four possible outcomes for these two brothers' scores:
Zach's score will be determined using algebraic formulas if Nathan's score is 81.
2Z - 11 = 81
2Z = 92
Z = 46
Zach's score will be 61 if Nathan receives a score of 111.
Zach's score will be 121 if Nathan's score is 231 or higher.
Zach's score will be 456 if Nathan's score is 901.
The formula 2Z - 11 = Z is a rule that connects Nathan's and Zach's scores.
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x+1 2/3 =2 3/8 what is x
Answer:
X=17/24
Step-by-step explanation:
first you need to find common denominators. To find it, you would multiply the denominator of the 1 2/3 and the 2 3/8.8*3=24, which means the denominator is 24. For 1 2/3, we multiplied 3*8 so we also have to do it for 2. The new equation is x+1 16/24=2 3/8. But remember, we still have to multiply 8*3, which means we have to multiply 3*3 too.
New equation:x+1 16/24=2 9/24
Now we can subtract 1 16/24 from each side
X=17/24
can anybody help me the process on how to convert fractions into decimals and decimals
into fractions.
Fractions into Decimals-
15/5 = 3
Decimals into Fractions-
0.5 = 5/10
How to convert fractions into decimals and decimals into fractions ?Place the decimal number above its place value to convert it to a fraction.
For instance, since the number six is in the tenths place in the fraction 0.6, we multiply it by 10 and get the comparable fraction 6/10.
Simplify the fraction if necessary.
The division is shown by the fractional bar between the "part" and the "whole."
By dividing the numerator by the denominator, any fractions can be transformed into decimals.
For instance, the fraction 45 denotes the ratio of 4 to 5, or 4/5.
By dividing 4 by 5, this fraction can be changed into a decimal.
Fractions into Decimals-
15/5 = 3
Decimals into Fractions-
0.5 = 5/10
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1. Passes through (6, 2) and (-3, 1)
The equation of line is found as y = 9x - 16.
What is described as the equation of the line?The "equation of a line" is an important topic in high school algebra. This is an x and y equation whose solution set is just a line in the (x,y) plane. The "slope-intercept" form is the most commonly used in algebra. y = mx + b, where, m is the slope and b is the y-intercept.For the given question;
The passing points of the line are (6, 2) and (-3, 1).
The slope of line is calculated as;
slope = m = (y₂ - y₁)/(x₂ - x₁)
Where,
(x₁, y₁) = (6, 2)
(x₂, y₂) = (-3, 1)
Put the values;
m = (-3 - 6)/(1 - 2)
m = -9/-1
m = 9
Then, the equation of line using slope intercept form is-
y - y₁ = m (x - x₁)
Put the values;
y - 2 = 9(x - 2)
Simplifying;
y -2 = 9x - 18
y = 9x - 16
Thus, the equation of line is found as y = 9x - 16.
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The complete question is -
What is the equation of the line that passes through P( 6,2) and S (- 3,1)?
solve 3x-1.5 ≤ 22.5
could i have a clear demonstration?
Answer:
x≤8
Step-by-step explanation:
3x-1.5≤22.5
Move the constant to the right side and change its sign to the opposite.
3x≤22.5+1.5
Add up the numbers.
3x≤24
Divide.
x=24/3
x≤8
Answer:
x= 8
Step-by-step explanation:
So this is not as hard as it looks
the aim of this question is to work out what x is
so we need to find x on it's own
therefore we must work on removing the number on the right and to do this we first of all have to get a number that is divisible by 3.
now this is not always the case but I think you can tell from this question that it is obvious.
so what you do first is reverse the -1.5 into a positive and if it was the other way round so positive to a negative
so we do 1.5 + 22.5 which equals to 24
now this is simple division so 24 ÷ 3 = 8
therefore making the answer x = 8
Determine the value of A so that x-1 is a factor of 2x^3 +x^2+2Ax+4
Answer:
When a polynomial f(x) is divided by ax + b and f(a/b) = 0, ax - b is a factor of f(x).
Let 2x³ + x² + 2Ax + 4 be f(x).
f(1) = 0
Substitute x = 1 into the equation.
2(1)³ + (1)² + 2A(1) + 4 = 0
2 + 1 + 2A + 4 = 0
2A = -7
A = -7/2
Solve the exponential equation
4^x = 7(3^x)
The solution to the given exponential equation is; x = 6.48
What is the solution to the exponential equation?
We want to solve the exponential equation;
4^(x) = 7 - (3^x)
We can use logarithm or inverse of logarithm to solve this but in this case we will use the logarithm to get;
x log 4 = 7 - (x log 3)
x log 4 + x log 3 = 7
x(log 4 + log 3) = 7
1.08x = 7
x = 7/1.08
x = 6.48
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–2.29(d + 1) = –6.87
Isolate the variable by dividing each side by factors that don't contain the variable.
[tex]-2.29(d+1)=-6.87[/tex]
[tex]d=2[/tex]
^Hence, our solution
________________________________________________
Hope this helps!
What is the zero of the function represented by this graph?
Answer:
Correct answer should be x= -6
Step-by-step explanation:
prove me wrong
Anyone know the answer for this
Answer: The question, please?
Step-by-step explanation:
Please help
Solve for x. Show each step of the solution.
2.54-x+12=21-42.5x+7
The value of the variables 'x' in the equation is 0. 32
What are algebraic expressions?Algebraic expressions can be defined as expressions consisting of constants, factors, coefficients, variables as well as terms.
They are also composed of certain mathematical operations such as;
AdditionSubtractionDivisionBracketParenthesesMultiplication, etcGiven the expression;
2.54 - x + 12 = 21 - 42.5x + 7
To determine the value of x, we have to follow the following steps;
collect like terms
-x + 42. 5x = 21 + 7 - 12 - 2. 54
Add or subtract like terms
41. 5x = 13. 46
Make 'x' the subject of formula by dividing both sides by the coefficient of x
x = 13. 46/41. 5
Divide the values
x = 0. 32
Hence, the value of x is 0. 32
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